id
stringlengths 40
40
| metadata
dict | text
stringlengths 9
2.66M
| created
timestamp[s]date 2025-03-04 00:00:00
2025-03-07 00:00:00
| source
stringclasses 1
value | attributes
dict |
|---|---|---|---|---|---|
d6a5ab0e19328fb731b463f6e1715e6b3fca3d55 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 5,
"total-fallback-pages": 0,
"total-input-tokens": 22352,
"total-output-tokens": 6730,
"fieldofstudy": [
"Mathematics"
]
} | A Shrinking Factor for Unitarily Invariant Norms under a Completely Positive Map
Alexey E. Rastegin
Department of Theoretical Physics, Irkutsk State University, Gagarin Bv. 20, Irkutsk 664003, Russia
A relation between values of a unitarily invariant norm of Hermitian operator before and after action of completely positive map is studied. If the norm is jointly defined on both the input and output Hilbert spaces, one defines a shrinking factor under the restriction of given map to Hermitian operators. As it is shown, for any unitarily invariant norm this shrinking factor is not larger than the maximum of two values for the spectral norm and the trace norm.
Keywords: Ky Fan’s maximum principle, symmetric gauge function, Choi-Kraus representation, Ky Fan’s norm
I. INTRODUCTION
In many disciplines, linear maps on a space of operators provide key tools for treatment of the subject. For several reasons the class of completely positive maps (CP-maps) is especially valuable [1]. The recent advances in quantum information theory have led to a renewed interest in this area [10]. In effect, it seems that all possible changes of quantum state is covered by contractive completely positive maps [8], though the monotonicity of relative entropy can be proved in more general framework [10]. Anyway, all the important examples are actually completely positive. Thus, studies of used quantitative measures under action of CP-maps form a very actual issue. Of course, other properties of CP-maps with respect to certain norms are subjects of active research [4, 7]. As a rule, distance measures are metrics induced by norms with handy properties. Unitarily invariant norms are very useful in this regard [6]. At the same time, some variety of measures is typically needed with respect to themes of interest. So, a question on contractivity of given map with respect to applied norm is significant in many different fields of physics (see [12] and references therein). Hence we may be interested in general results on a problem of contractivity without explicit specification of the measure. Below the result of such a kind will be given for the class of unitarily invariant norms. Namely, the norm of image of Hermitian operator is not greater than the norm of operator itself multiplied by some shrinking factor. For given CP-map and any norm from the considered class, this factor does not exceed the maximum of two exact values of shrinking factor for the spectral norm and the trace norm. The discussion is carried out entirely in finite dimensional setting.
II. DEFINITION AND NOTATION
Let \( H \) be \( d \)-dimensional Hilbert space. We denote by \( L(H) \) the space of all linear operators on \( H \), and by \( L_{s.a.}(H) \) the space of self-adjoint (Hermitian) operators on \( H \). For any \( X \in L(H) \) the operator \( X^\dagger X \) is positive semidefinite, and its unique positive square root is denoted by \( |X| \). The eigenvalues of \(|X|\) counted with multiplicities are the singular values of operator \( X \), in signs \( \sigma_i(X) \) [6]. Each unitarily invariant norm is generated by some symmetric gauge function of the singular values, i.e. \(||X|||_g = g(\sigma_1(X), \ldots, \sigma_d(X))\) (see, e.g., theorem 7.4.24 in [6]). The determining properties for a symmetric gauge function are listed in [6]. The two families, the Schatten norms and the Ky Fan norms, are most widely used. For any real \( p \geq 1 \), the Schatten \( p \)-norm is defined as [6]
\[
||X||_p := \left( \sum_{i=1}^{d} \sigma_i(X)^p \right)^{1/p}.
\]
This family recovers the trace norm \(||X||_1\) for \( p = 1 \), the Frobenius norm \(||X||_2\) for \( p = 2 \), and the spectral norm \(||X||_{\infty}\) for \( p \to \infty \) [6]. Let us use these signs, although \(||X||_{\infty} = ||X||_{(1)}\) and \(||X||_{1r} = ||X||_{(d)}\) as the Ky Fan norms though. For integer \( k \geq 1 \), the Ky Fan \( k \)-norm is defined by [6]
\[
||X||_{(k)} := \sum_{i=1}^{d} \sigma_i^k(X) \equiv g(k)(\sigma_1(X), \ldots, \sigma_d(X)),
\]
where the arrows down show that the singular values are put in the decreasing order. In terms of the norms (1), the partitioned trace distances have been introduced [15]. These measures enjoy similar properties to the trace norm distance. In the following, we will assume that \(||X||_{(k)} = ||X||_{1r}\) for \( k \geq d \). We shall now define the main object treated in this paper.
**Definition 2.1.** Let \( \Phi_{s.a.} \) be the restriction of CP-map \( \Phi : L(\mathcal{H}_A) \to L(\mathcal{H}_B) \) to Hermitian operators. Its shrinking factor with respect to given unitarily invariant norm \( \|X\|_g \) is defined as
\[
\eta_g(\Phi_{s.a.}) := \sup \left\{ \|\Phi(X)\|_g : X \in L_{s.a.}(\mathcal{H}_A), \|X\|_g = 1 \right\}.
\]
If \( \mathcal{H}_A = \mathcal{H}_B \) then on both the spaces a norm \( \|X\|_g \) is defined by the same symmetric gauge function. When \( \dim(\mathcal{H}_A) \neq \dim(\mathcal{H}_B) \), we append zero singular values so that the vectors \( \sigma(X) \) and \( \sigma(\Phi(X)) \) have the same dimensionality equal to \( \max\{d_A, d_B\} \). In this regard, our consideration is related to those symmetric gauge functions that are not changed by adding zeros. Only under this condition the same unitarily invariant norm is correctly defined on the spaces of different dimensionality. The needed property is provided by all the functions assigned to the Ky Fan gauge function that enjoys this property. Indeed, the symmetric gauge functions, providing the above property, form a convex set.
In Definition 2.1 the supremum is taken over Hermitian inputs \( X \). First, self-adjoint operators are very important in many applications including quantum information topics. Say, the difference between two density matrices is traceless Hermitian, and the restriction to such operators deserves attention. Second, a consideration of Hermitian \( X \) allows to simplify analysis. Third, some relations with positive or self-adjoint operators have later been extended to more general ones. So, our definition is suitable for such a generalization.
In the seminal paper \([5]\), Ky Fan obtained important results with respect to extremal properties of eigenvalues. One of his formulations is now known as Ky Fan’s maximum principle. The present author have applied this power to simplify analysis. Third, some relations with positive or self-adjoint operators have later been extended to more general ones \([2, 18]\). So, our definition is suitable for such a generalization.
In the seminal paper \([5]\), Ky Fan obtained important results with respect to extremal properties of eigenvalues. One of his formulations is now known as Ky Fan’s maximum principle. The present author have applied this power for stating the basic properties of the partial fidelities \([14]\), which were originally introduced by Uhlmann. The present author have applied this power for stating the basic properties of the partial fidelities \([14]\), which were originally introduced by Uhlmann\([17]\), and the partitioned trace distances \([15]\). Changing the proof of theorem 1 in \([2]\), we can merely prove
\[
\sum_{i=1}^{k} \lambda_i^k(X) = \max \{ \text{Tr}(PX) : 0 \leq P \leq I, \text{Tr}(P) = k \},
\]
where the maximum is taken over those positive operators \( P \) with trace \( k \) that satisfy \( P \leq I \). Alternately, the maximization may be over all projectors of rank \( k \), as in the original statement \([2]\). If operator \( X \) is positive semidefinite then the maximum can be taken under the condition \( \text{Tr}(P) \leq k \) or, for projectors, \( \text{rank}(P) \leq k \). Using the Jordan decomposition, we have the following result.
**Lemma 2.2.** For any \( X \in L_{s.a.}(\mathcal{H}) \) and \( k \geq 1 \), there exist two mutually orthogonal projectors \( P_Q \) and \( P_R \) such that \( \text{rank}(P_Q + P_R) \leq k \) and
\[
\|X\|_{(k)} = \text{Tr}[(P_Q - P_R)X].
\]
**Proof.** First, we suppose that \( k \leq d \). We write \( X = Q - R \) with positive semidefinite \( Q \) and \( R \) whose supports are orthogonal. These operators are positive and negative parts of \( X \) respectively. Putting the spectral decomposition
\[
|X| = Q + R = \sum_q q u_q u_q^\dagger + \sum_r r v_r v_r^\dagger,
\]
we see that \( \{q\} \cup \{r\} = \{\sigma_i(X)\} \). For given \( k \), we define two subspaces, namely
\[
\mathcal{K}_Q := \text{span}\{u_q : q \in \{\sigma_1^k, \sigma_2^k, \ldots, \sigma_k^k\}\}, \quad \mathcal{K}_R := \text{span}\{v_r : r \in \{\sigma_1^k, \sigma_2^k, \ldots, \sigma_k^k\}\}.
\]
If \( P_Q \) is projector onto \( \mathcal{K}_Q \) and \( P_R \) is projector onto \( \mathcal{K}_R \), then we at once get \( (P_Q - P_R)X = P|X| \) for projector \( P = P_Q + P_R \) of rank \( k \). By construction, the trace of \( P|X| \) sums just \( k \) largest singular values of \( X \). The case \( k > d \) is reduced to the trace norm for that the needed projectors are already built and \( \text{rank}(P_Q + P_R) = d < k \). \( \square \)
**III. MAIN RESULTS**
In this section, we will study a change of unitarily invariant norms under action of a CP-map. Since they are positive-valued, upper bounds are usually indispensable. Let \( \Phi : L(\mathcal{H}_A) \to L(\mathcal{H}_B) \) be a completely positive linear map. We shall use the Choi-Kraus representation \([2, 8]\).
\[
\Phi(X) = \sum_n E_n X E_n^\dagger, \quad E_n : \mathcal{H}_A \to \mathcal{H}_B.
\]
From the physical viewpoint, this result is examined in \([10]\). In the context of Stinespring’s dilation theorem, it is discussed in \([1]\). The Choi-Kraus representation is not unique, but a freedom is unitary in character (see theorem 8.2 in \([10]\)). Two sets \( \{E_n\} \) and \( \{G_m\} \) determine the same CP-map if and only if
\[
G_m = \sum_n v_{mn} E_n.
\]
where numbers $v_{mn}$ are entries of some unitary matrix of proper dimensionality. Then for given CP-map the two positive semidefinite operators
$$
M := \sum_n E_n^* E_n, \quad W := \sum_n E_n^T E_n
$$
are not dependent on a choice of the set $\{E_n\}$. The second operator has been used for another definition of the trace norm distance via extremal properties of contractive CP-maps [15].
**Theorem 3.1.** Let $\Phi : \mathcal{L}(\mathcal{H}_A) \to \mathcal{L}(\mathcal{H}_B)$ be a CP-map. For every $X \in \mathcal{L}_{s.a.}(\mathcal{H}_A)$ there holds
$$
|||\Phi(X)|||_k \leq \eta|||X|||_k, \quad k = 1, 2, \ldots, \max\{d_B, d_A\},
$$
where the factor $\eta := \max\{|||M|||_\infty, |||W|||_\infty\}$.
**Proof.** First, we assume that $d_B \leq d_A$. Let $X = Q - R$ be the Jordan decomposition of $X$, then $\Phi(X) = \Phi(Q) - \Phi(R)$. It follows from $\Phi(X)^\dagger = \Phi(X)$, Lemma 2.2 and properties of the trace that
$$
|||\Phi(X)|||_k = \text{Tr}_B \left[ (\Pi_Q - \Pi_R)(\Phi(Q) - \Phi(R)) \right] \leq \text{Tr}_B \left[ (\Pi_Q + \Pi_R)(\Phi(Q) + \Phi(R)) \right] = \eta \text{Tr}_A [(S + T)|X|]
$$
for two mutually orthogonal projectors with $\text{rank}(\Pi_Q + \Pi_R) \leq k$. In [15] we use $Q + R = |X|$ and positive semidefinite operators
$$
S = \eta^{-1} \sum_n E_n^T Q_n E_n, \quad T = \eta^{-1} \sum_n E_n^T R_n E_n.
$$
Denoting $\mu \equiv |||M|||_\infty$ and $\nu \equiv |||W|||_\infty$, we obviously write $\mu^{-1}M \leq I_B$ and $\nu^{-1}W \leq I_A$. Combining the former with properties of the trace, we have
$$
\text{Tr}_A (S + T) = \eta^{-1} \text{Tr}_B \left[ (\Pi_Q + \Pi_R)M \right] \leq \text{Tr}_B \left[ (\Pi_Q + \Pi_R) \mu^{-1}M \right] \leq k.
$$
Using $\Pi_Q + \Pi_R \leq I_B$ and $\nu^{-1}W \leq I_A$, we also obtain
$$
\langle u, (S + T)u \rangle = \eta^{-1} \sum_n \langle u, E_n^T (\Pi_Q + \Pi_R) E_n u \rangle \leq \langle u, \nu^{-1}W u \rangle \leq \langle u, \nu^{-1}W u \rangle \leq \langle u, u \rangle
$$
for each $u \in \mathcal{H}_A$. This implies $S + T \leq I_A$ and the truth of using Ky Fan’s principle for the right-hand side of [13]. So, the relations [13] and [11] provide the claim. When $d_B > d_A$, the calculations [15] remain valid for $k > d_A$, hence the right-hand side of [13] is not greater than $\eta|||X|||_\infty$.
As it is known, the role of particular symmetric gauge functions $g(k)(\cdot)$ is that norm inequalities can sometimes be extended to all unitarily invariant norms. Let $u, v \in \mathbb{C}^d$ be given vectors with $d = \max\{d_A, d_B\}$. In accordance with theorem 7.4.45 in [15], the inequality $g(u) \leq g(v)$ holds for all symmetric gauge functions $g(\cdot)$ on $\mathbb{C}^d$ if and only if $g(k)(u) \leq g(k)(v)$ for $k = 1, 2, \ldots, d$. By Theorem 3.1, for any symmetric gauge function we then obtain
$$
g(\sigma_i(\Phi(X))) \leq \eta g(\sigma_i(X)),$$
or merely $|||\Phi(X)|||_g \leq \eta|||X|||_g$, whenever $X \in \mathcal{L}_{s.a.}(\mathcal{H}_A)$. In terms of shrinking factors, the norm inequality can be reformulated as follows.
**Theorem 3.2.** For each unitarily invariant norm $|||\cdot|||_g$, defined on both the spaces $\mathcal{H}_A$ and $\mathcal{H}_B$, a corresponding shrinking factor satisfies
$$
\eta_g(\Phi_{s.a.}) \leq \max\{|||M|||_\infty, |||W|||_\infty\}.
$$
In the next section we will show that $|||M|||_\infty$ is the exact value of shrinking factor for the spectral norm and $|||W|||_\infty$ is the one for the trace norm. So, a degree of non-contraction of $\Phi_{s.a.}$ is quite revealed by these two values.
**IV. THE SPECTRAL NORM AND TRACE NORM**
Let $X$ be Hermitian operator such that $|||X|||_1 = 1$. Using the Jordan decomposition $X = Q - R$, we get
$$
|||\Phi(X)|||_\infty = \text{Tr}_B \left[ \Pi(\Phi(Q) - \Phi(R)) \right] \leq \text{Tr}_B \left[ \Pi(\Phi(Q) + \Phi(R)) \right]
$$
(6)
for corresponding projector $\Pi$ of rank one. Due to $|X| \leq I_A$ and Ky Fan’s maximum principle \cite{2}, the right-hand side of \eqref{10} can be treated as
\[ \text{Tr}_A \left( \sum_n E_n^\dagger \Pi E_n |X| \right) \leq \text{Tr}_A \left( \sum_n E_n^\dagger \Pi E_n \right) = \text{Tr}_B (M \Pi) \leq ||M||_\infty . \]
So, we have $||\Phi(X)||_\infty \leq ||M||_\infty$ for any $X \in \mathcal{L}_{s.a.}(\mathcal{H}_A)$ with $||X||_\infty = 1$. Noting $\Phi(I_A) = M$, the inequality between norms is saturated. Hence we obtain the exact value of shrinking factor
\[ \eta_\infty(\Phi_{s.a.}) = ||M||_\infty . \]
Note that this is a particular case of the Russo-Dye theorem (see, e.g., corollary 2.9 in \cite{11}). The above calculation is given here due to its simplicity and illustration of the method.
In line with \eqref{9}, for the trace norm there holds
\[ ||\Phi(X)||_{tr} \leq \text{Tr}_B \left[ (\Pi_Q + \Pi_R) (\Phi(Q) + \Phi(R)) \right] = \text{Tr}_A (W|X|) . \]
since $\Pi_Q + \Pi_R = I_B$ by rank($\Pi_Q + \Pi_R$) = $d_B$. If $||X||_{tr} = 1$ then the right-hand side of \eqref{8} does not exceed $||W||_\infty$. This value can actually be reached. Let $Y$ be projector onto 1-dimensional eigenspace corresponding to the largest eigenvalue of operator $W$. Then $\Phi(Y)$ is positive semidefinite and
\[ ||\Phi(Y)||_{tr} = \text{Tr}_B (\Phi(Y)) = \text{Tr}_A (WY) = ||W||_\infty . \]
In other words, the exact value of shrinking factor is given by
\[ \eta_{tr}(\Phi_{s.a.}) = ||W||_\infty . \]
Thus, for the spectral and trace norms the exact value of shrinking factor is simply calculated. For other norms a task is more difficult but the bound of Theorem 3.2 is useful for many aims. So, this bound can be rewritten as
\[ \eta_{tr}(\Phi_{s.a.}) \leq \max \{ \eta_\infty(\Phi_{s.a.}), \eta_{tr}(\Phi_{s.a.}) \} . \]
To sum up, we have a valuable conclusion. If the restriction $\Phi_{s.a.}$ is contractive with respect to both the spectral and trace norm then it is contractive with respect to all unitarily invariant norms. Moreover, a degree of non-contractivity can be measured by using these two norms.
Finally, we apply our results to the operation of partial trace. This operation is especially important in the context of quantum information processing. Hence we are interested in relations between norms before and after partial trace.
The writers of \cite{9} resolved a question for those unitarily invariant norms that are multiplicative over tensor products. The explicit Choi-Kraus representation of partial trace is given in \cite{10}. However, the operators $M$ and $W$ can be found directly. Let us take $\mathcal{H}_A = \mathcal{H}_B \otimes \mathcal{H}_C$ with partial tracing over $\mathcal{H}_C$, that is
\[ \Psi(X) := \text{Tr}_C(X) \]
for any $X \in \mathcal{L}(\mathcal{H}_B \otimes \mathcal{H}_C)$. First, this operation preserves trace, because
\[ \text{Tr}_B (\Psi(X)) = \text{Tr}_B \{\text{Tr}_C(X)\} = \text{Tr}_A(X) . \]
Combining this with $\text{Tr}_B (\Psi(X)) = \text{Tr}_A (W|X|)$ finally gives $W = I_A$. Second, the right-hand side of definition for $M$ is rewritten as
\[ \sum_n E_n I_A E_n^\dagger = \Phi(I_B \otimes I_C) = I_B \text{Tr}_C(I_C) . \]
So we obtain $M = d_C I_B$, where $d_C = \text{dim}(\mathcal{H}_C)$. Because $||M||_\infty = d_C$ and $||W||_\infty = 1$, the statement of Theorem 3.2 gives
\[ ||\Psi(X)||_g \leq d_C ||X||_g \]
for $X \in \mathcal{L}_{s.a.}(\mathcal{H}_A)$ and any unitarily invariant norm. For the spectral norm this relation coincides with the one given in \cite{3}. For the Frobenius norm the method of \cite{9} provides a more precise bound. On the other hand, the validity of \cite{12} is not restricted to those norms that are multiplicative over tensor product.
[1] Bhatia, R.: *Positive Definite Matrices*. Princeton: Princeton University Press, 2007
[2] Bhatia, R.: Some inequalities for norm ideals. Commun. Math. Phys. **111**, 33–39 (1987)
[3] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra Appl. **10**, 285-290 (1975)
[4] Devetak, I., Junge, M., King, C. and Ruskai, M.B.: Multiplicativity of completely bounded $p$-norms implies a new additivity result. Commun. Math. Phys. **266**, 37–63 (2006)
[5] Fan, K.: On a theorem of Weyl concerning eigenvalues of linear transformations. I. Proc. Nat. Acad. Sci. USA **35**, 652–655 (1949)
[6] Horn, R.A. and Johnson, C.R.: *Matrix Analysis*. Cambridge: Cambridge University Press, 1985
[7] Jenčová, A.: A relation between completely bounded norms and conjugate channels. Commun. Math. Phys. **266**, 65-70 (2006)
[8] Kraus, K.: General state changes in quantum theory. Ann. Phys. **64**, 311-335 (1971)
[9] Lidar, D.A., Zanardi, P. and Khodjasteh, K.: Distance bounds on quantum dynamics. Phys. Rev. A **78**, 012308 (2008)
[10] Nielsen, M.A. and Chuang, I.L.: *Quantum Computation and Quantum Information*. Cambridge: Cambridge University Press, 2000
[11] Paulsen, V.: *Completely Bounded Maps and Operator Algebras*. Cambridge: Cambridge University Press, 2002
[12] Peres-Garsia, D., Wolf, M.M., Petz, D. and Ruskai, M.B.: Contractivity of positive and trace preserving maps under $L_p$ norms. J. Math. Phys. **47**, 083506 (2006)
[13] Rastegin, A.E.: Trace distance from the viewpoint of quantum operation techniques. J. Phys. A: Math. Theor. **40**, 9533–9549 (2007)
[14] Rastegin, A.E.: Some properties of partial fidelities. Quantum Inf. Comput. **9**, 1069–1080 (2009)
[15] Rastegin, A.E.: Partitioned trace distances. Quantum Inf. Process. DOI 10.1007/s11128-009-0128-7
[16] Uhlmann, A.: Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory. Commun. Math. Phys. **54**, 21–32 (1977)
[17] Uhlmann, A.: On ”partial” fidelities. Rep. Math. Phys. **45**, 407–418 (2000)
[18] Watrous, J.: Notes on super-operator norms induced by Schatten norms. Quantum Inf. Comput. **5**, 58-68 (2005) | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4437,
1
],
[
4437,
9877,
2
],
[
9877,
13730,
3
],
[
13730,
17525,
4
],
[
17525,
19671,
5
]
]
} |
185f42965180f2707e790b9981f0e689e146bea3 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 16,
"total-fallback-pages": 0,
"total-input-tokens": 79971,
"total-output-tokens": 27158,
"fieldofstudy": [
"Computer Science"
]
} | Walk Message Passing Neural Networks and Second-Order Graph Neural Networks
Floris Geerts
University of Antwerp
[email protected]
Abstract
The expressive power of message passing neural networks (MPNNs) is known to match the expressive power of the 1-dimensional Weisfeiler-Leman graph (1-WL) isomorphism test. To boost the expressive power of MPNNs, a number of graph neural network architectures have recently been proposed based on higher-dimensional Weisfeiler-Leman tests. In this paper we consider the two-dimensional (2-WL) test and introduce a new type of MPNNs, referred to as \( \ell \)-walk MPNNs, which aggregate features along walks of length \( \ell \) between vertices. We show that 2-walk MPNNs match 2-WL in expressive power. More generally, \( \ell \)-walk MPNNs, for any \( \ell \geq 2 \), are shown to match the expressive power of the recently introduced \( W[\ell] \) procedure. Based on a correspondence between 2-WL and \( W[\ell] \), we observe that \( \ell \)-walk MPNNs can possibly distinguish pairs of graphs faster than 2-walk MPNNs.
When it comes to concrete learnable graph neural network (GNN) formalisms that match 2-WL or \( W[\ell] \) in expressive power, we consider second-order GNNs that allow for non-linear layers. In particular, to match \( W[\ell] \) in expressive power, we allow \( \ell - 1 \) matrix multiplications in each layer. We propose different versions of second-order GNNs depending on the type of features (i.e., coming from a countable set, or coming from an uncountable set) as this affects the number of dimensions needed to represent the features. Our results indicate that increasing non-linearity in layers by means of allowing multiple matrix multiplications does not increase expressive power. At the very best, it results in a faster distinction of input graphs.
1 Introduction
One of the most popular methods for deep learning on graphs are the message passing neural networks (MPNNs) introduced by Gilmer et al. (2017). An MPNN iteratively propagates vertex features based on the adjacency structure of a graph in a number of rounds. In each round, every vertex receives messages from its neighbouring vertices, based on the features computed in the previous round. Then, each vertex aggregates the received messages and performs an additional update based on the feature of the vertex itself. As such, new features are obtained for every vertex and the MPNN proceeds to the next round. When the features consist of tuples in \( \mathbb{R}^n \), an MPNN can be regarded as a means of computing an embedding of the vertices of a graph into \( \mathbb{R}^n \). An MPNN can also include an additional read-out phase in which the embedded vertices are combined to form a single representation of the entire graph. Important questions in this context relate to the expressive power of MPNNs, such as: “When can two vertices be distinguished by means of the computed embedding?” and “When can two graphs be distinguished?”.
In two independent works (Morris et al., 2019; Xu et al., 2019) such expressivity questions were addressed by connecting MPNNs to the one-dimensional Weisfeiler-Leman (1-WL) graph isomorphism test. Alike MPNNs, 1-WL also iteratively updates vertex features based on the graph’s adjacency structure. Morris et al. (2019) and Xu et al. (2019) show that MPNNs cannot distinguish more vertices by means of the computed embeddings than 1-WL does. In other words, the expressive power of MPNNs is bounded by 1-WL.
Furthermore, Morris et al. (2019) identify a simple class of MPNNs that is as expressive as 1-WL. In other words, for every graph there exists an MPNN in that class whose distinguishing power matches that of 1-WL. Similarly, by applying MPNNs on the direct sum of two graphs, these MPNNs can only distinguish the component graphs when 1-WL can distinguish them. In Geerts et al. (2020), similar results were established for an even simpler class of MPNNs and generalised to MPNNs that can use degree information (such as the graph convolutional networks by Kipf and Welling (2017)). There is a close correspondence between 1-WL and logic.
More precisely, two graphs are indistinguishable by 1-WL if and only if no sentence in the two-variable fragment of first-order logic with counting can distinguish those graphs. A more refined analysis of MPNNs based on this connection to logic can be found in Barceló et al. (2020). The impact of random features on the expressive power of MPNNs is considered in Sato et al. (2020).
Xu et al. (2019) propose another way of letting MPNNs match the expressive power of 1-WL. More specifically, they propose so-called graph isomorphism networks (GINs) and show that GINs can distinguish any two graphs (in some collection of graphs) whenever 1-WL does so. GINs crucially rely on the use of multi layer perceptrons (MLPs) and their universality (Cybenko, 1989; Hornik, 1991). To leverage this universality, the collection of graphs should have bounded degree and all features combined should originate from a finite set.
Since 1-WL fails to distinguish even very simple graphs the above results imply that MPNNs have limited expressive power. To overcome this limitation, higher-dimensional Weisfeiler-Leman graph isomorphism tests have recently been considered as inspiration for constructing graph embeddings. For a given dimension $k$, the $k$-WL test iteratively propagates features for $k$-tuples of vertices and again relies on the adjacency structure of the graph (Grohe and Otto, 2015; Grohe, 2017). From a logic perspective, two graphs are indistinguishable by $k$-WL if and only if they are indistinguishable by sentences in the $(k+1)$-variable fragment of first-order logic with counting and their expressive power is known to increase with increasing $k$ (Cai et al., 1992).
The focus of this paper on 2-WL. By using a graph product construction, MPNNs can be used to match the distinguishing power of 2-WL (Morris et al., 2019). The vertices on which the MPNN act are now triples of vertices and a notion of adjacency between such triples is considered (Maron et al., 2019b). Also here, $O(n^3)$ many embeddings are used. It is not known whether third-order GNNs are also bounded in expressive power by 2-WL\footnote{Perhaps the most promising approach related to 2-WL is the one presented in Maron et al. (2019b). In that paper, simple second-order invariant GNNs are introduced, using second-order tensors in $\mathbb{R}^{n^2 \times s}$ and MLPs, which can simulate 2-WL. A crucial ingredient in these networks is that the layers are non-linear. More specifically, the non-linearity stems from the use of a single matrix multiplication in each layer. This approach only requires to deal with $O(n^2)$ many embeddings making them more applicable than previous approaches. The downside is that the dimension of features needed increases in each round. In this paper we zoom in into those second-order non-linear GNNs and aim to provide some deeper insights. The contributions made in this paper can be summarised as follows.}. We recall from Maron et al. (2019b) that second-order non-linear invariant GNNs are also as expressive as one presented in Maron et al. (2019b). In that paper, the $k$-WL test iteratively propagates features for $k$-tuples of vertices and again relies on the adjacency structure of the graph (Grohe and Otto, 2015; Grohe, 2017). From a logic perspective, two graphs are indistinguishable by $k$-WL if and only if they are indistinguishable by sentences in the $(k+1)$-variable fragment of first-order logic with counting and their expressive power is known to increase with increasing $k$ (Cai et al., 1992).
The focus of this paper on 2-WL. By using a graph product construction, MPNNs can be used to match the distinguishing power of 2-WL (Morris et al., 2019). The vertices on which the MPNN act are now triples of vertices and a notion of adjacency between such triples is considered\footnote{Perhaps the most promising approach related to 2-WL is the one presented in Maron et al. (2019b). In that paper, simple second-order invariant GNNs are introduced, using second-order tensors in $\mathbb{R}^{n^2 \times s}$ and MLPs, which can simulate 2-WL. A crucial ingredient in these networks is that the layers are non-linear. More specifically, the non-linearity stems from the use of a single matrix multiplication in each layer. This approach only requires to deal with $O(n^2)$ many embeddings making them more applicable than previous approaches. The downside is that the dimension of features needed increases in each round. In this paper we zoom in into those second-order non-linear GNNs and aim to provide some deeper insights. The contributions made in this paper can be summarised as follows.}. A disadvantage of this approach is that one has to deal with $O(n^3)$ many embeddings. On the positive side, the dimension of the features is $O(n^2)$. More closely in spirit to GINs, Maron et al. (2019c) introduced higher-order (linear) invariant graph neural networks (GNNs) that use third-order tensors in $\mathbb{R}^{n^3 \times s}$ and MLPs to simulate 2-WL (Maron et al., 2019b). Also here, $O(n^3)$ many embeddings are used. It is not known whether third-order GNNs are also bounded in expressive power by 2-WL\footnote{Perhaps the most promising approach related to 2-WL is the one presented in Maron et al. (2019b). In that paper, simple second-order invariant GNNs are introduced, using second-order tensors in $\mathbb{R}^{n^2 \times s}$ and MLPs, which can simulate 2-WL. A crucial ingredient in these networks is that the layers are non-linear. More specifically, the non-linearity stems from the use of a single matrix multiplication in each layer. This approach only requires to deal with $O(n^2)$ many embeddings making them more applicable than previous approaches. The downside is that the dimension of features needed increases in each round. In this paper we zoom in into those second-order non-linear GNNs and aim to provide some deeper insights. The contributions made in this paper can be summarised as follows.}. We remark that the constructions provided in Morris et al. (2019) and Maron et al. (2019b) generalise to $k$-WL by using multiple graph products and higher-order tensors, respectively.
Perhaps the most promising approach related to 2-WL is the one presented in Maron et al. (2019b). In that paper, simple second-order invariant GNNs are introduced, using second-order tensors in $\mathbb{R}^{n^2 \times s}$ and MLPs, which can simulate 2-WL. A crucial ingredient in these networks is that the layers are non-linear. More specifically, the non-linearity stems from the use of a single matrix multiplication in each layer. This approach only requires to deal with $O(n^2)$ many embeddings making them more applicable than previous approaches. The downside is that the dimension of features needed increases in each round. In this paper we zoom in into those second-order non-linear GNNs and aim to provide some deeper insights. The contributions made in this paper can be summarised as follows.
1. We first introduce $\ell$-walk MPNNs in order to model second-order non-linear invariant GNNs. Walk MPNNs operate on pairs of vertices and can aggregate feature information along walks of a certain length $\ell$ in graphs. We show that $\ell$-walk MPNNs are bounded in expressive power by the $\ell$-walk refinement procedure ($W[\ell]$) recently introduced by Lichter et al. (2019). Furthermore, we show that $\ell$-walk MPNNs match the expressive power of $W[\ell]$.
2. We verify that second-order non-linear invariant GNNs are instances of 2-walk MPNNs. A direct consequence is that their expressive power is bounded by $W[2]$ which is known to correspond to 2-WL (Lichter et al., 2019). Intuitively, walks of length two correspond to the use of a single matrix multiplication in GNNs\footnote{We recall from Maron et al. (2019b) that second-order non-linear invariant GNNs are also as expressive as 2-WL.}. We recall from Maron et al. (2019b) that second-order non-linear invariant GNNs are also as expressive as 2-WL.
3. We generalise second-order non-linear invariant GNNs by allowing $\ell - 1$ matrix multiplications in each layer, for $\ell \geq 2$, and verify that these networks can be seen as instances of $\ell$-walk MPNNs. They are thus bounded in expressive power by $W[\ell]$. We generalise the construction given in Maron et al. (2019b) and show that they also match $W[\ell]$ in expressive power.
\footnote{What we refer to as $k$-WL is sometimes referred to as the “folklore” $k$-dimensional Weisfeiler-Leman test.}
\footnote{To be more precise: a set-based version of 2-WL was considered in Morris et al. (2019) where “vertices” $(u, v, w)$ correspond to a set of three vertices $\{u, v, w\}$, and two vertices $(u, v, w)$ and $(u', v', w')$ are adjacent if and only if $|\{u, v, w\} \cap \{u', v', w'\}| = 2$.}
\footnote{We remark that it has recently been shown in Chen et al. (2020) that second-order linear GNNs are bounded in expressive power by 1-WL on undirected graphs.}
\footnote{We recall that for an adjacency matrix $A_G$ of a graph $G$, the entries in $A_G^\ell$ correspond to the number of walks of length $\ell$ between pairs of vertices.}
4. Based on the properties of $W[\ell]$ and 2-WL reported in Lichter et al. (2019), we observe that allowing for multiple matrix multiplications does not increase the expressive power of second-order GNNs, but vertices and graphs can potentially be distinguished faster (in a smaller number of rounds) than when using only a single matrix multiplication.
5. In order to reduce the feature dimensions needed we consider the setting in which the features are taken from a countable domain, just as in Xu et al. (2019). In this setting, we observe that a constant feature dimension suffices to model 2-WL and $W[\ell]$. We recall that when the features are taken from the reals, the second-order GNNs mentioned earlier require increasing feature dimensions in each round, just as in Maron et al. (2019b). We obtain learnable architectures, similar to GINs, matching $W[\ell]$ in expressive power.
6. Finally, we show that the results in Morris et al. (2019) can be generalised by using non-linearity. As a consequence, we obtain a simple form of $\ell$-walk MPNNs that can simulate $W[\ell]$ (and thus also 2-WL) on a given graph using only $O(n^2)$ many embeddings. We recall that the higher-order graph neural networks in Morris et al. (2019) require $O(n^3)$ many embeddings. Furthermore, we preserve the nice property that the dimension of the features is of size $O(n^2)$.
Our results can be seen as partial answer to the question raised by Maron et al. (2019a), whether polynomial layers (of degree greater than two) increase the expressive power of second-order invariant GNNs. We answer this negatively in the restricted setting in which each layer consists of multiple matrix multiplications rather than general equivariant polynomial layers. Indeed, the use of multiple matrix multiplications can be simulated by single matrix multiplication at the cost of introducing additional layers.
For readers familiar with GNNs we summarise the proposed architectures in Table 1 and refer for details to Section 6. All architectures generalise to match $W[\ell]$ in expressive power. We note that the last architecture in Table 1 is the one proposed by Maron et al. (2019b).
### Organisation of the paper.
We start by introducing notation and describing the 2-dimensional Weisfeiler-Leman (2-WL) graph isomorphism test and walk refinement procedure ($W[\ell]$) in Section 2. To model $W[\ell]$ as a kind of MPNN we introduce $\ell$-walk MPNNs in Section 3. In Section 4 we verify that $\ell$-walk MPNNs are bounded in expressive power by $W[\ell]$. Matching lower bounds on the expressive power of $\ell$-walk MPNNs are provided in Section 5 in the case when labels originate from a countable domain, and when they come from an uncountable domain. The obtained insights are used in Section 6 to build learnable graph neural networks that match $W[\ell]$ (and 2-WL in particular) in expressive power. We conclude the paper in Section 7.
### 2 Preliminaries
We use $\{\}$ and $\{\}^\ast$ to indicate sets and multisets, respectively. The sets of natural, rational, and real numbers are denoted by $\mathbb{N}$, $\mathbb{Q}$, and $\mathbb{R}$, respectively. We write $\mathbb{P}^+$ to denote the subset of numbers from $\mathbb{P}$ which are strictly positive, e.g., $\mathbb{N}^+ = \mathbb{N} \setminus \{0\}$. For $n \in \mathbb{N}^+$, we denote with $[n]$ the set of numbers $\{1, \ldots, n\}$.
### Labelled graphs.
A labelled directed graph is given by $G = (V, E, \eta)$ with vertex set $V$, edge relation $E \subseteq V^2$, and where $\eta : E \rightarrow \Sigma$ is an edge labelling function into some set $\Sigma$ of labels. Without loss of generality we identify $V$ with $[n]$. For $\ell \in \mathbb{N}^+$, a walk in $G$ from vertex $i$ to vertex $j$ of length $\ell$ is a sequence of vertices
| Dimensions of $A^{(t)}$ | GNN |
|--------------------------|-----|
| $n \times n$ | $A^{(t)}_{ij} := \sum_{k \in [n]} \text{MLP}_{\theta}(\{A^{(t-1)}_{ik}, A^{(t-1)}_{kj}\})$ |
| $n \times n \times 2$ | $A^{(t)}_{ik} := \text{MLP}_{\theta(t)}(\sum_{k \in [n]} \text{MLP}_{\phi(t)}(A^{(t-1)}_{ik} \cdot \text{MLP}_{\phi(t)}(A^{(t-1)}_{kj})))$ |
| $n \times n \times s_t, s_t \in \mathcal{O}(n^2)$ | $A^{(t)}_{tjs} = \text{ReLU} \left( \sum_{k \in [n]} \sum_{c,d \in [s_{t-1}]} A^{(t-1)}_{ikc} \cdot A^{(t-1)}_{kjd} \cdot W^{(t)}_{tcs} - q_{tjs} \right)$ |
Table 1: Various graph neural network architectures matching 2-WL in expressive power.
\((i, i_1, i_2, \ldots, i_{t-1}, j)\) such that each consecutive pair of vertices is an edge in \(G\). For \(t \in \mathbb{N}^+\) we denote by \(W[t]_G(i, j)\) the set of walks of length \(t\) in \(G\) starting in \(i\) and ending at \(j\).
**Remark 2.1.** We opt to work with edge-labelled graphs rather than the more standard vertex-labelled graphs. This does not impose any restriction since we can always turn a vertex-labelled graph into an edge-labelled graph. More specifically, given a vertex-labelled graph \(G = (V, E, \nu)\) with \(\nu: V \rightarrow \Sigma\) one can define the corresponding edge-labelling \(\eta: E \rightarrow \Sigma \times \Sigma\) by \(\eta(i, j) := (\nu(i), \nu(j))\), and then simply consider \(G = (V, E, \eta)\) instead of \(G = (V, E, \nu)\).
Refinements of labellings. We will need to be able to compare two edge labellings and we do this as follows. Given two labellings \(\eta: E \rightarrow \Sigma\) and \(\eta': E \rightarrow \Sigma'\) we say that \(\eta\) refines \(\eta'\), denoted by \(\eta \sqsubseteq \eta'\), if for every \((i, j)\) and \((i', j')\) \(\in E\), \((\eta(i, j) = \eta(i', j'))\) implies that \(\eta'(i, j) = \eta'(i', j')\). If \(\eta \sqsubseteq \eta'\) and \(\eta' \subseteq \eta\) then \(\eta\) and \(\eta'\) are said to be equivalent, and we denote this by \(\eta \equiv \eta'\).
We next describe two procedures which iteratively generate refinements of edge labellings. First, we consider the \(2\)-dimensional Weisfeiler-Leman (2-WL) procedure. This procedure iteratively generates edge labellings, starting from an initial labelling \(\eta\), until no further changes to the edge labelling is made. The labelling produced in round \(t\) is denoted by \(\eta[t]_G\). Since 2-WL generates labellings for all pairs of vertices, it is commonly assumed that the input graph is a complete graph, i.e., \(E = V^2\). We remark that an incomplete graph \(G = (V, E, \eta)\) can always be regarded as a complete graph in which the (extended) edge labelling \(\eta: V^2 \rightarrow \Sigma\) assigns a special label to non-edges, i.e., those pairs in \(V^2 \setminus E\).
Let \(G = (V, E, \eta)\) be a (complete) labelled graph. Then the initial labelling produced by 2-WL is defined as \(\eta[0]_G := \eta\). For \(t > 0\) and \(i, j \in [n]\) we define:
\[
\eta[t]_G(i, j) := \text{HASH}\left(\eta[t−1]_G(i, j), \left\{\left(\eta[t−1]_G(i, k), \eta[t−1]_G(k, j)\right) \mid k \in [n]\right\}\right),
\]
where \(\text{HASH}\) injectively maps \((a, S)\) with \(a \in \Sigma\) and \(S\) a multiset of pairs of labels in \(\Sigma\) to a unique label in \(\Sigma\). It is known that \(\eta[t]_G \sqsubseteq \eta[t−1]_G\), for all \(t > 0\), and thus the 2-WL procedure indeed generates refinements of labellings.
We denote by \(\eta[t]_G\) the labelling \(\eta[t−1]_G\) such that \(\eta[t]_G \equiv \eta[t−1]_G\). It is known that \(\eta[2]_G\) is reached using at most \(t = O(n \log(n))\) rounds, where \(n = |V|\) (Lichter et al., 2019).
One can simplify 2-WL by assuming that the initial labelling \(\eta\) assigns different labels to loops (i.e., pairs of the form \((i, i)\) for \(i \in [n]\)) than to edges to other edges. In other words, when for every \(i, j, k \in [n]\) such that \(j \neq k\), \(\eta(i, i) \neq \eta(j, k)\) holds. Under this assumption, one can equivalently consider:
\[
\eta[t]_G(i, j) := \text{HASH}\left(\left\{\left(\eta[t−1]_G(i, k), \eta[t−1]_G(k, j)\right) \mid k \in [n]\right\}\right).
\]
In the following, we always assume that \(\eta\) treats loops differently from non-loops. One can always ensure this by modifying the labels of a given edge labelling.
To make 2-WL invariant under graph isomorphisms one requires that the initial edge-labelling respects transpose equivalence, i.e., for any \(i, j, i', j' \in [n]\), \(\eta(i, j) = \eta(i', j')\) implies that \(\eta(j, i) = \eta(j', i')\). In the following we always assume that this assumption holds. One can again ensure this by applying an appropriate modification to a given edge labelling. We also note that this assumption is satisfied when the edge labelling originates from a vertex labelling, as explained in Remark 2.1.
The second procedure which we consider is the \(\ell\)-walk refinement procedure \(W[\ell]\), recently introduced by Lichter et al. (2019). Similar to 2-WL, it iteratively generates labellings. The labelling produced by \(W[\ell]\) in round \(t\) is denoted by \(\eta[\ell]_G\). The initial labelling is defined as \(\eta[0]_G := \eta\) just as for 2-WL. For \(t > 0\) and \(i, j \in [n]\) we define:
\[
\eta[\ell]_G(i, j) := \text{HASH}\left(\left\{\left(\eta[\ell−1]_G(i, i_1), \eta[\ell−1]_G(i_1, i_2), \ldots, \eta[\ell−1]_G(i_{\ell−1}, j)\right) \mid i_1, \ldots, i_{\ell−1} \in [n]\right\}\right),
\]
where \(\text{HASH}\) now injectively maps multisets of \(\ell\) pairs of labels in \(\Sigma\) to a unique label in \(\Sigma\).
We observe that \(\eta[2]_G = \eta[2]_G\). Furthermore, for every \(t > 0\), \(\eta[\ell]_G \sqsubseteq \eta[\ell−1]_G\) and thus also \(W[\ell]\) generates refinements of labellings. We define \(\eta[k]_G\) as the labelling \(\eta[\ell]_G\) such that \(\eta[\ell]_G \equiv \eta[\ell]_G\). We further recall from Lichter et al. (2019) that \(\eta[\ell]_G \sqsubseteq \eta[\ell]_G\) for \(k \leq \ell\) and that \(\eta[\ell]_G \sqsubseteq \eta[\ell]_G\) for all \(t \geq 0\). In particular, \(\eta[k]_G \equiv \eta[2]_G\).
Remark 2.2. We thus see that both procedures generate the same labelling after a (possibly different) number of rounds. The labellings obtained by the two procedures may be different, however, in each round, except for \( t = 0 \), as is illustrated in Lichter et al. (2019). Furthermore, if \( \eta_{2\text{-WL}} \) is reached in \( T \) rounds by the 2-WL procedure, then it is reached in \( T/\lceil \log \ell \rceil \) rounds by the \( W[\ell] \) procedure.
Labellings and matrices. Given a tensor \( \mathbf{A} \in \mathbb{R}^{n^2 \times s} \) we denote by \( A_{ij,k} \in \mathbb{R} \) its entry at position \( i, j \in [n] \) and \( k \in [s] \), by \( \mathbf{A}_{ij} \in \mathbb{R}^s \) the vector at position \( i, j \in [n] \), and by \( \mathbf{A}_{\cdot \cdot} \in \mathbb{R}^{n^2 \times s} \) the matrix at position \( i \in [n] \).
Similar notions are in place for matrices and higher-order tensors. A tensor \( \mathbf{A} \in \mathbb{R}^{n^2 \times s} \) naturally corresponds to an edge labelling \( \eta: E \to \mathbb{R}^s \) by letting \( \eta(i, j) := \mathbf{A}_{ij} \), for \( i, j \in [n] \). Conversely, when given an edge labelling \( \eta: E \to \Sigma \), for \( E = V^2 \), we assume that we can encode the labels in \( \Sigma \) as vectors in some \( \mathbb{R}^s \). A common way to do this is by hot-encoding labels in \( \Sigma \) by basis vectors in \( \mathbb{R}^s \) for some \( s \in \mathbb{N} \). In this way, \( \eta \) can be regarded as a tensor in \( \mathbb{R}^{n^2 \times s} \). We interchangeably consider edge labels and edge labellings as vectors and tensors, respectively.
3 Walk Message Passing Neural Networks
We start by extending MPNNs such that they can easily model the walk-refinement procedure described above. This generalisation of MPNNs is such that message passing occurs between pairs of vertices and is restricted by walks in graphs, rather than between single vertices and their adjacent vertices as in standard MPNNs (Gilmer et al., 2017). We will refer to this generalisation as walk MPNNs.
Walk MPNNs iteratively compute edge labellings starting from an input labelled graph \( G = (V, E, \eta) \). We refer to each iteration as a round. Walk MPNNs are parametrised by a number \( \ell \in \mathbb{N} \), with \( \ell \geq 2 \), which bounds the length of walks considered, and we refer to them as \( \ell \)-walk MPNNs. We assume that the edge labelling of the input graph is of the form \( \eta: E \to \mathbb{R}^{s_0} \) for some \( s_0 \in \mathbb{N}^+ \). In what follows we fix the number of vertices to be \( n \).
After round \( t \geq 0 \), the labelling returned by an \( \ell \)-walk MPNN \( M \) is denoted by \( \eta_M^{(t)} \) and is of the form \( \eta_M^{(t)}: E \to \mathbb{R}^{s_t} \), for some \( s_t \in \mathbb{N}^+ \). We omit the dependency on the input graph \( G \) in the labellings unless specified otherwise. We next detail how \( \eta_M^{(t)} \) is computed.
Initialisation. We let \( \eta_M^{(0)} := \eta \).
Then, for every round \( t = 1, 2, \ldots \) we define \( \eta_M^{(t)} : E \to \mathbb{R}^{s_t} \), as follows:
**Message Passing.** Each pair \( (v, w) \in V^2 \) receives messages from ordered sequences of edges on walks in \( G \) of length \( \ell \) starting in \( v \) and ending at \( w \). These messages are subsequently aggregated. Formally, if \( (v, v_1, \ldots, v_{\ell-1}, w) \) is a walk of length \( \ell \) in \( G \) then the function \( MSG_M^{(t)} \) receives the labels (computed in the previous round) \( \eta_M^{(t-1)}(v, v_1), \eta_M^{(t-1)}(v_1, v_2), \ldots, \eta_M^{(t-1)}(v_{\ell-1}, w) \) of the edges in this walk, and outputs a label in \( \mathbb{R}^{s_t} \), for some \( s_t \in \mathbb{N}^+ \). Then, for every pair \( (v, w) \in V^2 \) we aggregate by summing all the received labels:
\[
\mathbf{m}_M^{(t)}(v, w) := \sum_{(v, v_1, \ldots, v_{\ell-1}, w) \in W^\ell_G(v, w)} MSG_M^{(t)}\left(\eta_M^{(t-1)}(v, v_1), \eta_M^{(t-1)}(v_1, v_2), \ldots, \eta_M^{(t-1)}(v_{\ell-1}, w)\right) \in \mathbb{R}^{s_t}.
\]
**Updating.** Each pair \( (v, w) \in V^2 \) further updates \( \mathbf{m}_M^{(t)}(v, w) \) based on its current label \( \eta_M^{(t-1)}(v, w) \):
\[
\eta_M^{(t)}(v, w) := UPD_M^{(t)}\left(\eta_M^{(t-1)}(v, w), \mathbf{m}_M^{(t)}(v, w)\right) \in \mathbb{R}^{s_t}.
\]
Here, the message functions \( MSG_M^{(t)} \) and update functions \( UPD_M^{(t)} \) are arbitrary functions. When a walk MPNN \( M \) only iterates for a finite number of rounds \( T \), we define the final labelling \( \eta_M : E \to \mathbb{R}^s \) with \( s = s_T \) returned by \( M \) on \( G = (V, E, \eta) \), as \( \eta_M(v, w) := \eta_M^{(T)}(v, w) \) for every \( v, w \in V \). If further aggregation over the entire graph is needed, e.g., for graph classification, an additional readout function \( READOUT_M(\{\eta_M(v, w) | v, w \in V\}) \) can be applied. We ignore the read-out function in this paper as most of the computation happens by means of the message and update functions. We do comment on read-out functions in Remark 6.4 in Section 6.
4 Upper bound on the expressive power of walk MPNNs
We start by showing that the expressive power of $\ell$-walk MPNNs is bounded by the expressive power of $W[\ell]$ just as MPNNs are bounded in expressive power by 1-WL. The proof of the following proposition is a straightforward modification of the proofs given in Xu et al. (2019) and Morris et al. (2019).
**Proposition 4.1.** For any $\ell$-walk MPNN $M$, any graph $G = (V,E,\eta)$, and every $t \geq 0$, $\eta^{(t)}_{W[\ell]} \subseteq \eta^{(t)}_M$.
**Proof.** Let $M$ be an $\ell$-walk MPNN. We verify the proposition by induction on the number of rounds $t$. Clearly, when $t = 0$, $\eta^{(0)}_{W[\ell]} = \eta = \eta^{(0)}_M$, so we can focus on $t > 0$. Suppose that $\eta^{(t-1)}_{W[\ell]} \subseteq \eta^{(t-1)}_M$ holds. We need to show that $\eta^{(t)}_{W[\ell]} \subseteq \eta^{(t)}_M$ holds as well.
Let $v, w, v', w'$ be vertices for which $\eta^{(t)}_{W[\ell]}(v, w) = s^{(t)}_{W[\ell]}(v', w')$ is satisfied. By definition of $W[\ell]$ this implies that
$$\left\{ \left( \eta^{(t-1)}_{W[\ell]}(v, v_1), \ldots, \eta^{(t-1)}_{W[\ell]}(v_{t-1}, w) \right) \right\}_{v_1, \ldots, v_{t-1} \in V} = \left\{ \left( \eta^{(t-1)}_{W[\ell]}(v', v_1), \ldots, \eta^{(t-1)}_{W[\ell]}(v_{t-1}, w') \right) \right\}_{v_1, \ldots, v_{t-1} \in V},$$
or in other words, there exists a bijection $\iota: [n]^{t-1} \rightarrow [t]^{t-1}$ such that for every $v_1, \ldots, v_{t-1}$ in $V$,
$$\left( \eta^{(t-1)}_{W[\ell]}(v, v_1), \ldots, \eta^{(t-1)}_{W[\ell]}(v_{t-1}, w) \right) = \left( \eta^{(t-1)}_{W[\ell]}(v', v_1), \ldots, \eta^{(t-1)}_{W[\ell]}(v_{t-1}, w') \right),$$
with $(v_1, \ldots, v_{t-1}) = \iota(v_1, \ldots, v_{t-1})$. By induction, this also implies that for every $v_1, \ldots, v_{t-1}$ there are unique $w_1, \ldots, w_{t-1}$ such that
$$\left( \eta^{(t-1)}_{M}(v, v_1), \ldots, \eta^{(t-1)}_{M}(v_{t-1}, w) \right) = \left( \eta^{(t-1)}_{M}(v', v_1), \ldots, \eta^{(t-1)}_{M}(v_{t-1}, w') \right)$$
holds. This in turn implies that for every $v_1, \ldots, v_{t-1}$ there are unique $w_1, \ldots, w_{t-1}$ such that
$$\text{MSG}^{(t)}_M \left( \eta^{(t-1)}_{M}(v, v_1), \ldots, \eta^{(t-1)}_{M}(v_{t-1}, w) \right) = \text{MSG}^{(t)}_M \left( \eta^{(t-1)}_{M}(v', v_1), \ldots, \eta^{(t-1)}_{M}(v_{t-1}, w') \right)$$
is satisfied. As a consequence, $m^{(t)}_M(v, w) = m^{(t)}_M(v', w')$ since these are defined by summing up the messages over all $v_1, \ldots, v_{t-1}$ and $w_1, \ldots, w_{t-1}$, respectively. We also note that if $\eta^{(t)}_{W[\ell]}(v, w) = \eta^{(t)}_{W[\ell]}(v', w')$ holds, then $\eta^{(t-1)}_{W[\ell]}(v, w) = \eta^{(t-1)}_{W[\ell]}(v', w')$ (Lichter et al., 2019). Hence also $\eta^{(t-1)}_{M}(v, w) = \eta^{(t-1)}_{M}(v', w')$ holds by induction.
We may thus conclude that
$$\eta^{(t)}_{M}(v, w) = \text{UPD}^{(t)}_M \left( \eta^{(t-1)}_{M}(v, w), m^{(t)}_M(v, w) \right) = \text{UPD}^{(t)}_M \left( \eta^{(t-1)}_{M}(v', w'), m^{(t)}_M(v', w') \right) = \eta^{(t)}_{M}(v', w'),$$
holds, as desired. \qed
As already mentioned in the preliminaries, $\eta^{(t)}_{W[2]} \equiv \eta^{(t)}_{2\text{-WL}}$ and $\eta^{(t\log(\ell))}_{W[\ell]} \leq \eta^{(t)}_{W[\ell]}$ for all $t \geq 0$. We may thus also infer the following.
**Corollary 4.1.** For every $\ell$-walk MPNN $M$, any graph $G = (V,E,\eta)$, and $t \geq 0$, $\eta^{(t\log(\ell))}_{W[\ell]} \subseteq \eta^{(t)}_M$. \qed
We may thus conclude that for $\ell \geq 2$, $\ell$-walk MPNNs are limited in their distinguishing power by 2-WL, but they may reach the final labelling $\eta^{(t)}_{2\text{-WL}}$ faster than by using 2-walk MPNNs. This comes at the cost, however, of a computationally more intensive messaging passing phase. We next show that $\ell$-walk MPNNs can also simulate $W[\ell]$ from which we can infer that $\ell$-walk MPNNs match $W[\ell]$ in their expressive power.
5 Lower bound on the expressive power of $\ell$-walk MPNNs
We next show how to simulate $W[\ell]$ by means of $\ell$-walk MPNNs. In particular, we show that they can simulate $W[\ell]$ on all graphs of a fixed size ($|V| = n$). We provide two simulations, one for when the labels come from a countable domain, and one for when the labels come from an uncountable domain, such as $\mathbb{R}^a$ for some $a \in \mathbb{N}^+$.
The challenge is to simulate the hash function used in $W[\ell]$ by means of message and update functions, hereby taking into consideration that $\ell$-walk MPNNs always perform a sum aggregation over the received messages\(^\ddagger\). For the countable case we generalise the technique underlying GINs (Xu et al., 2019); for the uncountable case we use multi-symmetric polynomials underlying higher-order graph neural networks (Maron et al., 2019b).
5.1 Simulating $W[\ell]$: Countable case
We first consider the setting in which graphs $G = (V, E, \eta)$ have a labelling $\eta : E \to \mathcal{X}$ for some countable domain $\mathcal{X}$. Without loss of generality we assume that $\mathcal{X} = \mathbb{N}$. Indeed, since $\mathcal{X}$ is countable the elements in $\mathbb{N}$ can be mapped to elements in $\mathbb{N}$ by means of an injection. The following result shows that $\ell$-walk MPNNs can simulate $W[\ell]$ on the set of of graphs with $n$ vertices with labels from $\mathbb{N}$.
Proposition 5.1. For every $\ell \in \mathbb{N}$, $\ell \geq 2$, there exists an $\ell$-walk MPNN $M$ such that $\eta^{(t)}_{W[\ell]} \equiv \eta^{(t)}_{M}$ holds for all $t \geq 0$, on any given input graph $G = (V, E, \eta)$ with $\eta : E \to \mathbb{N}$ and $|V| = n$.
Proof. We define the $\ell$-walk MPNN $M$ by induction on $\ell$. More specifically, we inductively define the message and update functions of $M$ and verify that $\eta^{(t)}_{W[\ell]} \equiv \eta^{(t)}_{M}$ holds for all $t$ on any given input graph $G = (V, E, \eta)$ with $\eta : E \to \mathbb{N}$. Furthermore, along the way we verify that for $t > 0$, $\eta^{(t)}_{M} : E \to \mathbb{N}$, i.e., the labels remain to be elements in $\mathbb{N}$.
Clearly, by definition, $\eta^{(0)}_{W[\ell]} = \eta = \eta^{(0)}_{M}$ so we can focus on $t > 0$. Assume that we have specified $M$ up to round $t - 1$ such that $\eta^{(t-1)}_{W[\ell]} \equiv \eta^{(t-1)}_{M}$ holds, where $\eta^{(t-1)}_{M} : E \to \mathbb{N}$. We next consider round $t$.
The labels of a walk of length $\ell$ correspond to an element in $\mathbb{N}^\ell$. We want to map these to elements in $\mathbb{N}$ by means of an injection. We can use any pairing function $\tau : \mathbb{N}^\ell \to \mathbb{N}$ for this purpose\(^\dagger\). Given such a pairing function, we define the function $h : \mathbb{N}^\ell \to \mathbb{N}$ as
$$h(a_1, \ldots, a_\ell) := (n^\ell - 1 + 1)^\tau(a_1, \ldots, a_\ell).$$
Then, any multiset $S$ consisting of at most $n^{\ell-1}$ elements in $\mathbb{N}^\ell$ can be mapped to a number in $\mathbb{N}$ by means of the injective function
$$\varphi(S) := \sum_{(a_1, \ldots, a_\ell) \in S} h(a_1, \ldots, a_\ell).$$
Indeed, we here just represent a multiset by its unique $(n^{\ell-1} + 1)$-ary representation, just as in Xu et al. (2019). It now suffices to define $M$ to consist of the following message and update functions\(^\ddagger\) in round $t$: For every $a_1, \ldots, a_\ell \in \mathbb{R}$:
$$\text{MSG}^{(t)}_{M}(a_1, \ldots, a_\ell) := h(a_1, \ldots, a_\ell) \in \mathbb{R},$$
and for every $a, b \in \mathbb{R}$,
$$\text{UPD}^{(t)}_{M}(a, b) := b \in \mathbb{R}.$$
It remains to verify that $\eta^{(t)}_{W[\ell]} \equiv \eta^{(t)}_{M}$ holds. In other words, we need to show that for every $v, w, v', w' \in V$,
$$\eta^{(t)}_{W[\ell]}(v, w) = \eta^{(t)}_{M}(v', w') \iff \eta^{(t)}_{M}(v, w) = \eta^{(t)}_{M}(v', w').$$
We define for every $v, w \in V$, the multiset
$$S_{v, w} := \left\{ \left( \eta^{(t-1)}_M(v, v_1), \ldots, \eta^{(t-1)}_M(v_{\ell-1}, v_\ell) \right) \left| v_1, v_2, \ldots, v_{\ell-1} \in [n] \right. \right\}.$$
Hence, \( \eta_M^{(t)}(v, w) = \eta_M^{(t)}(v', w') \) if and only if \( S_{v,w} = S_{v',w'} \). It now suffices to observe that
\[
\eta_M^{(t)}(v, w) = \sum_{v_1, \ldots, v_{t-1} \in V} h(\eta_M^{(t-1)}(v, v_1), \ldots, \eta_M^{(t-1)}(v_{t-1}, w)) = \varphi(S_{v,w})
\]
and,
\[
\eta_M^{(t)}(v', w') = \sum_{v_1, \ldots, v_{t-1} \in V} h(\eta_M^{(t-1)}(v', v_1), \ldots, \eta_M^{(t-1)}(v_{t-1}, w')) = \varphi(S_{v',w'})
\]
Since the multiplicity of every element in the multisets \( S_{v,w} \) is bounded by \( n^{t-1} \), \( \varphi \) is an injection and thus \( S_{v,w} = S_{v',w'} \) if and only if \( \varphi(S_{v,w}) = \varphi(S_{v',w'}) \) if and only if \( \eta_M^{(t)}(v, w) = \eta_M^{(t)}(v', w') \), from which the proposition follows. We note that when the labels assigned by \( \eta^{(t-1)} \) belong to \( \mathbb{N} \), then so do the labels assigned by \( \eta_M^{(t)} \), by the definition of \( \varphi \). As a consequence, the \( \ell \)-walk MPNN \( M \) generates labels in \( \mathbb{N} \) in every round.
We note that in the simulation above the message and update functions can be fixed, independent of \( t \).
**Remark 5.1.** The function \( \varphi \) used in the proof of Proposition 5.1 is similar to the one motivating the definition of GINs (Xu et al., 2019). The difference is that Xu et al. (2019) incorporate the initial injective mapping from \( X \) to \( N \) in the first round, and that instead of a representation in \( N \), a representation in \( Q \) is used. Translated to our setting this corresponds to defining \( h(a_1, \ldots, a_\ell) \) as \( (n^{t-1}+1)^{-\tau} \) with \( \tau \) a pairing function and \( \pi : X \rightarrow N \) an injection from \( X \) to \( N \). Since labels now take rational values, one needs to incorporate an injective mapping from \( Q \) to \( N \) in each round \( t > 1 \). By contrast, our simulation produces labels in \( N \) for all \( t \).
**Remark 5.2.** In the standard MPNN setting, MPNNs are known to simulate 1-WL on all graphs with labels in \( N \) and that have bounded degree. As such MPNNs can simulate 1-WL on graphs of arbitrary size. In our setting, \( W'[\ell] \) assigns labels to all pairs of vertices and the degree is thus always \( n \) because the input graphs are complete graphs. Hence, the bounded degree condition reduces to the graphs having a fixed size.
### 5.2 Simulating \( W'[\ell] \): Uncountable case
We next consider graphs \( G = (V,E,\eta) \) with \( \eta : E \rightarrow \mathbb{R}^n \) for some \( s_0 \in \mathbb{N}^+ \). We first recall from Maron et al. (2019b) how to, by using multi-symmetric polynomials, assign a unique value in \( \mathbb{R}^b \) to multisets of \( m \) elements in \( \mathbb{R}^a \) for some \( a, b \in \mathbb{N} \). Let \( a, m \in \mathbb{N} \) and let \( \alpha \in [m]^a \) be a multi-index, i.e., \( \alpha = (\alpha_1, \ldots, \alpha_a) \) with \( \alpha_i \in [m] \) for \( i \in [a] \). For an element \( x = (x_1, \ldots, x_a) \in \mathbb{R}^a \) we write \( x^\alpha := \prod_{i \in [a]} x_i^{\alpha_i} \) and define \( |\alpha| = \sum_{i \in [a]} |\alpha_i| \). Consider a multiset \( X = \{x_1, \ldots, x_m\} \) with each \( x_i \in \mathbb{R}^a \). We represent such a multiset by a matrix, also denoted by \( X \), by choosing an arbitrary order on the elements \( x_1, \ldots, x_m \). More precisely, \( X \in \mathbb{R}^{m \times a} \) and \( x_i \) corresponds to one of the \( x_i \)'s for each \( i \in [m] \). We next define \( p_\alpha(X) := \sum_{j \in [m]} (X_{j,i})^\alpha \) and let \( u(X) := (p_\alpha(X) \mid |\alpha| \leq m) \in \mathbb{R}^b \), where \( b \) corresponds to the number of multi-indexes \( \alpha \in [m]^a \) with \( |\alpha| \leq m \). More precisely, \( b = \binom{m+a}{a} \). Then, for \( X \) and \( X' \) in \( \mathbb{R}^{m \times a} \), \( u(X) = u(X') \) if and only if there exists a permutation \( \pi \) of \( [m] \) such that \( X_{\pi(i), i} = X'_{\pi(i), i} \) for all \( j \in [m] \) (see Proposition 1 in Maron et al. (2019b)). In other words, by regarding \( X \) and \( X' \) as multisets, \( u(X) = u(X') \) if and only if \( X \) and \( X' \) represent the same multiset.
**Proposition 5.2.** For every \( \ell \in \mathbb{N}, \ell \geq 2 \), there exists an \( \ell \)-walk MPNN \( M \) such that \( \eta_M^{(t)} = \eta_M^{(t)} \) for all \( t \geq 0 \), on any given an input graph \( G = (V,E,\eta) \) with \( \eta : E \rightarrow \mathbb{R}^n \) and \( |V| = n \).
**Proof.** For each \( \ell \in \mathbb{N}, \ell \geq 2, n \in \mathbb{N}^+ \) and \( s_0 \in \mathbb{N}^+ \) we define an \( \ell \)-walk MPNN \( M \) such that \( \eta_M^{(t)} = \eta_M^{(t)} \) holds on any given an input graph \( G = (V,E,\eta) \) with \( |V| = n \) and \( \eta : E \rightarrow \mathbb{R}^n \). We define \( M \) by induction on \( t \). More specifically, we inductively define the message and update functions of \( M \) and verify that \( \eta_M^{(t)} = \eta_M^{(t)} \) holds for all \( t \) on any given an input graph \( G = (V,E,\eta) \) with \( |V| = n \) and \( \eta : E \rightarrow \mathbb{R}^n \).
Clearly, by definition, \( \eta_M^{(0)} = \eta = \eta_M^{(0)} \), so we can focus on \( t > 0 \). Assume that we have specified \( M \) up to round \( t - 1 \) such that \( \eta_M^{(t-1)} = \eta_M^{(t-1)} \) holds, where \( \eta_M^{(t-1)} : E \rightarrow \mathbb{R}^{s_{t-1}} \). We next consider round \( t \).
We use the injective function \( u \) as described above. We will apply it to the setting whether \( a = \ell s_{t-1} \) and \( m = n^{t-1} \). More precisely, we consider the multi-index set \( \{ \alpha \mid \alpha \in [n^{t-1}]^{s_{t-1}}, |\alpha| \leq n^{t-1} \} \) of cardinality \( s_t = \binom{n^{t-1}+\ell s_{t-1}}{s_{t-1}} \). We denote the elements in this set by \( \alpha_s \) for \( s \in [s_t] \). We define for \( x_1, \ldots, x_{s_t} \) in \( \mathbb{R}^{s_t} \),
\[
MS_G^{(t)}(x_1, \ldots, x_{s_t}) := \{(x_1, \ldots, x_{s_t})^\alpha \mid s \in [s_t] \} \in \mathbb{R}^{s_t}.
\]
When evaluated on an input graph $G = (V, E, \eta)$, for any $v, w \in V$:
$$m_M^{(t)}(v, w) = \sum_{v_1, \ldots, v_{t-1} \in V} \text{MSG}^{(t)} \left( \eta_M^{(t-1)}(v, v_1), \eta_M^{(t-1)}(v_1, v_2), \ldots, \eta_M^{(t-1)}(v_{t-1}, w) \right)$$
$$= \left( p_{\alpha_s}(X^{(t-1)}_{v,w}) \mid s \in [s_t] \right) =: u^{(t)}(X^{(t-1)}_{v,w}) \in \mathbb{R}^{s_t},$$
with $X^{(t-1)}_{v,w}$ the $\mathbb{R}^{n^{t-1} \times s_{t-1}}$ matrix whose rows are indexed by $(v_1, v_2, \ldots, v_{t-1}) \in [n]^{t-1}$ and such that
$$(X^{(t-1)}_{v,w}(v_1, v_2, \ldots, v_{t-1}), \cdot) := \left( \eta_M^{(t-1)}(v, v_1), \eta_M^{(t-1)}(v_1, v_2), \ldots, \eta_M^{(t-1)}(v_{t-1}, w) \right).$$
We have mentioned above that $u^{(t)}(X^{(t-1)}_{v,w}) = u^{(t)}(X^{(t-1)}_{v',w'})$ if and only if
$$\left\{ \left( \eta_M^{(t-1)}(v, v_1), \eta_M^{(t-1)}(v_1, v_2), \ldots, \eta_M^{(t-1)}(v_{t-1}, w) \right) \right\}_{v_1, v_2, \ldots, v_{t-1} \in [n]} = \left\{ \left( \eta_M^{(t-1)}(v', v_1), \eta_M^{(t-1)}(v_1, v_2), \ldots, \eta_M^{(t-1)}(v_{t-1}, w') \right) \right\}_{v_1, v_2, \ldots, v_{t-1} \in [n]}.$$
From the induction hypothesis we know that $\eta_M^{(t-1)} = \eta_M^{(t-1)}$ and hence, $m_M^{(t)}(v, w) = m_M^{(t)}(v', w')$ if and only if $u^{(t)}(X^{(t-1)}_{v,w}) = u^{(t)}(X^{(t-1)}_{v',w'})$ if and only if $\eta_M^{(t)}(v, w) = \eta_M^{(t)}(v', w')$. It now suffices to define for any $x \in \mathbb{R}^{s_{t-1}}$ and $y \in \mathbb{R}^{s_t}$:
$$\text{UPD}_M^{(t)}(x, y) := y \in \mathbb{R}^{s_t},$$
such that when evaluated on the input graph,
$$\eta_M^{(t)}(v, w) := \text{UPD}_M^{(t)}(\eta_M^{(t-1)}(v, w), m_M^{(t)}(v, w)) := m_M^{(t)}(v, w) = u^{(t)}(X^{(t-1)}_{v,w}).$$
Hence, $\eta_M^{(t)}(v, w) = \eta_M^{(t)}(v', w')$ if and only if $\eta_M^{(t)}(v, w) = \eta_M^{(t)}(v', w')$, as desired. \hfill \square
We remark that the dimensions $s_t$ needed in each round grow very fast. For example, for $n = 10$, $\ell = 2$ and with initial $s_0$ set to 1, we have $s_1 = \binom{12}{2} = 66$ and $s_2 = \binom{14}{2} = 664226242466073$. This is in sharp contrast to $s_t = 1$ for all $t \geq 1$ in the countable case. It is an interesting open problem how to treat the real number case with constant (or small) $s_t$ dimensions. A preliminary investigation in dimensionality aspects of representations of multi-sets with elements from the reals is reported in Wagstaff et al. (2019) and Seo et al. (2019).
### 6 Simulation of W[\ell] by graph neural networks
We next propose a couple of learnable graph neural network (GNN) models, each of which can be seen as walk MPNNs, and match W[\ell] in expressive power. More specifically, we first revisit the GNNs proposed by Morris et al. (2019) and show that they can simulate W[\ell] on a specific input graph. We next propose two GNNs, one close in spirit to the GNNs of Xu et al. (2019), and one close to the higher-order GNNs of Maron et al. (2019b), and show that these can simulate W[\ell] on all graphs of a fixed size $n$ provided that all labels combined form a finite set. The latter restriction is to ensure that the approximations of functions by MLPs are injective. This is needed since these approximations will substitute the hash functions used in W[\ell].
#### 6.1 Simulating W[\ell] on a single graph
When dealing with a single graph, we can generalise the GNN architecture from Morris et al. (2019). As already mentioned in the introduction, Morris et al. (2019) propose higher-order GNNs that, in order to simulate 2-WL, require maintaining $O(n^2)$ many labels. It would be desirable to need at most $O(n^2)$ many dimensions. We achieve this by allowing non-linear layers in the GNN architecture. We show the simulation for $\ell = 2$, and thus 2-WL, but the construction can be generalised easily to W[\ell] for arbitrary $\ell \geq 2$. We comment on this generalisation later in this section.
Let $G = (V, E, \eta)$ be the input graph with $\eta : E \to \mathbb{R}^{s_0}$ for some $s_0 \in \mathbb{N}^+$. We represent $G$ by means of a tensor $A \in \mathbb{R}^{n^2 \times s_0}$ such that $A_{ij} = \eta(i, j) \in \mathbb{R}^{s_0}$ for each $i, j \in [n]$.认同
Similarly to Morris et al. (2019) we say that a tensor $A \in \mathbb{R}^{n^2 \times s}$ for $s \in \mathbb{N}^+$ is label-independent modulo equality\footnote{Morris et al. (2019) use the notion of row-independence modulo equality because the row dimension correspond to the labels. Since we work with tensors, we use label-independence modulo equality. We always assume that the labels are stored in the last dimension in the tensors.} if the set of unique labels $\{A_{ij} \mid i, j \in [n]\}$ consists of linearly independent vectors in $\mathbb{R}^s$. We remark that the input tensor $A$ can always be assumed to satisfy this property by hot-one encoding the labelling $\eta$. In the worst case, we need labels in $\mathbb{R}^{n^2}$ to do so\footnote{This is really worst case as it corresponds to every pair in $[n]^2$ to have a distinct label.}. Generalising the GNNs from Morris et al. (2019), we define $A^{(0)} := A$ and for $t > 0$ we define a tensor $A^{(t)} \in \mathbb{R}^{n^2 \times s}$ for some $s_t \in \mathbb{N}^+$ based on a tensor $A^{(t-1)} \in \mathbb{R}^{n^2 \times s_{t-1}}$. More specifically, for $i, j \in [n]$ and $s \in [s_t]$:
$$A^{(t)}_{ij} := \text{ReLU} \left( \sum_{k \in [n]} \sum_{c, d \in [s_{t-1}]} A^{(t-1)}_{ikc} A^{(t-1)}_{kdj} W_{c ds} - q_{j, i s} \right),$$
(1)
where $W(t) \in \mathbb{R}^{s_{t-1} \times s_{t-1} \times s_t}$ is a (learnable) weight matrix, $J \in \mathbb{R}^{n^2 \times s_t}$ is a tensor consisting of all ones, and $q$ is (learnable) scalar in $\mathbb{R}$. A first observation is that we can cast the update rules (1) as a 2-walk MPNN $M$. Indeed, it suffices to define for each $t > 0$ and $a, b \in \mathbb{R}^{n^2}$:
$$\text{Msg}^{(t)}_M(a, b) := \left( \sum_{c, d \in [s_{t-1}]} a_{c} b_{d} W_{c ds} - q \mid s \in [s_t] \right) \in \mathbb{R}^{n^2}$$
and for $a \in \mathbb{R}^{n^2}$ and $b \in \mathbb{R}^{n^2}$:
$$\text{UPD}^{(t)}_M(a, b) := \text{ReLU}(b).$$
Clearly, when using these message and update functions the corresponding 2-walk MPNN $M$ will compute the labelling $\eta_M(i, j) := A^{(t)}_{ij}$ for $i, j \in [n]$ and each $t \geq 0$. Proposition 4.1 thus implies that the expressive power of architectures of the form (1) are bounded by 2-WL. We next provide a matching lower bound.
**Proposition 6.1.** For a given input graph $G = (V, E, \eta)$ with $\eta : E \to \mathbb{R}^{s_0}$ and such that the labels are label-independent modulo equality, there exists a scalar $q \in \mathbb{R}$ and, for each $t > 0$, there exists a weight tensor $W(t)$ such that $\text{Msg}^{(t)}_M \equiv A^{(t)}$ holds, where $A^{(t)}$ is defined as in (1). Furthermore, $A^{(t)}$ is label-independent modulo equality.
**Proof.** The base case $t = 0$ is satisfied by assumption. We next assume that the induction hypothesis is satisfied for $t - 1$ and consider round $t$. We define $W(t)$ as the product of a number of tensors, which we define next. In a similar way as in Morris et al. (2019) we first map each label in $A^{(t-1)}$ to a canonical vector encoding that label. Here, with a canonical vector we mean a binary vector with precisely one occurrence of the value 1. Intuitively, the canonical vector in which 1 appears in position $i$ corresponds to the $i$th label, relative to some ordering on the labels. By the induction hypothesis, $A^{(t-1)}$ is label-independent modulo equality. So, if we assume that there are $c_t$ distinct labels $a_{c_1}, \ldots, a_{c_t}$ in $A^{(t-1)}$, then we know that these vectors in $\mathbb{R}^{n^2}$ are linearly independent. We denote by $\text{uniq}(A^{(t-1)})$ the $c_t \times s_{t-1}$ matrix consisting of these distinct labels. Due to linear independence, there exists a $s_{t-1} \times c_t$ matrix $V(t)$ such that $\text{uniq}(A^{(t-1)}) V(t) = \text{Id} \in \mathbb{R}^{c_t \times c_t}$. As a first step, we multiply each label in $A^{(t-1)}$ with $V(t)$. More specifically, we define a tensor $B \in \mathbb{R}^{n^2 \times c_t}$ such that for $i, j \in [n]$ and $c \in [c_t]$: $B_{ijc} := \sum_{s \in [s_{t-1}]} A^{(t-1)}_{ij s} V(t)_{s c}$.
In other words, for $i, j \in [n]$ and $c \in [c_t]$:
$$B_{ijc} = \begin{cases} 1 & \text{if } (A^{(t-1)})_{ij} = a_c \\ 0 & \text{otherwise.} \end{cases}$$
We next define a tensor $C^{(t)} \in \mathbb{R}^{n^2 \times c_t \times c_t}$ such that for $i, j \in [n]$, $c, d \in [c_t]$:
$$C^{(t)}_{ijcd} := \sum_{k \in [n]} B_{ikc}^{(t)} B_{kdj}^{(t)}.$$
As a consequence, for $i, j \in [n], c, d \in [c_t]$:
$$C_{ijcd}^{(t)} := \text{number of } k \in [n] \text{ such that } A_k^{(t-1)} = a_c \text{ and } A_{dk}^{(t-1)} = a_d.$$
By the induction hypothesis, $\eta_{2\text{WL}}^{(t-1)} \equiv A^{(t-1)}$, and we may assume that there is a bijection between the unique labels in $A^{(t-1)}$ and those assigned by $\eta_{2\text{WL}}^{(t-1)}$. Let us assume that this bijection is such that for $c \in [c_t], a_c$ corresponds to the label $\ell_c$. We remark that $C_{ij\ell_c\ell_d}^{(t)} = C_{ij\ell_c\ell_d}^{(t)} \in \mathbb{R}^{c_t \times c_t}$ if and only if for each pair of labels $a_c$ and $a_d$ in $A^{(t-1)}$,
$$N(i, j, c, d) = N(i', j', c, d).$$
By the induction hypothesis, this in turn is equivalent to
$$\{k \in [n] | \eta_{2\text{WL}}^{(t-1)}(i, k) = \ell_c, \eta_{2\text{WL}}^{(t-1)}(k, j) = \ell_d\} = \{s \in [n] | \eta_{2\text{WL}}^{(t-1)}(i', k) = \ell_c, \eta_{2\text{WL}}^{(t-1)}(k, j') = \ell_d\},$$
for every $c, d \in [c_t]$. Since this holds for any pair of labels $\ell_c$ and $\ell_d$, this is equivalent to $\eta_{2\text{WL}}^{(t)}(i, j) = \eta_{2\text{WL}}^{(t)}(i', j')$. So, at this point we already know that $\eta_{2\text{WL}}^{(t)} \equiv C^{(t)}$. In what follows, we turn $C^{(t)}$ into a tensor in $\mathbb{R}^{n^2 \times s_t}$ which is label-independent modulo equality whilst preserving equivalence to $\eta_{2\text{WL}}^{(t)}$.
The first thing we do is to turn each of the labels in $C^{(t)}$ into a single number in $\mathbb{N}^+$. Similarly as in Morris et al. (2019) we identify the maximum entry max in $C^{(t)}$ and define the vector $M^{(t)} \in \mathbb{R}^{c_t}$ such that for $d \in [c_t]$:
$$M_d^{(t)} := (\text{max} + 1)^{d-1}.$$
We next define the tensor $D^{(t)} \in \mathbb{R}^{n^2 \times c_t}$ such that for $i, j \in [n]$ and $c \in [c_t]$:
$$D_{ijc}^{(t)} := \sum_{d \in [c_t]} C_{ijcd}^{(t)} M_d^{(t)}.$$
In other words,
$$D_{ijc}^{(t)} := \sum_{d \in [c_t]} N(i, j, c, d)(\text{max} + 1)^{d-1}$$
and we thus have represented each vector $C_{ij\ell_c\ell_d}^{(t)}$ by its $(\text{max} + 1)$-ary representation. Since all $N(i, j, c, d) \leq \text{max}$, we have that $C_{ij\ell_c\ell_d}^{(t)} = C_{ij\ell_c\ell_d}^{(t)}$ if and only if $D_{ijc} = D_{ijc}$ and thus $C_{ij\ell_c\ell_d}^{(t)} = C_{ij\ell_c\ell_d}^{(t)}$ if and only if $D_{ijc} = D_{ijc}$. As a consequence, also $\eta_{2\text{WL}}^{(t)} \equiv D^{(t)}$ holds. We perform the same reduction once more, but this time using the maximum entry max' in $D^{(t)}$. That is, we define $\mathbf{N}^{(t)}$ just like $M^{(t)}$ but using max' instead of max and consider the matrix $E^{(t)} \in \mathbb{R}^{n \times n}$ such that for $i, j \in [n]$:
$$E_{ij}^{(t)} := \sum_{c \in [c_t]} D_{ijc}^{(t)} N_c^{(t)}.$$
A similar argument as before shows that $\eta_{2\text{WL}}^{(t)} \equiv E^{(t)}$. Let $e_1 > e_2 > \cdots > e_{s_t}$ be the unique values in $E^{(t)}$. By construction of $E^{(t)}$, each $e_s > 0$. We next consider the vector $U_s^{(t)} \in \mathbb{R}^{s_t}$ define as $U_s^{(t)} = \frac{1}{e_s}$ for $s \in [s_t]$. We define the tensor $F^{(t)} \in \mathbb{R}^{n^2 \times s_t}$ such that for $i, j \in [n]$ and $s \in [s_t]$:
$$F_{ij}^{(t)} := E_{ij}^{(t)} U_s^{(t)}.$$
In other words, for $i, j \in [n]$ and $s \in [s_t]$:
$$F_{ij}^{(t)} = \frac{E_{ij}^{(t)}}{e_s}.$$
We are now ready to define $W^{(t)} \in \mathbb{R}^{n \times s_t - 1 \times s_t - 1 \times s_t}$. Indeed, for $c, d \in [s_t - 1]$ and $s \in [s_t]$:
$$W_{cds}^{(t)} := \sum_{c', d' \in [c_t]} V_{c'}^{(t)} V_{d'}^{(t)} M_{cd}^{(t)} N_{c}^{(t)} U_{s}^{(t)}.$$
11
Hence, we can write $F^{(t)}$ as
$$F_{ijs}^{(t)} = \sum_{k \in [n]} \sum_{c,d \in [s_{t-1}]} A_{ikc}^{(t-1)} A_{kjd}^{(t-1)} W_{cds}^{(t)}.$$
It remains to identify a scalar $q$ such that
$$A_{ijs}^{(t)} = \text{ReLU} \left( \sum_{k \in [n]} \sum_{c,d \in [s_{t-1}]} A_{ikc}^{(t-1)} A_{kjd}^{(t-1)} W_{cds}^{(t)} - qJ_{ijs} \right)$$
is label-independent modulo equality. To this aim, let $q^{(t)}$ be the greatest value in $F^{(t)}$ smaller than 1 and consider the tensor $G^{(t)} \in \mathbb{R}^{n^2 \times s_t}$ such that for $i,j \in [n]$ and $s \in [s_t]$, $G_{ijs}^{(t)} := F_{ijs}^{(t)} - q^{(t)}$. Hence,
$$G_{ijs}^{(t)} = \begin{cases} 1 - q^{(t)} & \text{if } E_{ijs}^{(t)} = e_s \\ > 0 & \text{if } E_{ijs}^{(t)} > e_s \\ \leq 0 & \text{if } E_{ijs}^{(t)} < e_s. \end{cases}$$
Hence, for $i,j \in [n]$, $s \in [s_t]$:
$$A_{ijs}^{(t)} := \text{ReLU} \left( G_{ijs}^{(t)} \right) = \begin{cases} 1 - q^{(t)} & \text{if } E_{ijs}^{(t)} = e_s \\ > 0 & \text{if } E_{ijs}^{(t)} > e_s \\ 0 & \text{if } E_{ijs}^{(t)} < e_s. \end{cases}$$
It is again easily verified that $\eta_{2,\text{WL}}^{(t)} = A^{(t)}$. Indeed, $\eta_{2,\text{WL}}^{(t)} \subseteq A^{(t)}$ follows immediately from $\eta_{2,\text{WL}}^{(t)} = E^{(t)}$. To show $A^{(t)} \subseteq \eta_{2,\text{WL}}^{(t)}$ it suffices to observe that when $A_{ijs}^{(t)} = A_{i'j'}^{(t)}$, holds, these vectors contain $1 - q^{(t)}$ at the same (unique) position, say at position $s \in [s_t]$. Hence, $E_{ijs}^{(t)} = e_s = E_{i'j'}^{(t)}$, and again due to $\eta_{2,\text{WL}}^{(t)} = E^{(t)}$, $\eta_{2,\text{WL}}^{(t)}(i,j) = \eta_{2,\text{WL}}^{(t)}(i',j')$.
The unique labels in $A^{(t)}$ are also linearly independent. To see this, we note that the unique labels correspond to the unique elements $e_1, e_2, \ldots, e_{s_t}$ in $E^{(t)}$. As a consequence, the value $e_s$ corresponds to the label
$$(0, \ldots, 0, 1 - q^{(t)}, > 0, \ldots, > 0)$$
in $A^{(t)}$. In other words, these form (up to a permutation) an upper-triangular matrix with $1 - q^{(t)} \neq 0$ on its diagonal, and this is known to be a non-singular matrix. As a consequence, the unique labels in $A^{(t)}$ are linearly independent.
We further observe that $q^{(t)}$ can be chosen to be any number satisfying
$$\frac{n^{2n^2} - 1}{n^{2n^2}} < q < 1.$$ This follows from upper bounding $\max_{i,j} E_{ijs}$ by $n$, and $c_{ik}$ by $n^2$ which results in an upper bound for $\max'_{i,j}$ as $n^{n^2}$. Hence, $\frac{n^{2n^2} - 1}{n^{2n^2}}$ is an upper bound on the largest value in $F^{(t)}$ smaller than 1 for any $t > 0$. As a consequence, $q^{(t)}$ can be chosen uniformly across all layers. All combined, this shows that architectures of the form of (1) can simulate 2-WL on $G = (V, E, \eta)$.
\begin{remark}
To generalise the construction to simulate $W[\ell]$ for $\ell > 2$ it suffices to consider $\ell - 1$ matrix multiplications of $A^{(t-1)}$ in the architecture (1) and to extend the weight tensor to be of dimensions $\ell s_{t-1} \times s_t$. The construction of $W^{(t)}$ is entirely similar, with the exception that the matrix $E^{(t)}$, which will now be in $\mathbb{R}^{n^\ell}$, is obtained by encoding each of its $\ell$ dimensions as a number in $\mathbb{N}$. So instead of only two matrices $M^{(t)}$ and $N^{(t)}$, we need $\ell$ such matrices. Finally, $q$ is lower bounded by $\frac{n^{2n^2} - 1}{n^{2n^2}} \ell$ times.
\end{remark}
We note that we can use GNNs of the form (1) to distinguish graphs by simply running the GNN on the direct sum of the two graphs, just as for 1-WL.
6.2 Simulating $W[\ell]$ on a collection of graphs
We have seen two different ways of simulating $W[\ell]$ by $\ell$-walk MPNNs in Section 5. We next turn these simulations into learnable GNNs by replacing the message functions by multi layer perceptrons (MLPs), just as in (Xu et al., 2019) and (Maron et al., 2019b). MLPs are known to approximate any continuous bounded function. In order to approximate the message functions by MLPs we need to ensure that the message functions are continuous and that the approximations returned by the MLPs inherit the crucial injectivity properties (on multisets) of the functions being approximated.
Let us first consider the simulation presented in Section 5.1. In that simulation we used an arbitrary pairing function $\tau: \mathbb{N}^\ell \rightarrow \mathbb{N}$ and defined $MSG^{(\ell)}(a_1, \ldots, a_\ell) := (n^{(\ell-1)} + 1)^{\tau(a_1, \ldots, a_\ell)}$. To ensure continuity we choose $\tau: \mathbb{N}^\ell \rightarrow \mathbb{N}: (a_1, a_2, \ldots, a_\ell) \mapsto p_1^{a_1} p_2^{a_2} \cdots p_\ell^{a_\ell}$ with $p_i$ the $i$th prime number. Clearly, its extension $\tau: \mathbb{R}^\ell \rightarrow \mathbb{R}: (x_1, \ldots, x_\ell) \mapsto 2^{x_1} 3^{x_2} \cdots p_\ell^{x_\ell}$ is a continuous function and similarly, $h: \mathbb{R}^\ell \rightarrow \mathbb{R}: (x_1, \ldots, x_\ell) \mapsto (n^{(\ell-1)} + 1)^{h(x_1, \ldots, x_\ell)}$ is continuous. We remark that other continuous pairing functions $\mathbb{N}^\ell \rightarrow \mathbb{N}$ can be used instead.
There are now various ways of using MLPs to approximate $h$ and $\tau$. We recall that the simulation in Section 5.1 concerns graphs $G = (V, E, \eta)$ with $\eta: E \rightarrow \mathbb{N} \subseteq \mathbb{R}$. Hence, we can represent $G$ by means of a matrix $A^{(0)}$ such that $(A^{(0)})_{ij} := \eta(i, j)$ for all $i, j \in [n]$. We then define for $t > 0$, the matrix $A^{(t)} \in \mathbb{R}^{n \times n}$, as follows:
$$ (A^{(t)})_{ij} := \sum_{i_1, \ldots, i_\ell \in [n]} MLP_{\theta^{(t)}} (A^{(t-1)})_{i1i1}, \ldots, (A^{(t-1)})_{i_{\ell-1}i_{\ell-1}}, $$
where $MLP_{\theta^{(t)}}: \mathbb{R} \rightarrow \mathbb{R}$ is an MLP with parameters $\theta^{(t)}$. The MLP is to be trained to approximate $\eta$, just as for GINs (Xu et al., 2019). Alternatively, we can define $A^{(t)} \in \mathbb{R}^{n \times n}$, as follows:
$$ A^{(t)}_{ij} := \sum_{i_1, \ldots, i_\ell \in [n]} MLP_{\eta^{(t)}} (MLP_{\theta^{(t)}}(A^{(t-1)})_{i1i1} \cdot MLP_{\theta^{(t)}}(A^{(t-1)})_{i1i2} \cdot \ldots MLP_{\theta^{(t)}}(A^{(t-1)})_{i_{\ell-1}i_{\ell-1}]), $$
where $MLP_{\eta^{(t)}}: \mathbb{R} \rightarrow \mathbb{R}$ is an MLP with parameters $\eta^{(t)}$ used to approximate the function $x \mapsto (n^{(\ell-1)} + 1)^x$ and $MLP_{\theta^{(t)}} : \mathbb{R} \rightarrow \mathbb{R}$, for $i \in [\ell]$, is an MLP with parameters $\theta^{(t)}_i$ used to approximate the function $x \mapsto p_i^x$ with $p_i$ the $i$th prime number. Yet another alternative could be to encode $G$ as the tensor $A^{(0)} \in \mathbb{R}^{n \times n \times \ell}$ with $(A^{(0)})_{ij} := p_i^{\eta(i, j)}$ with $p_s$ the $s$th prime number, for $s \in [\ell]$, and then define for $t > 0$, the tensor $A^{(t)} \in \mathbb{R}^{n \times n \times \ell}$ with for $i, j \in [n]$ and $s \in [\ell]$:
$$ A^{(t)}_{ij} := MLP_{\theta_1^{(t)}} \left( \sum_{i_1, \ldots, i_\ell \in [n]} MLP_{\theta_2^{(t)}} (A^{(t-1)})_{i1i1} \cdot (A^{(t-1)})_{i1i2} \cdot \ldots (A^{(t-1)})_{i_{\ell-1}i_{\ell-1}} \right), $$
where $MLP_{\theta_1^{(t)}} : \mathbb{R} \rightarrow \mathbb{R}^\ell$ is an MLP with parameters $\theta_1^{(t)}$ used to approximate the function $x \mapsto (2^x, 3^x, \ldots, p_\ell^x)$ and $MLP_{\theta_2^{(t)}} : \mathbb{R} \rightarrow \mathbb{R}$ is an MLP with parameters $\theta_2^{(t)}$ used to approximate the function $x \mapsto (n^{(\ell-1)} + 1)^x$.
In all three formulations the MLPs have to be learned based on the available labels. In general, one could approximate the functions up to arbitrary precision provided that the set of labels belong to some compact set. We also need, however, to ensure injectivity. One way to guarantee this is by assuming that only a finite number of labels are present in the collection of graphs (Maron et al., 2019b; Sato, 2020). We thus can guarantee the following.
**Proposition 6.2.** For each $n, \ell, t \in \mathbb{N}$ with $\ell \geq 2$, there exists parameters of the MLPs in (2), (3) and (4), such that $A^{(t)} \equiv \eta_{W[\ell]}^{(t)}$ for any graph $G = (V, E, \eta)$ with $|V| = n$, $\eta: E \rightarrow \Gamma \subseteq \mathbb{N}$, where $\Gamma$ is a finite set of numbers.
We can proceed in a similar way using the simulation given in Section 5.2. As already observed by Maron et al. (2019b) for 2-WL, one can decompose the function $u^{(t)}$ in that simulation as a product of $\ell$ other functions. More precisely, let $G = (V, E, \eta)$ with $|V| = n$ and $\eta: E \rightarrow \mathbb{R}^{s_0}$ for some $s_0 \in \mathbb{N}^+$. We encode $G$ as a tensor $A^{(0)} \in \mathbb{R}^{n^2 \times s_0}$ as before. Then for $t > 0$, assume that $A^{(t-1)} \in \mathbb{R}^{n^2 \times s_{t-1}}$ and define
$$ A^{(t)}_{ij} := \sum_{i_1, \ldots, i_{\ell-1} \in [n]} g^{(t)}_1 (A^{(t-1)})_{i1i1} \cdot g^{(t)}_2 (A^{(t-1)})_{i1i2} \cdot \ldots g^{(t)}_\ell (A^{(t-1)})_{i_{\ell-1}i_{\ell-1}} $$
13
for continuous functions \( g_{p}^{(t)} : \mathbb{R}^{s_{t}} \to \mathbb{R}^{s_{t}} \), for \( p \in [\ell] \), which we define next. Consider again the multi-index set \( \{\alpha \mid \alpha \in [n^{\ell-1}]^{s_{t-1}}, |\alpha| \leq n^{\ell-1}\} \) of cardinality \( s_{t} = \binom{n^{\ell-1} + s_{t-1}}{s_{t-1}} \) used in the simulation of \( \mathcal{W}[\ell] \) in Section 5.2. We can represent each multi-index \( \alpha_{s} \) in this set, for \( s \in [s_{t}] \), in the form \( \alpha_{s} = (\alpha_{1}, \ldots, \alpha_{\ell}) \) where for \( j \in [\ell] \), \( \alpha_{j} \in [n^{\ell-1}]^{s_{t-1}} \) and furthermore, \( \sum_{j \in [\ell]} |\alpha_{j}| \leq n^{\ell-1} \). We next define for \( p \in [\ell] \), \( g_{p}^{(t)} : \mathbb{R}^{s_{t-1}} \to \mathbb{R}^{s_{t}} \) such that for \( x \in \mathbb{R}^{s_{t-1}} \),
\[
g_{p}^{(t)}(x) := (x^{\alpha_{p}} \mid s \in [s_{t}]) \in \mathbb{R}^{s_{t}}.
\]
Hence, for \( x_{1}, \ldots, x_{\ell} \in \mathbb{R}^{s_{t}} \) we have
\[
\prod_{p=1}^{\ell} g_{p}^{(t)}(x_{p}) = \left( (x_{1}, \ldots, x_{\ell})^{\alpha_{s}} \mid s \in [s_{t}] \right) \in \mathbb{R}^{s_{t}},
\]
which precisely corresponds to the message function used in Section 5.2. As a consequence, \( A^{(t)} \) as defined in (5) is equivalent to \( \eta_{\mathcal{W}[\ell]}^{(t)} \). To turn (5) into a learnable graph neural network we define
\[
A_{ij}^{(t)} := \sum_{i_{1}, \ldots, i_{\ell-1} \in [n]} \text{MLP}_{\theta_{1}^{(t)}}(A^{(t-1)})_{ii_{1}s} \cdot \text{MLP}_{\theta_{2}^{(t)}}(A^{(t-1)})_{i_{1}i_{2}s} \cdots \text{MLP}_{\theta_{\ell}^{(t)}}(A^{(t-1)})_{i_{\ell-1}j_{s}},
\]
(6)
where for \( p \in [\ell] \), \( \text{MLP}_{\theta_{p}^{(t)}} : \mathbb{R}^{s_{t-1}} \to \mathbb{R}^{s_{t}} \) is a multi layer perceptron applied to the labels in \( A^{(t-1)} \). More specifically, \( \text{MLP}_{\theta_{p}^{(t)}}(A^{(t-1)})_{i_{j}s} := (\text{MLP}_{\theta_{p}^{(t)}}(A^{(t-1)}))_{ii}, s \), for \( p \in [\ell] \) and \( s \in [s_{t}] \). Furthermore, for \( p \in [\ell] \), \( \text{MLP}_{\theta_{p}^{(t)}} \) is used to approximate the function \( g_{p}^{(t)} \). We may thus conclude that:
**Proposition 6.3.** For each \( n, \ell, t \in \mathbb{N} \) with \( \ell \geq 2 \), there exists parameters of the MLPs in (6) such that \( A^{(t)} = \eta_{\mathcal{W}[\ell]}^{(t)} \) for any graph \( G = (V, E, \eta) \) with \( |V| = n, \eta : E \to \Gamma \subseteq \mathbb{R}^{n}, \) where \( \Gamma \) is a finite set of real vectors.
We note that the graph neural network models (2), (3), (4), (5) and (6) can all be cast as \( \ell \)-walk MPNNs, which implies that their expressive power is bounded by \( \mathcal{W}[\ell] \) as well.
**Remark 6.2.** We remark that the second-order non-linear invariant GNNs proposed in Maron et al. (2019b) are a special case of (6) by letting \( \ell = 2 \), and hence they are bounded by 2-WL in expressive power. We observe that allowing for multiple matrix multiplications in second-order GNNs, as in (6), does not increase expressive power. Instead, it may only result in a faster convergence towards the final 2-WL labelling. This partially answers a question raised in Maron et al. (2019a) related to the impact of polynomial layers on the expressive power of higher-order invariant GNNs.
**Remark 6.3.** If one desires to start from a vertex-labeled graph, one can add an initialisation step in the GNNs which converts the graph into and edge-labeled graph, as explained in Remark 2.1. Furthermore, this initialisation step can be performed by tensor computations as shown in Maron et al. (2019b).
**Remark 6.4.** So far, we only considered the expressive power of walk MPNNs related to distinguishing edges (or pairs of vertices to be more precise). As mentioned earlier, we may also use walk MPNNs to distinguish graphs. In the setting of walk MPNNs this corresponds to running the walk MPNN for multiple rounds \( T \) and then use a read-out function READOUT on the obtained multiset of labels. More precisely, for \( \mathcal{W}[\ell] \), two graphs \( G = (V, E, \eta) \) and \( H = (V', E', \eta') \) with \( \eta : E \to \Sigma \) and \( \eta' : E' \to \Sigma \) are said to be indistinguishable after round \( T \) if
\[
\left\{ \left\{ \eta_{\mathcal{W}[\ell]}^{(T)}(i, j) \mid i, j \in [n] \right\} \right\} = \left\{ \left\{ \eta'^{T}_{\mathcal{W}[\ell]}(i, j) \mid i, j \in [n] \right\} \right\}
\]
holds. Hence, to check whether this equality holds, it suffices to consider a read-out function which assigns a unique value in \( \mathbb{N} \) to multisets of elements in \( \mathbb{N} \) of size \( n^{2} \), for the case when labels are in \( \mathbb{N} \), and a unique value in \( \mathbb{R}^{b} \) for some \( b \in \mathbb{N}^{+} \), to multisets of elements in \( \mathbb{R}^{s_{t}} \) of size \( n^{2} \), for the case when labels are reals. Alternatively, one can define a read-out function which assigns to each possible label a unique basis vector in \( \mathbb{R}^{b} \), and then simply sum these up to create a histogram. In each of these cases, an additional MLP can be used to approximate such a read-out function, as described in Maron et al. (2019b).
7 Conclusion
We introduced \(\ell\)-walk MPNNs as a general formalism for iteratively constructing graph embeddings based on walks of length \(\ell\) between pairs of vertices. In terms of expressive power, \(\ell\)-walk MPNNs match with the walk refinement procedure \(W[\ell]\) of Lichter et al. (2019). When \(\ell = 2\), this procedure coincides with 2-WL and as such, 2-walk MPNNs are equally expressive as 2-WL. In fact, \(\ell\)-walk MPNNs are also bounded in expressive power by 2-WL but can possibly distinguish graphs faster because more information is taken into account in each iteration. We provide a number of concrete learnable GNNs, all of which can be cast as \(\ell\)-walk MPNNs. These GNNs use non-linear layers and only require \(O(n^2)\) many embeddings. All proposed GNNs are equally expressive as \(W[\ell]\) and 2-WL in particular. It would be interesting to see how the proposed GNNs perform in practice.
References
Pablo Barceló, Egor V. Kostylev, Mikael Monet, Jorge Pérez, Juan L. Reutter, and Juan Pablo Silva. The logical expressiveness of graph neural networks. In Proceedings of the 8th International Conference on Learning Representations, ICLR, 2020. URL https://openreview.net/forum?id=r1lZ7AEKvB.
Jin-Yi Cai, Martin Fürer, and Neil Immerman. An optimal lower bound on the number of variables for graph identifications. Combinatorica, 12(4):389–410, 1992. URL https://doi.org/10.1007/BF01305232.
Zhengdao Chen, Lei Chen, Soledad Villar, and Joan Bruna. Can graph neural networks count substructures? arXiv, 2020. URL https://arxiv.org/abs/2002.04025.
George Cybenko. Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals and Systems, 5(4):303–314, 1989. URL https://doi.org/10.1007/BF02134016.
Floris Geerts, Filip Mazowiecki, and Guillermo A. Prez. Let’s agree to degree: Comparing graph convolutional networks in the message-passing framework. arXiv, 2020. URL https://arxiv.org/abs/2004.02593.
Justin Gilmer, Samuel S. Schoenholz, Patrick F. Riley, Oriol Vinyals, and George E. Dahl. Neural message passing for quantum chemistry. In Proceedings of the 34th International Conference on Machine Learning, ICML, volume 70, pages 1263–1272, 2017. URL http://proceedings.mlr.press/v70/gilmer17a/gilmer17a.pdf.
Martin Grohe. Descriptive Complexity, Canonisation, and Definable Graph Structure Theory. Lecture Notes in Logic. Cambridge University Press, 2017. URL https://doi.org/10.1017/9781139028868.
Martin Grohe and Martin Otto. Pebble games and linear equations. The Journal of Symbolic Logic, 80(3):797844, 2015. URL https://doi.org/10.1017/jsl.2015.28.
Kurt Hornik. Approximation capabilities of multilayer feedforward networks. Neural Networks, 4(2):251–257, 1991. URL https://doi.org/10.1016/0893-6080(91)90009-T.
Thomas N. Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. In Proceedings of the 5th International Conference on Learning Representations, ICLR, 2017. URL https://openreview.net/forum?id=SJU4ayYgl.
Moritz Lichter, Ilia Ponomarenko, and Pascal Schweitzer. Walk refinement, walk logic, and the iteration number of the Weisfeiler-Leman algorithm. In Proceedings of the 34th Annual IEEE Symposium on Logic in Computer Science LICS, pages 1–13, 2019. URL https://doi.org/10.1109/LICS.2019.8785694.
Haggai Maron, Heli Ben-Hamu, and Yaron Lipman. Open problems: Approximation power of invariant graph networks. In NeurIPS 2019 Graph Representation Learning Workshop, 2019a. URL https://grilearning.github.io/papers/31.pdf.
Haggai Maron, Heli Ben-Hamu, Hadar Serviansky, and Yaron Lipman. Provably powerful graph networks. In Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS, pages 2153–2164, 2019b. URL http://papers.nips.cc/paper/8488-provably-powerful-graph-networks.
Haggai Maron, Hel\,I Ben-Hamu, Nadav Shamir, and Yaron Lipman. Invariant and equivariant graph networks. In Proceedings of the 7th International Conference on Learning Representations, ICLR, 2019c. URL https://openreview.net/forum?id=Syx72jC9tm.
Christopher Morris, Martin Ritzert, Matthias Fey, William L. Hamilton, Jan Eric Lenssen, Gaurav Rattan, and Martin Grohe. Weisfeiler and Leman go neural: Higher-order graph neural networks. In Proceedings of The 33rd AAAI Conference on Artificial Intelligence, AAAI, pages 4602–4609, 2019. URL https://doi.org/10.1609/aaai.v33i01.33014602.
Ryoma Sato. A survey on the expressive power of graph neural networks. arXiv, 2020. URL https://arxiv.org/abs/2003.04078.
Ryoma Sato, Makoto Yamada, and Hisashi Kashima. Random features strengthen graph neural networks. arXiv, 2020. URL https://arxiv.org/abs/2002.03155.
Younjoo Seo, Andreas Loukas, and Nathanal Perraudin. Discriminative structural graph classification. arXiv, 2019. URL http://arxiv.org/abs/1905.13422.
Edward Wagstaff, Fabian Fuchs, Martin Engelcke, Ingmar Posner, and Michael A. Osborne. On the limitations of representing functions on sets. In Kamalika Chaudhuri and Ruslan Salakhutdinov, editors, Proceedings of the 36th International Conference on Machine Learning, ICML, volume 97, pages 6487–6494, 2019. URL http://proceedings.mlr.press/v97/wagstaff19a.html.
Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? In Proceedings of the 7th International Conference on Learning Representations, ICLR, 2019. URL https://openreview.net/forum?id=ryGs6iASKm. | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4148,
1
],
[
4148,
13313,
2
],
[
13313,
17792,
3
],
[
17792,
23244,
4
],
[
23244,
28340,
5
],
[
28340,
32635,
6
],
[
32635,
36269,
7
],
[
36269,
42312,
8
],
[
42312,
46460,
9
],
[
46460,
50890,
10
],
[
50890,
54527,
11
],
[
54527,
58080,
12
],
[
58080,
63458,
13
],
[
63458,
68645,
14
],
[
68645,
72529,
15
],
[
72529,
74144,
16
]
]
} |
3c1e8c4fb8eebf881c5b06798c58cc581c2be844 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 10,
"total-fallback-pages": 0,
"total-input-tokens": 37423,
"total-output-tokens": 13313,
"fieldofstudy": [
"Computer Science"
]
} | Towards Driving-Oriented Metric for Lane Detection Models
Takami Sato
University of California, Irvine
[email protected]
Qi Alfred Chen
University of California, Irvine
[email protected]
Abstract
After the 2017 TuSimple Lane Detection Challenge, its dataset and evaluation based on accuracy and F1 score have become the de facto standard to measure the performance of lane detection methods. While they have played a major role in improving the performance of lane detection methods, the validity of this evaluation method in downstream tasks has not been adequately researched. In this study, we design 2 new driving-oriented metrics for lane detection: End-to-End Lateral Deviation metric (E2E-LD) is directly formulated based on the requirements of autonomous driving, a core downstream task of lane detection; Per-frame Simulated Lateral Deviation metric (PSLD) is a lightweight surrogate metric of E2E-LD. To evaluate the validity of the metrics, we conduct a large-scale empirical study with 4 major types of lane detection approaches on the TuSimple dataset and our newly constructed dataset Comma2k19-LD. Our results show that the conventional metrics have strongly negative correlations (≤ -0.55) with E2E-LD, meaning that some recent improvements purely targeting the conventional metrics may not have led to meaningful improvements in autonomous driving, the core downstream task. For example, SCNN always has higher accuracy than PolyLaneNet, but its detection results are making it much harder to achieve lane centering (detailed in §4.2).
Figure 1. Examples of lane detection results and the accuracy metric in benign and adversarial attack scenarios on TuSimple Challenge dataset [8]. As shown, the conventional accuracy metric does not necessarily indicate drivability if used in autonomous driving, the core downstream task. For example, SCNN always has higher accuracy than PolyLaneNet, but its detection results are making it much harder to achieve lane centering (detailed in §4.2).
1. Introduction
Lane detection is one of the key technologies today for realizing autonomous driving. For lane detection, camera is the most frequently used sensor because it is a natural choice as lane lines are visual patterns [26]. Like most other computer vision areas, lane detection has been significantly benefited from the recent advances of deep neural networks (DNNs). In the 2017 TuSimple Lane Detection Challenge [8], DNN-based lane detection shows substantial performance as all top 3 teams opt for DNN-based lane detection. After this competition, its dataset and evaluation method based on accuracy and F1 score became the de facto standard in lane detection evaluation. These metrics are inherited by the subsequent datasets [13, 37].
However, the validity of this evaluation method in practical contexts, i.e., whether this is representative of practicality in real-world downstream applications, has not been adequately researched. Specifically, the main real-world applications of lane detection are for autonomous driving (AD), e.g., online detection for automated lane centering (for lower-level AD such as in ’Tesla AutoPilot [6]), and offline detection for high-definition map creation (for both low-level [5] and high-level AD [50]). With such an application domain as its main target, the robustness of lane detection is highly critical as errors from it could be fatal. Unfortunately, we find that the conventional evaluation metrics (i.e., accuracy and F1 score) have limitations in correctly reflecting the performance of lane detection models in such main downstream application domain, especially in more challenging scenarios (e.g., when under adversarial attacks). Fig. 1 shows a few such examples that motivate this study. In the adversarial attack settings, the lane lines detected by SCNN [37] are largely disrupted, but their performance measured by the conventional accuracy metric is
always higher than the one of PolyLaneNet [48], which are generally aligned with actual lane lines (and indeed lead to less lane center deviation than SCNN when used with driving models as quantified later in §4.2). In the benign settings, PolyLaneNet has the lowest accuracy and is underestimated, despite its seemingly perfect detection for humans. As lane detection has been evaluated using mainly relatively clean and homogeneous driver’s view images, it is not easy to identify such a great discrepancy at the metric level. Considering the criticality of robust lane detection to correct and safe AD, it is important to address such a metric-level limitation since (1) the cornerstone of real-world deployment and commercialization of AD today is exactly on the handling of those more challenging driving scenarios [21, 30, 53]; and (2) with increasingly more discoveries of physical-world adversarial attack on lane detection in AD context [31, 44], it is desired to have a more downstream task-aware performance metric when judging the model robustness (and its enhancement).
Motivated by such critical needs, we design 2 new driving-oriented metrics, End-to-End Lateral Deviation metric (E2E-LD) and Per-frame Simulated Lateral Deviation metric (PSLD), to measure the performance of lane detection models in AD, especially in Automated Lane Centring (ALC), a Level-2 driving automation that automatically steers a vehicle to keep it centered in the traffic lane [7]. E2E-LD is designed directly based on the requirements of driving automation by ALC. PSLD is a lightweight surrogate metric of E2E-LD that estimates the impact of lane detection results on driving from a single frame. This per-frame lightweight design allows the metric to be usable during upstream lane detection model training. To evaluate the validity of the metrics, we conduct a large-scale empirical study of the 4 major types of lane detection approaches on the TuSimple dataset and our newly constructed dataset, Comma2k19-LD, which contains both lane line annotation and driving information. To simulate corner-case but physically-realizable scenarios as in Fig. 1 for lane detection, we utilize and extend physical-world adversarial attacks against the 4 major types of lane detection approaches. Through this study, we find that the conventional metrics have strongly negative correlations ($r \leq 0.55$) with E2E-LD in the benign scenarios, meaning that some recent improvements purely targeting the conventional metrics may not have led to meaningful improvements in AD, but rather may actually have made it worse by overfitting to the conventional metrics. In the attack scenarios, while we observe a slight positive correlation ($r \leq 0.08$), it is not statistically significant. Consequently, we find that the conventional metrics tend to overestimate less robust models. On the contrary, our newly-designed PSLD metric is always strongly positively correlated with E2E-LD ($r \geq 0.38$), and all correlations are statistically significant ($p \leq 0.001$).
While the TuSimple Challenge dataset and its evaluation metrics have played a substantial role in developing performant lane detection methods, the recent improvement on the conventional metrics does not lead to the improvement on the core downstream task AD. We thus want to inform the community of such limitations of the conventional evaluation and facilitate research to conduct more downstream task-aware evaluation for lane detection, as the gap between upstream evaluation metrics and downstream application performance may hinder the sound development of lane detection methods for real-world application scenarios.
In summary, our contributions are as follows:
- We design 2 new driving-oriented metrics, E2E-LD and PSLD, that can more effectively measure the performance of lane detection models when used for AD, their core downstream task.
- We design a methodology to fairly generate physical-world adversarial attacks against the 4 major types of lane detection models.
- We build a new dataset Comma2k19-LD that contains lane annotations and driving information.
- We are the first to conduct a large-scale empirical study to measure the capability of 4 major types of lane detection models in supporting AD.
- We highlight and discuss the critical limitations of the conventional evaluation and demonstrate the validity of our new downstream task-aware metrics.
**Code and data release.** All our codes and datasets are available on our project websites.
1. 2. Related Work
2.1. DNN-based Lane Detection
We taxonomize state-of-the-art DNN-based lane detection methods into 4 approaches. Similar taxonomy is also adopted in prior works [35, 47].
**Segmentation approach.** Segmentation approach handles lane detection as a segmentation task, which classifies whether each pixel is on a lane line or not. Since this approach achieved the state-of-the-art performance in the 2017 TuSimple Lane Detection Challenge [8] (all top-3 winners adopt the segmentation approach [29, 36, 37]), it has been applied in many recent lane detection methods [28, 54, 55]. This segmentation approach is also used in the industry. A reverse-engineering study reveals that Tesla Model S adopts this segmentation-based approach [31]. The major drawback of this approach is its higher computational and memory cost than the other approaches. Due to the nature of the segmentation approach, it needs to predict the classification results for every pixel, the majority of
---
1. https://github.com/ASGuard-UCI/ld-metric
https://sites.google.com/view/cav-sec/ld-metric
which is just background. Additionally, this approach requires a postprocessing step to extract the lane line curves from the pixel-wise classification result.
**Row-wise classification approach.** This approach [27, 35, 39, 52] leverages the domain-specific knowledge that the lane lines should locate the longitudinal direction of driving vehicles and should not be so curved to have more than 2 intersections in each row of the input image. Based on the assumption, this approach formulates the lane detection task as multiple row-wise classification tasks, i.e., only one pixel per row should have a lane line. Although it still needs to output classification results for every pixel similar to the segmentation approach, this divide-and-conquer strategy enables to reduce the model size and computation while keeping high accuracy. For example, UltraFast [39] reports that their method can work at more than 300 FPS with a comparable accuracy 95.87% on the TuSimple Challenge dataset [8]. On the other hand, SAD [28], a segmentation approach, works at 75 frames per second with 96.64% accuracy. This approach also requires a postprocessing step to extract the lane lines similar to the segmentation approach.
**Curve-fitting approach.** The curve-fitting approach [38, 48] fits the lane lines into parametric curves (e.g., polynomials and splines). This approach is applied in an open-source production driver assistance system, OpenPilot [4]. The main advantage of this approach is lightweight computation, allowing OpenPilot to run on a smartphone-like device without GPU. To achieve high efficiency, the accuracy is generally not high as other approaches. Additionally, prior work mentions that this approach is biased toward straight lines because the majority of lane lines are straight [48].
**Anchor-based approach.** Anchor-based approach [34, 40, 47] is inspired by region-based object detectors such as Faster R-CNN [42]. In this approach, each lane line is represented as a straight proposal line (anchor) and lateral offsets from the proposal line. Similar to the row-wise classification approach, this approach takes advantage of the domain-specific knowledge that the lane lines are generally straight. This design enables to achieve state-of-the-art latency and performance. LaneATT [47] reports that it achieves a higher F1 score (96.77%) than the segmentation approaches (95.97%) [28, 37] on the TuSimple dataset.
### 2.2. Evaluation Metrics for Lane Detection
All lane detection methods we discuss in §2.1 evaluate their performance on the accuracy and F1 score metrics used in the 2017 TuSimple Challenge [8]. The accuracy is calculated by $\sum_{i \in H} \frac{|y|}{y}$, where $H$ is a set of sampled y-axis points in the driver’s view image and $t_{p_i}$ is 1 if the difference of a predicted lane line point and the ground truth point at $y = i$ is within $\alpha$ pixels; otherwise is 0. $\alpha$ is set to 20 pixels in the TuSimple Challenge. The detected lane line is associated with a ground truth line with the highest accuracy. In other datasets [13, 37], IoU (Intersection over Union) is also used instead of accuracy. However, the ground-truth area is only defined as a 30-pixel wide line based on lane points, and this metric is almost equivalent to accuracy. The F1 score is a common metric to measure the performance of binary classification tasks. This is the harmonic mean of precision and recall: $F1 = \frac{2 \cdot \text{precision} \cdot \text{recall}}{\text{precision} + \text{recall}}$. In the TuSimple Challenge, the precision and recall are calculated at the lane line level: The precision is the true positive ratio of detected lane lines and the recall is the true positive ratio of ground truth lines. The true positive is defined if the accuracy of a pair of the ground truth line and detected line is $\geq \beta$. $\beta$ is set to 0.85 in the TuSimple Challenge. Although the accuracy and F1 score can measure the capability of lane detection at a certain level, these metrics do not fully represent the performance in the main real-world downstream application, AD [5, 6, 50], as concretely shown later in §4.2.
Specifically, to reflect its performance if used in AD, or drivability, accuracy and F1 score metrics have 2 major limitations: (1) There is no justification of $\alpha = 20$ pixels and $\beta = 0.85$ accuracy thresholds. For example, the ALC system can keep at the lane center even if the detection error is more than 20 pixels, as long as the detected lane lines are parallel with actual lane lines. Furthermore, the importance of detected lane line points should not be equal, i.e., closer points to the vehicle should be more important than the distance points to control a vehicle. (2) The current metrics treat all lane lines in the driver’s view equally, e.g., detection errors for the ego lane’s left line are treated the same as the detection errors for the left lane’s left line. However, the former is much more important to ALC systems than the latter, as the former can directly impact the downstream calculation of the lane center. For example, if a model cannot detect the left lane’s left line but can still detect the ego lane’s left line, it won’t affect its use for ALC. However, if it cannot detect the latter but can detect the former, the accuracy metric remains the same but the downstream modules in ALC may consider the left lane’s left line as ego lane’s left line and thus mistakenly deviate to the left.
### 2.3. Automated Lane Centering
Automated Lane Centering (ALC) is a Level-2 driving automation technology that automatically steers a vehicle to keep it centered in the traffic lane [7]. Recently, ALC is widely adopted in various vehicle models such as Tesla [6] and thus one of the most popular downstream applications of lane detection. Typical ALC systems [4, 10, 33] operate in 3 modules: lane detection, lateral control, and vehicle acceleration. More details of ALC are in the supplementary materials (Appendix G). While there is a line of research that designs end-to-end DNNs for ALC or higher driving automation [12, 14, 16], the current industry-standard solutions
Adversarial Attack on ALC. After researchers found DNN models generally vulnerable to adversarial attacks [24, 46], the following work further explored such attacks in the physical world [15, 23]. A recent study demonstrates that ALC systems are also vulnerable to physical-world adversarial attacks [44]. Their attack, dubbed Dirty Road Patch (DRP) attack, targets industry-grade DNN-based ALC systems, and is designed to be robust to the vehicle position and heading changes caused by the attack in the earlier frames. We use the DRP attack to simulate challenging but realizable scenarios in our evaluations.
3. Methodology
In this section, we motivate the design of 2 new downstream task-aware metrics to measure the performance of lane detection models in ALC. To evaluate the validity of the metrics even in challenging scenarios, we formulate attack objective functions to fairly generate adversarial attacks against the 4 major types of lane detection methods.
3.1. End-to-End Lateral Deviation Metric
As the name of ALC indicates, the performance of ALC should be evaluated by how accurately it can drive in the lane center, i.e., the lateral (left or right) deviation from the lane center. In particular, the maximum lateral deviation from the lane center in continuous closed-loop perception and control is the ultimate downstream-task performance metric for lane detection. Such deviation is directly safety-critical as large lateral deviations can cause a fatal collision with other driving vehicles or roadside objects. We call it End-to-End Lateral Deviation metric (E2E-LD), shown in Fig. 2 (a). The E2E-LD at \( t = 0 \) is obtained as follows.
\[
\max_{t \leq T_E} |L_t - C_t|
\]
, where \( L_t \) is the lateral (y-axis) coordinate of the vehicle at \( t \). \( C_t \) is the lane center lateral (y-axis) coordinate corresponding to the vehicle position at \( t \). We use the vehicle coordinate system at \( t = 0 \). \( T_E \) is a hyperparameter to decide the time duration. If \( T_E = 1 \) second, the E2E-LD is the largest deviation within one second. To obtain \( L_t \), it requires a closed-loop mechanism to simulate a driving by ALC, such as AD simulators [3, 22]. Starting from \( t = 0 \), the vehicle position and heading at \( t = 1 \) is calculated based on the camera frame at \( t = 0 \) (\( X_0 \)): The lane detection model detects lane lines from the frame, the lateral control interprets it by a steering angle, and vehicle actuation operates the steering wheel. This procedure repeats until \( t = T_E \). Hence, multiple (consecutive) camera frames \( X_0, ..., X_{T_E} \) are required and they are dynamically changed based on the lane detection results in the earlier frames.
However, such AD simulations are too computationally expensive for large-scale evaluations. Thus, we simulate vehicle trajectories by following prior work [44], which combines vehicle motion model [41] and perspective transformation [25, 49] to dynamically synthesize camera frames from existing frames according to a driving trajectory.
3.2. Per-Frame Simulated Lateral Deviation Metric
The E2E-LD metric is defined as the desired metric based on the requirements of downstream task ALC. However, it is still too computationally intensive to be monitored during training of the upstream lane detection model. This overhead is mainly due to the camera frame inter-dependency that the camera frames are dynamically changed based on the lane detection results in the earlier frames. To address this limitation, we design the Per-Frame Simulated Lateral Deviation metric (PSLD), which simulates E2E-LD only with a single camera input at the current frame (\( X_0 \)) and the geometry of the lane center.
The overview of PSLD is shown in Fig. 2 (b). The calculation consists of two stages: (1) update the vehicle position with the current camera frame at \( t = 0 \) (\( X_0 \)) and its lane detection result, and (2) apply the closed-loop simulation using the ground-truth lane center as waypoints from \( t = 1 \) to \( t = T_p \). Note that we do not need camera frames in (2) as the vehicle just tries to follow the ground-truth waypoints with lateral control, i.e., we bypass the lane detection assuming we know the ground-truth in \( t \geq 1 \). We then take the maximum lateral deviation from the lane center as a metric as with E2E-LD. For convenience, we normalize the maximum lateral deviation by \( T_p \) to make it a per-frame metric. The definition of PSLD is as follows:
\[
\frac{1}{T_p} \max_{1 \leq t \leq T_p} (\tilde{L}_t - C_t)
\]
(2)
, where the \( \tilde{L}_t \) is the simulated lateral (y-axis) coordinate of the vehicle at \( t \). For example, for \( T_p = 1 \), it is just a single-step simulation with the current lane detection result. The longer \( T_p \) can simulate the tailing effect of the current frame result in the later frames, but it may suffer from accumulated errors. In §4.3, we explore which \( T_p \) achieves the best correlation between PSLD and E2E-LD. More details are in the supplementary material (Appendix A).
3.3. Attack Generation
In this study, we utilize and extend physical-world adversarial attacks to evaluate the robustness of the lane detection system against challenging but realizable scenarios. To fairly generate adversarial attacks for all 4 major types of lane detection methods, we design an attack objective that can be commonly applicable to them. We name it the expected road center, which averages all detected lane lines weighted with their probabilities. Intuitively, the average of all lane lines is expected to represent the road center. If the expected center locates at the center of the input image, its value will be 0.5 in the normalized image width. We maximize the expected road center to attack to the right and minimize it to attack to the left. Detailed calculation of the expected road center for each method is as follows.
Segmentation & row-wise classification approaches:
\[
\frac{1}{L \cdot H} \sum_{l=1}^{L} \sum_{i=1}^{W} \sum_{j=1}^{H} i \cdot P_{ij}^l
\]
(3)
, where \( H \) and \( W \) are the height and width of probability map, \( L \) is the number of probability maps (channels), and \( P_{ij}^l \) is the lane line existence probability of the pixel in the \((i, j)\) element of the probability map.
Curve-fitting approach:
\[
\frac{1}{L \cdot |H|} \sum_{l=1}^{L} \sum_{j \in \mathcal{H}} \left[ j^d, j^{d-1}, \ldots, j, 1 \right] p_l
\]
(4)
, where \( L \) is the number of detected lane lines, \( d \) is the degrees of polynomial (\( d = 3 \) used in PolyLaneNet [48]), \( \mathcal{H} \) is a set of sampled y-axis values, and \( p_l \in \mathbb{R}^{d+1} \) is the coefficient of detected lane line \( l \).
Anchor-based approach:
\[
\sum_{A \in \Lambda} \left[ \frac{1}{|A|} \sum_{j \in A} \left( a_j^l + \delta_j^l \right) \right] \cdot \pi^l
\]
(5)
, where \( A \) is a set of the anchor proposals, \( \Delta^l \) is an index set of y-axis value for anchor proposal \( l \), \( \pi^l \) is the probability of anchor proposal \( l \), and \( a_j^l \) and \( \delta_j^l \) are the x-axis value and its offset of anchor proposal \( l \) at y-axis index \( j \) respectively.
We incorporate this expected road center functions into DRP attack [44] procedure to generate adversarial attacks that are effective for multiple frames.
4. Experiments
We conduct a large-scale empirical study to evaluate the validity of the conventional metrics and our PLSD by comparing them with the ultimate downstream-task performance metric E2E-LD. We evaluate the 4 major types of lane detection approaches. We select a representative model for each approach as shown in Table 1. The pretrained weights of all models are obtained from the authors’ or publicly available websites\(^2\). All pretrained weights are trained on the TuSimple Challenge training dataset [8].
4.1. Conventional Evaluation on TuSimple Dataset
Evaluation Setup. We first evaluate the lane detection models with the conventional accuracy and F1 score metrics on the TuSimple dataset [8], which has 2,782 one-second-long video clips as test data. Each clip consists of 20 frames, and only the last frame is annotated and used for evaluation. We randomly select 30 clips from the test data. For each clip, we consider two attack scenarios: attack to the left, and to the right. Thus, in total, we evaluate 60 different attack scenarios. In each scenario, we place 3.6 m x 3.6 m patches 7 m away from the vehicle as shown in Fig. 1. To know the world coordinate, we manually calibrate the camera matrix based on the size of lane width and lane marking. To deal with the limitation (2) discussed in §2.2, we remove lane lines other than the ego-left and ego-right lane lines to evaluate the applicability to ALC systems more correctly. More details of each attack implementation and parameters are in the supplementary materials (Appendix B).
Results. Table 2 shows the accuracy and F1 score metrics in the benign and attacks scenarios. In the benign scenarios, LaneATT has the best accuracy (94%) and F1 score (88%). SCNN and UltraFast show also high accuracy and F1 score while UltraFast has the lowest F1 score (8%) in the attack scenarios. PolyLaneNet has lower accuracy and F1 score than the others in both benign and attack scenarios. These results are generally consistent with the reported performance as in Table 1. However, when we visually look into the detected lane lines under attack, we find quite some cases suggesting vastly different conclusions if used in AD as the downstream task. For example, as shown in Fig. 1,
\(^2\)LaneATT https://github.com/lucastabelini/LaneATT
SCNN https://github.com/harryhandi18/SCNN-PyTorch
UltraFast https://github.com/cfzd/Ultra-Fast-Lane-Detection
PolyLaneNet https://github.com/lucastabelini/PolyLaneNet
Table 1. Target lane detection methods. Acc. is the accuracy of the TuSimple Challenge dataset [8] in the reference papers.
| Approach | Selected Method | Acc. |
|-------------------|-----------------------|---------------|
| Segmentation | SCNN [37] | 96.53% |
| Row-wise classification | UltraFast (ResNet18) [39] | 95.87% |
| Curve-fitting | PolyLaneNet (b0) [48] | 88.62% |
| Anchor-based | LaneATT (ResNet34) [47] | 95.63% |
The higher score means the higher performance.
Even though SCNN has the highest accuracy in all three scenarios, its detected lane lines are heavily curved by the attack. In contrast, the detection of PolyLaneNet looks like the most robust among the 4 models, as the detected lane lines are generally parallel to the actual lane lines. However, its accuracy (63%) is smaller than the one of SCNN (51%) in the attack to the right scenario. In the benign scenario, PolyLaneNet has a lower accuracy (16% margin) than the others, but it is hard to find meaningful differences for humans as the detected lines are well-aligned with actual lane lines. We provide more examples in the supplementary material (Appendix G). Hence, the conventional accuracy and F1 score-based evaluation may not be well suitable to judge the performance of the lane detection model in representative downstream tasks such as AD.
4.2. Consistency of TuSimple Metrics with E2E-LD
To more systematically evaluate the consistency of the conventional accuracy and F1 score with the performance in AD as the downstream task, we conduct a large-scale empirical study on our newly-constructed dataset.
New Dataset: Comma2k19-LD. To evaluate both the conventional metrics and the downstream task-centric metrics E2E-LD and PSLD on the same dataset, we need both lane line annotations and driving information (e.g., position, steering angle, and velocity). Unfortunately, there is no existing dataset that satisfies the requirements to our best knowledge. Thus, we create a new dataset, coined Comma2k19-LD, in which we manually annotate the left and right lane lines for 2,000 frames (100 scenarios of 1-second clips at 20 Hz). The selected scenarios are randomly selected from the scenarios with more than 30 mph (≈ 48 km/h) in the original Comma2k19 dataset [45]. Fig 3 shows the example frames of the Comma2k19-LD dataset. These frames are the first frames of the scenario. The following 20 frames are also annotated and the same patch is used for each attack. More details are in our supplementary materials (Appendix C). The Comma2k19-LD dataset is published on our website [11].
Evaluation Setup. We conduct the evaluation on the Comma2k19-LD dataset. For the attack generation, we attack to the left in randomly selected 50 scenarios and attack to the right in the other 50 scenarios. For the lateral control, we use the implementation of MPC [43] in OpenPilot v0.6.6, which is an open-source production ALC system. For the longitudinal control, we used the velocity in the original driving trace. For the motion model, we adopt the kinematic bicycle model [32], which is the most widely-used motion model for vehicles [2, 32, 51]. The vehicle parameters are from Toyota RAV4 2017 (e.g., wheelbase), which is used to collect the traces of the comma2k19 dataset. To make the model trained on the TuSimple dataset work on the Comma2k19-LD dataset, we manually adjust the input image size and field-of-view to be consistent with the TuSimple dataset. We place a 3.6 m x 36 m patch at 7 m away from the vehicle at the first frame. For the E2E-LD metric, we use $T_F = 20$ frames (1 second). It follows the result that the average attack success time of the DRP attack is nearly 1 sec [44]. More setup details are in the supplementary materials (Appendix B, D, and G).
Results. Table 3 shows the evaluation results of conventional accuracy and F1 score and E2E-LD. We calculate the Pearson correlation coefficient $r$ and its p value. As shown, there are substantial inconsistencies between the downstream-task performance (from the heavy-weight E2E-LD metric) and the conventional metrics. In the benign scenarios, SCNN has the highest accuracy (0.59) and F1 score (0.84) under the original parameters ($\alpha = 20, \beta = 0.85$). However, SCNN is one of the methods with the lowest E2E-LD (0.21), and instead UltraFast has the highest E2E-LD (0.18). In the attack scenarios, the inconsistency is more obvious: PolyLaneNet has the highest E2E-LD (0.38), but PolyLaneNet achieves the 2nd lowest accuracy (0.59) and the highest F1 score (0.13) with the original parameters. Hence, the E2E-LD draws quite different conclusions.
Table 3. Evaluation results of the E2E-LD and the conventional metrics, accuracy and F1 in the benign and attack scenarios. For each metric, the corresponding Pearson correlation coefficient with E2E-LD in the bottom rows. The original parameters are the ones used in the TuSimple challenge. The best parameters are those that have the highest correlation between E2E-LD with respect to F1 score. The bold and underlined letters indicate the highest and lowest performance or correlation, respectively.
| Metric | Original Parameters | Best Parameters | Original Parameters | Best Parameters |
|--------|---------------------|-----------------|---------------------|-----------------|
| | (α = 20, β = 0.85) | (α = 5, β = 0.9) | (α = 20, β = 0.85) | (α = 50, β = 0.65) |
| SCNN [37] | E2E-LD [m] | 0.21 | 0.93 | 0.64 | 0.59 | 0.68 | 0.31 | 0.82 | 0.77 |
| UltraFast [39] | Accuracy | 0.18 | 0.92 | 0.81 | 0.55 | 0.10 | 0.58 | 0.60 | 0.21 |
| PolyLaneNet [48] | F1 | 0.20 | 0.78 | 0.50 | 0.44 | 0.01 | 0.72 | 0.51 | 0.14 |
| LaneATT [47] | F1 | 0.21 | 0.89 | 0.75 | 0.54 | 0.06 | 0.79 | 0.60 | 0.48 |
Corr. | SCNN [37] | - | -0.55*** | -0.60*** | -0.33*** | -0.13*** | -0.13*** | -0.06*** | -0.06*** |
| UltraFast [39] | - | -0.58*** | -0.59*** | -0.38*** | -0.24* | -0.24* | -0.14** | -0.20* | -0.13** |
| PolyLaneNet [48] | - | -0.60*** | -0.55*** | -0.46*** | 0.10** | -0.27** | -0.28** | -0.06** | 0.01** |
| LaneATT [47] | - | -0.57*** | -0.58*** | -0.34*** | -0.14** | -0.08** | -0.10** | 0.11** | 0.12** |
*Not Significant (p > 0.05), *p ≤ 0.05, **p ≤ 0.01, ***p ≤ 0.001
from the conventional metrics. If we adopt the conventional metrics, SCNN should be preferred as the best performer model. This is consistent with the results in Table 1 and §4.1 since SCNN, UltraFast, and LaneATT show close performance in the conventional metrics (SCNN may have slight advantages in Comma2k19-LD). On the other hand, if we adopt E2E-LD, PolyLaneNet should be preferred since there is only a slight difference between the 4 lane detection models in the benign scenarios and PolyLaneNet clearly outperforms the other methods in the attack scenarios.
The inconsistency between the E2E-LD and the conventional metrics can be more systematically quantified using Pearson correlation coefficient $r$. Generally, the E2E-LD and the conventional metrics have strongly negative correlations ($r \leq 0.55$) with high statistical significance ($p \leq 0.001$), meaning that some recent improvements in the conventional metrics may not have led to improvements in AD, but rather may have made it worse by overfitting to the metrics. SCNN, the segmentation approach, is the only one that does not use domain knowledge, e.g., lane lines are smooth lines (§2.1). This high degree of freedom in the model may lead to overfitting of the human annotations with noise.
Finally, we evaluate the parameters in the conventional metrics: $\alpha$ for the accuracy and $\beta$ for F1 score. For $\alpha$, we explore every 5 pixels from 5 pixels to 50 pixels. For $\beta$, we explore every 0.05 from 0.5 to 0.9. In the benign scenarios, $(\alpha = 20, \beta = 0.85)$ has the best correlation between the E2E-LD and F1 score. In the attack scenarios, $(\alpha = 50, \beta = 0.65)$ has the best correlation between the E2E-LD and F1 score. However, the results are still similar to those using the original parameters: SCNN shows the highest accuracy; UltraFast has a higher F1 score than the others, but the correlation is still negative. Thus, such a naive parameter tuning does not resolve the limitations of the conventional metrics.
### 4.3. Consistency of E2E-LD with PSLD
In this section, we evaluate the validity of PSLD as a per-frame surrogate metric of E2E-LD.
Figure 4. Pearson correlation coefficient $r$ between E2E-LD and PSLD when $T_p$ is varied from 1 to 20 in the benign and attack scenarios. The red vertical lines are $T_p$ with the largest average $r$.
Figure 5. PSLD for the 4 major lane detection models when $T_p$ is varied from 1 to 20 frames in the benign and attack scenarios.
**Evaluation Setup.** We follow the same setup as in §4.2. We generate the DRP attacks for 100 scenarios in the Comma2k19-LD dataset with the same parameters. For the PSLD, we obtain the ground truth waypoints by the following procedure. We generate a trajectory with the bicycle model and OpenPilot’s MPC by using the human driving trajectory as waypoints. We then use the generated trajectory as a ground-truth road center. While we can directly use the human driving trajectory as ground truth, human driving sometimes is not smooth and this approach can cancel the effect of motion models, which have differences from real vehicle dynamics. For the benign scenarios, we calculate the PSLD for each frame in the original human driving. For the attack scenarios, we use the frames synthesized by the method described in 3.1 instead of the original frames because the attacked trajectory and its camera frames are largely changed from the original human driving. For example, to obtain the PSLD at frame $t = N$, we simulate the trajectory until $t = N - 1$ and we then calcu-
late the PSLD with the synthesized frame at \( t = N \).
**Results.** Fig. 4 shows the Pearson correlation coefficient \( r \) between E2E-LD and PSLD when \( T_p \) is varied from 1 to 20 frames. As shown, the E2E-LD, PSLD has strong positive correlations in both benign and attack scenarios. In particular, there are significant correlations (>0.8) in the attack scenarios. This is because the direction of lateral deviation generally coincides with the attack direction. By contrast, in the benign scenarios, the vehicle drives around the road center with overshooting, and thus the direction of lateral deviation heavily depends on the initial states. Nevertheless, the PSLD has always high positive correlations with E2E-LD (>0.2). In particular, SCNN has strong correlations (>0.8) with E2E-LD in all \( T_p \). We consider that the high correlation can be due to the segmentation approach, which is the only method among the 4 methods that do not use the domain-specific knowledge the lane lines are generally smooth (§2.1). The detection of SCNN at the same location tends to be consistent across different frames, i.e., SCNN is less dependent on global information.
Finally, we explore the best \( T_p \) for PSLD to proxy E2E-LD. As shown in Fig. 4, the average of the correlation coefficients of the 4 methods achieves the maximum at \( T_p = 10 \) in the benign scenarios and \( T_p = 5 \) in the attack scenarios respectively. We list the E2E-LD and PSLD with \( T_p = 10 \) and the corresponding \( r \) in Table 4. As shown, there are strong, statistically significant (\( p \leq 0.001 \)) positive correlations (\( \geq 0.38 \)) between E2E-LD and PSLD in both cases. The results strongly suggest that PSLD can measure the performance of lane detection in ALCs based solely on the single camera frame and ground-truth road center geometry. We note that the PSLD is not so sensitive to the choice of \( T_p \). As shown in Fig. 5, the magnitude relation of the 4 methods is generally consistent for all \( T_p \).
### 5. Discussion
**Alternative Metric Design.** To improve the existing metrics, we explored other possible design choices. One of the most intuitive approaches is the \( L_1 \) or \( L_2 \) distance in the bird’s eye view. We evaluated the designs and confirmed that these metrics are still leading to erroneous judgment on downstream AD performance similar to the conventional metrics. Details are in the supplementary materials (Appendix F). We note that our metrics are specific to AD, the main downstream task of lane detection. For other downstream tasks, other metric designs can be more suitable.
**Domain Shift.** In this work, we use lane detection models pretrained on the TuSimple dataset and evaluate them on the Comma2k19-LD. To evaluate the impact of domain shift, we conduct further evaluation and confirm that our observations are generally consistent. Detailed results and discussions are in the supplementary material (Appendix E).
**Closed-loop Simulation.** To obtain driving-oriented metrics, there are multiple parameters and design choices in the closed-loop simulation. In this study, we follow the parameters in the Comma2k19 datasets and select simple and popular designs, e.g., bicycle model and MPC. Meanwhile, we think that such design differences should only have minor effects on our observations because ALC, Level-2 driving automation, just follows the lane center line, which is designed to be smooth on normal roads.
**Evaluation on Other Datasets.** Our metrics are applicable to any dataset set that contains position data (e.g. GPS) and its camera frames, but ideally, velocity and ground-truth lane centers should be available. Such information is available in relatively new datasets such as [9,17]. However, lane annotations are not directly available in the datasets and require considerable effort to obtain from map data and camera frames. To our knowledge, our Comma2k19-LD is so far the only dataset with both lane line annotation and driving information. We hope our work will facilitate further research to build datasets including them.
### 6. Conclusion
In this work, we design 2 new lane detection metrics, E2E-LD and PSLD, which can more faithfully reflect the performance of lane detection models in AD. Throughout a large-scale empirical study of the 4 major types of lane detection approaches on the TuSimple dataset and our new dataset Comma2k19-LD, we highlight critical limitations of the conventional metrics and demonstrate the high validity of our metrics to measure the performance in AD, the core downstream task of lane detection. In recent years, a wide variety of pretrained models have been used in many downstream application areas such as AD [1], natural language processing [19], and medical [18]. Reliable performance measurement is essential to facilitate the use of machine learning responsibly. We hope that our study will help the community make further progress in building a more downstream task-aware evaluation for lane detection.
**Acknowledgments**
This research was supported in part by the NSF CNS-1850533, CNS-1932464, CNS-1929771, CNS-2145493, and USDOT UTC Grant 69A3552047138.
References
[1] Baidu Apollo. https://github.com/ApolloAuto/apollo. 8
[2] Introduction to Self-Driving Cars. https://www.coursera.org/learn/intro-self-driving-cars. 6
[3] LGSVL Simulator: An Autonomous Vehicle Simulator. https://github.com/lgsvl/simulator/. 4
[4] OpenPilot: Open Source Driving Agent. https://github.com/commaai/openpilot. 3
[5] Super Cruise - Hands Free Driving — Cadillac Ownership. https://www.cadillac.com/world-of-cadillac/innovation/super-cruise. 1, 3
[6] Tesla Autopilot. https://www.tesla.com/autopilot. 1, 3
[7] Taxonomy and Definitions for Terms Related to Driving Automation Systems for On-Road Motor Vehicles. SAE International, (J3016), 2016. 2, 3
[8] TuSimple Lane Detection Challenge. https://github.com/TuSimple/tusimple-benchmark/tree/master/doc/lane_detection, 2017. 1, 2, 3, 5
[9] Waymo Open Dataset: An Autonomous Driving Dataset. https://www.waymo.com/open. 2019. 8
[10] Lane Keeping Assist System Using Model Predictive Control. https://www.mathworks.com/help/mpc/ug/lane-keeping-assist-system-using-model-predictive-control.html. 2020. 3
[11] Comma2k19 LD. https://www.kaggle.com/tkm22/comma2k19-lD. 2022. 6
[12] Mayank Bansal, Alex Krizhevsky, and Abhijit S. Ogale. ChauffeurNet: Learning to Drive by Imitating the Best and Synthesizing the Worst. In RSS, 2019. 3
[13] Karsten Behrendt and Ryan Soussan. Unsupervised Labeled Lane Marker Dataset Generation Using Maps. In IEEE International Conference on Computer Vision, 2019. 1, 3
[14] Mariusz Bojarski, Davide Del Testa, Daniel Dworakowski, Bernhard Firner, Beat Flepp, Prasoon Goyal, Lawrence D Jackel, Mathew Monfort, Urs Muller, Jiakai Zhang, et al. End to End Learning for Self-Driving Cars. arXiv preprint arXiv:1604.07316. 2016. 3
[15] Tom Brown, Dandelion Mane, Aurko Roy, Martin Abadi, and Justin Gilmer. Adversarial Patch. arXiv preprint arXiv:1712.09665. 2017. 4
[16] Sergio Casas, Abbas Sadat, and Raquel Urtasun. MP3: A Unified Model to Map, Perceive, Predict and Plan. In CVPR, 2021. 3
[17] Ming-Fang Chang, John Lambert, Patsorn Sangkloy, Jageet Singh, Slawomir Bak, Andrew Hartnett, De Wang, Peter Carr, Simon Lucey, Deva Ramanan, et al. Argoverse: 3D Tracking and Forecasting with Rich Maps. In CVPR, 2019. 8
[18] Sihong Chen, Kai Ma, and Yefeng Zheng. Med3d: Transfer Learning for 3D Medical Image Analysis. arXiv preprint arXiv:1904.00625. 2019. 8
[19] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding. In NAACL, 2019. 8
[20] Richard C Dorf and Robert H Bishop. Modern Control Systems. Pearson, 2011. 4
[21] Alexey Dosovitskiy, German Ros, Felipe Codevilla, Antonio Lopez, and Vladlen Koltun. CARLA: An Open Urban Driving Simulator. In CoRL, 2017. 2
[22] Alexey Dosovitskiy, German Ros, Felipe Codevilla, Antonio Lopez, and Vladlen Koltun. CARLA: An Open Urban Driving Simulator. In CoRL, pages 1–16. 2017. 4
[23] Kevin Eykholt, Ivan Evtimov, Earlene Fernandes, Bo Li, Amir Rahmati, Florian Tramer, Atul Prakash, Tadayoshi Kohno, and Dawn Song. Physical Adversarial Examples for Object Detectors. In WOOT, 2018. 4
[24] Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and Harnessing Adversarial Examples. arXiv preprint arXiv:1412.6572. 2014. 4
[25] Richard Hartley and Andrew Zisserman. Multiple View Geometry in Computer Vision. Cambridge University Press, 2 edition, 2003. 4
[26] Aharon Bar Hillel, Ronen Lerner, Dan Levi, and Guy Raz. Recent Progress in Road and Lane Detection: A Survey. Machine vision and applications, 25(3):727–745, 2014. 1
[27] Yuenan Hou, Zheng Ma, Chunxiao Liu, Tak-Wai Hui, and Chen Change Loy. Inter-Region Affinity Distillation for Road Marking Segmentation. In CVPR, 2020. 3
[28] Yuenan Hou, Zheng Ma, Chunxiao Liu, and Chen Change Loy. Learning Lightweight Lane Detection CNNs by Self Attention Distillation. In CVPR, 2019. 2, 3
[29] Yen-Chang Hsu, Zheng Xu, Zsolt Kira, and Jiawei Huang. Learning to Cluster for Proposal-Free Instance Segmentation. In IJCNN, 2018. 2
[30] Ashesh Jain, Luca Del Pero, Hugo Grimmert, and Peter Ondruska. Autonomy 2.0: Why Is Self-Driving Always 5 Years Away? arXiv preprint arXiv:2107.08142. 2021. 2
[31] Pengfei Jing, Qiyi Tang, Yuefeng Du, Lei Xue, Xiapu Luo, Ting Wang, Sen Nie, and Shi Wu. Too Good to Be Safe: Tricking Lane Detection in Autonomous Driving with Crafted Perturbations. In USENIX Security, 2021. 2
[32] Jason Kong, Mark Pfeiffer, Georg Schildbach, and Francesco Borrelli. Kinematic and Dynamic Vehicle Models for Autonomous Driving Control Design. In IV, 2015. 6
[33] Jin-Woo Lee and Bakhtiar Litkouhi. A Unified Framework of the Automated Lane Centering/Changing Control for Motion Smoothness Adaptation. In ITSC, 2012. 3
[34] Xiang Li, Jun Li, Xiaolin Hu, and Jian Yang. Line-CNN: End-to-End Traffic Line Detection with Line Proposal Unit. ITSC, 2019. 3
[35] Lizhe Liu, Xiaohao Chen, Siyu Zhu, and Ping Tan. Conditioned LaneNet: A Top-To-Down Lane Detection Framework Based on Conditional Convolution. In ICCV, 2021. 2, 3
[36] Davy Neven, Bert De Brabandere, Stamatis Georgoulis, Marc Proesmans, and Luc Van Gool. Towards End-to-End Lane Detection: An Instance Segmentation Approach. In IV, 2018. 2
[37] Xingang Pan, Jianping Shi, Ping Luo, Xiaogang Wang, and Xiaoou Tang. Spatial as Deep: Spatial CNN for Traffic Scene Understanding. In AAAI, 2018. 1, 2, 3, 5, 6, 7, 8
[38] Jonah Philion. FastDraw: Addressing the Long Tail of Lane Detection by Adapting a Sequential Prediction Network. In CVPR, 2019. 3
[39] Qin, Zequn and Wang, Huanyu and Li, Xi. Ultra Fast Structure-Aware Deep Lane Detection. In ECCV, 2020. 3, 5, 6, 7, 8
[40] Zhan Qu, Huan Jin, Yang Zhou, Zhen Yang, and Wei Zhang. Focus on Local: Detecting Lane Marker From Bottom Up via Key Point. In CVPR, 2021. 3
[41] Rajesh Rajamani. Vehicle Dynamics and Control. Springer Science & Business Media, 2011. 4
[42] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun. Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks. In NeurIPS, 2015. 3
[43] Richalet, J. and Rault, A. and Testud, J. L. and Papon, J. Paper: Model Predictive Heuristic Control. Automatica, 14(5):413–428, Sept. 1978. 4, 6
[44] Takami Sato, Junjie Shen, Ningfei Wang, Yunhan Jia, Xue Lin, and Qi Alfred Chen. Dirty Road Can Attack: Security of Deep Learning based Automated Lane Centering under Physical-World Attack. USENIX Security Symposium, 2021. 2, 4, 5, 6
[45] Harald Schafer, Eder Santana, Andrew Haden, and Riccardo Biasini. A Commute in Data: The comma2k19 Dataset. arXiv preprint arXiv:1812.05752, 2018. 6
[46] Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus. Intriguing Properties of Neural Networks. In ICLR, 2014. 4
[47] Lucas Tabelini, Rodrigo Berriel, Thiago M. Paix ao, Claudine Badue, Alberto Ferreira De Souza, and Thiago Oliveira-Santos. Keep your Eyes on the Lane: Real-time Attention-guided Lane Detection. In CVPR, 2021. 2, 3, 5, 6, 7, 8
[48] Lucas Tabelini, Rodrigo Berriel, Thiago M Paixao, Claudine Badue, Alberto F De Souza, and Thiago Oliveira-Santos. Polylanenet: Lane Estimation via Deep Polynomial Regression. In ICPA, 2021. 2, 3, 5, 6, 7, 8
[49] Shiho Tanaka, Kenichi Yamada, Toshio Ito, and Takenao Okawa. Vehicle Detection Based on Perspective Transformation Using Rear-View Camera. Hindawi Publishing Corporation International Journal of Vehicular Technology, 9, 03 2011. 4
[50] Jigang Tang, Songbin Li, and Peng Liu. A Review of Lane Detection Methods Based on Deep Learning. Pattern Recognition, 111:107623, 2021. 1, 3
[51] Daniel Watzenig and Martin Horn. Automated Driving: Safer and More Efficient Future Driving. Springer, 2016. 6
[52] Seungwoo Yoo, Hee Seok Lee, Heesoo Myeong, Sungrack Yun, Hyoungwoo Park, Janghoon Cho, and Duck Hoon Kim. End-to-End Lane Marker Detection via Row-Wise Classification. In CVPR Workshops, 2020. 3
[53] Fisher Yu, Hao Feng Chen, Xin Wang, Wengu Xian, Yingying Chen, Fangchen Liu, Vashishth Madhavan, and Trevor Darrell. Bdd100k: A Diverse Driving Dataset for Heterogeneous Multitask Learning. In CVPR, 2020. 2
[54] Tu Zheng, Hao Fang, Yi Zhang, Wenjian Tang, Zheng Yang, Haifeng Liu, and Deng Cai. RESA: Recurrent Feature-Shift Aggregator for Lane Detection, 2020. 2
[55] Tu Zheng, Hao Fang, Yi Zhang, Wenjian Tang, Zheng Yang, Haifeng Liu, and Deng Cai. RESA: Recurrent Feature-Shift Aggregator for Lane Detection. AAAI, 2021. 2 | 2025-03-06T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3937,
1
],
[
3937,
9559,
2
],
[
9559,
15743,
3
],
[
15743,
20258,
4
],
[
20258,
26120,
5
],
[
26120,
30321,
6
],
[
30321,
35493,
7
],
[
35493,
40699,
8
],
[
40699,
46084,
9
],
[
46084,
49152,
10
]
]
} |
44bfaa1bcf189b5f7c02434921b89cf83e909e33 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 28,
"total-fallback-pages": 0,
"total-input-tokens": 116117,
"total-output-tokens": 34024,
"fieldofstudy": [
"Materials Science"
]
} | Review
Undoped Sr$_2$MMoO$_6$ Double Perovskite Molybdates (M = Ni, Mg, Fe) as Promising Anode Materials for Solid Oxide Fuel Cells
Lubov Skutina 1, Elena Filonova 2*, Dmitry Medvedev 1,3,* and Antoine Maignan 2,4
1 Laboratory of Electrochemical Devices Based on Solid Oxide Proton Electrolytes, Institute of High Temperature Electrochemistry, 620137 Yekaterinburg, Russia; [email protected]
2 Institute of Natural Sciences and Mathematics, Ural Federal University, 620002 Yekaterinburg, Russia; [email protected] (E.F.); [email protected] (A.M.)
3 Institute of Chemical Engineering, Ural Federal University, 620002 Yekaterinburg, Russia
4 Laboratoire Crismat, UMR 6508 Normandie Université, CNRS, Ensicaen, Unicaen, 6 bd du Maréchal Juin, CEDEX 4, 14050 Caen, France
* Correspondence: [email protected]
Abstract: The chemical design of new functional materials for solid oxide fuel cells (SOFCs) is of great interest as a means for overcoming the disadvantages of traditional materials. Redox stability, carbon deposition and sulfur poisoning of the anodes are positioned as the main processes that result in the degradation of SOFC performance. In this regard, double perovskite molybdates are possible alternatives to conventional Ni-based cermets. The present review provides the fundamental properties of four members: Sr$_2$NiMoO$_{6-δ}$, Sr$_2$MgMoO$_{6-δ}$, Sr$_2$FeMoO$_{6-δ}$ and Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_{6-δ}$. These properties vary greatly depending on the type and concentration of the 3d-element occupying the B-position of AB'O$_6$. The main emphasis is devoted to: (i) the synthesis features of undoped double molybdates, (ii) their electrical conductivity and thermal behaviors in both oxidizing and reducing atmospheres, as well as (iii) their chemical compatibility with respect to other functional SOFC materials and components of gas atmospheres. The information provided can serve as the basis for the design of efficient fuel electrodes prepared from complex oxides with layered structures.
Keywords: SOFC; double perovskite; molybdates; anode materials; redox stability; tolerance; electrochemistry; LSGM; carbon deposition; sulfur poisoning
1. Introduction
The development of solid oxide fuel cells (SOFCs) capable of generating electricity by means of a single-step electrochemical approach has been an urgent task since the mid-nineteenth century. Currently, considerable efforts have been devoted to the study of both individual materials (electrolytes, anodes, cathodes, collectors, sealants) and the design and testing of SOFCs [1–3]. It is now extremely important to scale-up from laboratory activity to commercial device. Although many promising fundamental, theoretical and applied problems have been solved, others constantly arise, initiating the development of new technological approaches. For example, with the development of conventional SOFCs, in which YSZ (yttria-stabilized zirconia) acts as an electrolyte and Ni-based cermets serve as anodes, a cheaper and more accessible hydrocarbon fuel (natural gas, biogas, etc.) cannot be used. This is due to the degradation of nickel-based anodes caused by carbonization and sulfur poisoning, which leads to a decrease in SOFC lifetime [4–9]. The solution to this problem involves either modifying the Ni–YSZ composites by introducing various additives (thus preventing carbon deposition and improving chemical stability [10,11]) or searching for new anode materials that do not exhibit these disadvantages [12–17].
In terms of chemical design, there are many alternative materials for Ni-based composites. They include Mo-containing double perovskites with the general formula Sr$_2$MMoO$_{6-δ}$ [18–30].
The use of these compounds as anodes, in combination with La$_{1-x}$Sr$_x$Ga$_{1-y}$Mg$_y$O$_{3-δ}$ (LSGM) electrolytes, allows for the operating temperatures of SOFCs to be lowered down to 800 °C (or even lower). This is due to the high electrical conductivity of LSGM electrolytes [31–33]. This aspect, along with the possibility of using Sr$_2$MMoO$_{6-δ}$ in hydrocarbon fuels, [34–47] opens up new directions for designing carbon- and sulfur-tolerant SOFCs.
The present review seeks to highlight and systemize information on the functional properties of Sr$_2$MMoO$_{6-δ}$ double perovskite molybdates (where M = Ni, Mg, Fe) in terms of their applicability to SOFCs. Special attention is devoted to analyzing their functional properties in both oxidizing and reducing conditions, both of which are used in SOFC fabrication and testing. On the basis of this analysis, the main advantages and problems are identified and future solutions proposed.
2. Brief Descriptions of SOFCs
The extensive body of research on SOFCs is mostly motivated by the fact that they can efficiently generate electricity over a wide temperature range, do not contain liquid phases, do not require the presence of noble metals and allow for the use of various types of fuels [48–56]. An SOFC unit is a multilayered structure consisting of an ionic conductor (electrolyte) between two electrodes, an anode and a cathode (Figure 1).
During the operation of an SOFC, the cathode produces an oxygen reduction reaction (Reaction (1)) and delivers O$^{2-}$ ions to the contact point with the electrolyte.
$$\text{O}_2 + 4e^- = 2\text{O}^{2-}$$
(1)
The function of the gas-tight electrolyte is to electrochemically transport the formed oxygen ions from the cathode to the anode, where they oxidize the fuel (Reactions (2)–(4)) and form generate electrons; the latter go through an external circuit to the cathode, thus forming potentially a power source. It should be noted that the electrolyte must block the flow of electrons from the anode to the cathode inside the cell, thus exhibiting unipolar (ionic) conductivity.
$$\text{H}_2 + \text{O}^{2-} = \text{H}_2\text{O} + 2e^-$$
(2)
$$\text{CO} + \text{O}^{2-} = \text{CO}_2 + 2e^-$$
(3)
$$\text{CH}_4 + 4\text{O}^{2-} = \text{CO}_2 + 2\text{H}_2\text{O} + 8e^-$$
(4)
The overall reactions occurring in SOFCs when hydrogen, a synthesis gas or methane are used can be expressed by Equations (5)–(7), respectively.
$$2\text{H}_2 + \text{O}_2 = 2\text{H}_2\text{O}$$
(5)
\[
H_2 + CO + O_2 = H_2O + CO_2 \quad (6)
\]
\[
CH_4 + 2O_2 = CO_2 + 2H_2O \quad (7)
\]
As SOFCs are not a heat engine, their efficiency is not limited by the Carnot cycle. However, such devices suffer from internal losses, especially at lower operating temperatures (\(T \leq 800 \, ^\circ C\)). These losses are due to insufficient ionic conductivity and/or the slow kinetics of electrode processes. Therefore, traditional SOFCs containing YSZ as a supporting electrolyte and Ni-YSZ as an anode generally operate at temperatures around 900 \(^\circ C\), where the electrolyte’s electrical conductivity reaches a sufficient level (~0.1–0.2 S cm\(^{-1}\) [31,51]). On the other hand, lowering the temperature to 800 \(^\circ C\) would simplify SOFC fabrication, reduce operating costs and extend their long-term lifespan. However, it is necessary to use other oxygen-conducting materials, since the ionic conductivity of YSZ strongly declines with cooling, reaching ~0.05 S cm\(^{-1}\) at 800 \(^\circ C\) [16]. As electrolyte alternatives, compounds based on ceria (Ce\(_{1-x}\)Gd\(_x\)O\(_{2-\delta}\), GDC, or Ce\(_{1-x}\)Sm\(_x\)O\(_{2-\delta}\), SDC) and LSGM [38,39] can be used, since their conductivity at 800 \(^\circ C\) is several times higher than that of YSZ [38]. From these compositions, it is possible to obtain sufficiently dense ceramics that are mechanically and thermally stable [31–33,57,58].
3. Anode Materials for SOFCs
Pure hydrogen, synthesis gas (\(H_2 + CO\)), simple hydrocarbons and ammonia can serve as fuel for SOFCs. The commercialization of SOFCs operating on hydrocarbon fuels has recently become promising due to the abundance of cheaper and easily stored natural gas. In this regard, the development of new anode materials is a key challenge for achieving efficient operations in the presence of methane, which can be used either directly (Reaction (4)) or after preliminary reforming to obtain syngas according to Equations (8)–(10):
\[
CH_4 + 1/2O_2 = CO + 2H_2 \quad (8)
\]
\[
CH_4 + H_2O = CO + 3H_2 \quad (9)
\]
\[
CH_4 + CO_2 = 2CO + 2H_2 \quad (10)
\]
When using hydrocarbons, however, the problem of the carbonization of the anode material arises. During the direct supply of the methane-containing fuel (Reaction (4)), carbon deposition can occur due to cracking from a lack of oxygen ions (Equation (11)).
\[
CH_4 \rightarrow C + 2H_2 \quad (11)
\]
In a synthesis gas environment, the accumulation of carbon at the anode occurs due to the Boudouard reaction, which is a result of the high concentration of CO:
\[
2CO \rightarrow C + CO_2 \quad (12)
\]
and also due to the reduction of carbon monoxide with hydrogen:
\[
CO + H_2 \rightarrow C + H_2O \quad (13)
\]
Carbon can envelop electro-active anode particles and form carbon sediments both on the surface and in the bulk of the electrode material, causing its expansion and deactivation. To prevent the formation of a coke deposit, it is necessary to facilitate the electrochemical oxidation of CO on the surface of the anode (Equation (3)). Additionally, it is possible to supply some O\(_2\) to the feed gas, which will lead to CO oxidation or forced carbon burnout:
\[
2CO + O_2 = 2CO_2 \quad (14)
\]
\[
C + O_2 = CO_2 \quad (15)
\]
Along with carbon accumulation, there is the problem of poisoning the anode materials with sulfur compounds, which are often present in small amounts in natural gas and can interact with electrode components. Moreover, sulfur prevents the reagents from accessing the electrode, blocking targeted electrochemical reactions.
Recognizing the prospects of using hydrocarbons in SOFCs, it is necessary to solve a number of problems in order to develop anode materials with a high level of stability and other important functional properties, including:
1. High catalytic activity in relation to fuel oxidation. In the case of hydrocarbon fuels, the catalytic properties of the material are preliminarily studied before using it as an anode. This is done to determine the mechanism and degree of fuel oxidation, synthesis gas yield and the possibility of carbon deposition after tests [36,41,42,45,47].
2. Sufficient electron conductivity. Electrons formed as a result of electrochemical reactions at anode/electrolyte interface must be transported to the external circuit not only through current collectors, but also through the supported anode with high conductivity to suppress any unwanted ohmic losses in the electrodes.
3. Thermal compatibility. The thermal expansion of the anode must be consistent with similar behavior in both the electrolyte and the current collector. This is required to prevent cracking between SOFC components during operation, heating, cooling or thermal cycling.
4. Chemical stability. The anode must be chemically stable at operating temperatures not only in oxidizing and reducing atmospheres, but also in relation to the electrolyte and the current collector. Otherwise, the resulting impurities can block the transfer of electrons or oxygen ions along the corresponding paths in the SOFCs. It should be noted that chemical stability must also be verified by sintering the SOFCs, where temperatures are higher compared to working temperatures.
5. Porosity. Since the fuel is a gas that must reach a triple-phase boundary (TPB) or the surface of a mixed-ionic conductor, the anode must exhibit a porous structure that retains its natural microstructural characteristics over a prolonged operating period.
Non-compliance to the listed requirements would kill the interest for application as anode materials.
The most common anode materials for SOFCs are porous Ni-YSZ cermets, in which nickel provides electrical conductivity and YSZ oxygen-ion conductivity. The main advantages of this composite include good chemical and thermal compatibility with YSZ electrolytes, high electrical conductivity and excellent electro-catalytic properties with respect to the oxidation of the hydrogen used as a fuel. However, there are some disadvantages: (i) instability of the microstructure during redox cycling, which causes the porous YSZ framework to lose mechanical strength due to the destruction of nickel–nickel contacts during reoxidation and reduction; (ii) the agglomeration of nickel particles using elevated temperatures and high current densities; such an agglomeration leads to the formation of isolated Ni-particles, with the subsequent loss of the electrical connection with the current collector [1]. In addition, the morphology and electrochemical activities of nickel-cermet composite electrodes strongly depend on the ratio and sizes of Ni and YSZ particles, as well as on the methods used to obtain the components [59,60].
Since the metallic nickel catalyzes a cracking reaction (Equation (11)), using Ni-YSZ ceramics in hydrocarbon fuels is difficult. This produces carbon fibers that can block pores and cause mechanical stress, with the subsequent destruction of the electrode and loss of SOFC performance [6–8]. In addition, nickel interacts with fuel impurities, especially sulfur. Even a very small amount of sulfur (as a part of H₂S or S-containing organic compounds) poisons the catalyst, blocking electrochemically active zones and reducing SOFC performance. In this regard, many have sought either to improve cermets by introducing various additives (CaO, SrO [10]; Co, Fe, Cu [11]) and replacing YSZ with doped ceria [61] or to find new anode materials that can overcome the disadvantages of traditional cermets.
Perovskites with mixed ion-electronic conductivity (general formula ABO$_3$) could be an alternative, since they can have an extended TPB compared to purely electronic or purely ionic conductors. In addition, oxide materials are good catalysts in hydrocarbon oxidation and can prevent carbon deposition due to the ability to exchange lattice oxygen with the gaseous phase [6,62].
To date, the existing data offer a wide range of perovskite anode materials with good performances in hydrocarbon fuels. The titanates (ATiO$_3$) [63–65], chromites (ACrO$_3$) [63], manganites (AMnO$_3$) [63,66,67], ferrites (AFeO$_3$) [63,68,69] and vanadates (AVO$_3$) [70] of alkaline earth metals (A = Ca, Sr, Ba) are the best studied perovskites. Among double perovskites, strontium molybdates with general formula Sr$_2$MMoO$_6$ (M = Ni, Mg, Fe) have attracted particular interest over the last decade due to their ability to achieve the required combination of functional properties.
4. General Features of Sr$_2$MMoO$_6$ (M = Ni, Mg, Fe)
Double perovskites (Sr$_2$MMoO$_6$) have a modified perovskite structure (ABO$_3$), where the BO$_6$ and MoO$_6$ octahedra are located in two alternating face-centered cubic sublattices described by the space group Fm3m (Figure 2). Factors involved in the MMo ordering are the differences in cation oxidation states and/or ionic radii. The octahedral voids are occupied by A-cations (Sr$^{2+}$ in the present case).
*Figure 2. Cubic structure of double Sr$_2$MMoO$_6$ perovskites. Reproduced with permission [71]. Copyright 2006, Elsevier.*
The cubic structure is usually distorted due to a mismatch between the sizes of Sr-, M- and Mo-cations, attaining the most energetically favorable form. When the BO$_6$ and MoO$_6$ octahedra rotate relative to each other by an angle, the value of which is determined by the displacement of oxygen atoms within the ab plane, the tetragonal lattice becomes more stable (Figure 3).
The cubic structure is usually distorted due to a mismatch between the sizes of Sr-, M- and Mo-cations, attaining the most energetically favorable form. When the BO$_6$ octahedra rotate relative to each other by an angle, the value of which is determined by the displacement of oxygen atoms within the ab plane, the tetragonal lattice becomes more stable (Figure 3). In this case, monoclinic (α ≠ β ≠ γ ≠ 90°) or orthorhombic (α ≠ β ≠ γ ≠ 90°) polymorphs are formed.
The double perovskite structure can also exhibit a lower degree of symmetry associated with octahedra tilting (Figure 4). In this case, monoclinic (α ≠ b ≠ c, α = β = 90°, γ ≠ 90°), triclinic (α ≠ b ≠ c, α ≠ β ≠ γ ≠ 90°) or orthorhombic (α ≠ b ≠ c, α = β = γ = 90°) polymorphs are formed.
The crystallographic structure of ABO$_3$ (and A$_2$BB’O$_6$) perovskites can be predicted if we consider the discrepancy between the size of the A-site cations and the remaining space inside the oxygen octahedra. For this purpose, the value of the tolerance factor, $t$, is calculated, taking two A-O and B-O distances into account:
$$t = \frac{r_A + r_O}{\sqrt{2}(r_B + r_O)}$$ \hspace{1cm} (16)
where $r_A$, $r_B$ and $r_O$ are the effective ionic radii of A-, B- and O-ions, according to Shannon [73].
Excluding rare examples that arise due to the difficulty of determining variable oxidation states of the cations, the A$_2$MMo’O$_6$ compounds are found to be crystalized in various crystal structures [74]: hexagonal (space groups P6$_3$/mmc, P6$_2$c) at $t > 1.05$, cubic (Fm$ar{3}$m) at $1.00 < t < 1.05$, tetragonal at $0.97 < t < 1.00$ and, finally, triclinic (P$ar{1}$), monoclinic
 **Figure 3.** Structural phase transition of Sr$_2$MMoO$_6$ from cubic to tetragonal lattice associated with the rotation angle of the MO$_6$ and MoO$_6$ octahedra. Reproduced with permission [32]. Copyright 2003, Elsevier.
 **Figure 4.** Monoclinic structure of Sr$_2$MMoO$_6$ formed during the octahedra tilting. Reproduced with permission [72]. Copyright 2013, AIP Publishing.
(P21/n) or orthorhombic (Pmm2) at t < 0.97. For the double perovskites of Sr₂NiMoO₆₋δ, Sr₂MgMoO₆₋δ, and Sr₂FeMoO₆₋δ, the theoretically calculated t values are 0.984, 0.977 and 0.963, respectively [20]. However, these often do not coincide with the experimentally calculated t values (Equation (17)). For example, in the following sections, it will be shown that the Sr₂MgMoO₆₋δ and Sr₂FeMoO₆₋δ compounds can be also formed in triclinic and tetragonal systems.
\[
t = \frac{d_{A-O}}{\sqrt{2}d_{B-O}}\tag{17}
\]
where \(d_{A-O}\) and \(d_{B-O}\) are the average distances between corresponding atoms.
From the viewpoint of defect chemistry, the Sr₂MMoO₆₋δ perovskites exhibit commonalities: the presence of a Mo⁶⁺/Mo⁵⁺ redox pair and a certain amount of oxygen vacancies formed according to Equation (18). In addition, the MO₆ octahedra in the Sr₂MMoO₆₋δ oxides determine their electronic properties, as, for instance, the ordering between Mg²⁺ and Mo⁶⁺ cations is hindering the charge delocalization on the M-O-Mo network, whereas charge carrier exchange between Fe²⁺/Fe³⁺ and Mo⁶⁺/Mo⁵⁺ is a charge carrier delocalization promotor. Therefore, replacing the B-position elements also allows for the modification of their structural, thermal, electric transport, catalytic and other functional properties.
\[
2\text{Mo}^{O_{6}} + O_{2} \iff 2\text{Mo}'_{6} + V_{6}^{\bullet\bullet} + 1/2O_{2}. ag{18}
\]
where \(V_{6}^{\bullet\bullet}\) is the oxygen vacancy, \(\text{Mo}^{6} \) is the Mo⁶⁺-ion (oxidized state) and \(\text{Mo}'_{6} \) is the Mo⁵⁺-ion (reduced state).
For non-composite (i.e., single-phase) anode materials, oxygen vacancies are critical for realizing oxygen-ion transport. The Mo⁶⁺/Mo⁵⁺ redox pairs also provide for electron transport in case of the absence of other transition elements. The ability of these materials to prevent carbon deposition is due to carbon interaction with the lattice oxygen [6,62].
Analyzing the data from the literature, it can be noted that the most promising and studied molybdates are strontium molybdates, where the M-position is occupied by nickel, magnesium and iron. The SOFCs based on these molybdates and LSGM electrolytes yield very high power densities (Table 1).
**Table 1.** Performance of SOFCs based on double Sr₂MMoO₆₋δ molybdates and La₃₋ₓSrₓGa₁₋yMg₄O₁₅₋δ (LSGM) electrolytes.
| Electrolyte Thickness, µm | Cathode Composition | Conditions | \(P_{\text{max}}, \text{mW cm}^{-2}\) | Ref. |
|---------------------------|---------------------|------------|---------------------------------|-----|
| | Sr₂NiMoO₆₋δ | | | |
| 300 | SrCo₀.₈Fe₀.₂O₃₋δ | H₂, 800 °C | 480 | [24]|
| | | 3% H₂O/CH₄, 800 °C | 110 | |
| | | CH₄, 800 °C | 270 | |
| | Bₐ₀.₅Sr₀.₅Co₀.₈Fe₀.₂O₃₋δ | H₂, 850 °C | 820 | |
| | | H₂, 800 °C | 595 | [75]|
| | | H₂, 750 °C | 400 | |
| | Sr₂MgMoO₆₋δ | | | |
| 280 | Bₐ₀.₅Sr₀.₅Co₀.₈Fe₀.₂O₃₋δ | H₂, 800 °C | 660 | [76]|
| 300 | SrCo₀.₈Fe₀.₂O₃₋δ | H₂, 800 °C | 840 | [77]|
| | | CH₄, 800 °C | 440 | |
| 300 | Bₐ₀.₅Sr₀.₅Co₀.₈Fe₀.₂O₃₋δ | H₂, 850 °C | 860 | [40]|
| | | H₂, 800 °C | 600 | |
| | | CH₄, 850 °C | 605 | |
| | | CH₄, 800 °C | 430 | |
| | | H₂, 850 °C | 830 | |
| | | H₂, 800 °C | 830 | |
| | | H₂, 750 °C | 585 | [78]|
| | SmBaCo₂O₅₋δ | H₂, 800 °C | 585 | |
| | | H₂, 750 °C | 410 | |
| 300 | Bₐ₀.₅Sr₀.₅Co₀.₈Fe₀.₂O₃₋δ | H₂, 800 °C | 520 | [79]|
| 1200 | Sr₂Fe₁.₅Mo₀.₅O₀.₅₋δ | 3% H₂O/H₂, 800 °C | 375 | [80] |
Table 1. Cont.
| Electrolyte Thickness, µm | Cathode Composition | Conditions | \(P_{\text{max}}\), mW cm\(^{-2}\) | Ref. |
|---------------------------|---------------------|---------------------|------------------------------------|------|
| 30 | \(\text{La}_{0.8}\text{Sr}_{0.2}\text{MnO}_3\)-YSZ | \(\text{H}_2\), 850 °C | 667 | [81] |
| 30 | \(\text{La}_{0.8}\text{Sr}_{0.2}\text{MnO}_3\)-YSZ | biogas, 850 °C | 520 | [81] |
| 400 | \(\text{Sr}_2\text{MnMoO}_6\)\(_{\delta}\)/\(\text{NiO-Ce}_{0.8}\text{Sm}_{0.2}\text{O}_2\)\(_{\delta}\) | \(\text{CH}_4\), 800 °C | 245 | [28] |
In Table 1 the power density values for the traditional Ni-YSZ cermet anodes are also presented. From this comparison one can see that molybdates \(\text{Sr}_2\text{MMoO}_6\)\(_{\delta}\) (M = Ni, Mg, Fe) are not inferior to the traditional anode in terms of power densities. Moreover, in case of the Ni-cermet anodes, the carbon particles formed during hydrocarbon fuel pyrolysis are deposited on the electrode surface that leads to the cell degradation [82]. The problem of coke formation may be solved by incorporating a catalyst (Au, Pd, Ru) into the Ni-based cermet anodes to avoid the conditions of coke formation. Obviously, it will increase the cost of the Ni-cermet anodes, which does not seem to be economically viable. The investigations of carbon deposition behaviors of the Ni-YSZ-based anodes after treatment in biogas [83] and the \(\text{Sr}_2\text{MnMoO}_6\)\(_{\delta}\)/\(\text{NiO-Ce}_{0.8}\text{Sm}_{0.2}\text{O}_2\)\(_{1.9}\) composite in methane [28] illustrate the undoubted advantages of the molybdate-based anodes.
The electrochemical characteristics of anode materials largely depend on their functional properties: stability in a fuel gas environment, electrical conductivity and chemical and thermal compatibility with electrolyte materials. Therefore, in the following sections, the main emphasis will be devoted to summarizing the results achieved for \(\text{Sr}_2\text{NiMoO}_6\)\(_{\delta}\), \(\text{Sr}_2\text{MgMoO}_6\)\(_{\delta}\), \(\text{Sr}_2\text{FeMoO}_6\)\(_{\delta}\) and \(\text{Sr}_2\text{Fe}_{1.5}\text{Mo}_{0.5}\text{O}_6\)\(_{\delta}\).
5. Functional Properties of \(\text{Sr}_2\text{MMoO}_6\) (M = Ni, Mg, Fe)
The present section, aiming at properties of the \(\text{Sr}_2\text{MMoO}_6\)\(_{\delta}\) phases, has the following common structure of description: preparation, crystal features, thermodynamic stability, thermal and electrical properties, and chemical compatibility with the state-of-the-art electrolyte materials.
5.1. \(\text{Sr}_2\text{NiMoO}_6\)\(_{\delta}\)
The double perovskite \(\text{Sr}_2\text{NiMoO}_6\)\(_{\delta}\) has been considered as the basis for promising anode materials, since the corresponding SOFCs show quite high levels of performance (Table 1). This compound can be easily obtained in a single-phase form in air using various techniques, including the easy and simple method of solid state synthesis [71,84–87]. The starting materials of \(\text{SrCO}_3\), \(\text{NiO}\), and \(\text{MoO}_3\) are mixed and ground together over a long period with subsequent annealing. The final annealing temperatures are rather high in the case of solid state synthesis: 1300 °C for 6 h [84], 1250–1350 °C for 12 h [86] or 48 h [71,87].
The most widely used method for synthesizing \(\text{Sr}_2\text{NiMoO}_6\)\(_{\delta}\) is sol-gel technology [24,34,39,75,88,89]. A crystalline hydrate of ammonium heptamolybdate (\(\text{NH}_4\)\(_7\)\(\text{Mo}_7\text{O}_{24}\)·\(4\text{H}_2\text{O}\) is used as an Mo-containing component; together with \(\text{Sr(NO}_3\)\(_2\) and \(\text{Ni(NO}_3\)\(_2\)·\(6\text{H}_2\text{O}\), this is dissolved in water. In some works, strontium carbonate (\(\text{SrCO}_3\)) and nickel oxide (\(\text{NiO}\)) are used instead of nitrates for the dissolution of which nitric acid is required [88]. Ethylenediaminetetraacetic acid (EDTA) is added to the prepared solution as a chelating agent and then a pH (~7) is tailored with an aqueous ammonia solution. The resulting mixture is converted into a sol during the heat treatment, and then into a gel, which is subsequently dried and calcined. The calcination is usually carried out with two steps: first at 400 °C to remove organic residues, and then at higher temperatures, which can vary greatly: at 1250 °C for 24 h [24], at 800 °C for 10 h [34], at 1300 °C for 24 h [39] or at 1000 °C for 12 h [88] in air.
The citrate-nitrate method was used in [90] to synthesize the complex oxide \(\text{Sr}_2\text{NiMoO}_6\)\(_{\delta}\); this method consists of the thermolysis of a mixture of nitrates and citric acid, which acts as both a chelating agent and fuel. Thermal treatment was conducted in the same way as in
EDTA. The resulting powder was calcined at 850 °C for 12 h. After the synthesis, the sample contained a small amount of a SrMoO₄ impurity phase (which remained even after sintering in air at 1350 °C for 12 h).
In work [91], the authors used the lyophilization of an aqueous solution of cations to obtain Sr₂NiMoO₆δ. Sr(NO₃)₂ and Ni(NO₃)₂·6H₂O were dissolved in water, while MoO₃ was dissolved in dilute nitric acid, with EDTA and ammonia added subsequently. The resulting solution was frozen dropwise to liquid nitrogen. The frozen drops were dehydrated by vacuum sublimation in a freeze dryer for 2 days until an amorphous state was formed. It was then heated three times: at 300 °C to burn organic residue, at 800 °C to remove carbon-containing particles and at 1200 °C for 1 h until crystallization was achieved.
The crystal lattice of Sr₂NiMoO₆δ is described within the framework of a tetragonal system with the space group of I4/m [71,87,88,90–92] and lattice parameters of a = 5.540 Å, c = 7.890 Å [71,87,88]. This compound is characterized by the presence of a second-order transition from the tetragonal I4/m to the cubic Fm3m structure when temperature increases. This transition is associated with the rotation of the NiO₆ and MoO₆ octahedra (Figure 3) and takes place at a temperature of 235 °C [92], 250 °C [91] or 277 °C [87].
The stability of Sr₂NiMoO₆δ under reducing conditions was studied in [24,34,91]. According to X-ray diffraction (XRD) data [34], this material is single phase after sintering at 1200 °C in a forming 5%H₂/N₂ gas (here and below, the volume units are used). However, energy dispersive X-ray spectroscopy analysis showed the presence of metallic nickel nanoparticles. The authors of [24] have shown that Sr₂NiMoO₆δ decomposes in an atmosphere of 5%H₂/Ar above 800 °C. This is in agreement with other data [91], which show the complete decomposition of Sr₂NiMoO₆δ into Sr₃MoO₆, SrMoO₃, SrMoO₄ and Ni after prolonged treatment of the double perovskite in an atmosphere of 5%H₂/Ar (Figure 5). In pure CO₂, double perovskite is destroyed at 600 °C; in this case, the formation of SrCO₃ and SrMoO₄ impurity phases occurs [91].
![Figure 5. XRD patterns recorded for Sr₂NiMoO₆δ calcined in 5%H₂/Ar at different temperatures for 24 h. Reproduced with permission [91]. Copyright 2013, Elsevier.](image-url)
structure until the formation of metallic Ni-particles and unstable “Sr$_2$MoO$_6$” residue that decomposes into a number of more simple molybdates.
The thermal expansion coefficients of Sr$_2$NiMoO$_{6-\delta}$ in air (Table 2) are in agreement with similar parameters for LSGM materials (11.4 $\times$ 10$^{-6}$ K$^{-1}$ for LSGM [93–95]).
Table 2. Thermal expansion coefficients of Sr$_2$NiMoO$_{6-\delta}$ in air. These data are also presented in Figure A1.
| Temperature Range, °C | $\alpha$ $\times$ 10$^6$, K$^{-1}$ | Ref. |
|-----------------------|----------------------------------|------|
| 27–950 | 12.1 | [75] |
| 30–575 | 12.4 | [92] |
| 575–1100 | 14.0 | [92] |
| 20–1300 | 12.9 | [93] |
The values of the electrical conductivity of Sr$_2$NiMoO$_{6-\delta}$ (Table 3) are low enough for practical use in SOFCs. The high conductivity achieved in [75] is probably associated with the formation of highly conductive impurity phases (Ni and SrMoO$_3$ in pure hydrogen at 850 °C).
Table 3. Conductivity of Sr$_2$NiMoO$_{6-\delta}$. These data are also presented in Figure A2.
| Measuring Conditions | $\sigma$, S cm$^{-1}$ | Ref. |
|---------------------|-----------------------|------|
| 5%H$_2$/Ar, 800 °C | 0.1 | [24] |
| H$_2$, 800 °C | 1.1 | [24] |
| CH$_4$, 800 °C | 1.1 | [24] |
| H$_2$, 800 °C | 1.6 | [39] |
| H$_2$, 850 °C | 49 | [75] |
| pO$_2$ = 1 $\times$ 10$^{-6}$ Pa, 600 °C | 7 $\times$ 10$^{-4}$ | [88] |
The revealed varieties in structure, stability and functional properties of the same material (Sr$_2$NiMoO$_{6-\delta}$) can be explained by its pre-history. As shown in works [25,84], the synthesis methods of the Sr$_2$MMoO$_{6-\delta}$ compounds determine their phase compositions, crystal structures, microstructural morphologies, and physico-chemical properties; in particular, electrical transport properties and thermodynamic stability can be considerably varied. This comes from the fact that the preparation pathways and the synthesis/sintering conditions of Sr$_2$MMoO$_{6-\delta}$ determine the content of Mo$^{5+}$ ions (Equation (18)) in the obtained phases [75]. As a result, a high content of Mo$^{5+}$ ions in Sr$_2$MMoO$_{6-\delta}$ governs stability of the final oxides in reducing atmospheres [25] and high values of electrical conductivity [75]. Therefore, when characterizing the structure and properties of Sr$_2$MMoO$_{6-\delta}$, their preparation details should be thoroughly analysed.
Proposing Sr$_2$NiMoO$_{6-\delta}$ as an alternative anode material, most authors recommend using it in combination with LSGM [24,75], CGO [34] or CSO [39] electrolytes. However, the temperature of sintering the anode suspension to the LSGM electrolyte should not exceed 1000 °C. On the contrary, they interact chemically with each other [91], leading to the formation of poorly conducting impurity phases, LaSrGaO$_4$ and SrLaGa$_3$O$_7$ (Figure 6). Sr$_2$NiMoO$_{6-\delta}$ does not react with oxide-based materials (CGO and CSO) even at 1200 °C; therefore, CGO and CSO can also be used as protective layers between the LSGM electrolyte and the anode, formed at temperatures above 1000 °C. According to [82,91,96], the double perovskite molybdates interact with YSZ electrolytes with the formation of SrMoO$_4$ (at temperatures above 800 °C) and SrZrO$_3$ (at temperatures above 1000 °C) phases. For this reason, Sr$_2$MMoO$_6$ cannot be considered as anode material for high-temperature SOFCs.
The chemical stability of Sr$_2$NiMoO$_6$-$\delta$ in hydrocarbon fuels has been insufficiently discussed in the literature. Some works indicate that this material is unstable in a methane atmosphere and in conditions containing sulfur. In [39], it was reported that this perovskite is unstable in a 0.1\%H$_2$S/H$_2$ environment, even at 650 °C (Figure 7). In addition, with an increase in temperature in this medium, the grain boundaries of the sintered Sr$_2$NiMoO$_6$-$\delta$ ceramic were covered with needles and filamentous inclusions, which may be related to metal sulfide(s). Upon testing the SOFC, the Sr$_2$NiMoO$_6$-$\delta$ anode was identified to be chemically unstable when methane CH$_4$ was supplied as a fuel [34]. In addition, an undesirable carbonization reaction (Equation (11)) was also detected.
5.2. Sr$_2$MgMoO$_6$-$\delta$
There is not a single comprehensive study on the properties of the Sr$_2$MgMoO$_6$-$\delta$ oxide. Separate works have been devoted to either electric transport or thermal properties or the design and testing of a fuel cell. The results obtained are quite distinct, which can be explained by the conditions of synthesis and the subsequent sintering of the material, which affects the phase composition, density, microstructure, and consequently other properties.
As Sr$_2$NiMoO$_{6-δ}$, Sr$_2$MgMoO$_{6-δ}$ can be obtained through different synthesis methods: solid state synthesis [19,97–103], solution methods (including sol-gel technology using citric acid [24,37,45,72,104–107] and EDTA [20,76,77,108,109]), the combustion method using glycine as a fuel and complexing agent [110,111] and the freeze-drying method [88,108]. The main disadvantage of this compound is its non-single phase after synthesis in air (Figure 8). Therefore, in almost all works, Sr$_2$MgMoO$_{6-δ}$ was additionally treated in 5%H$_2$/inert gas (Ar or N$_2$) at elevated temperatures. The temperature and exposure time varied from 1000 °C to 1300 °C and from 10 to 40 h, respectively. Sr$_2$MgMoO$_{6-δ}$ was obtained in a single-phase form in air only in [104] after annealing at 1450 °C for 10 h and in [111] at a certain fuel and oxidizer ratio with final annealing at 1000 °C for 6 h.
![Figure 8. XRD patterns recorded for Sr$_2$MgMoO$_{6-δ}$ calcined in air at different exposure times. Reproduced with permission [98]. Copyright 2017, John Wiley & Sons.](image)
It should also be noted that Sr$_2$MgMoO$_{6-δ}$ does not decompose (in contrast to Sr$_2$NiMoO$_{6-δ}$) in H$_2$-containing atmospheres at high temperatures. However, it is also unstable in a CO$_2$ environment at 600 °C [91].
Discussing the crystal structure of Sr$_2$MgMoO$_{6-δ}$, the compound can exhibit cubic (Fm3m [89]), tetragonal (I4/m [19,72,97,98,106,112,113]), monoclinic (P2 [37], P21/n [77,109]) or triclinic I-1 [101,103,104,108,111] crystal structures, depending on the synthesis methods. The triclinic structure was proved by neutron diffraction analysis [101]. According to [108], the cell parameters for the triclinic Sr$_2$MgMoO$_{6-δ}$ at room temperature were: $a = 5.5702$ Å, $b = 5.5709$ Å, $c = 7.9228$ Å, $α = 89.96^\circ$, $β = 90.01^\circ$, $γ = 90.00^\circ$. The phase transitions of Sr$_2$MgMoO$_{6-δ}$ were studied in [72,108]. It was reported that this material undergoes a structural phase transition from the tetragonal (I4/m) to the cubic (Fm3m) structure at 300 °C [72], or from the triclinic (I-1) to the cubic (Fm3m) structure with cubic cell parameter $a = 7.9308$ Å at 250 °C [108].
Tables 4 and 5 list electrical and thermomechanical properties of Sr$_2$MgMoO$_{6-δ}$. The functional properties of this compound are closely dependent on the preparation method and the reduction degree. An acceptable value of electrical conductivity was obtained in [100] when synthesizing the sample via solid state synthesis, followed by firing in 5%H$_2$/N$_2$ in two stages, both at 1300 °C for 4 h. The lower conductivity values obtained in [77,97,104,113] might be associated with the fact that Sr$_2$MgMoO$_{6-δ}$ was subject to reduction at temperatures from 800 °C to 1200 °C. These conditions probably lead to the incomplete reduction of the molybdate; as a consequence, an insignificant concentration of Mo$^{5+}$-ions was achieved (Equation (18)).
Table 4. Thermal expansion coefficients of Sr$_2$MgMoO$_6$-δ in air. These data are also presented in Figure A1.
| Temperature Range, °C | $\alpha \cdot 10^6$, K$^{-1}$ | Ref. |
|-----------------------|-------------------------------|------|
| 109–360 | 11.7 | [77] |
| 360–800 | 12.7 | [77] |
| 25–800 | 15.1 | [100]|
| 50–1300 | 12.9 | [104]|
| n/a | 13.6 | [113]|
Table 5. Conductivity of Sr$_2$MgMoO$_6$-δ. These data are also presented in Figure A2.
| Measuring Conditions | $\sigma$, S cm$^{-1}$ | Ref. |
|----------------------|------------------------|------|
| pO$_2$ = 10$^{-24}$, 800 °C | 3.5 | [18] |
| 5%H$_2$/Ar, 800 °C | 9.5 | [45] |
| 5%H$_2$/Ar, 800 °C | 4 | [77] |
| H$_2$, 800 °C | 10 | [77] |
| 5%H$_2$/Ar, 800 °C | 0.07 | [97] |
| 5%H$_2$/N$_2$, 800 °C | 50 | [100]|
| 5%H$_2$/Ar, 900 °C | 0.5 | [104]|
| 5%H$_2$/Ar, 800 °C | 1.5 | [113]|
The thermal behavior for Sr$_2$MgMoO$_6$-δ was studied only in air, despite the fact that this material was synthesized in a hydrogen atmosphere and that it becomes non-single phase under oxidizing conditions. More precisely, the impurity phases of SrMoO$_4$ and Sr$_3$MoO$_6$ are formed along with the target Sr$_2$MgMoO$_6$-δ compound after its synthesis in an air atmosphere [98]. Although Mg-ions exhibit very high chemical stability due to the constant oxidation state (+2), they cannot compensate for an excess of the lattice oxygen upon the oxidation of Sr$_2$MgMoO$_6$-δ, leading to phase decomposition.
The thermal compatibility of Sr$_2$MgMoO$_6$-δ with an LSGM electrolyte was studied in [99]. It was found that an insignificant interaction between these components begins after annealing at 700 °C (Figure 9). In this regard, a protective layer of doped ceria must be applied between the anode and the electrolyte when designing SOFCs. However, in most of the works devoted to the testing of SOFCs, no protective layers were used [76,77].
Figure 9. XRD patterns recorded for mixtures of Sr$_2$MgMoO$_6$-δ and LSGM calcined in air at different temperatures. Reproduced with permission [99]. Copyright 2018, The Ceramic Society of Japan.
Particular attention has been paid to Sr$_2$MgMoO$_6$-δ due to its good catalytic properties in the oxidation of hydrocarbons and acceptable tolerance with regards to carbonization.
and sulfur poisoning. For example, Sr$_2$MgMo$_{1-x}$V$_x$O$_{6-\delta}$ ($x = 0–0.2$) materials were verified in catalytic tests in biogas [45]. Two types of mixtures were fed into a reactor at temperatures of 300–600 °C: 6% CH$_4$, 6% O$_2$, 4% CO$_2$, balanced with N$_2$ and 6% CH$_4$, 6% O$_2$, 4% CO$_2$, 1% H$_2$S balanced with N$_2$. After isothermal holding, CO$_2$, H$_2$O and a small amount of SO$_2$ were detected as reaction products for the reaction mixture with 1% H$_2$S; the methane conversion rate reached 50% (Figure 10). According to the calculation of the sulfur balance, apart from sulfur oxide SO$_2$ and hydrogen sulfide H$_2$S, no compounds were formed, which proves the stability of Sr$_2$MgMoO$_{6-\delta}$ with regards to sulfur poisoning. The phase stability of Sr$_2$MgMoO$_{6-\delta}$ in a 10%C$_4$H$_4$/Ar medium was proved using the XRD analysis [109]: no traces of carbon were found during testing this sample in comparison to an Ni-GDC ceramic taken as a blank sample.
![Figure 10. Temperature dependence of the conversion degree of biogas in the case of using Sr$_2$MgMoO$_{6-\delta}$ (SMM) or Sr$_2$MgMo$_{0.95}$V$_{0.05}$O$_{6-\delta}$ (SMMV0.05): 1–6% CH$_4$, 6% O$_2$, 4% CO$_2$, 84 % N$_2$; 2–6% CH$_4$, 6% O$_2$, 4% CO$_2$, 83 % N$_2$, 1% H$_2$S. Reproduced with permission [45]. Copyright 2015, Elsevier.](image)
The effect of sulfur poisoning on the SOFC performance of a fuel cell with a Sr$_2$MgMoO$_{6-\delta}$ anode was studied in [37]. After feeding a mixture containing 100 ppm H$_2$S in H$_2$ at 800 °C for 90 h, the anode material remained in its single phase, but the performance of the SOFC decreased, which was attributed to the accumulation of sulfur on the buffer layer. The high sulfur tolerance of Sr$_2$MgMoO$_{6-\delta}$ was also reported in other works [77,113,114].
5.3. Sr$_2$FeMoO$_{6-\delta}$
Iron-containing molybdates have attracted increased attention due to the presence of Fe-Mo pairs, in which a mixed valence is characteristic of both the molybdenum (Mo$^{5+}$/Mo$^{6+}$) and iron (Fe$^{2+}$/Fe$^{3+}$) ions. This peculiarity causes high electron transport. For example, the complex Sr$_2$FeMoO$_{6-\delta}$ oxide, having a metallic type of conductivity (Figure 11), is very different from the other double perovskites. The conductivity values for a given compound in a reducing atmosphere vary in a wide range, from 100 to 300 S cm$^{-1}$ at 800 °C [18,115].
The Sr$_2$FeMoO$_{6-\delta}$ complex oxide can be prepared in the same manner as the previous Ni- and Mg-containing systems. Sr$_2$FeMoO$_{6-\delta}$ was synthesized by solid state synthesis in [18,19,78]. A mixture of the starting reagents (SrCO$_3$, Fe$_2$O$_3$, and MoO$_3$) was first calcined in air and then in a 5%H$_2$/Ar gas at 1100 °C for 10 h [78], 30 h [18] or at 1250 °C for 12 h [18]. Solution methods were used in [40,47,114–117]. (NH$_4$)$_6$Mo$_7$O$_{24}$·4H$_2$O, Sr(NO$_3$)$_2$ and Fe(NO$_3$)$_3$·9H$_2$O were used as starting salts, which were dissolved in water. EDTA, citric acid and ammonia were added in sequence. After the evaporation of the resulting solution and spontaneous combustion, the obtained powder was annealed first at low temperatures (300–400 °C) to remove organic components and then at higher temperatures. The final heat treatment was carried out in 5%H$_2$/Ar at 1100 °C for 20 h [40], 24 h [116] or 2 h [47]. In [117] the finishing powder was heat-treated in air and atmosphere of 5%H$_2$/N$_2$ for 3 h at 800 °C. Similar to the double perovskite Sr$_2$MgMoO$_{6-\delta}$, the complex Sr$_2$FeMoO$_{6-\delta}$ oxide is highly stable in a hydrogen atmosphere, while in air it tends to decompose. According to [116,118] the Sr$_2$FeMoO$_{6-\delta}$ oxide remains a single phase in the pO$_2$ range 10$^{-12}$–10$^{-14}$ atm. Chemical stability of Sr$_2$FeMoO$_{6-\delta}$ as a representative of a Sr$_2$Fe$_{1-x}$Mo$_x$O$_{6-\delta}$ family [116,118,119] is caused by the existence of two redox active elements showing a variety in their oxidation states (+2, +3 and +4 for iron and +5 and +6 for molybdenum). In reducing atmospheres, these cations exist in reduced states (Fe$^{+2}$, Fe$^{+3}$, Mo$^{+5}$, Mo$^{+6}$), adjusting the oxygen content below 6.0 (i.e., $\delta$ > 0). In atmospheres with high oxygen partial pressures, the content of oxidized cations (Fe$^{+5}$, Fe$^{+4}$, Mo$^{+6}$) increase, leading to unstable over-stoichiometry products decomposed until the formation of a SrMoO$_4$ impurity.
The crystal structure of Sr$_2$FeMoO$_{6-\delta}$ is described by tetragonal symmetry with the space group I4/m [19,78,113], P4/mmm [116], or I4/mmm [47]. Manasa et al. [115] reported that this material has a cubic unit cell (sp. gr. Fm3m) after reduction and a tetragonal unit cell (sp. gr. I4/m) after annealing in air. The parameters for the tetragonal structure were refined in [116]: $a = b = 5.575$ Å, $c = 7.907$ Å; and in [47]: $a = b = 5.564$ Å, $c = 7.888$ Å. Possessing high electrical conductivity (nearly 100 S cm$^{-1}$ in the temperature range 25–827 °C), the double Sr$_2$FeMoO$_{6-\delta}$ perovskite also demonstrates quite acceptable TEC values (13.7(4)·10$^{-6}$ K$^{-1}$) in N$_2$ and 5%H$_2$/Ar atmospheres [40,78,116]. However, its thermal behavior in air remains unstudied.
Research on the stability of the Sr$_2$FeMoO$_{6-\delta}$ anode material in hydrocarbon fuel was carried out in [40,78,114]. It was shown that an SOFC consisting of Sr$_2$FeMoO$_{6-\delta}$ | La$_{0.8}$Sr$_{0.2}$Ga$_{0.83}$Mg$_{0.17}$O$_{3-\delta}$ | Ba$_{0.5}$Sr$_{0.5}$Co$_{0.8}$Fe$_{0.2}$O$_{3-\delta}$ operated stably when methane was supplied at 850 °C, and the maximal specific power densities decreased only by 5% after the 20th cycle [40]. The catalytic activity of Sr$_2$FeMoO$_{6-\delta}$ during methane oxidation with oxygen was investigated in [35,47]. It was found that methane is completely oxidized according to Reaction (7) at a high conversion rate, reaching 50% at 750 °C [35]. In cases of partial oxidation of the anode material in hydrocarbon fuel was carried out in [40,78]. The catalytic activity of Sr$_2$FeMoO$_{6-\delta}$ during methane oxidation with oxygen was investigated in [35,47]. It was found that methane is completely oxidized according to Reaction (7) at a high conversion rate, reaching 50% at 750 °C [35].
to Reaction (7) at a high conversion rate, reaching 50% at 750 °C [35]. In cases of partial oxidation (reaction when a CH₄/O₂ mixture is fed in a 1:1 ratio), the methane is completely oxidized according to Equation (10), while the conversion rate reaches 50% at 750 °C [35]. In cases of partial oxidation (Equation (8)) when using a mixture of CH₄/O₂ at a ratio of 2:1, a maximal conversion degree of 36.6% was achieved at 900 °C with a corresponding CO selectivity of 97.2% (Figure 12) [47].
![Figure 12. Catalytic activity of Sr₂FeMoO₆–δ. Reproduced with permission [47]. Copyright 2018, John Wiley & Sons.](image)
5.4. Sr₂Fe₁.5Mo₀.5O₆–δ
The most studied iron-containing molybdate is Sr₂Fe₁.5Mo₀.5O₆–δ with an oxygen nonstoichiometry level (δ) of 0.10 [116]. Oxygen vacancies in this material are mainly transported through the Fe-O-Fe bonds instead of the Mo-O-Fe and Mo-O-Mo bonds; at the same time, the Fe-O bonds are relatively weak, which contributes to a high level of oxygen conductivity. This material has attracted significant attention due to its stability in both oxidizing and reducing atmospheres, as well as the possibility of using it not only as an anode, but also as a cathode [120–122].
In most works, Sr₂Fe₁.5Mo₀.5O₆–δ was synthesized by dissolving the initial salts ((NH₄)₆Mo₇O₄·4H₂O, Sr(NO₃)₂ and Fe(NO₃)₃·9H₂O) in water, adding glycine and citric acid and annealing the precursors obtained after spontaneous combustion at 950–1100 °C in air [21,80,122–132]. This material was also obtained via solid state synthesis in [102,133,134].
The double perovskite Sr₂Fe₁.5Mo₀.5O₆–δ has a cubic face-centered (Fm3m) [80,127,133,135,136] or primitive (Pm3m) [21,91,122] crystal structure after sintering in air. The lattice parameters (a = b = c) calculated within the Fm3m space group are 7.852 Å [127], 7.860 Å [80], 7.845 Å [135], 7.349 Å [136], 7.843 Å [133]; for the Pm3m space group, they are equal to 3.928 Å [21]. A tetragonal structure with an I4/mcm space group was proved by neutron diffraction analysis in [137]; when Sr₂Fe₁.5Mo₀.5O₆–δ was heated in 5%H₂/Ar, it underwent phase transformations into a cubic system (sp. gr. Pm3m). However, it reverted to a tetragonal system after cooling. It is interesting that in the structure of the Sr₂Fe₁.5Mo₀.5O₆–δ perovskite, the iron and molybdenum atoms in a ratio of 3:1 are distributed randomly: iron-molybdenum ordering stops. Perhaps this is the reason why Sr₂Fe₁.5Mo₀.5O₆–δ differs strongly from other double perovskites in terms of its properties, as it is no longer a double perovskite but a simple one and should be rather formulated SrFe₀.75Mo₀.25O₃–δ/2.
When analyzing the electrical transport properties of Sr₂Fe₁.5Mo₀.5O₆–δ, different authors have produced quite distinct results. The electrical conductivity values vary from 9 to 310 S cm⁻¹ in hydrogen and from 10 to 550 S cm⁻¹ in air (Figure 13, Table 6). One of the requirements for anode materials [50] is their high electronic conductivity for effective electrical connectivity with interconnectors. From Tables 3 and 5 and Figure 13a, it can be concluded that the electrical conductivity of the Sr₂M₂O₆ (M = Ni, Mg, Fe) molybdates...
are below the required values (10 S cm$^{-1}$) in reducing atmospheres at low temperatures; therefore, they can be used for intermediate-temperature SOFCs.
 Conductivity values of the Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_6$–δ ceramic in reducing (a) and oxidizing (b) atmospheres.
**Table 6.** Conductivity of Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_6$–δ. These data are also presented in Figure A2.
| Measuring Conditions | $\sigma$, S cm$^{-1}$ | Ref. |
|----------------------|-----------------------|------|
| H$_2$, 800 °C | 9 | [78] |
| Air, 800 °C | 13 | [80] |
| Air, 800 °C | 10 | [98] |
| H$_2$, 800 °C | 16 | [125]|
| Air, 800 °C | 17 | [126]|
| H$_2$ (3 % H$_2$O), 800 °C | 13 | [127]|
| H$_2$, 780 °C | 310 | [135]|
| Air, 780 °C | 550 | [135]|
| H$_2$, 800 °C | 41 | [136]|
A similar disagreement also occurs when considering the thermal properties (Table 7): some authors gave TEC values calculated over the entire temperature range, while others identified several sections in the dilatometric curve with different slopes. It should be noted that the TEC values are rather high compared to electrolyte materials, which could be a significant drawback from application viewpoints.
**Table 7.** Thermal expansion coefficients of Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_6$–δ in air. These data are also presented in Figure A1.
| Temperature Range, °C | $\alpha 10^6$, K$^{-1}$ | Ref. |
|-----------------------|--------------------------|------|
| 200–760 | 14.5 | [122]|
| 760–1200 | 21.4 | [122]|
| 200–1200 | 18.1 | [122]|
| 40–350 | 11.6 | [123]|
| 500–800 | 18.6 | [123]|
| 40–950 | 16.3 | [124]|
| 50–450 | 12.8 | [126]|
| 650–900 | 20.2 | [126]|
The chemical stability of Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_6$–δ in various atmospheres has been widely studied. According to the data from the literature, this is stable in a hydrogen atmosphere even after annealing at 1000 °C for 24 h [91,135] and in pure CO$_2$ at 800 °C [91]. However, there is a significant drawback: the sample is unstable in humid atmospheres at low temperatures. The authors of [128] noted that this double perovskite easily reacts with water to form strontium hydroxide Sr(OH)$_2$, decomposing into Fe$_3$O$_4$, SrMoO$_4$ and SrO$_2$ (Figure 14). It was noted that upon repeated heating to 800 °C, the formed impurities...
could again react with each other, forming Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_{6-\delta}$. This behavior is extremely undesirable for the real application of this molybdate in SOFCs, since the corresponding anode can decompose in a humid environment when heated or cooled, causing possible mechanical stress between the anode and electrolyte.
**Figure 14.** XRD patterns of Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_{6-\delta}$ before and after its treatment in a boiling water. Reproduced with permission [128]. Copyright 2013, Elsevier.
The chemical compatibility of Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_{6-\delta}$ with state-of-the-art electrolyte materials was studied in detail in [91]. It was found that Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_{6-\delta}$ does not react with Ce$_{0.8}$Gd$_{0.2}$O$_{2-\delta}$ even at 1200 °C; interaction with the YSZ electrolyte begins at 1000 °C. The study of chemical compatibility with LSGM is difficult because the diffraction peaks of the two phases overlap. However, a noticeable shift in their position was not observed at different sintering temperatures, and no impurity phases were found (Figure 15).
**Figure 15.** XRD patterns of different mixtures at room temperature and after high-temperature treatment: Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_{6-\delta}$ and YSZ (a), Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_{6-\delta}$ and LSGM (b) Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_{6-\delta}$ and GDC (c). Reproduced with permission [91]. Copyright 2013, Elsevier.
The tolerance of the Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_{6-δ}$ phase to a fuel containing sulfur was investigated in [21,46,137,138]. In work [46], during testing of an SOFC based on the Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_{6-δ}$-Ce$_{0.9}$Gd$_{0.1}$O$_{2-δ}$ composite anode (Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_{6-δ}$-Ce$_{0.9}$Gd$_{0.1}$O$_{2-δ}$ | Ce$_{0.9}$ Gd$_{0.1}$O$_{2-δ}$ | La$_{0.6}$Sr$_{0.4}$Co$_{0.2}$Fe$_{0.8}$O$_{3-δ}$), it was found that after adding 50 ppm H$_2$S to hydrogen, the power densities decreased over the first 46 h due to sulfur poisoning and the formation of a needle-like iron sulfide structure. However, over the next 300 h of operations, power density stabilized, which may be associated with the established equilibrium between the formation and removal of sulfides in the form of sulfur oxide SO$_2$. Similar results were obtained in [21]: when testing a symmetrical SOFC (Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_{6-δ}$ | LSGM | Sr$_2$Fe$_{1.5}$ Mo$_{0.5}$O$_{6-δ}$, SFM | LSGM | SFM), its power characteristics decreased by 10% after replacing pure H$_2$ with 100 ppm H$_2$S; however, after electrode regeneration in air at 800 °C, the power densities reached their initial values (Figure 16).
With the direct supply of methane to the same symmetric cell, power density deterioration was also registered. However, the power density stabilized after annealing in air at 800 °C (Figure 16). This effect was attributed to the formation of carbon by Reaction (11), which subsequently burns in oxygen at high temperatures. In conclusion, the authors noted that Sr$_2$Fe$_{1.5}$Mo$_{0.5}$O$_{6-δ}$ is a highly promising candidate.
6. Conclusions
According to the literature overview, double perovskites (Sr$_2$MMoO$_{6-δ}$, where M = Ni, Mg, Fe) are promising materials for use as fuel electrodes in SOFCs. More precisely, some of them demonstrate a high tolerance for sulfur poisoning and carbonization. However, the optimal compositions have not yet been identified for undoped double molybdates, which is due to the difficulty of achieving the required set of target properties. For example, some complex oxides are stable in oxidizing conditions (which are realized during the joint sintering of SOFCs), but decompose in reducing atmospheres (in which anodes must operate effectively). Others, in contrast, exhibit a single phase form in a reduced state, but become a multiphase system when in oxidizing conditions, which, as a rule, leads to the degradation of many functional properties. It is evident that optimization strategies rest on the further modification of Sr$_2$MMoO$_{6-δ}$ using single or multi-doping (see examples in Table 8). Although the effects of such doping were not considered within the present review, this work gives basic data on the natural properties of Sr$_2$MMoO$_{6-δ}$, acting a starting point for designing modernized double perovskite molybdate derivatives for energy conversion and electrochemical purposes.
Table 8. Doping strategies performed for tailoring the functional properties of Sr$_2$MMoO$_{6-δ}$.
| System | Concentration, x | Ref. |
|-------------------------|------------------|---------------|
| Sr$_2$NiMoO$_{6-δ}$ | | |
| Sr$_2$Ce$_{x}$NiMoO$_{6-δ}$ | x ≤ 0.02 | [139] |
| Sr$_2$Fe$_{x}$NiMoO$_{6-δ}$ | 0 ≤ x ≤ 0.05 | [140] |
| Sr$_2$Mn$_{x}$NiMoO$_{6-δ}$ | 0 ≤ x ≤ 0.05 | [90] |
| Sr$_2$La$_{x}$NiMoO$_{6-δ}$ | 0 ≤ x ≤ 0.1 | [141] |
| Sr$_2$Ba$_{x}$NiMoO$_{6-δ}$ | 0 ≤ x ≤ 1 | [142] |
| Sr$_2$Ni$_{1-x}$Mg$_x$MoO$_{6-δ}$ | 0 ≤ x ≤ 0.25 | [143-147] |
| Sr$_2$Ni$_1-x$Mg$_x$MoO$_{6-δ}$ | x = 0.3 | [148] |
| Sr$_2$Ni$_1-x$Mg$_x$MoO$_{6-δ}$ | 0 ≤ x ≤ 0.75 | [149-151] |
| Sr$_2$Ni$_1-x$Mg$_x$MoO$_{6-δ}$ | 0 ≤ x ≤ 1 | [25] |
| Sr$_2$Ni$_1-x$Mg$_x$MoO$_{6-δ}$ | 0 ≤ x ≤ 1 | [142] |
| Sr$_2$MgMoO$_{6-δ}$ | x = 0.1 | [110,152,153] |
| Sr$_2$Mg$_{1-x}$Co$_x$O$_{6-δ}$ | x = 0.1 | [110,152,153] |
| Sr$_2$Mg$_{1-x}$Ni$_{1-x}$O$_{6-δ}$ | x = 0.1 | [110,152-154] |
| Sr$_2$Ca$_{1-x}$MgMoO$_{6-δ}$ | 0 ≤ x ≤ 0.5 | [113] |
| Sr$_2$Fe$_{1-x}$Mo$_x$O$_{6-δ}$ | x = 1/3 | [155] |
| Sr$_2$Fe$_{1-x}$Mg$_x$O$_{6-δ}$ | 0 ≤ x ≤ 1 | [156] |
| Sr$_2$Fe$_{1-x}$Mg$_x$O$_{6-δ}$ | 0 ≤ x ≤ 0.05 | [157] |
| Sr$_2$Fe$_{1-x}$Mg$_x$O$_{6-δ}$ | 0 ≤ x ≤ 1 | [120,158] |
| Sr$_2$Fe$_{1-x}$Mg$_x$O$_{6-δ}$ | 0 ≤ x ≤ 2 | [120,159] |
| Sr$_2$Fe$_{1.5-x}$Cu$_x$Mo$_{1.5}$O$_{6-δ}$ | 0 ≤ x ≤ 0.3 | [160] |
| Sr$_2$Fe$_{1.5-x}$Ni$_x$Mo$_{1.5}$O$_{6-δ}$ | 0 ≤ x ≤ 0.4 | [123,161,162] |
| Sr$_2$Fe$_{1.5-x}$Ga$_x$Mo$_{1.5}$O$_{6-δ}$ | x = 0.2 | [163] |
| Sr$_2$Fe$_{1.5-x}$Co$_x$Mo$_{1.5}$O$_{6-δ}$ | x = 0.2 | [164] |
| Sr$_2$Fe$_{1.5-x}$Co$_x$Mo$_{1.5}$O$_{6-δ}$ | 0 ≤ x ≤ 1.0 | [126] |
| Sr$_2$Fe$_{1.5-x}$Ni$_x$Mo$_{1.5}$O$_{6-δ}$ | x = 0.1 | [80] |
| Sr$_2$Fe$_{1.5-x}$Mn$_x$Mo$_{1.5}$O$_{6-δ}$ | x = 0.1 | [165] |
| Sr$_2$Fe$_{1.5-x}$Mn$_x$Mo$_{1.5}$O$_{6-δ}$ | 0 ≤ x ≤ 0.1 | [166] |
| Sr$_2$Fe$_{1.5-x}$Mn$_x$Mo$_{1.5}$O$_{6-δ}$ | x = 0.1 | [167] |
| Sr$_2$Fe$_{1.5-x}$Mn$_x$Mo$_{1.5}$O$_{6-δ}$ | x = 0.05 | [168] |
| Sr$_2$La$_{1-x}$Fe$_{1.5}$Mo$_{1.5}$O$_{6-δ}$ | x = 0.5 | [169,170] |
| Sr$_2$Ca$_{1-x}$Fe$_{1.5}$Mo$_{1.5}$O$_{6-δ}$ | 0 ≤ x ≤ 0.6 | [171] |
| Sr$_2$Fe$_{1.5-x}$Mn$_{1-x}$Cl$_x$ | 0 ≤ x ≤ 0.4 | [172] |
| Sr$_2$Fe$_{1.5-x}$Mn$_{1-x}$Cl$_x$ | 0 ≤ x ≤ 0.3 | [173] |
Author Contributions: Conceptualization, L.S. and D.M.; formal analysis, L.S., E.F. and A.M.; data curation, D.M. and E.F.; writing—original draft preparation, L.S. and E.F.; writing—review and editing, D.M. and A.M.; visualization, L.S.; supervision, D.M.; project administration, D.M.; funding acquisition, E.F. and A.M. All authors have read and agreed to the published version of the manuscript.
Funding: The work was funded by a grant from the Ministry of Science and Higher Education of the Russian Federation (Agreement No. 075-15-2019-1924).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Data sharing not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
Figure A1. Thermal expansion coefficients ($\alpha$) of Sr$_2$MMoO$_{6-\delta}$ materials in air. Visualization of Tables 2, 4 and 7. The $\alpha$ values were calculated within entire- (●), low- (■) and high- (▼) temperature ranges. The ► marker indicates that the data are not applicable.
Figure A2. Total conductivity of Sr$_2$MMoO$_{6-\delta}$ materials in reducing (●), pO$_2$-intermediate (■) and oxidizing (▼) atmospheres. Visualization of Tables 3, 5 and 6.
References
1. Da Silva, F.S.; de Souza, T.M. Novel materials for solid oxide fuel cell technologies: A literature review. Int. J. Hydrog. Energy 2017, 42, 26020–26036. [CrossRef]
2. Dwivedi, S. Solid oxide fuel cell: Materials for anode, cathode and electrolyte. Int. J. Hydrog. Energy 2020, 45, 23988–24013. [CrossRef]
3. Istomin, S.Y.; Lyskov, N.V.; Mazo, G.N.; Antipov, E.V. Electrode materials based on complex d-metal oxides for symmetrical solid oxide fuel cell. Russ. Chem. Rev. 2021, 90. [CrossRef]
32. Kharton, V.V.; Shaula, A.L.; Vyshatko, N.P.; Marques, F.M.B. Electron-hole transport in (La0.9Sr0.1)0.98Gao.8Mg0.2O3-δ electrolyte: Effects of ceramic microstructure. *Electrochim. Acta* 2003, 48, 1817–1828. [CrossRef]
33. Morales, M.; Roa, J.J.; Tartaj, J.; Segarra, M. A review of doped lanthanum gallates as electrolytes for intermediate temperature solid oxides fuel cells: From materials processing to electrical and thermo-mechanical properties. *J. Eur. Ceram. Soc.* 2016, 36, 1–16. [CrossRef]
34. Gwan, M.A.; Yun, J.W. Carbon tolerance effects of Sr2NiMoO6-δ as an alternative anode in solid oxide fuel cell under methane fuel condition. *J. Electroceram.* 2018, 40, 171–179. [CrossRef]
35. Li, C.; Wang, W.; Xu, C.; Liu, Y.; He, B.; Chen, C. Double perovskite oxides Sr2Mg1-xFe1-xMoO6-δ for catalytic oxidation of methane. *Nat. Gas Chem.* 2011, 156, 345–349. [CrossRef]
36. Li, C.; Wang, W.; Zhao, N.; Liu, Y.; He, B.; Hu, F.; Chen, C. Structure properties and catalytic performance in methane combustion of double perovskites Sr2Mg1-xMn3MoO6-δ. *Appl. Catal. B* 2010, 102, 78–84. [CrossRef]
37. Howell, T.; Kuhnell, C.; Reitz, T. A summary survey of double perovskites Sr3LaGa2O7 for use as sulfur tolerant anodes. *J. Power Sources* 2013, 231, 279–284. [CrossRef]
38. Zheng, K.; Świerzczek, K.; Carcases, N.M.; Norby, T. Coking study in anode materials for SOFCs: Physicochemical properties and behavior of Mo-containing perovskites in CO and CH4 fuels. *J. Electrochem. Soc.* 2014, 64, 103–116. [CrossRef]
39. Tan, W.; Pan, C.; Yang, S.; Zhong, Q. Application of symmetric solid oxide fuel cell in fuel containing sulfur: I. Effect of electrodes. *J. Power Sources* 2015, 277, 416–425. [CrossRef]
40. Wang, Z.; Tian, Y.; Li, Y. Direct CH4 fuel cell using Sr2FeMoO6 as an anode material. *J. Power Sources* 2011, 196, 6104–6109. [CrossRef]
41. Escudero, M.; Gómez de Parada, I.; Fuerte, A.; Daza, L. Study of Sr2Mg(Mo0.8Nb0.2)O6-δ as anode material for solid oxide fuel cells using hydrocarbons as fuel. *J. Power Sources* 2013, 243, 645–660. [CrossRef]
42. Falcon, H.; Barbero, J.A.; Araujo, G.; Casais, M.T.; Martínez-Lope, M.J.; Alonso, J.A.; Fierro, J.L. Double perovskite oxides 2FeMoO6-δ (A = Ca, Sr and Ba) as catalysts for methane combustion. *J. Appl. Catal. B* 2004, 53, 37–45. [CrossRef]
43. Goodenough, J.; Huang, Y.H. Alternative anode materials for solid oxide fuel cells. *J. Power Sources* 2007, 173, 1–10. [CrossRef]
44. Ji, Y.; Huang, Y.-H.; Ying, J.R.; Goodenough, J.B. Electrochemical performance of La-doped Sr2MgMoO6-δ in natural gas. *Electrochem. Commun.* 2007, 9, 1881–1885. [CrossRef]
45. Wang, F.Y.; Zhong, G.B.; Luo, S.; Xia, L.; Fang, L.-H.; Song, X.; Hao, X.; Yan, G. Porous Sr2MgMo1-xVxO6 ceramics as anode materials for SOFCs using biogas fuel. *Catal. Commun.* 2015, 67, 108–111. [CrossRef]
46. Chen, Y.; Zhang, Y.; Xiao, G.; Yang, Z.; Han, M.; Chen, F. Sulfur-tolerant hierarchically porous ceramic anode-supported solid-oxide fuel cells with self-precipitated nanocatalyst. *ChemElectroChem* 2015, 2, 672–678. [CrossRef]
47. Chang, H.; Chen, H.; Yang, G.; Shi, J.; Zhou, W.; Bai, J.; Li, S.-D. Enhanced coking resistance of Ni cermet anodes for solid oxide fuel cells based on methane on-cell reforming by a redox-stable double-perovskite Sr2FeMoO6-δ. *Int. J. Energ. Res.* 2018, 43, 1–11. [CrossRef]
48. Li, G.; Gou, Y.; Qiao, J.; Sun, W.; Wang, Z.; Sun, K. Recent progress of tubular solid oxide fuel cell: From materials to applications. *J. Power Sources* 2020, 477, 228693. [CrossRef]
49. Sobyanin, V.A. High-temperature solid oxide fuel cells and methane conversion. *Ross. Khim. Zh.* 2003, 47, 62–70. (In Russian)
50. Kawada, T.; Mizusaki, J. Current electrolytes and catalysts. In *Handbook of Fuel Cells-Fundamentals, Technology and Application*; Vielstich, W., Lamm, A., Gasteiger, A., Eds.; Wiley and Sons: Chichester, UK, 2003; Volume 4, pp. 987–1001.
51. Ramadhani, F.; Hussain, M.A.; Mokhils, H.; Hajimolana, S. Optimization strategies for solid oxide fuel cell (SOFC) application: A literature survey. *Renew. Sust. Energ. Rev.* 2017, 76, 460–484. [CrossRef]
52. Saadabadi, S.A.; Thattai, A.T.; Fan, L.; Lindeboom, R.E.F.; Spanjers, H.; Aravind, P.V. Solid oxide fuel cells fuelled with biogas: Potential and constraints. *J. Renew Energy* 2019, 134, 194–214. [CrossRef]
53. Shi, N.; Xie, Y.; Yang, Y.; Xue, S.; Li, X.; Zhu, K.; Huan, D.; Peng, R.; Xia, C.; Lu, Y. Review of anodic reactions in hydrocarbon fueled solid oxide fuel cells and strategies to improve anode performance and stability. *Mater. Renew. Sustain. Energy* 2020, 9, 6. [CrossRef]
54. Veluswamy, G.K.; Laycock, C.J.; Shah, K.; Ball, A.S.; Guwy, A.J.; Dinsdale, R.M. Biohythane as an energy feedstock for solid oxide fuel cells. *Int. J. Hydrog. Energy* 2019, 44, 27896–27906. [CrossRef]
55. Thiruveli, D.A.; Kumar, P.S.B.; Kumar, M.A.C.; Lay, C.H.; Aathika, S.A.; Mani, Y.A.; Jagadiswary, D.G.; Dhanasekaran, A.H.; Shanmugam, P.I.; Sivanesan, S.A.; et al. A critical review on global trends in biogas scenario with its up-gradation techniques for fuel cell and future perspectives. *Int. J. Hydrog. Energy* 2021. [CrossRef]
56. Yu, F.; Han, T.; Wang, Z.; Xie, Y.; Wu, Y.; Jin, Y.; Yang, N.; Xiao, J.; Kawi, S. Recent progress in direct carbon solid oxide fuel cell: Advanced anode catalysts, diversified carbon fuels, and heat management. *Int. J. Hydrog. Energy* 2021, 46, 4283–4300. [CrossRef]
57. Badwal, S.P.S.; Giddey, S.; Munnings, C.; Kulkinari, A. Review of progress in high temperature solid oxide fuel cells. *J. Aust. Ceram. Soc.* 2014, 50, 23–37. [CrossRef]
58. Jaiswal, N.; Tanwar, K.; Suman, R.; Kumar, D.; Uppadhyya, S.; Parkash, O. A brief review on ceria based solid electrolytes for solid oxide fuel cells. *J. Alloys Compd.* 2019, 781, 984–1005. [CrossRef]
59. Kawashima, T.; Miyoshi, S.; Shibuta, Y.; Yamaguchi, S. Particle size dependence of polarization of Ni/YSZ cermet anodes for solid oxide fuel cells. *J. Power Sources* 2013, 234, 147–153. [CrossRef]
60. Barnett, S.A.; Park, B.-K.; Scipioni, R. Effect of infiltration on performance of Ni-YSZ fuel electrodes. ECS Transact. 2019, 91, 1791–1797. [CrossRef]
61. Rösch, B.; Tu, H.; Störmer, A.O.; Müller, A.C.; Stimming, U. Electrochemical characterization of Ni-Ce0.9Gd0.1O2-δ for SOFC anodes. Solid State Ion. 2004, 175, 113–117. [CrossRef]
62. Siang, T.J.; Jalil, A.A.; Hambali, H.U.; Hussain, I.; Azami, M.S. Catalytic partial oxidation of methane to syngas over perovskite catalysts. EWS Conf. 2019, 90, 01006. [CrossRef]
63. Shu, L.; Sunarso, J.; Hashim, S.S.; Mao, J.; Zhou, W.; Liang, F. Advanced perovskite anodes for solid oxide fuel cells: A review. Int. J. Hydrog. Energy 2019, 44, 31275–31304. [CrossRef]
64. Alvarado Flores, J.J.; Avalos Rodriguez, M.L.; Andrade Espinosa, G.; Alcaraz Vera, J.V. Advances in the development of titanates for anodes in SOFC. Int. J. Hydrog. Energy 2019, 44, 12529–12542. [CrossRef]
65. Zhou, X.W.; Yan, N.; Chuang, K.T.; Luo, J.L. Progress in La-doped SrTiO3 (LST)-based anode materials for solid oxide fuel cells. RSC Adv. 2014, 4, 118–131. [CrossRef]
66. Channu, V.S.R.; Holze, R.; Walker, E.H.; Kalluru, R.R. Synthesis and characterization of La0.75Sr0.25Co0.5Mn0.5O3-δ nanoparticles using a combustion method for solid oxide fuel cells. New J. Glass Ceram. 2011, 1, 58–62. [CrossRef]
67. Royer, S.; Alamdari, H.; Duprez, D.; Kaliaguine, S. Oxygen storage capacity of La1-xAxB6O7 perovskites with A′ = Sr, Ce; B = Co, Mn—relation with catalytic activity in the CH4 oxidation reaction. Appl. Catal. B 2005, 58, 273–288. [CrossRef]
68. Li, J.; Wei, B.; Cao, Z.; Yue, X.; Zhang, Y.; Liu, Z. Niobium doped lanthanum strontium ferrite as a redox-stable and sulfur-tolerant anode for solid oxide fuel cells. ChemSusChem 2017, 11, 254–263. [CrossRef]
69. Cao, Z.; Fan, L.; Zhang, G.; Shao, K.; He, C.; Zhang, Q.; Zhu, B. Titanium-substituted ferrite perovskite: An excellent sulfur-resisting and coking tolerant anode catalyst for SOFCs. Catal. Today 2019, 330, 217–221. [CrossRef]
70. Cheng, Z.; Zha, S.; Aguilar, L.; Wang, D.; Winnick, J.; Liu, M. A solid oxide fuel cell running on H2S/CH4 fuel mixtures. Electrochem. Solid State Lett. 2006, 9, A31–A33. [CrossRef]
71. Eriksson, A.K.; Eriksson, S.-G.; Ivanov, S.A.; Knee, C.S.; Eriksen, J.; Rundlöf, H.; Tseggai, M. High temperature phase transition of the magnetoelectric double perovskite Sr2CoMoO6 by neutron diffraction. Mat. Res. Bull. 2006, 41, 144–157. [CrossRef]
72. Troncoso, L.; Martínez-Lope, M.J.; Alonso, J.A.; Fernández-Díaz, M.T. Evaluation of Sr2MnMoO6 (M = Mg, Mn) as anode materials in solid-oxide fuel cells: A neutron diffraction study. J. Appl. Phys. 2013, 113, 023511. [CrossRef]
73. Shannon, R.D.; Prewitt, C.T. Effective ionic radii in oxides and fluorides. Acta Cryst. 1969, 25, 925–946. [CrossRef]
74. Serrate, D.; Teresa, J.M.D.; Barra, M.R. Double perovskites with ferromagnetism above room temperature. J. Phys. Condens. Matter 2006, 19, 023202. [CrossRef]
75. Wei, T.; Ji, Y.; Meng, X.; Zhang, Y. Sr2NiMoO6.8 as anode material for LaGaO3-based solid oxide fuel cell. J. Electrochem. Commun. 2008, 10, 1369–1372. [CrossRef]
76. Jiang, L.; Liang, G.; Han, J.; Huang, Y. Effects of Sr-site deficiency on structure and electrochemical performance in Sr2MgMoO6 for solid-oxide fuel cell. J. Power Sources 2014, 270, 441–448. [CrossRef]
77. Huang, Y.-H.; Dass, R.J.; Deniszyn, J.C.; Goodenough, J.B. Synthesis and characterization of Sr2MgMoO6.8 as an anode material for the solid oxide fuel cell. J. Electroch. 2016, 153, 1266–1272. [CrossRef]
78. Zhang, L.; Zhou, Q.; He, Q.; He, T. Double-perovskites A2FeMoO6.8 (A = Ca, Sr, Ba) as anodes for solid oxide fuel cells. J. Power Sources 2010, 159, 6356–6366. [CrossRef]
79. Li, H.; Tian, Y.; Wang, Z.; Qie, F.; Li, Y. An all perovskite direct methanol solid oxide fuel cell with high resistance to carbon formation at the anode. RSC Adv. 2012, 2, 3857. [CrossRef]
80. Gou, M.; Ren, R.; Sun, W.; Xu, C.; Meng, X.; Wang, Z.; Sun, K. Nb-doped Sr2Fe1.5Mo0.5O5-δ electrode with enhanced stability and electrochemical performance for symmetrical solid oxide fuel cells. Ceram. Int. 2019, 45, 15696–15704. [CrossRef]
81. Wang, F.; Wang, W.; Ran, R.; Tade, M.O.; Shao, Z. Aluminum oxide as a dual-functional modifier of Ni-based anodes of solid oxide fuel cells for operation on simulated biogas. J. Power Sources 2014, 268, 787–793. [CrossRef]
82. Ma, M.; Yang, X.; Qiao, J.; Sun, W.; Wang, Z.; Sun, K. Progress and challenges of carbon-fueled solid oxide fuel cells anode. J. Energy Chem. 2021, 56, 209–222. [CrossRef]
83. Zhang, L.; Chen, G.; Dai, R.; Lv, X.; Yang, D.; Geng, S. A review of the chemical compatibility between oxide electrodes and electrolytes in solid oxide fuel cells. J. Power Sources 2021, 492, 229630. [CrossRef]
84. Prasatkhetragarn, A.; Kaowphong, S.; Yimmirun, R. Synthesis, structural and electrical properties of double perovskite Sr2NiMoO6 ceramics. Appl. Phys. A 2012, 107, 117–121. [CrossRef]
85. Sereda, V.V.; Tsvetkov, D.S.; Sednev, A.L.; Druzhchina, A.I.; Malyskhina, D.A.; Zuev, A.Y. Thermodynamics of Sr2NiMoO6 and Sr2CoMoO6 and their stability under reducing conditions. Phys. Chem. Chem. Phys. 2018, 20, 20108–20116. [CrossRef]
86. Gagulin, V.V.; Korchagina, S.K.; Ivanova, V.V.; Shevchuk, Y.A. Synthesis and properties of Sr2NiMoO6. Adv. Sci. Lett. 2014, 20, 647–649. [CrossRef]
87. Eriksson, A.K.; Eriksson, S.G.; Ivanov, S.A. Phase transitions of the magnetoelectric A2NiMoO6 (A = Ba, Sr) and Ca2NiWO6 by neutron diffraction. Ferroelectrics 2014, 339, 235–243. [CrossRef]
88. Kumar, P.; Kumar, R.; Singh, P. Structural and electrical behavior of double perovskite material Sr2NiMoO6. Adv. Sci. Lett. 2014, 20, 647–649. [CrossRef]
89. Bijelic, J.; Tatar, D.; Hajra, S.; Sahu, M.; Kim, S.J.; Jagličić, Z.; Djerdi, I. Nanocrystalline antiferromagnetic high-κ dielectric Sr2NiMoO6 (M = Te, W) with double perovskite structure type. Molecules 2020, 25, 3996. [CrossRef]
90. Kumar, P.; Presto, S.; Sinha, A.S.K.; Varma, S.; Viviani, M.; Singh, P. Effect of samarium (Sm\(^{3+}\)) doping on structure and electrical conductivity of double perovskite Sr\(_2\)NiMoO\(_6\) as anode material for SOFC. J. Alloys Compd. 2017, 725, 1123–1129. [CrossRef]
91. Dos Santos-Gómez, L.; León-Reina, L.; Porrás-Vázquez, J.M.; Lozisilla, E.R.; Marrero-López, D. Chemical stability and compatibility of double perovskite anode materials for SOFCs. Solid State Ion. 2013, 239, 1–7. [CrossRef]
92. Filonova, E.A.; Dmitriev, A.S. Physicochemical properties of potential cathode La\(_{1-x}\)Ba\(_x\)Mn\(_{1-y}\)Cr\(_y\)O\(_3\) and anode Sr\(_2\)NiMoO\(_6\) materials for solid-oxide fuel cells. J. Electrochem. Soc. 2012, 114, 139–145. [CrossRef]
93. He, B.; Wang, Z.; Zhao, L.; Pan, X.; Wu, X.; Xia, C. Ti-doped molybdenum-based perovskites as anodes for solid oxide fuel cells. J. Power Sources 2013, 241, 627–633. [CrossRef]
94. Tietz, F. Thermal expansion of SOFC materials. Ionics 1999, 5, 129–139. [CrossRef]
95. Tisipis, E.V.; Karton, V.V.; Frade, J.R. Electrochemical behavior of mixed-conducting oxide cathodes in contact with apatite–type La\(_{10}\)Sr\(_5\)AlO\(_{25.5}\) electrolyte. Electrochim. Acta 2007, 52, 4428–4435. [CrossRef]
96. Marrero-López, D.; Peña-Martínez, J.; Ruiz-Morales, J.C.; Gabás, M.; Nuñez, P.; Aranda, M.A.G.; Ramos-Barrado, J.R. Redox behavior, chemical compatibility and electrochemical performance of Sr\(_2\)MgMoO\(_6\)\(_{\delta}\) as SOFC anode. Solid State Ion. 2010, 180, 1672–1682. [CrossRef]
97. Sasaki, K.; Shin-Mura, K. Electrical conductivity of Sr\(_2\)MgMoO\(_6\) for solid oxide fuel cell anodes. J. Ceram. Soc. Jpn. 2017, 125, 487–493. [CrossRef]
98. Kinoshiita, M.; Hara, K.; Onozawa, T.; Shin-Mura, K.; Otani, Y.; Ogawa, S.; Niwa, E.; Hashimoto, T.; Sasaki, K. Synthesis of Sr\(_2\)MgMoO\(_6\) by atmosphere-controlled calcination method and characterization for solid oxide fuel cells. In Advances in Solid Oxide Fuel Cells and Electronic Ceramics II: Ceramic Engineering and Science Proceedings XXXVII; Kusnezoff, M., Bansal, N.P., Shimamura, K., Eds.; John Wiley & Sons: Hoboken, NJ, USA, 2017; Volume 37. [CrossRef]
99. Takano, S.; Shin-Mura, K.; Niwa, E.; Hashimoto, T.; Sasaki, K. Chemical compatibility of Sr\(_2\)MgMoO\(_6\) with representative electrolyte materials and interlayer materials for solid oxide fuel cells. J. Ceram. Soc. Jpn. 2018, 126, 482–487. [CrossRef]
100. Thomas, T.; Qi, H.; Liua, X.; Zonldo, J.; Sabolsky, E.M.; Hart, R. Effect of Mg/Mo rRatio in a stoichiometric Sr\(_2\)MgMoO\(_6\)\(_{\delta}\) (SMM) redox-stable anode. J. Electrochem. Soc. 2017, 78, 1205–1215. [CrossRef]
101. Bernu–Lopez, C.; Allix, M.; Bridges, C.A.; Claridge, J.B.; Rosseinsky, M.J. Sr\(_3\)MgMoO\(_6\) as a perspective anode for solid oxide fuel cells. Inorganic Materials; Elsevier: Oxford, UK, 2006; Volume 26, pp. 265–270. [CrossRef]
102. Vasala, S.; Lehtimaki, S.; Haw, S.W.; Chen, J.M.; Liu, R.S.; Yamauchi, H.; Karppinen, M. Role of SrMoO\(_3\) in Sr\(_2\)MgMoO\(_6\) synthesis. J. Solid State Chem. 2011, 184, 1312–1315. [CrossRef]
103. Vasala, S.; Lehtimaki, S.; Haw, S.W.; Chen, J.M.; Liu, R.S.; Yamauchi, H.; Karppinen, M. Isovalent and aliovalent substitution effects on redox chemistry Sr\(_2\)MgMoO\(_6\)\(_{\delta}\) SOFC-anode material. Solid State Ion. 2010, 181, 754–759. [CrossRef]
104. Xie, Z.; Zhao, H.; Du, Z.; Chen, T.; Chen, N.; Liu, X.; Skinner, S.J. Effects of Co doping on the electrochemical performance of double perovskite oxide Sr\(_2\)MgMoO\(_6\)\(_{\delta}\) as an anode material for solid oxide fuel cells. J. Phys. Chem. 2012, 36, 9734–9743. [CrossRef]
105. Xie, Z.; Zhao, H.; Chen, T.; Zhou, X.; Du, Z. Synthesis and electrical properties of Al-doped Sr\(_2\)MgMoO\(_6\) as an anode material for solid oxide fuel cells. Int. J. Hydrog. Energy 2011, 36, 7257–7264. [CrossRef]
106. Zhang, L.; He, T. Performance of double-perovskite Sr\(_{2-x}\)Sm\(_x\)MgMoO\(_6\)\(_{\delta}\) as solid-oxide fuel-cell anodes. J. Power Sources 2011, 196, 8352–8359. [CrossRef]
107. Durai, A.K.; Masuda, Y.; Joo, J.H.; Woo, S.K.; Kim, S.D. Influence of Fe doping on the electrical properties of Sr\(_2\)MgMoO\(_6\). Mater. Chem. Phys. 2013, 139, 360–363. [CrossRef]
108. Marrero-López, D.; Pená-Martínez, J.; Ruiz-Morales, J.C. High temperature phase transition in SOFC anodes based on Sr\(_2\)MgMoO\(_6\)\(_{\delta}\). J. Solid State Chem. 2009, 182, 1027–1034. [CrossRef]
109. Matsuda, Y.; Karppinen, M.; Yamazaki, Y.; Yamauchi, H. Oxygen-vacancy concentration in A\(_2\)MgMoO\(_6\)\(_{\delta}\) double-perovskite oxides. J. Solid State Chem. 2009, 182, 279–284. [CrossRef]
110. Montenegro-Hernández, A.; Dager, P.; Caneiro, A.; Mogli, L. Structural properties and electrical conductivity of perovskite type oxides in SOFCs. J. Phys. Conf. Ser. 2019, 1219, 012001. [CrossRef]
111. Dager, P.K.; Chanquía, C.M.; Mogli, L.; Caneiro, A. Synthesis of pure-phase Sr\(_2\)MgMoO\(_6\) nanostructured powder by the combustion method. Mater. Lett. 2015, 141, 248–251. [CrossRef]
112. Marrero-López, D.; Pená-Martínez, J.; Ruiz-Morales, J.C.; Pérez-Coll, D.; Aranda, M.A.G.; Nuñez, P. Synthesis, phase stability and electrical conductivity of Sr\(_2\)MgMoO\(_6\)\(_{\delta}\). Mat. Res. Bull. 2008, 43, 2441–2450. [CrossRef]
113. Osinkin, D.A.; Zabolotskaya, E.V.; Kellerman, D.G.; Sunstov, A.Y. The physical properties and electrochemical performance of Ca-doped Sr\(_2\)MgMoO\(_6\)\(_{\delta}\) as perspective anode for solid oxide fuel cells. J. Solid State Electrochem. 2018, 22, 1209–1215. [CrossRef]
114. Huang, Y.-H.; Dass, R.L.; Xing, Z.-L.; Goodenough, J.B. Double perovskites as anode materials for solid-oxide fuel cells. Science 2006, 312, 254–257. [CrossRef]
115. Rath, M.K.; Lee, K.-T. Superior electrochemical performance of non-precious Co-Ni-Mo alloy catalyst-impregnated Sr\(_2\)FeMoO\(_6\) as an electrode material for symmetric solid oxide fuel cells. Electrochim. Acta 2016, 212, 678–685. [CrossRef]
116. Rager, J.; Zipperle, M.; Sharma, A.; MacManus-Driscoll, J.L. Oxygen stoichiometry in Sr\(_2\)FeMoO\(_6\), the determination of Fe and Mo valence states, and the chemical phase diagram of SrO–Fe\(_2\)O\(_3–\)MoO\(_3\). J. Am. Ceram. Soc. 2004, 87, 1330–1335. [CrossRef]
117. Farzin, Y.A.; Babaei, A.; Ataie, A. Low-temperature synthesis of Sr\(_2\)FeMoO\(_6\) double perovskite; structure, morphology, and magnetic properties. Ceram. Int. 2020, 46, 16867–16878. [CrossRef]
118. Tsvetkov, D.S.; Ivanov, I.L.; Malyskhin, D.A.; Steparuk, A.S.; Zuev, A.Y. The defect structure and chemical lattice strain of the double perovskites Sr₂BMoO₆₋₈ (B = Mg, Fe). *Dalton Trans.* 2016, 45, 12906–12913. [CrossRef]
119. Kircheisen, R.; Töpfer, J. Nonstoichiometry, point defects and magnetic properties in Sr₂FeMoO₆₋₈ double perovskites. *J. Solid State Chem.* 2012, 185, 76–81. [CrossRef]
120. Sugahara, T.; Ohtaki, M.; Souma, T. Thermoelectric properties of double-perovskite oxides Sr₂₋ₓM₆FeMoO₆ (M = Ba, La). *J. Ceram. Soc. Jpn.* 2008, 116, 1278–1282. [CrossRef]
121. Muñoz-García, A.B.; Pavone, M.; Carter, E.A. Effect of antisite defects on the formation of oxygen vacancies in Sr₂FeMoO₆: Implications for ion and electron transport. *Chem. Mater.* 2011, 23, 4525–4536. [CrossRef]
122. Xiao, G.; Liu, Q.; Zhao, F.; Zhang, L.; Xi, C.; Chen, F. Sr₂Fe₁₋ₓNiₓMoO₆ as cathodes for intermediate-temperature solid oxide fuel cells with La₀.₅Sr₂Ga₀.₅Mg₀.₅O₃ electrolyte. *J. Electrochem. Soc.* 2011, 158, B455. [CrossRef]
123. Dai, N.; Feng, J.; Wang, Z.; Jiang, T.; Sun, W.; Qiao, J.; Sun, K. Synthesis and characterization of B-site Ni-doped perovskites Sr₂Fe₁₋ₓNiₓMoO₆ (x = 0, 0.05, 0.1, 0.2, 0.4) as cathodes for SOFCs. *J. Mater. Chem. A* 2013, 1, 14147–14153. [CrossRef]
124. Qiao, J.; Chen, W.; Wang, W.; Wang, Z.; Sun, W.; Zhang, J.; Sun, K. The Ca element effect on the enhancement performance of Sr₂Fe₁₋ₓMoO₆₋₈ based perovskite as cathode for intermediate-temperature solid oxide fuel cells. *J. Power Sources* 2016, 331, 400–407. [CrossRef]
125. Feng, J.; Yang, G.; Dai, N.; Wang, Z.; Sun, W.; Rooney, D.; Qiao, J.; Sun, K. Investigation into the effect of Fe-site substitution on the performance of Sr₂Fe₁₋ₓNiₓMoO₆ anodes for SOFCs. *J. Mater. Chem.* 2014, 2, 17628–17634. [CrossRef]
126. Feng, J.; Yang, G.; Dai, N.; Wang, Z.; Sun, W.; Rooney, D.; Qiao, J.; Sun, K. Investigation into the effect of Fe-site substitution on the performance of Sr₂Fe₁₋ₓNiₓMoO₆ anodes for SOFCs. *J. Mater. Chem.* 2014, 2, 17628–17634. [CrossRef]
127. Pan, X.; Wang, Z.; He, B.; Wang, S.; Wu, X.; Xi, C. Effect of Co doping on the electrochemical properties of Sr₂Fe₁₋ₓMoO₆₋₈ electrocatalyst for solid oxide fuel cell. *Int. J. Electrochem. Sci.* 2013, 8, 4108–4115. [CrossRef]
128. Wright, J.H.; Virkar, A.V.; Liu, Q.; Chen, F. Electrical characterization and water sensitivity of Sr₂Fe₁₋ₓMoO₆₋₈ as a possible solid oxide fuel cell electrode. *J. Power Sources* 2013, 237, 13–18. [CrossRef]
129. Muñoz-García, A.B.; Pavone, M.; Carter, E.A. Effect of antisite defects on the formation of oxygen vacancies in Sr₂FeMoO₆: Implications for ion and electron transport. *Chem. Mater.* 2011, 23, 4525–4536. [CrossRef]
130. Qi, H.; Lee, Y.-L.; Yang, T.; Li, W.; Li, H.; Zhao, Y.; Li, Y. Synthesis and enhanced electrochemical performance of Sm-doped Sr₂Fe₁₋ₓMoO₆₋₈ electrode for solid state electrochemical devices. *J. Power Sources* 2019, 418, 17–23. [CrossRef]
131. Wang, Y.; Li, P.; Li, H.; Zhao, Y.; Li, Y. Synthesis and enhanced electrochemical performance of Sm-doped Sr₂Fe₁₋ₓMoO₆₋₈ electrode for solid state electrochemical devices. *J. Power Sources* 2019, 418, 17–23. [CrossRef]
132. Osinkin, D.A. Kinetics of CO oxidation and redox cycling of Sr₂Fe₁₋ₓMoO₆₋₈ electrode for symmetrical solid state electrochemical devices. *J. Power Sources* 2019, 418, 17–23. [CrossRef]
133. Osinkin, D.A.; Kolchugin, A.A.; Bogdanovich, N.M.; Beresnev, S.M. Performance and redox stability of a double-layer Sr₂Fe₁₋ₓMoO₆₋₈-based electrode for solid oxide electrochemical application. *Electrochim. Acta* 2020, 361, 137058. [CrossRef]
134. Liu, Q.; Dong, X.; Xiao, G.; Zhao, F.; Chen, F. A novel electrode material for symmetrical SOFCs. *Adv. Mater.* 2010, 22, 5478–5482. [CrossRef]
135. Liu, H.; Zhao, Y.; Wang, Y.; Li, Y. Sr₂Fe₁₋ₓMoO₆₋₈ perovskite as an anode in a solid oxide fuel cell: Effect of the substitution ratio. *Catal. Today* 2016, 259, 417–422. [CrossRef]
136. Bugaris, D.E.; Hodges, J.P.; Huq, A.; Chance, W.M.; Heyden, A.; Chen, F.; zur Loye, H.-C. Investigation of the high-temperature redox chemistry of Sr₂Fe₁₋ₓMoO₆₋₈ via in situ neutron diffraction. *J. Mater. Chem. A* 2014, 2, 4045–4054. [CrossRef]
137. Walker, E.; Ammal, S.C.; Suthirakun, S.; Chen, F.; Terejanu, G.A.; Heyden, A. Mechanism of sulfur poisoning of Sr₂Fe₁₋ₓMoO₆₋₈ perovskite anode under solid oxide fuel cell conditions. *J. Phys. Chem. C* 2014, 118, 23545–23552. [CrossRef]
138. Presto, S.; Kumar, P.; Varma, S.; Viviani, M.; Singh, P. Electrical conductivity of NiMoO₃-based double perovskites under SOFC anodic conditions. *Int. J. Hydrog. Energy* 2018, 43, 4528–4533. [CrossRef]
139. Kumar, P.; Singh, N.K.; Sinha, A.S.K.; Singh, P. Structural and electrical characterizations of cerium (Ce³⁺)-doped double perovskite system Sr₅NiMoO₁₂₋₈. *Appl. Phys. A* 2016, 122, 828. [CrossRef]
140. Kumar, P.; Singh, N.K.; Gupta, G.; Singh, P. Effect of lanthanum (La³⁺) doping on the structural and electrical properties of double perovskite Sr₅NiMoO₁₂₋₈. *Solid State Ion.* 2016, 229–230, 2101–2109. [CrossRef]
141. Filiponova, E.A.; Skutina, L.S.; Medvedev, D.A. Phase transitions and thermal expansion of Sr₂₋ₓBaₓNiMoO₆ and Sr₂₋ₓNi₋ₓZnₓMoO₆ solid solutions. *Inorg. Mat.* 2016, 52, 57–62. [CrossRef]
142. Filiponova, E.A.; Gilev, A.R.; Skutina, L.S.; Vylkov, A.I.; Kuznetsov, D.K.; Shur, V.Y. Double Sr₂₋ₓNi₋ₓMgₓMoO₆ perovskites (x = 0, 0.25) as perspective anode materials for LaGaO₃-based solid oxide fuel cells. *Solid State Ion.* 2018, 314, 112–118. [CrossRef]
143. Filiponova, E.A.; Dmitriev, A.S.; Pikalov, P.S.; Medvedev, D.A.; Pikalova, E.Y. The structural and electrical properties of Sr₂₋ₓNi₋ₓMgₓMoO₆ and its compatibility with solid state electrolytes. *Solid State Ion.* 2014, 262, 365–369. [CrossRef]
144. Skutina, L.S.; Vylkov, A.I.; Grzhegorzhievskii, K.V.; Chuikin, A.Y.; Ostroushko, A.A.; Filiponova, E.A. Crystal structure and phase transitions of Sr₂₋ₓNi₋ₓMo₃O₉ solid solutions. *Inorg. Mat.* 2017, 53, 1293–1299. [CrossRef]
146. Gilev, A.R.; Kiselev, E.A.; Cherepanov, V.A. Performance of the lanthanum gallate based solid oxide fuel cells with the La_{2-x}Ca_xNi_{1-x}Fe_xO_{4+δ} cathodes and Sr_2Ni_{0.75}Mg_{0.25}MoO_6δ anode. Solid State Ion. 2019, 339, 115001. [CrossRef]
147. Skutina, L.S.; Vylkov, A.; Kuznetsov, D.K.; Medvedev, D.A.; Shur, V.Y. Tailoring Ni and Sr_2Mg_{0.25}Ni_{0.75}MoO_6δ cermets compositions for designing the fuel electrodes of solid oxide electrochemical cells. Energies 2019, 12, 2394. [CrossRef]
148. Filonova, E.A.; Russikh, O.V.; Skutina, L.S.; Vylkov, A.J.; Maksimchuk, T.Y.; Ostroushko, A.A. Sr_2Ni_{0.7}MoO_{3.5}δ: Correlation between synthesis conditions and functional properties as anode material for intermediate-temperature SOFCs. Int. J. Hydrog. Energy 2021, in press. [CrossRef]
149. Urusova, N.; Kumar, M.R.; Semkin, M.; Filonova, E.; Kratochvilova, M.; Neznakhin, D.; Grzhegorzhevskii, K.; Ostroushko, A.; Park, J.G.; Pirogov, A. Crystal structure and magnetic properties of the Sr_2Ni_{1-x}Mg_xO_6 (x = 0, 0.25, 0.5, and 0.75) polycrystals. Solid State Sci. 2020, 99, 106008. [CrossRef]
150. Xia, T.; Meng, X.; Luo, T.; Zhan, Z.-L. Synthesis and evaluation of Ca-doped Sr_2Mg_{0.25}MgMoO_6δ anode in SOFCs. Ceram. Int. 2018, 44, 2539–2546. [CrossRef]
151. Dager, P.K.; Mogni, L.V.; Zampieri, G.; Caneiro, A. High temperature properties of Sr_2Ni_{0.75}Mg_{0.25}MoO_6δ-δ. J. Alloys Compd. 2018, 705, 671–678. [CrossRef]
152. Dager, P.K.; Mogni, L.V.; Zampieri, G.; Tobia, D.; Caneiro, A. Effect of transition metal doping on the crystal structure and oxidation state of Sr_2MgMo_{0.9}TM_{0.1}O_{6+δ} compounds (TM = Co, Mn or Ni). J. Phys. Chem. Solids 2019, 135, 109084. [CrossRef]
153. Dager, P.K.; Mogni, L.V.; Soria, S.; Caneiro, A. High temperature properties of Sr_2MgMo_{0.9}TM_{0.1}O_{6+δ} (TM = Mn, Co and Ni). Ceram. Int. 2018, 44, 106008. [CrossRef]
154. Park, J.G.; Pirogov, A. Crystal structure and magnetic properties of Sr_2Ni_{1-x}Mg_{x}O_6 (x = 0, 0.25, 0.5, and 0.75) polycrystals. Solid State Sci. 2020, 99, 106008. [CrossRef]
155. Chen, F.; Ni-doped Sr_2Mg_{0.25}MgMoO_6δ anode for SOFCs. ACS Appl. Energy Mater. 2020, 3, 4914–4922. [CrossRef]
156. Rosas, J.L.; León-Flores, J.; Escamilla, R.; Cervantes, J.M.; Carvajal, E.; Verdín, E.; Romero, M. LDA+U study of the electronic and magnetic properties of the Sr_2FeMo_{1–x}Nb_xO_6 compound. Mater. Today Commun. 2020, 23, 101155. [CrossRef]
157. Hu, Y.; Zhao, X.; Wang, X.; Wang, S. Effects of Nd doping on the magnetocaloric properties of double perovskite Sr_2FeMoO_6. J. Magn. Magn. Mater. 2019, 499, 166212. [CrossRef]
158. Reyes, A.M.; Montoya, J.A.; Navarro, O. Demise of half-metallicity upon increasing of disorder in the double perovskite Sr_2-yLa_yFeMoO_6. J. Magn. Magn. Mater. 2019, 495, 165877. [CrossRef]
159. Kim, S.B.; Hahn, E.J.; Kim, C.S. Crystallographic and magnetic properties of double perovskite oxide Ba_2-xSr_xFeMoO_6 as SOFC anode. ECS Trans. 2017, 78, 1367–1374. [CrossRef]
160. Tian, C.; Zheng, J.; Yang, J. A highly active cathode material of Cu-doped SrFe_{1.5}Mg_{0.5}O_6 for symmetrical solid oxide fuel cell. J. Mater. Sci. Mater. Electron. 2021, 32, 1258–1264. [CrossRef]
161. Meng, X.; Wang, Y.; Zhao, Y.; Zhang, T.; Yu, N.; Chen, X.; Miao, M.; Liu, T. In-situ exsolution of nanoparticles from Ni substituted SrFe_{1.5}Mg_{0.5}O_6 perovskite oxides with different Ni doping contents. Electrochim. Acta 2020, 348, 136351. [CrossRef]
162. Xiao, G.; Wang, S.; Lin, Y.; Chen, F. Ni-doped SrFe_{1.5}Mg_{0.5}O_6 as anode materials for solid oxide fuel cells. ECS Trans. 2013, 58, 255–264. [CrossRef]
163. Xu, C.; Sun, Q.; Yang, X.; Ma, M.; Ren, R.; Qiao, J.; Wang, Z.; Zhen, S.; Sun, W. Highly active and CO_2-tolerant SrFe_{1.3}Ga_{0.2}Mg_{0.3}O_6δ cathode for intermediate-temperature solid oxide fuel cells. J. Power Sources 2020, 450, 227722. [CrossRef]
164. Yang, Y.; Wang, Y.; Yang, Z.; Lei, Z.; Jin, C.; Liu, Y.; Wang, Y.; Peng, S. Co-substituted SrFe_{1.5}Mg_{0.5}O_6δ as anode materials for solid oxide fuel cells: Achieving high performance via nanoparticle exsolution. J. Power Sources 2019, 438, 226989. [CrossRef]
165. Jiang, Y.; Yang, Y.; Xia, C.; Bouwmeester, H.J.M. SrFe_{1.4}Mg_{0.1}Mg_{0.5}O_6δ perovskite cathode for highly efficient CO_2 electrolysis. J. Mater. Chem. A 2019, 7, 22939. [CrossRef]
166. Zheng, K. Ti-doped SrFe_{1.4}Ti_{0.6}Mg_{0.5}O_6δ double perovskites with improved stability as anode materials for solid oxide fuel cells. Mat. Res. Bull. 2020, 128, 110877. [CrossRef]
167. Ren, R.; Wang, Z.; Meng, X.; Wang, X.; Xu, C.; Qiao, J.; Sun, W.; Sun, K. Tailoring the oxygen vacancy to achieve fast intrinsic proton transport in perovskite cathode for protonic ceramic fuel cells. ACS Appl. Energy Mater. 2020, 3, 4914–4922. [CrossRef]
168. Lv, H.; Lin, L.; Zhang, X.; Song, Y.; Matsumoto, H.; Zeng, C.; Ta, N.; Liu, W.; Gao, D.; Wang, G.; et al. In situ investigation of reversible exsolution/dissolution of CoFe alloy nanoparticles in a Co-doped SrFe_{1.5}Mg_{0.5}O_6δ cathode for CO_2 electrolysis. Adv. Mater. 2020, 32, e1906193. [CrossRef]
169. Qi, H.; Xia, F.; Yang, T.; Li, W.; Li, W.; Ma, L.; Collins, G.; Shi, W.; Tian, H.; Hu, S.; et al. In situ exsolved nanoparticles on La_{0.5}Sr_{1.5}Fe_{1.5}Mg_{0.5}O_6δ anode enhance the hydrogen oxidation reaction in SOFCs. J. Electrochem. Soc. 2020, 167, 024510. [CrossRef]
170. Qi, H.; Yang, T.; Li, W.; Ma, L.; Hu, S.; Shi, W.; Sabolsky, E.M.; Zondlo, J.; Hart, R.; Hackett, G.A.; et al. Reversible in-situ exsolution of Fe catalyst in La_{0.5}Sr_{1.5}Fe_{1.5}Mg_{0.5}O_6δ anode for SOFCs. ECS Trans. 2019, 91, 1701–1710. [CrossRef]
171. Xia, T.; Meng, X.; Luo, T.; Zhan, Z.-L. Synthesis and evaluation of Ca-doped SrFe_{1.5}Mg_{0.5}O_6δ as symmetrical electrodes for high performance solid oxide fuel cells. J. Inorg. Mater. 2019, 34, 1109–1114. [CrossRef]
172. Zhang, Y.; Zhu, Z.; Gu, Y.; Chen, H.; Zheng, Y.; Ge, L. Effect of Cl doping on the electrochemical performance of Sr$_{2}$Fe$_{1.5}$Mo$_{0.5}$O$_{6-\delta}$ cathode material for solid oxide fuel cells. *Ceram. Int.* **2020**, *46*, 22787–22796. [CrossRef]
173. Zhang, L.; Sun, W.; Xu, C.; Ren, R.; Yang, X.; Qiao, J.; Wang, Z.; Sun, K. Attenuating metal-oxygen bond of double perovskite oxide via anion doping to enhance its catalytic activity for oxygen reduction reaction. *J. Mater. Chem. A* **2020**, *8*, 14091–14098. [CrossRef] | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3726,
1
],
[
3726,
6326,
2
],
[
6326,
9574,
3
],
[
9574,
13844,
4
],
[
13844,
15859,
5
],
[
15859,
17943,
6
],
[
17943,
22819,
7
],
[
22819,
27779,
8
],
[
27779,
30118,
9
],
[
30118,
33849,
10
],
[
33849,
35163,
11
],
[
35163,
38136,
12
],
[
38136,
40812,
13
],
[
40812,
43249,
14
],
[
43249,
47145,
15
],
[
47145,
50322,
16
],
[
50322,
53133,
17
],
[
53133,
54966,
18
],
[
54966,
57917,
19
],
[
57917,
61376,
20
],
[
61376,
62362,
21
],
[
62362,
62362,
22
],
[
62362,
68376,
23
],
[
68376,
74370,
24
],
[
74370,
80870,
25
],
[
80870,
86915,
26
],
[
86915,
92806,
27
],
[
92806,
93345,
28
]
]
} |
e3930f3083bd78f59db291ed2f5825bdf3eb0a82 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 20,
"total-fallback-pages": 0,
"total-input-tokens": 66685,
"total-output-tokens": 23376,
"fieldofstudy": [
"Agricultural And Food Sciences"
]
} | Volatile Fingerprinting and Sensory Profiles of Coffee Cascara Teas Produced in Latin American Countries
Juliana DePaula 1, Sara C. Cunha 2, Adriano Cruz 3, Amanda L. Sales 1, Ildi Revi 4, José Fernandes 2, Isabel M. P. L. V. O. Ferreira 2, Marco A. L. Miguel 5 and Adriana Farah 1,*
1 Laboratório de Química e Bioatividade de Alimentos & Núcleo de Pesquisa em Café Professor Luiz Carlos Trugo—NuPeCafé, Instituto de Nutrição Josué de Castro, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-902, Brazil
2 LAQV/REQUIMTE, Laboratório de Bromatologia e Hidrologia, Departamento de Ciências Químicas, Faculdade de Farmácia da Universidade do Porto, 4099-030 Porto, Portugal
3 Instituto Federal de Educação, Ciência e Tecnologia do Rio de Janeiro, Rio de Janeiro 20260-100, Brazil
4 Purity Coffee, Greenville, SC 29609, USA
5 Laboratório de Microbiologia de Alimentos, Instituto de Microbiologia Paulo de Góes, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-902, Brazil
* Correspondence: [email protected]
Abstract: Coffee is one of the most produced and consumed food products worldwide. Its production generates a large amount of byproducts with bioactive potential, like the fruit skin and pulp, popularly called cascara. This study aimed to evaluate the volatile and sensory profiles and the consumption potential of commercial Coffea arabica cascara teas by Rio de Janeiro consumers. Analyses of volatile organic compounds in unfermented (n = 2) and fermented (n = 4) cascara tea infusions were performed by GC-MS. RATA and acceptance sensory tests were performed with untrained assessors (n = 100). Fifty-three volatile organic compounds distributed in 9 classes were identified in different samples. Aldehydes, acids, alcohols, esters, and ketones prevailed in order of abundance. With mild intensity, the most cited aroma and flavor attributes were sweet, herbal, woody, prune, fruity, honey, toasted mate and black tea for unfermented teas. For the fermented teas, sweet, woody, black tea, prune, herbal, citric, fruity, honey, raisin, peach, toasted maté, tamarind, and hibiscus were rated as intense. A good association between the attributes selected by the assessors and the volatile compounds was observed. Unfermented teas, with a mild flavor and traditional characteristics, showed better mean acceptance (6.0–5.9 points) when compared to fermented teas (6.0–5.3 points), with exotic and complex attributes. These were well accepted (>8.0 points) by only about 20% of the assessors, a niche of consumers that appreciate gourmet foods.
Keywords: coffee cherry tea; coffee husk; volatile compounds; coffee fruit; infusion; fermentation
1. Introduction
In response to the growing demand from the consumer market, world coffee production is constantly expanding, having surpassed 10 million tons in 2021, from which approximately 60% corresponded to the production of Coffea arabica (arabica coffee) and 40% of Coffea canephora (robusta coffee) [1].
Several steps are involved in coffee production. After the fruits are harvested, they may undergo different types of processing to release the seeds that are traditionally roasted and ground for the coffee beverage extraction. While in the wet postharvest processing the skin and pulp are fermented or enzymatically digested to release the seeds, in the dry and semi-dry processing, they are mechanically separated from the seeds after washing and drying [2]. The coffee pulp alone corresponds to approximately 28% of the coffee fruit on a dry weight basis, the skin approximately 12%, and the seeds 50–55% [3] (Figure 1).
When improperly discarded, these residues may negatively impact the ecosystem [5], which impregnate the seeds and remaining parts of the fruit and add value to them [2]. In this sense, alternatives are proposed to reuse these byproducts in the production of eatable flours [3] (Figure 1).
Tons of this byproduct are generated from coffee fruit processing and discarded annually. It has been estimated that for every million 60 kg bags of dried coffee seeds, about 218,400 tons of dried coffee cherry skin and pulp (the hull or cascara) are generated [4]. When improperly discarded, these residues may negatively impact the ecosystem [5], especially the freshwaters where byproducts from coffee processing usually are drained [6]. Looking from another perspective, these byproducts are rich in bioactive compounds [7] and represent a significant resource that can improve the quality of living of small coffee producers [8–11]. In this sense, alternatives are proposed to reuse these byproducts in the food industry, for example, extraction of anthocyanins for food coloring [12] and production of eatable flours [13] and tea [8]. In fact, for centuries, the cascara has been used to prepare medicinal infusions in producing countries, where they received different names. Examples are “hashara” in Ethiopia, “qishr” in Yemen, “sultana” in Bolivia, and “cascara” in El Salvador, Colombia [11], and in most parts of the world where it is marketed.
In recent years, controlled fermentation of varying intensities has been carried out during the postharvest processing of coffee fruits. In the process, the whole fruit is fermented, sometimes with the addition of different types of yeast, which resembles grape processing for wine production. Such fermentation results in rich aromatic, fruity and sweet notes, which impregnate the seeds and remaining parts of the fruit and add value to them [2].
In 2017, the European Union interrupted the marketing of C. arabica cascara tea because it was considered a “Novel Food”—that had not been consumed to a significant degree in the European Union before 1997—and therefore needed authorization [14]. For this, scientific information involving the determination of chemical composition, microbiological and toxin screening, and safety assessment that proved that people who had previously consumed the product have not developed health problems was necessary [14]. In 2021, considering the nature of coffee cascara and the history of its use as food, the EFSA Panel on Nutrition [15] considered that no more toxicological studies were required, and the risk of allergic reactions was low. The Panel concluded that C. arabica cascara was a safe ingredient for preparing non-alcoholic drinks and infusions. Despite this validation as a safe food ingredient, consumption is still overlooked in the West, and very few studies on chemical characterization have been published, especially on its volatile composition. Nevertheless, the considerable content of bioactive compounds and the variable sensory notes make it promising food ingredient or product, providing that it is produced under the health regulatory agencies.
This study evaluated the volatile and sensory profiles of infusions of C. arabica cascara teas produced in Latin American countries.
2. Materials and Methods
2.1. Samples and Study Design
Seven samples of arabica coffee cascara tea were acquired directly from producers. Four originated from wet processed and fermented fruits and three from dehulling from...
dry/semi-dry processed fruits [2] (Table 1). Samples were ground to pass through an 850 µm sieve for chemical and microbiological analyses. Infusions were prepared using the cascara as bulk. All samples underwent preliminary microbiological analyses. Based on these results, six were selected for volatile and sensory tests with untrained assessors. Instrumental color, soluble solids, pH, and titratable acidity were determined as complementary analyses.
Table 1. Samples of commercial fermented and unfermented coffee cascara teas produced in Latin America countries.
| Sample | Origin/Cultivar |
|--------|-----------------------------------------------------|
| 1 | Brazil/Mix of six cultivars: Iapar 59, Bourbon Amarelo, Caturra, IcatuPrecoce/Sold in Brazil |
| 2 | Bolivia/Nr/Sold in Canada |
| 3 | El Salvador/Nr/Sold in the USA |
| 4 | Nicaragua/Caturra and Bourbon/Sold in the USA |
| 5 | Brazil/Mix of six cultivars: Iapar 59, Bourbon Amarelo, Caturra Açu, Catuai 44, Caturra/Sold in Brazil |
| 6 | Nicaragua/Caturra/Sold in Brazil |
| 7 | Brazil/IcatuPrecoce/Sold in Brazil |
Nr: not reported.
2.2. Infusions Preparation
Infusions were prepared under the food safety requirements of the Brazilian Health Surveillance Agency (ANVISA) [16] and the Food and Agriculture Organization of the US (FAO)/World Health Organization (WHO) [17]. After preliminary sensory tests to adjust the amount of tea and water, 1 L of 90 °C spring water (pH 5.8; bicarbonate: 7.53 mg/L; potassium: 1.669 mg/L; sodium: 1.212 mg/L; nitrate: 4.53 mg/L; chloride: 0.58 mg/L; calcium: 1.402 mg/L; magnesium: 0.585 mg/L; barium: 0.065 mg/L; sulphate: 0.06 mg/L; fluoride: 0.04 mg/L) was poured over 35 g cascara and let steep for 5 min before removing them with a traditional sieve for the preparation of bulk infusions. Samples of the infusions were collected for microbiological, chemical, and physical analyses. The remaining amount was then placed in thermoses for sensory analyses, where it was kept for up to 20 min to ensure a temperature of 68 °C ± 2 °C [18–20].
2.3. Physical-Chemical Analyses
A portable colorimeter (Konica Minolta, CR-410, Tokyo, Japan) was used to determine the instrumental color of the infusions by the \( L^* \) (lightness), \( C^* \) (chroma), \( H^\circ \) (hue angle) system [21]. Soluble solids were determined in the infusions using the Atago® digital refractometer (model PAL-1, Tokyo, Japan), and results were expressed in °Brix. pH was evaluated using a pH meter (Macherey-Nagel®, Düren, Nordrhein-Westfalen, Germany); titratable acidity was determined by titration with 0.1 N NaOH, using phenolphthalein as an indicator, according to Adolfo Lutz Institute [22]. Results were expressed in mEq NaOH/L of infusion.
2.4. Analyses of Volatile Organic Compounds
Extraction of the volatile organic compounds from the infusions was performed by HS-SPME, using a 50/30 µm divinylbenzene/carboxen/polydimethylsiloxane fiber (DVB/CAR/PDMS, Supelco®), and analyzed by a gas chromatograph (Agilent, 6890 Little Falls, DE, USA) coupled to a mass spectrometer (Agilent 5975) (GC-MS), according to the methodology described by Wang et al. [23]. Before use, the fiber was conditioned according to the manufacturer’s recommendations. 2 mL of each sample were placed in a 20 mL SPME vial, which was immediately sealed with silicone septa and conditioned for 5 min at 50 °C under continuous agitation. Then, the fiber was exposed to the vial headspace for 30 min, in agitation, and heated at 50 °C. After this period, the fiber was retracted, and inserted into the chromatographic injector, in splitless mode, for 2 min, for desorption of volatile compounds, with the aid of a carrier gas (helium) and transferred directly into the chromatographic column (SPB-5, 60 m × 0.32 mm, film thickness df = 1 µm 5%diphenyl—95%dimethylpolysiloxane, Supelco, Bellefonte, PA, USA) at 1 mL min/ for 10 min, 250 °C. The chromatographic separation conditions were: 40 °C for 3 min, ramped to 200 °C at 5 °C/min, subsequently ramped to 250 °C at 10 °C/min, and held at final temperature for 3 min. The transfer line, ion source, and MS quadrupole temperature were 250, 230, and 150 °C, respectively. Electron impact mass spectra were measured at the acceleration energy of 70 eV. Data acquisition was performed in full-scan mode from m/z 50 to 550. Analytes were tentatively identified by the linear retention indices (LRI) and confirmed by the National Institute of Standards and Technology (ChemdataNIST V2.2, Gaithersburg, MD, USA) library database [24]. Agilent Chem Station (Agilent Technologies, Santa Clara, CA, USA) was used for data collection and processing. In addition, high purity external standards, when available, were injected. The LRI of each compound was calculated using the respective retention time (RT) compared against the RTs of a series of standard n-alkanes. The compounds were identified based on their LRI, the mass spectra of the NIST library [24], or authentic standards measured under the same conditions. To identify the compounds, substances with a probability greater than 50% were selected. To improve the accuracy of compounds’ identification, only those substances that provided a match factor higher than 600 and a match factor versus reversed match factor ratio greater than 0.8 were selected for data processing [25]. LRI available from previous publications were also used for comparison.
2.5. Microbiological Analyses for Food Safety
Before sensory tests, microbiological analyses for molds and yeasts, total and thermotolerant coliforms, and Salmonella spp. were carried out in duplicate, following the standards established by ANVISA [26] and EFSA [15]. Samples (25 mL) were diluted in a culture medium (BHI broth—Brain Heart Infusion, Difco) and homogenized (Stomacher—Splabor®), before the analyses. Escherichia coli ATCC (American type culture collection) 25922 and Salmonella enteritidis ATCC 13076 were used as control strains.
2.6. Sensory Analysis
The sensory tests were previously approved by the Research Ethics Committee of Clementino Fraga Filho University Hospital (# 21776619.8.0000.5257). One hundred assessors, who consumed plant infusions habitually, took part in the acceptance, purchasing intention, and Rate All That Apply (RATA) tests. They were students, teachers, visitors, and employees at the Federal University of Rio de Janeiro-UFRJ Health Sciences Center and Technology Center. After being informed of the procedures and expressing their agreement, they signed the Informed Consent Form. Assessors performed the tests on individual benches in the UFRJ Food and Dietetics Lab under white light. Before receiving the samples, demographic information was collected, including gender, age, educational level, occupation, family monthly income, frequency, and habits of infusions consumption. Approximately 30 mL of each infusion were presented at a time in 50 mL polystyrene plastic cups, coded with three-digit random numbers, and distributed in a balanced way to avoid the consistent
influence of neighboring samples on the sensory sensation. Assessors were instructed to drink the infusions with or without sweeteners as they habitually did. They could use table sugar or artificial sweetener (saccharin or aspartame). They were advised (and monitored) to use the same type and amount of sweetener in all samples. Crackers and spring water at room temperature were offered between samples to clean the palate.
2.6.1. Consumer Acceptance and Purchase Intention
Assessors evaluated the infusions using the nine-point hedonic scale ranging from 1 (extremely disliked) to 9 (extremely liked), followed by a five-point hedonic scale ranging from 1 (certainly would not buy) to 5 (certainly would buy) [27]. The Acceptability Index (AI) was calculated using the following equation: \( AI = \frac{X \times 100}{N} \), where: \( X \) = Average score given by assessors and \( N \) = Highest score given by assessors. AI equal to or greater than 70% was considered satisfactory [27].
2.6.2. Rate All that Apply (RATA)
After marking the hedonic scales, assessors were given a pre-prepared checklist with 30 sensory attributes related to appearance, aroma, flavor, and mouth feel, which were identified in the preliminary session performed by the trained panel. Following, they were required to select all terms they considered appropriate to describe the infusions. Given that fermented coffee cascara infusions had a more pronounced aroma, flavor, and taste attributes than the unfermented ones, we investigated whether the assessors perceived such differences by asking them to score the attributes according to their intensity (RATA scores: 0 = no perception; 1 = low intensity; and 2 = high intensity) [28,29]. The attributes used in the study were organized by alphabetical order as follows: acidic, apricot, astringent, bitter, black tea, brown, burnt, citrus, fermented, floral, fruity, green coffee, green leaf, herbal, hibiscus, honey, jasmine, liquor, mouthfeel, orange-brown, toasted maté, peach, prune, raisin, sweet, tamarind, toasted leaf, tobacco, wine, and woody.
2.7. Statistical Analysis
Data from physical and chemical analyses were analyzed using GraphPad Prism (Version 8.4.2, Informer Technologies, Los Angeles, CA, USA) and presented as mean ± standard deviation. They were compared for differences by one-way ANOVA, followed by the Tukey test, at a 5% significance level. Pearson’s correlation was used to compare soluble solids and color parameters. Data from sensory tests were analyzed using XLSAT for Windows (Version 2019.3, Boston, MA, USA). ANOVA was used for acceptance and purchase intention tests, with two sources of variance and a distribution histogram, considering the socio-demographic and consumption data obtained through questions. Cluster analysis based on the hierarchical grouping of acceptance scores was carried out to identify segments of consumers with similar likings.
RATA scores were analyzed as continuous data, with Principal Component Analysis (PCA), through the arithmetic mean values of the sensory descriptors for all assessors. Non-applicable attributes were marked as intensity 0 [28,29]; the mean overall liking scores and the quantitative analysis of each organic function detected on the volatile profiling were considered as supplementary. 95% confidence ellipse generated by virtual panels using Bootstrap techniques were used. For each consumer panel, linear mixed-effects models were performed for overall liking and sensory attribute intensities to examine if there were significant differences across the samples, with the sample as a fixed effect and the assessor as a random effect. Tukey’s HSD test was used for post-hoc pairwise comparisons of sample means [30].
3. Results and Discussion
3.1. Microbiological Analysis
Among the seven analyzed samples, one (sample 7) contained the number of total coliforms \( (2.4 \times 10^4 \text{ Most Probable Number—MPN/g}) \) and thermotolerant coliforms at
Results from physical-chemical analyses of commercial coffee cascara infusions produced in Latin American countries. (A): sample 3—El Salvador (F); (B): sample 1—Brazil (F); (C): sample 4—Nicaragua (F); (D): sample 5—Brazil (UF); (E): sample 6—Nicaragua (UF); (F): sample 2—Bolivia (F). Note: F—fermented; UF—unfermented.
Because hot water is used for tea preparation, all the infusions, including the one from Sample 7, were microbiologically safe, with zero counts of thermo-tolerant coliforms at 45 °C, E. coli, Salmonella spp. and molds and yeasts. According to the Food and Agriculture Organization [35], the limit of viability and multiplication of pathogenic strains of E. coli in foods is between 6.5–49.4 °C. Despite the death of yeasts and molds, a concern is the susceptibility of coffee cascara to contamination by mycotoxin-producing microorganisms [36]. Ochratoxin A (OTA) is the most studied mycotoxin in coffee and the only one regulated by European legislation [37]. A recent study has detected OTA (4.3 µg/kg) in a coffee cascara tea from Nicaragua at a lower level than that established by the EC (maximum 5 µg/kg) [13]. Hot water cannot destroy mycotoxins, which are reasonably soluble [38]. Therefore, coffee cascara may present food security risks common to those observed in dried fruits. Considering the microbiological results, Sample 7 was excluded from the remaining parts of the study. It is worth noting that in the case of iced tea preparation, coffee cascara should always be extracted with hot water and then refrigerated, never cold brewed.
3.2. Physical-Chemical Analyses
Figure 2 shows the visual appearance of the coffee cascara infusions evaluated in this study. Table 2 contains the instrumental soluble solids, color pH, and titratable acidity data.
Table 2. Results from physical-chemical analyses of commercial coffee cascara infusions produced in Latin American countries.
| Samples | L* | C* | H* | SS (°Brix) | pH | TA (mEq NaOH/L) |
|---------|------|------|------|------------|-----|-----------------|
| 1 | 70.97 ± 0.86 d | 52.11 ± 1.39 b | 88.47 ± 0.88 d | 1.17 ± 0.06 ab | 4.21 ± 0.01 a | 6.0 ± 0.3 c |
| 2 | 79.69 ± 0.50 a | 32.54 ± 1.50 d | 97.58 ± 0.70 a | 1.13 ± 0.06 c | 4.22 ± 0.01 a | 6.5 ± 0.0 b |
| 3 | 56.69 ± 1.50 f | 51.42 ± 0.23 b | 76.71 ± 1.61 f | 1.30 ± 0.00 a | 4.20 ± 0.00 a | 6.5 ± 0.1 b |
| 4 | 68.98 ± 1.19 e | 58.01 ± 1.46 a | 85.56 ± 1.19 e | 1.27 ± 0.06 a | 4.19 ± 0.01 ab | 7.2 ± 0.3 a |
| 5 | 73.68 ± 0.45 e | 45.75 ± 0.92 c | 90.96 ± 0.49 c | 1.20 ± 0.00 ab | 4.18 ± 0.01 b | 6.2 ± 0.3 bc |
| 6 | 77.89 ± 0.69 b | 34.27 ± 1.40 d | 96.03 ± 0.38 b | 1.10 ± 0.00 c | 4.22 ± 0.02 a | 7.0 ± 0.4 ab |
Note: L* (lightness), C* (chroma), H* (hue angle); SS (soluble solids); TA (titratable acidity). Different letters over the bars indicate statistical differences among samples by ANOVA (p ≤ 0.05). Samples 1—Brazil (F); 2—Bolivia (F); 3—El Salvador (F); 4—Nicaragua (F); 5—Brazil (UF); 6—Nicaragua (UF). F—fermented; UF—unfermented.
Soluble solids values (range 1.10–1.30 °Brix, using 3.5 g cascara/100 mL) were higher in Samples 3 and 4 (both fermented). The present results are higher than those previously reported for arabica coffee cascara infusion (0.54) prepared using 1 g cascara/100 mL water [39], bulk black tea (0.45) and bulk mate tea (0.23) (both using 1.6 g/100 mL) [40].
The colorimetric data varied for the different infusions. L* represents the lightness measured as brightness, with 100 and 0 values corresponding to absolute white and black, respectively [41]. The L* values of infusions were found to be significantly lower (darker) in Sample 3 (56.7 ± 1.5) and higher (lighter) in Sample 2 (79.7 ± 0.5) (both fermented) compared to the other samples, as visually perceived in Figure 2. C* represents the chroma or intensity or saturation, the degree of color relative to a similarly illuminated neutral grey [41]. C* values were the highest in Samples 4, 1 and 3. This indicates that these fermented samples had more vivid colors. H* represents the hue [41]. H* values of fermented infusions varied between 76.71° and 97.58°, while the values of unfermented infusions were 90.96° and 96.03°. The lower H* value in Sample 3 indicates that the infusion was more reddish and less yellowish, and the higher H* value in Sample 2 indicates the infusion was more yellowish. Although the fermented cascaras were darker than the unfermented ones (exemplified in Table 1), this was not necessarily reflected in the infusions. In Figure 2, the infusions in cups A and F were from fermented cascaras. However, while cup A presented the highest soluble solids value (1.30 °Brix), cup F presented one of the lowest values (1.13 °Brix) (Table 2). Nevertheless, positive correlations were observed between soluble solids and L* (r = 0.7908, p = 0.014), C* (r = 0.6757, p = 0.047), and H* (r = 0.8549, p = 0.0083). The variety and intensity of colors observed in the infusions are related to the presence of anthocyanins, responsible for the red, yellow, and purple colors observed in coffee fruit skin, mainly cyanidin-3-rutinoside, and, in small amounts, cyanidin-3-glycoside [12].
In the present study, pH and TA values were generally similar in all infusions. The pH values (ranged 4.18–4.22) are relatively similar to those previously reported for arabica cascara infusions prepared using 2 g cascara/100 mL (range 4.55–4.62) [42] and lower than those prepared using 1 g cascara/100 mL [39], confirming the acidic characteristics of cascara coffee tea and showing that the pH values are related to the amount of cascara used to prepare the infusions.
3.3. Volatile Organic Compounds
Considering all infusions, 53 compounds (corresponding to 89.3–97.1% of the total peak areas of the chromatograms) were accurately identified (Table 3). They were grouped into 9 chemical classes: 16 aldehydes, 9 acids, 8 esters, 6 alcohols, 4 terpenoids, 3 ketones, 3 furans, 2 pyrroles and 2 pyrazines. Of the 53 compounds, only 6 were present in all samples, 9 in both unfermented and 13 in the four fermented samples. The remaining compounds were differently distributed among samples, which differed not only concern-
ing the number of compounds but also in chemical classes (especially aldehydes, acids, alcohols, and ketones) and peak areas. Most identified compounds, a few reported as odoriferous components of other foods, were generated by fermentation, which is a key step in aroma development [43].
Despite the significant variation in the volatile profiles among samples, most identified compounds have been recently reported by Pua et al. [44] who have examined infusions from five coffee cascara teas, also from different countries. A few compounds reported by these authors have been detected in this study but did not meet the peaks confirmation criteria; therefore, they were not considered. No other study investigating the volatile composition of coffee cascara infusions was found. Two studies have investigated the volatile profile of fresh *C. arabica* [45] and *C. canephora* [46] pulps. Of the 45 and 55 volatile compounds reported in these studies, only 4 and 10 were identified in the present study, respectively, suggesting that the volatile profile of coffee cascara changes considerably as the fruit is fermented and or dried.
Table 3. Volatile compounds identified in infusions of fermented and unfermented commercial coffee cascara teas from Latin American countries and their classical odor description.
| Volatile Compound | Odor Description | aCAS# | bELRI | cLRI | Samples | | | | | | | |
|-------------------|------------------|------|-------|------|---------|---|---|---|---|---|---|---|
| **Aldehydes** | | | | | | 2 | 3 | 4 | | | | |
| Pentanal | Almond, pungent, coffee, chocolate [47,48] | 110-62-3 | 749 | 873 | d,e | | | | | | | |
| Hexanal * | Green, vegetable, fruity, tallow, fat [47,48] | 66-25-1 | 759 | 874 | d,e | | | | | | | |
| Hexenal | Apple, green [47] | 505-57-7 | 892 | 920 | | | | | | | | |
| Heptanal * | Fresh, herbal, fruity, citrus, wine-lee [47,48] | 111-71-7 | 785 | 843 | d,e | | | | | | | |
| Octanal | Citrus, soap, lemon, herbal, honey [47,48] | 124-13-0 | 726 | 805 | d,e | | | | | | | |
| Nonanal * | Fat, citrus, fresh, orange, green [47,48] | 124-19-6 | 798 | 880 | d,e | | | | | | | |
| Decanal * | Sweet, citrus, floral, soap, orange [47,48] | 112-31-2 | 797 | 838 | d,e | | | | | | | |
| Undecanal | Floral, citrus, green, fresh [47] | 112-44-7 | 847 | 901 | d,e | | | | | | | |
| Dodecanal * | Citrus, green, floral [47] | 112-54-9 | 839 | 922 | d,e | | | | | | | |
| Benzaldehyde * | Almond, burnt sugar, tropical fruit [47,48] | 100-52-7 | 689 | 875 | d,e | | | | | | | |
| α-methylbutanal | Cocoa, almond, malt, fermented [47,48] | 96-17-3 | 683 | 836 | d,e | | | | | | | |
| β-methylbutonal | Chocolate, peach [48] | 590-86-3 | 742 | 861 | d,e | | | | | | | |
| Phenylethanal | Honey, sweet, floral, fermented [47,48] | 122-78-1 | 741 | 880 | d,e | | | | | | | |
| Safranal | Herb, sweet, fresh, spicy [47,48] | 116-26-7 | 762 | 882 | d,e | | | | | | | |
| (E)-cinnamaldehyde | Sweet, cinnamon, balsamic, honey [47,48] | 14371-10-9 | 767 | 868 | d,e | | | | | | | |
| Vanilllin * | Sweet, vanilla, creamy, chocolate [47,48] | 121-33-5 | 652 | 721 | d,e | | | | | | | |
| **Acids** | | | | | | | | | | | | |
| Acetic acid * | Acidic, sour, pungent, vinegar [47,48] | 64-19-7 | 589 | 600 | d,e | | | | | | | |
| Hexanoic acid | Sour, fatty, sweet, cheesy [47,48] | 142-62-1 | 817 | 848 | d,e | | | | | | | |
| Heptanoic acid | Rancid, sour, cheesy, sweat [48] | 111-14-8 | 785 | 750 | d,e | | | | | | | |
| Octanoic acid | Acid, sweet, cheese, fruity [47,48] | 124-07-2 | 789 | 837 | d,e | | | | | | | |
| Nonanoic acid | Green, cheese, fatty [47,48] | 112-05-0 | 800 | 830 | d,e | | | | | | | |
| Decanoic acid | Rancid, fatty, sour, citrus [47,48] | 334-48-5 | 773 | 814 | d,e | | | | | | | |
| Isovaleric acid | Sweet, acid, fermented, berry [47,48] | 503-74-2 | 792 | 859 | d,e | | | | | | | |
| Isobutyric acid | Acidic, sour, cheese, rancid [47,48] | 79-31-2 | 754 | 870 | d,e | | | | | | | |
| Methylbutyric acid | Fruity, cheese, sweet [47,48] | 759-05-7 | 787 | 839 | d,e | | | | | | | |
### Table 3. Cont.
| Volatile Compound | Odor Description | aCAS# | bELRI | cLRI | 1 | 2 | 3 | 4 | 5 | 6 |
|-------------------|------------------|-------|-------|------|----|----|----|----|----|----|
| **Alcohols** | | | | | | | | | | |
| 1,2-epoxylinalool | Floral, alcohol | 14049-11-7 | 755 | 767 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| Phenylethylalcohol* | Honey, spice, rose, lilac, floral, fresh | 60-12-8 | 740 | 849 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| 3-methylpentanol | Pungent, green, fruity | 589-35-5 | 790 | 919 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| Ethylhexanol | Citrus, fresh, floral, rose, green | 104-76-7 | 819 | 906 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| Benzyl alcohol | Floral, rose, balsamic, sweet | 100-51-6 | 830 | 855 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| Lauryl alcohol | Fatty, waxy, honey, coconut | 112-53-8 | 797 | 929 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| **Esters** | | | | | | | | | | |
| Methyl salicylate | Peppermint | 119-36-8 | 690 | 865 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| Ethyl salicylate | Wintergreen, mint, floral, spicy | 118-61-6 | 792 | 955 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| Methyl octanoate | Orange, vegetable, herbal | 111-11-5 | 632 | 742 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| Ethyl octanoate | Fruity, banana, pear | 106-32-1 | 690 | 854 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| **Esters** | | | | | | | | | | |
| Methyl palmitate | Waxy, fatty, candle | 112-39-0 | 851 | 888 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| Ethyl palmitate | Fruity, milky, balsamic | 628-97-7 | 573 | 635 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| Benzyl acetate | Fresh, boiled vegetable, fruity, floral | 140-11-4 | 622 | 722 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| Isopropyl myristate | Faint, oily, fatty | 110-27-0 | 714 | 782 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| **Terpenoids** | | | | | | | | | | |
| Linalool * | Citrus, floral, lavender, sweet, green | 78-70-6 | 788 | 838 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| α-terpineol | Oil, anise, mint, lemon, citrus | 98-55-5 | 730 | 838 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| Menthol | Fresh, peppermint | 2216-51-5 | 761 | 801 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| β-ionone * | Sweet, violet, floral, raspberry | 14901-07-6 | 708 | 807 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| **Ketones** | | | | | | | | | | |
| β-damascenone * | Apple, rose, honey, sweet, tobacco | 23726-93-4 | 823 | 927 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| γ-nonalactone | Coconut, peach, sweet | 104-61-0 | 827 | 899 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| Geranyl acetone | Magnolia, fruity, rose, pear, guava | 3796-70-1 | 758 | 873 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| **Furans** | | | | | | | | | | |
| Furfural | Bread, almond, sweet, woody | 98-01-1 | 867 | 902 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| 5-methylfurfural | Almond, caramel, burnt sugar | 620-02-0 | 696 | 863 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| 2-acetylpyran | Balsamic, almond, nutty, toasted | 1192-62-7 | 670 | 848 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| **Pyroles** | | | | | | | | | | |
| 2-acetylpyrrole | Nutty, walnut, bread | 1072-83-9 | 680 | 835 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| Formyl pyrrole | Chocolate | 1003-29-8 | 657 | 819 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| **Pyrazines** | | | | | | | | | | |
| 2,3,5-trimethylpyrazine | Roast, potato, musty, nutty, cocoa | 14667-55-1 | 689 | 865 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
| 2,6-dimethylpyrazine | Nutty, butter, cocoa, caramel | 5910-89-4 | 695 | 845 | □ □ | □ □ | □ □ | □ □ | □ □ | □ □ |
Note: Samples: 1—Brazil (F); 2—Bolivia (F); 3—El Salvador (F); 4—Nicaragua (F); 5—Brazil (UF); 6—Nicaragua (UF); F—fermented; UF—unfermented. * Impact compounds according to Wang et al. [24]; Xiao et al. [49]; González-Mas et al. [50]; Márquez et al. [51]; Yang et al. [52]; Dongmo et al. [53]; Schieberle and Schuh [54]. Odor description according to Flavornet [47]; and The Good Scents Company Information System [48]. aCAS# (Chemical Abstracts Service) Registry Available in the NIST database [24]. bELRI: Experimental Linear Retention Index; cLRI: Linear Retention Index based on literature and NIST database [24]; d,e Compounds identified with probability more than 50%; * Compounds that provided a match factor higher than 600 and a match factor versus reversed match factor ratio greater than 0.8.
Aldehydes represented about 19.5–39.0% of the total peak areas, with higher percentages in the infusions from fermented teas, especially Sample 2. Aldehydes contribute remarkably to citrus, fruity, floral, fresh, and herbaceous notes [55]. Some of these com-
pounds, such as octanal, decanal and dodecanal, identified in this study, have been listed as impact compounds in citrus fruits and have attractive sensory qualities, according to aroma and flavor assessments [49,50]. Octanal has also been listed as one of the main aroma-active compounds responsible for the unique aroma of toasted maté leaf [51]. Hexanal, heptanal, nonanal and benzaldehyde have been listed as key aroma and flavor compounds in black tea [23,52]. Hexanal has been previously identified in fresh C. arabica [45] and C. canephora [46] cherry pulps. Nonanal, which also has been identified in fresh C. canephora cherry pulp [46], contributes to citrus, fresh, orange, and green characteristics [53,54]. This aldehyde was the most relevant concerning the chromatogram peak areas in all evaluated teas, accounting, in the fermented samples, for 9–15% of the total chromatogram peak area and, in the unfermented samples, for 15–20%. Because of their high chemical reactivity, the concentration of aldehydes is significantly altered during thermal processing [56] and, therefore, boiling these teas is probably not recommended.
Acids accounted for 11.0–33.4% of the total chromatogram peak area, with the highest percentages found in infusions from fermented teas, especially Samples 2 and 3. Acids contribute pungent, vinegar, sour, fermented, and acidic notes. Acetic acid, also identified in the fresh C. canephora pulp [46], has been listed as a key aroma compound in fermented beverages [51]. Octanoic and nonanoic acids were the most relevant in all samples concerning peak area, except for Sample 5 (unfermented), in which decanoic acid was more relevant. These compounds generally impart acid, sweat, and fruit characteristics to the beverage [53,54].
Alcohols accounted for 3.3–11.4% of the total peak area of the volatile fraction of different samples, with higher percentages in the infusions from fermented teas, especially Sample 2. Phenylethyl alcohol, identified in fresh C. canephora pulp [46], has been reported as key aroma compound in black tea [23,52]. Together with ethyl hexanol, it was the most relevant alcohol in all samples. Alcohols, in general, contribute honey, floral, fresh, rose, citrus and alcohol notes [53,54].
Esters comprised 3.0–23.5% of the total peak area of the chromatograms. The highest percentages of esters were observed in the fermented infusions. These compounds are essential volatile components in many fruits, and most of them have a strong fruity and floral odor and contribute to the “mature” flavor [57,58]. Methyl and ethyl salicylate have been previously identified in fresh pulps of C. arabica [45,59] and C. canephora [46]. Methyl salicylate has also been identified in Pu-erh tea samples and reported as an important component for the overall tea aroma formation [60].
Terpenoids comprised 2.8–8.5% of the total peak area of the chromatograms. Although these compounds are characterized by poor aroma, they still impart sweet, citrus, fruity, woody, and herbal characteristics [55]. However, they are susceptible to degradation reactions when exposed to air (oxygen), light, heat and undergo consequent conversion to terpenic alcohols or oxides [55]. Linalool, the most relevant terpenoid in the cascara teas, has been identified in fresh C. arabica [45] and C. canephora [46] pulps. It has been reported as key aroma compound in black tea [23,50,52]. β-ionone, only identified in Sample 2 (fermented), has also been listed as one of the main aroma-active compounds in toasted maté leaf [49].
Ketones comprised 3.0–13.3% of the total peak area of the volatile fraction of the different teas, with the highest proportion found in infusions from fermented samples, especially Samples 1, 2 and 3. Biogenetically, ketone components are derived from alcohols through oxidation reactions catalyzed by different enzymes, which exert dehydrogenase activity, and have a relevant contribution to the taste and fragrance of the essential citrus fruit oils [56]. In general, they contribute sweet, fruity, rose, and honey notes [53,54]. γ-nonalactone was only identified in Sample 5 (fermented). β-damascenone, identified in the present study only in fermented teas, has been reported as key aroma compound in black tea [52], toasted maté leaf [49] and fruits, vegetables, and derived products, including wine, where it imparts a pleasant “stewed apple”, “fruity” and honey-like character [61]. β-damascenone and γ-nonalactone have been cited as compounds responsible for prune
Only hot Only cold Hot and cold Yes No Yes**** No
Only bulk teas
There is no significant difference among samples by ANOVA (p ≤ 0.05) (n = 100 assessors). Samples: 1—Brazil (F); 2—Bolivia (F); 3—El Salvador (F); 4—Nicaragua (F); 5—Brazil (UF); 6—Nicaragua (UF). F—fermented; UF—Unfermented.
3.4. Sensory Tests
As far as the authors know, this is the first study reporting the characterization, acceptance, and purchase intention evaluation of coffee cascara infusions by consumers.
3.4.1. Assessors’ Characteristics
The study assessors’ main characteristics are presented in Table 4. Although the high participation of females in the study can be attributed to their higher willingness to take part in it, it is worth mentioning that women are now responsible for purchasing decisions in most Brazilian homes, and they drink more tea (51.6 mL/day) than men (45.0 mL/day) [65]. Moreover, women around the world traditionally consume more tea and herbal infusions than men, although, with the world’s increase in the availability and consumption of exotic and gourmet products, men tend to consume more herbal infusions increasingly [66].
3.4.2. Consumer Acceptance and Purchase Intention Test Scores
The mean acceptance scores for all infusions ranged from 5.3 (nor liked neither disliked) to 6.1 (liked slightly) (Figure 3A). No significant difference was observed between the genders’ scores. The mean Acceptability Index (AI) ranged from 67.8% to 59.4%.
Figure 3. Mean acceptance (A) and purchase intention (B) scores given for coffee cascara infusions by Brazilian consumers living in Rio de Janeiro. Different letters over the bars indicate statistical differences among samples by ANOVA (p ≤ 0.05) (n = 100 assessors). Samples: 1—Brazil (F); 2—Bolivia (F); 3—El Salvador (F); 4—Nicaragua (F); 5—Brazil (UF); 6—Nicaragua (UF). F—fermented; UF—Unfermented.
...
Table 4. Assessor’s characteristics.
| Gender | Age | Level of education | Family income (MW: minimum wages) | Frequency of tea/herbal tea consumption | Types of teas commonly consumed | Drinking temperature | Consumption of ready-to-drink infusions | Habit of sweetening tea |
|--------|---------|--------------------|-----------------------------------|---------------------------------------|-----------------------------------|-----------------------|----------------------------------------|-------------------------|
| | Male | Female | 18–24 | 25–34 | 34–44 | 45–59 | | |
| 26% | 74% | | 39% | 47% | 8% | 6% | | |
| 18–24 | | | 26% | 31% | 7% | 46% | | |
| | Basic education | Complete high school | Incomplete graduation | Complete graduation | Master’s or Doctoral degree | 1 MW | 2–3 MW | 4–5 MW | >5 MW | | |
| 6% | 10% | | 31% | 7% | 46% | 1% | 25% | 25% | 46% | |
| | Daily | Twicedaily | Weekly | 50 mL | Regular cup (150 mL) | Largecup (240 mL) | | |
| 30% | 16% | 54% | 12% | 33% | 55% | 35% | 27% | 65% | 50% | 44% | 28% |
| | Black tea | Green tea | White Tea | Toasted maté | Chamomile | Lemonbalm | Fruity | Other teas * | | |
| 35% | | | 6% | 57% | 65% | 50% | 44% | 28% | | |
| | Only sachets | Only bulk teas ** | Sachet and bulk teas | Only traditional | Only imported | Traditional and imported | | |
| 48% | 7% | 45% | 82% | 6% | 12% | 85% | | |
| | Drinking temperature | Consumption of ready-to-drink infusions *** | | | | | |
| 51% | 4% | 45% | 53% | 47% | 45% | 55% | | |
* Other infusions such as hibiscus, mint, bilberry, and horsetail. ** Consuming only bulk teas purchased in natural food stores or even from their gardens. *** Traditionally served cold and sweetened. **** Among those who sweetened, 77% reported using sugar and 23% sweeteners.
According to Meilgaard et al. [27], for a sample to be considered “well-accepted”, it must obtain 70% AI or higher. Therefore, considering the mean scores from all assessors, the tested infusions failed to reach 70%, although Sample 6 (unfermented infusion) (68%) was close to reaching it. As usual, the purchase intention results (Figure 3B) were associated with those from the acceptance test. Sample 2 (fermented) received a lower score, probably because of the high degree of fermentation.
As individual preferences may differ considerably concerning foods and are not reflected in the mean scores, cluster analysis was carried out to identify consumer segments with similar likings. This analysis is relevant for distinguishing different market niches. Three groups of consumers were identified.
Cluster 1 (n = 22, mean score = 8—“liked very much”, and AI ≈ 87%) consistently attributed the highest scores, especially to the unfermented samples. Cluster 1 was primarily composed of females (73%) aged between 25 and 34 years old (64%), with postgraduate education (68%), family monthly income > 5 MW (59%). They habitually consumed caffeinated infusions such as toasted maté (55%) and black tea (32%), and herbal infusions such as lemon balm (64%) and chamomile (59%). They also reported consuming fruity teas, such as hibiscus, lavender, and roses (50%). Most assessors usually consumed imported teas and did not have the habit of sweetening teas.
Cluster 2 (n = 30, mean score = 4—“disliked slightly”) was composed mostly of female (66.7%), 18–24 years old (56.7%), with incomplete higher education (60%), and family monthly income of 2 to 3 MW (46.7%). They habitually consumed infusions such as toasted maté (53.3%) and herbal or fruit infusions (40.0%).
Cluster 3 (n = 48, mean score = 6—“liked” or “slightly liked”), the largest cluster, was composed mostly of females (81.3%), 18–24 years old (54.2%), with incomplete higher education (47.9%), family monthly income between 2 and 3 MW (47.1%). They habitually consumed infusions of toasted maté (60.4%), chamomile (43.8%) and lemon balm (43.8%).
These findings suggest that post-graduate women aged 25–34 years with family monthly incomes higher than 5 MW are potential consumers of cascara coffee tea. This consumer tends to appreciate exotic and expensive gourmet products [67]. On the other hand, young consumers aged 18–24 years, with lower income and education, are not good candidates.
3.4.3. Rate All that Apply (RATA) Test
RATA test results are presented in Figures 4 and 5. Considering all samples, Figure 4 presents the main sensory attributes and the number of times the assessors checked them.
Figure 4. Main aroma (A), flavor (B) and taste (C) attributes selected for all coffee cascara infusions by the assessors.
Figure 5. Principal component analysis (PCA): bi-dimensional plot of samples of cascara coffee tea infusions ($n = 6$) (A) and sensory characteristics attributed by consumers ($n = 100$) through RATA sensory test, distributing volatile compounds and attributes that make up the best acceptance of samples among consumers (B). Overall liking and the volatile compounds were considered as supplementary variables. Samples: 1—Brazilfermented (F); 2—Bolivia (F); 3—El Salvador (F); 4—Nicaragua (F); 5—Brazilunfermented (UF); 6—Nicaragua (UF).
Considering the results for each sample individually, on the right side of Figure 5a, the superimposition of the ellipses around samples 2, 3 and 4 (fermented samples) indicate that they present very similar characteristics. Samples 5 and 6 (unfermented samples) are located on the left side of the figure and carry similar characteristics, although Sample 6 exhibited a few attributes similar to the fermented samples; Sample 1 was placed in an intermediate position given its hybrid characteristics (mildly fermented). Figure 5b presents the sensory attributes reported for the individual samples by the assessors in association with the acceptance scores and classes of volatile compounds used as secondary variables. The individual volatile compounds and their characteristic attributes are presented in Table 3.
Looking at Figures 4 and 5, it is notable that, in general, the fermented teas showed more richness of sensory attributes when compared to the unfermented ones, which still maintained some of the characteristics of green coffee seeds. Nevertheless, the attributes leading to higher acceptance (overall liking) were closer to the unfermented samples because most of these assessors are used to consuming unfermented teas with poor (weak) flavor characteristics. Most Brazilians generally do not expect a fermented beverage when consuming teas because fermented attributes often resemble spoiled foods. Even fruity and flowery teas are not very popular among these consumers. Mostly, the niche of consumers that appreciate gourmet foods and look for exotic and complex attributes will appreciate this type of beverage. Similar situations have been observed in our studies with specialty coffee beverages.
It is worth noting that the distribution of chemical classes in Figure 4B only considered the number of volatile compounds in each chemical class, together with the attributes and their RATA scores, but it did not consider the chromatogram peak areas or the odor threshold of the compounds. Nevertheless, the distribution of the classes is reasonably similar to the odor and flavor descriptions in the literature, which can be revisited in Table 3.
The aroma, flavor and taste of coffee cascara tea vary considerably and are not easy to reproduce, as they depend not only on genetics but also on the terroir, edaphoclimatic conditions and the postharvest processing method applied, including fermentation [2]. The perceived intensity and the number of assessors who perceived the attributes also varied among samples. However, considering the number of volatile compounds commonly identified in the unfermented and or fermented samples, that 26 attributes were frequently checked for all samples and that most volatile compounds identified in this study were also reported by Pua et al. [44], it appears that the volatile profiles presented in this study can characterize coffee cascara teas generically. Nonetheless, it is expected that the cascara teas will most often show unique profiles depending on the conditions aforementioned.
For the unfermented infusions, sweet, herbal, woody, prune, fruity, and honey aromas, and citrus, woody, prune, toasted maté, and black tea flavors were most cited but with mild intensity. Orange-brown color, sweetness and light body were often perceived in unfermented teas. Aldehydes and linalool, a terpenoid compound, are related to sweet, herbal, and citrus attributes, while phenyl-ethanal and phenyl-ethyl alcohol are related to honey notes [53,54]. Hexanal, benzaldehyde and octanoic acid are related to fruit notes and furfural to woody attributes [53,54] (Table 3).
A variety of aromas (sweet, woody, black tea, prune, herbal, citric, fruity, honey, raisin, peach) and flavor (citric, woody, prune, black tea, toasted leaf, toasted maté, herbal, tamarind, hibiscus, burnt) attributes in fermented teas were marked as intense. In addition to the volatile compounds and attributes observed in the unfermented teas, esters, such as ethyl octanoate and ethyl palmitate and ketones, such as β-damascenone, γ-nonalactone, and geranyl acetone are mainly related to intense fruity aroma and flavor [53,54]. These are the chief compounds responsible for the aroma of prune [62], raisin [64,68], and peach [69]. Furans, mainly 5-methyl-furfural and 2-acetyl-furan and pyrazines, are related to toasted and burnt attributes [53,54]. Color attributes were also, in general, more intense in fermented than in unfermented teas. Additional perceived attributes were: acidic, bitter, astringent, and medium body.
The least mentioned attributes were wine, liquor, jasmine, green coffee, and tobacco. This may result either from low concentration and or high odor threshold of the compounds associated with these attributes or from the fact that these assessors do not experience these aromas habitually, given that only those who are used to consuming those foods or have them in their olfactory memory can recognize them. Although only a few assessors marked these attributes, a few compounds which agree with these attributes were identified in the analyses of volatile compounds. For example, 1,2-epoxylinalool, an alcohol compound only identified in fermented samples, contributes alcohol characteristics, while heptanal, an aldehyde identified in Samples 1, 2, 3 (all fermented) and in one unfermented (Sample 6), contributes wine notes. Benzyl alcohol, linalool, and benzyl acetate are key volatile compounds in jasmine tea [70]. Hexanal, benzaldehyde and hexanoic acid, have been reported in green coffee seeds [71]. In addition to impart pleasant characteristics, such as fruity, sweet and honey, β-damascenone may also contribute to unpleasant tobacco notes (Table 3).
As for taste attributes, bioactive compounds from coffee seeds such as caffeine, trigonelline, and a few polyphenols also identified in coffee cascara teas [7] are related to bitterness [2]. Astringency usually involves the association of polyphenols with proteins in the saliva to form precipitates [2]. Like other polyphenols, such as procyanidins and tannins, chlorogenic acids, the main phenolic compounds in coffee cascara tea [7], generate astringency in the mouth, which, depending on the intensity, may contribute negatively to flavor [72]. During processing, fermentation tends to degrade phenolic compounds and other components in coffee mucilage, providing positive changes in flavor development, including a decrease in astringency [73]. The main compounds responsible for acidity in coffee are non-volatile organic acids, but low-molecular-mass organic acids also contribute to acid and formation of aroma and flavor [2]. Organic acids contribute specific types and intensity of acidity in different ways, depending on the sensory characteristics, concentration in the beverage and their strengths [2]. To date, citric, malic, citramalic and gluconic acids have been identified in coffee pulp [74].
4. Concluding Remarks
In this study, coffee cascara teas were characterized in terms of volatile profiles and sensory attributes. The role of fermentation in flavor development is undeniable, just like for coffee seeds, transforming simple and mild flavor attributes into rich, exotic, and intense flavors. However, traditional caffeinated and herbal teas consumers from Rio de Janeiro did not expect such complexity, which affected acceptability. These consumers may need to dilute the infusions to experience more mild flavors. We believe that if adequately processed from a microbiological and sensory point of view and diluted, coffee cascara infusions, especially those using unfermented cascara, with poor flavor characteristics, can be accepted by the general consumers of Rio de Janeiro, as well as by gourmet foods consumers. Particularly, adult women with greater purchasing power and higher education appreciated all cascara teas, including those with intense exotic and fruity flavor. Thus, each tea singularity and individual preferences should be considered when choosing the preparation method.
Just as there is a fast-growing niche of specialty coffee consumers worldwide who appreciate flavor complexity, we expect a similar trend happening with cascara teas. In addition to the pleasure of drinking a flavorful beverage, coffee cascara tea is a source of bioactive compounds and a way of supporting sustainability in coffee production. Nevertheless, the risk of cascara contamination by mycotoxin-producing microorganisms does exist, and we hope farmers and agronomists will improve their methods to produce “clean” cascara teas to be appreciated by a growing number of consumers. The potential presence of soluble pesticides in the cascara is another concern. Despite the higher costs of organic coffee production, supporting consumers’ health and the environment aggregates product value, and therefore, cascara teas from organic coffee production show potential.
Author Contributions: J.D.: formal analysis, writing original draft, reviewing, and editing; S.C.C.: methodology, formal analysis, validation; A.C.: formal analysis; A.L.S.: formal analysis; I.R.: samples acquisition and reviewing; J.F.: formal analysis; I.M.P.L.V.O.: funding acquisition, analysis supervision; M.A.L.M.: analysis, supervision; A.F.: conceptualization, funding acquisition, supervision, writing, reviewing, and editing. All authors have read and agreed to the published version of the manuscript.
Funding: The authors are thankful for the financial support and scholarship from the National Research Council (CNPq, Brazil reg. #309091/2016-0); the Rio de Janeiro ResearchSupport Foundation (FAPERJ: E-26/2018#241762; E-26/2021#2599919) and Fundação para a Ciência e a Tecnologia: NORTE-01-0145-FEDER-00041 and UIDB/04423/2020.
Data Availability Statement: The data presented in this study are available on request from the corresponding author.
Acknowledgments: The authors would like to thank Jonas Toledo Guimarães for assistance with colorimetric analyses and Uilda Fava Pimentel for assistance with titratable acidity analyses. Sara C. Cunha acknowledges FCT for IF/01616/2015 contract.
Conflicts of Interest: The authors declare no conflict of interest.
References
1. International Coffee Organization. World Coffee Production. Available online: https://ico.org/prices/po-production.pdf (accessed on 19 July 2022).
2. Farah, A. Flavor development during roasting. In Drying and Roasting of Cocoa and Coffee, 1st ed.; Hii, C.L., Borém, F.M., Eds.; CRC Press: New York, NY, USA, 2019; pp. 267–309, ISBN 9781315113104.
3. Heuzé, V.; Tran, G. Coffee Hulls, Fruit Pulp and by-Products. Feediédir, a Programme by INRAE, CIRAD. AFZ and FAO. 2015. Available online: https://www.feedipedia.org/node/549 (accessed on 15 August 2022).
4. Veenstra, S. Recovery of biogas from landfill sites. IHE Delft. In Curso Taller Internacional Sobre Tratamiento Anaerobio de Aguas Residuales; SFC: Santiago de Cali, Colombia, 1995.
5. Beyene, A.; Kassahun, Y.; Addis, T.; Assefa, F.; Amsalu, A.; Legesse, W.; Kloos, H.; Triest, L. The impact of traditional coffee processing on river water quality in Ethiopia and the urgency of adopting sound environmental practices. Environ. Monit. Assess. 2012, 184, 7053–7063. [CrossRef]
6. Awoke, A.; Beyene, A.; Kloos, H.; Goethals, P.L.; Triest, L. River water pollution status and water policy scenario in Ethiopia: Raising awareness for better implementation in developing countries. Environ. Monag. 2016, 58, 694–706. [CrossRef] [PubMed]
7. DePaula, J.; Farah, A. Phenolic compounds in coffee and by-products. In Coffee Science: Biotechnological Advances, Economics, and Health Benefits, 1st ed.; Ramakrishna, A., Parvatam, G., Jeszka-Skowron, M., Eds.; CRC Press: Boca Raton, FL, USA, 2022; pp. 119–134, ISBN 9781003043133.
8. Heeger, A.; Kosiriwna-Cagnazzo, A.; Cantergiani, E.; Andlauer, W. Bioactives of coffee cherry pulp and its utilisation for production of Cascara beverage. Food Chem. 2017, 212, 969–975. [CrossRef] [PubMed]
9. Alves, R.C.; Rodrigues, F.; Nunes, M.A.; Vinha, A.F.; Oliveira, M.B.P. State of the art in coffee processing by-products. In Handbook of Coffee Processing By-Products, 1st ed.; Galanakis, C.M., Ed.; Academic Press: Cambridge, MA, USA, 2017; pp. 1–26, ISBN 9780128112908.
10. Dorsey, B.M.; Jones, M.A. Healthy components of coffee processing by-products. In Handbook of Coffee Processing By-Products, 1st ed.; Galanakis, C.M., Ed.; Academic Press: Cambridge, MA, USA, 2017; pp. 27–62, ISBN 9780128112908.
11. del Castillo, M.D.; Fernandez-Gomez, B.; Martinez-Saez, N.; Iriondo-DeHond, A.; Mesa, M.D. Coffee by-products. In Coffee: Production, Quality and Chemistry, 1st ed.; Farah, A., Ed.; Royal Society of Chemistry: London, UK, 2019; Volume 1, pp. 309–334. [CrossRef]
12. Prata, E.R.; Oliveira, L.S. Fresh coffee husks as potential sources of anthocyanins. J. IVT Food Sci. Technol. 2007, 40, 1555–1560. [CrossRef]
13. Iriondo-DeHond, A.; Aparicio Garcia, N.; Fernandez-Gomez, B.; Guisantes-Batan, E.; Velázquez Escobar, F.; Blanch, G.P.; Velázquez Escobar, M.I.; Sanchez-Fortun, S.; del Castillo, M.D. Validation of coffee by-products as novel food ingredients. Innov. Food Sci. Emerg. Technol. 2019, 51, 194–204. [CrossRef]
14. EFSA. Panel on Dietetic Products Guidance on the preparation and presentation of an application for authorisation of a novel food in the context of Regulation (EU) 2015/2283. EFSA J. 2016, 14, e04594. [CrossRef]
15. EFSA Panel on Nutrition; Novel Foods and Food Allergens (NDA); Turck, D.; Bohn, T.; Castenmiller, J.; De Henauw, S.; Hirsch-Ernest, K.I.; Maciuk, A.; Mangelsdorf, I.; Mc Ardle, H.J.; et al. Scientific opinion on the safety of dried coffee husk (cascara) from Coffea arabica L. as a Novel food pursuant to Regulation (EU) 2015/2283. EFSA NDA Panel (EFSA Panel on Nutrition, Novel Foods and Food Allergens). EFSA J. 2022, 20, 7085. [CrossRef]
16. Brasil-ANVISA: Resolution of the Collegiate Board of Directors (RDC) 216/2004. Available online: https://bvsms.saude.gov.br/bvs/saudelegis/anvisa/2004/res0216_15_09_2004.html (accessed on 20 August 2022).
17. Food and Agriculture Organization of the United Nations. Codex Alimentarius Commission. 1997. Available online: https://www.fao.org/3/W6419E/W6419EB0.htm#Contents (accessed on 20 August 2022).
18. American Society for Testing and Materials. Proceedings. 1973, Volume 73. Available online: https://books.google.com.br/books/about/Proceedings_American_Society_for_Testing.html?id=GEFLAQAAIAJ&redir_esc=y (accessed on 20 August 2022).
19. Loomis, D.; Guyton, K.Z.; Grosse, Y.; Lauby-Secretan, B.; El Ghissassi, F.; Bouvard, V.; Benbrahim-Tallaa, L.; Guha, N.; Mattock, H.; Straif, K. International Agency for Research on Cancer Monograph Working Group. Carcinogenicity of drinking coffee, mate, and very hot beverages. *Lancet Oncol.* 2016, 17, 877–878. [CrossRef]
20. Adhikari, J.; Chambers, E.; Koppel, K. Impact of consumption temperature on sensory properties of hot brewed coffee. *Food Res. Int.* 2019, 115, 95–104. [CrossRef] [PubMed]
21. Sui, X.; Bary, S.; Zhou, W. Changes in the color, chemical stability and antioxidant capacity of thermally treated anthocyanin aqueous solution over storage. *Food Chem.* 2016, 192, 516–524. [CrossRef]
22. Instituto Adolfo Lutz. Métodos Fisico-Químicos para Análise de Alimentos; ANVISA: São Paulo, Brazil, 2008.
23. Wang, Z.; Han, B.; Jing, W.; Yi, Z.; Zhang, Y.; Ren, D.; Yi, L. Effects of Different Steeping Temperatures on the Leaching of Aroma Components in Black Tea by SPME–GC–MS Coupled with Chemometric Method. *J. AOAC Int.* 2019, 102, 1834–1844. [CrossRef] [PubMed]
24. NIST V2.2 (National Institute of Standards and Technology, USA) Library Database. Available online: https://webbook.nist.gov/chemistry/name-ser/ (accessed on 15 August 2022).
25. Galvan-Lima, A.; Cunha, S.C.; Martins, Z.E.; Soares, A.G.; Ferreira, I.M.; Farah, A. Headspace volatolome of peel flours from citrus fruits grown in Brazil. *Food Res. Int.* 2021, 150, 110801. [CrossRef]
26. Brasil-ANVISA: Resolution of the Collegiate Board of Directors (RDC) 724/2022 and Normative Instruction (IN) 161/2022. Available online: https://antigo.anvisa.gov.br/documents/10181/2718376/RDC_724_2022_.pdf/33c61081-4f32-43c2-9105-c318fa0699ce (accessed on 20 August 2022).
27. Meilgaard, M.; Civille, G.V.; Carr, B.T. techniques. In *Sensory Evaluation Techniques*, 4th ed.; CRC Press: Boca Raton, FL, USA, 2006; Volume 1, pp. 173–186.
28. Ares, G.; Bruzzzone, F.; Vidal, L.; Cadena, R.S.; Giménez, A.; Pineau, B.; Hunter, D.C.; Paisley, A.G.; Jaeger, S.R. Evaluation of a rating-based variant of check-all-that-apply questions: Rate-all-that-apply (RATA). *Food Qual. Prefer.* 2014, 36, 87–95. [CrossRef]
29. Meyners, M.; Jaeger, S.R.; Ares, G. On the analysis of Rate-All-That-Apply (RATA) data. *Food Qual. Prefer.* 2016, 49, 1–10. [CrossRef]
30. Kuznetsova, A.; Brockhoff, P.B.; Christensen, R.H.B. ImerTest Package: Tests in linear mixed effects models. *J. Stat. Softw.* 2017, 82, 1–26. [CrossRef]
31. Vital, P.G.; Caballes, M.B.D.; Rivera, W.L. Antimicrobial resistance in *Escherichia coli* and *Salmonella* spp. isolates from fresh produce and the impact to food safety. *J. Environ. Sci. Health B* 2017, 52, 683–689. [CrossRef]
32. Zhang, G.; Chen, Y.; Hu, L.; Melka, D.; Wang, H.; Laasri, A.; Brown, E.W.; Strain, E.; Allard, M.; Bunning, V.K.; et al. Survey of Foodborne Pathogens, Aerobic Plate Counts, Total Coliform Counts, and *Escherichia coli* Counts in Leafy Greens, Sprouts, and Melons Marketed in the United States. *J. Food Prot.* 2018, 81, 400–411. [CrossRef]
33. Food and Agriculture Organization. Microbiological hazards in fresh leafy vegetables and herbs. In *Microbiological Risk Assessment Series*; World Health Organization: Geneva, Switzerland, 2008.
34. Beuchat, L.R.; Mann, D.A. Comparison of new and traditional culture-dependent media for enumerating foodborne yeasts and molds. *J. Food Prot.* 2016, 79, 95–111. [CrossRef]
35. Food and Drug Administration. Fish and Fishery Products Hazards and Controls. Appendix 4: Bacterial Pathogen Growth and Inactivation. 2022. Available online: https://www.fda.gov/media/159301/download (accessed on 20 August 2022).
36. Gamboa-Gaitán, M.A. Presencia de aspergillus y otros simbiontes fúngicos en granos de café procedentes de Colombia. *Acta Biol. Colomb.* 2012, 17, 39–49. [CrossRef]
37. European Commission. Commission Regulation (EC) No 123/2005 of 26 January 2005 amending Regulation (EC) No 466/2001 as regards ochratoxin. *A. Off. J. Eur. Union* 2005, 2005, 2004–2006.
38. Malir, F.; Ostry, V.; Pfohl-Leszkowicz, A.; Malir, J.; Toman, J. Ochratoxin A: 50 Years of Research. *Toxins* 2016, 8, 191. [CrossRef] [PubMed]
39. Murlida, E.; Noviasari, S.; Nilda, C.; Rohaya, S.; Rahmi, F.; Muzai'a, M. Chemical characteristics of cascara tea from several varieties of coffee in Aceh Province. *IOP Conf. Series: Earth Environ. Sci.* 2021, 667, 012078. [CrossRef]
40. Lima, J.D.P.; Farah, A. Methylxanthines in stimulant foods and beverages commonly consumed in Brazil. *J. Food Compos. Anal.* 2019, 78, 75–85. [CrossRef]
41. Xu, Y.-Q.; Zou, C.; Gao, Y.; Chen, J.-X.; Wang, F.; Chen, G.-S.; Yin, J.-F. Effect of the type of brewing water on the chemical composition, sensory quality and antioxidant capacity of Chinese teas. *Food Chem.* 2017, 236, 142–151. [CrossRef]
42. Maharanis, S.; Mustikawati, I.; Nailufahr, L.; Istimahom, S. The effect of brewing time on pH values, polyphenols content, and antioxidant activities of coffee husk tea (cascara tea). *J. Physics: Conf. Ser.* 2021, 1869, 012050. [CrossRef]
43. Rahardjo, Y.P.; Syamsu, K.; Rahardja, S.; Samsudin; Mangunwijaya, D. Impact of controlled fermentation on the volatile aroma of roasted cocoa. *Braz. J. Food Technol.* 2022, 25. [CrossRef]
44. Pua, A.; Choo, W.X.D.; Goh, R.M.V.; Liu, S.Q.; Cornuz, M.; Ee, K.-H.; Sun, J.; Lassabliere, B.; Yu, B. A systematic study of key odourants, non-volatile compounds, and antioxidant capacity of cascara (dried Coffea arabica pulp). *LWT* 2021, 138, 110630. [CrossRef]
45. Mathieu, F.; Malosse, C.; Frérot, B. Identification of the volatile components released by fresh coffee berries at different stages of ripeness. *J. Agric. Food Chem.* 1998, 46, 1106–1110. [CrossRef]
46. Buck, N.; Wohlt, D.; Winter, A.; Ortner. E. Aroma-Active compounds in robusta coffee pulp puree—Evaluation of physicochemical and sensory properties. *Molecules* 2021, 26, 3925. [CrossRef] [PubMed]
47. Flavornet and Human Odor Space. Available online: http://www.flavornet.org (accessed on 15 August 2022).
48. The Good Scents Company Information System. Available online: https://www.thegoodscentsofcompany.com/ (accessed on 15 August 2022).
49. Xiao, Z.; Ma, S.; Niu, Y.; Chen, F.; Yu, D. Characterization of odour-active compounds of sweet orange essential oils of different regions by gas chromatography-mass spectrometry, gas chromatography-olfactometry and their correlation with sensory attributes. *Flavour Fragr. J.* 2015, 31, 41–50. [CrossRef]
50. González-Mas, M.C.; Rambla, J.L.; López-Gresa, M.P.; Blázquez, M.A.; Granell, A. Volatile Compounds in Citrus Essential Oils: A Comprehensive Review. *Front. Plant Sci.* 2019, 10, 12. [CrossRef] [PubMed]
51. Márquez, V.; Martínez, N.; Guerra, M.; Faríña, L.; Boido, E.; Dellacassa, E. Characterization of aroma-impact compounds in yerba mate (ilex paraguariensis) using GC–olfactometry and GC–MS. *Food Res. Int.* 2013, 53, 808–815. [CrossRef]
52. Yang, Y.; Zhu, H.; Chen, J.; Xie, J.; Shen, S.; Deng, Y.; Zhu, J.; Yuan, H.; Jiang, Y. Characterization of the key aroma compounds in black teas with different aroma types by using gas chromatography electronic nose, gas chromatography-ion mobility spectrometry, and odor activity value analysis. *LWT* 2022, 163, 113492. [CrossRef]
53. Dongmo, S.N.; Sacher, B.; Kollmannsberger, H.; Becker, T. Key volatile aroma compounds of lactic acid fermented malt based beverages—impact of lactic acid bacteria strains. *Food Chem.* 2017, 229, 565–573. [CrossRef]
54. Schieberle, P.; Schuh, C. Aroma compounds in black tea powders of different origins-changes induced by preparation of the infusion. In *Developments in Food Science*; Bredie, W.L.P., Petersen, M.A., Eds.; Elsevier: London, UK, 2006; Volume 43, pp. 151–156.
55. Wang, Y.; Wang, S.; Fabroni, S.; Feng, S.; Rapisarda, P.; Rouseff, R. The genus citrus. In *Chemistry of Citrus Flavor*; Talon, M., Caruso, M., Gmitter, F.G., Eds.; Elsevier: London, UK, 2020; pp. 447–470. [CrossRef]
56. Schwab, W.; Davidovich-Rikanati, R.; Lewinsohn, E. Biosynthesis of plant-derived flavor compounds. *Plant J.* 2008, 54, 712–732. [CrossRef]
57. Rouseff, R.; Perez-Cacho, P.R. Citrus flavor. In *Flavours and Fragrances: Chemistry, Bioprocessing and Sustainability*; Berger, R.G., Ed.; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2007; pp. 117–134. [CrossRef]
58. Selli, S.; Kelebek, H. Aromatic profile and odour-activity value of blood orange juices obtained from Moro and Sanguinello (*Citrus sinensis* L. Osbeck). *Ind. Crop. Prod.* 2011, 33, 727–733. [CrossRef]
59. Mathieu, F.; Malosse, C.; Cain, A.-H.; Frérot, B. Comparative headspace analysis of fresh red coffee berries from different cultivated varieties of coffee trees. *J. High Resolut. Chromatogr.* 1996, 19, 298–300. [CrossRef]
60. Lv, S.; Wu, Y.; Zhou, J.; Lian, M.; Li, C.; Xu, Y.; Liu, S.; Wang, C.; Meng, Q. The Study of Fingerprint Characteristics of Dayi Pu-erh Tea using a Fully Automatic HS-SPME/GC–MS and Combined Chemometrics Method. *PLoS ONE* 2014, 9, e116428. [CrossRef]
61. Rodrigues, J.; Almeida, P.E-2-nonenal and ß-Damascenone in beer. In *Beer in Health and Disease Prevention*; Preedy, V.R., Ed.; Academic Press: Cambridge, MA, USA, 2009; pp. 395–402, ISBN 9780123738912. [CrossRef]
62. Pons, A.; Lavigne, V.; Eric, F.; Darriet, P.; Dubourdieu, D. Identification of Volatile Compounds Responsible for Prune Aroma in Prematurely Aged Red Wines. *J. Agric. Food Chem.* 2008, 56, 5285–5290. [CrossRef]
63. Greger, V.; Schieberle, P. Characterization of the key aroma compounds in apricots (*Prunus armeniaca*) by application of the molecular sensory science concept. *J. Agric. Food Chem.* 2007, 55, 5221–5228. [CrossRef]
64. Wang, D.; Duan, C.-Q.; Shi, Y.; Zhu, B.-Q.; Javed, H.U.; Wang, J. Free and glycosidically bound volatile compounds in sun-dried raisins made from different fragrance intensities grape varieties using a validated HS-SPME with GC–MS method. *Food Chem.* 2017, 228, 125–135. [CrossRef] [PubMed]
65. Brazilian Institute of Geography and Statistics IBGE. Pesquisa de Orçamentos Familiares 2017–2018. 2020. Available online: https://biblioteca.ibge.gov.br/visualizacao/livros/liv101742.pdf (accessed on 15 August 2022).
66. Supplements 101, Tea Statistics. 2021. Available online: https://supplements101.net/tea-statistics/ (accessed on 15 August 2022).
67. Market Research. Gourmet Food Market Research Reports & Industry Analysis. Available online: https://www.marketresearch.com/food-beverage/c84/food-c167/Gourmet-Food-c487/ (accessed on 15 August 2022).
68. Wang, D.; Cai, J.; Zhu, B.-Q.; Wu, G.-F.; Duan, C.-Q.; Chen, G.; Shi, Y. Study of free and glycosidically bound volatile compounds in air-dried raisins from three seedless grape varieties using HS–SPME with GC–MS. *Food Chem.* 2015, 177, 346–353. [CrossRef]
69. Zhu, J.; Xiao, Z. Characterization of the key aroma compounds in peach by gas chromatography–olfactometry, quantitative measurements and sensory analysis. *Eur. Food Res. Technol.* 2019, 245, 129–141. [CrossRef]
70. An, H.; Ou, X.; Zhang, Y.; Li, S.; Xiong, Y.; Li, Q.; Huang, J.; Liu, Z. Study on the key volatile compounds and aroma quality of jasmine tea with different scented technology. *Food Chem.* 2022, 385, 132718. [CrossRef]
71. Toci, A.; Farah, A. Volatile fingerprint of Brazilian defective coffee seeds: Corroboration of potential marker compounds and identification of new low quality indicators. *Food Chem.* 2014, 153, 298–314. [CrossRef] [PubMed]
72. Ye, J.-H.; Ye, Y.; Yin, J.-F.; Jin, J.; Liang, Y.-R.; Liu, R.-Y.; Tang, P.; Xu, Y.-Q. Bitterness and astringency of tea leaves and products: Formation mechanism and reducing strategies. *Trends Food Sci. Technol.* **2022**, *123*, 130–143. [CrossRef]
73. Neto, D.P.D.C.; Pereira, G.V.D.M.; Tanobe, V.O.A.; Soccol, V.T.; Da Silva, B.J.G.; Rodrigues, C.; Soccol, C.R.; Da Silva, B.G. Yeast Diversity and Physicochemical Characteristics Associated with Coffee Bean Fermentation from the Brazilian Cerrado Mineiro Region. *Fermentation* **2017**, *3*, 11. [CrossRef]
74. Duangjai, A.; Suphrom, N.; Wungrath, J.; Ontawong, A.; Nuengchamnong, N.; Yosboonruang, A. Comparison of antioxidant, antimicrobial activities and chemical profiles of three coffee (*Coffea arabica* L.) pulp aqueous extracts. *Integr. Med. Res.* **2016**, *5*, 324–331. [CrossRef] [PubMed] | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3620,
1
],
[
3620,
7274,
2
],
[
7274,
10177,
3
],
[
10177,
14489,
4
],
[
14489,
18478,
5
],
[
18478,
20270,
6
],
[
20270,
24738,
7
],
[
24738,
29399,
8
],
[
29399,
34611,
9
],
[
34611,
39152,
10
],
[
39152,
41027,
11
],
[
41027,
47355,
12
],
[
47355,
48040,
13
],
[
48040,
48579,
14
],
[
48579,
53147,
15
],
[
53147,
57511,
16
],
[
57511,
62694,
17
],
[
62694,
68392,
18
],
[
68392,
74651,
19
],
[
74651,
75513,
20
]
]
} |
71110be140fd2e75e34a0dd5d0e0f7f72c9c06ed | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 10,
"total-fallback-pages": 0,
"total-input-tokens": 29218,
"total-output-tokens": 8519,
"fieldofstudy": [
"Computer Science"
]
} | Research Article
Research on Virtual Interactive Animation Design System Based on Deep Learning
Bing Liu
JMU College of Arts & Design, Xiamen 361000, China
Correspondence should be addressed to Bing Liu; [email protected]
Received 15 April 2022; Accepted 25 May 2022; Published 25 June 2022
Academic Editor: Le Sun
Copyright © 2022 Bing Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
With the rapid development of computer network technology, the advantages of virtual reality technology in the field of instant messaging are becoming more and more significant. Virtual reality technology plays an important role in communication networks, including enhanced resource utilization, device redundancy, immersion, interactivity, conceptualization, and holography. In this paper, we use the basic theory of Restricted Boltzmann Machine to establish a semisupervised spatio-temporal feature model through the animation capture data style recognition problem. The bottom layer can be pretrained with a large amount of unlabeled data to enhance the model’s feature perception capability of animation data, and then train the high-level supervised model with the labeled data to finally obtain the model parameters that can be used for the recognition task. The layer-by-layer training method makes the model have good parallelism, that is, when the layer-by-layer training method makes the model well parallelized, that is, when the bottom features cannot effectively represent the animation features, such as overfitting or underfitting, only the bottom model needs to be retrained, while the top model parameters can be kept unchanged. Simulation experiments show that the design assistance time of this paper’s scheme for animation is reduced by 10 minutes compared to baseline.
1. Introduction
Video communication in instant messaging systems usually requires high real time and stability; otherwise, it is prone to data delay, playback lag, and other instability [1]. Due to the influence of unstable network environment, the data is easily disturbed by various factors during transmission, resulting in the data not being broadcasted properly at the receiving end [2]. And the goal of this paper is to design a virtual video chat system combined with virtual reality, which needs to transform from the original transmission video data to the transmission user’s face key point data based on the application scenario and handle the transmission abnormality [3]. At the same time, because the content of this paper is not based on video streaming instant messaging, but 3D virtual animation video chat, the user sees the expression animation of the virtual animation model during the chat, so the data format transmitted in the network is the data set of face keypoints and voice data, and this paper has high requirements for noise reduction and echo cancellation of voice based on the actual application scenario, thus making the voice and animation [4]. Therefore, the synchronization of voice and animation and speech optimization become the urgent problem in the subject.
In recent years, the research on face keypoint localization has become more and more abundant and mature, and the research on deep learning has also made many breakthroughs, bringing better innovative methods and more opportunities for other related research fields [5]. Face keypoint localization is the basis of face recognition and other research, and the application scenarios are very broad. Researchers have proposed many algorithms for face keypoint localization and achieved good results in related fields, but in practical applications, faces are often affected by various internal and external factors such as expression, posture, illumination, and occlusion, making it very difficult to achieve accurate face keypoint localization, which is still a great challenge [6, 7]. This paper will address the design and
optimization of the face keypoint localization model and its application in mobile based on practical application scenarios [8].
Virtual reality technology is an important part of the computer field and has important applications in biochemistry, social entertainment, aerospace, and military industries [9]. However, virtual reality technology is less present in the current popular instant messaging-related research, which indicates that researchers in the field of instant messaging have paid less attention to virtual reality technology and have not well combined the two [10]. In this paper, we combine virtual reality technology and instant messaging, and the client drives the expression animation of 3D virtual model by parsing the key point data of human face to realize the virtual animation real-time communication [11].
In summary, the design of combining virtual reality technology with instant messaging and combining human-computer interaction with video chat will be a very important research direction in the future communication field [12].
2. Related Work
At present, domestic and foreign research in instant communication has made great progress, and communication among people has become more and more convenient and colorful [13]. At the same time, people are more and more willing to try various diversified and personalized instant communication methods, such as using 3D virtual animation models instead of real faces to communicate in real time, and the expression animation of 3D virtual animation models is driven by the real expressions of users in real time [14, 15].
In this paper, we combine deep machine learning-based face keypoint localization technology, virtual reality technology, and instant messaging to design and implement a more personalized instant messaging system [16].
2.1. Face Key Points. Face keypoint localization is the basis of face recognition and expression analysis and has a very broad development and application prospect. Researchers have proposed many face keypoint localization algorithms based on various methods. In [17], a fast face alignment method based on a layer-by-layer model is proposed, which converges after 8–10 iterations and the alignment time of each face image is tested within 40 ms on a Samsung I9300 smartphone. Reference [18] proposed a multitask cascaded convolutional neural network to achieve face detection while achieving face key point localization. Reference [12] et al. used a cascaded convolutional neural network-based method to achieve the localization of five key points of faces with an average localization error of 1.264 pixels, and it only takes 15.9 ms to process a face image. Reference [19] proposed a new cascaded deep design warp network, where the input of the previous cascaded neural network is a certain part of the image, unlike the previous ones, the input of each stage of the DAN (Deep Alignment Network) network is the whole image, which can extract features from the whole image. The features can be extracted from the whole image to obtain more accurate localization. Reference [20] proposed an edge-aware face alignment algorithm based on the edge as the geometric structure of the face for localization of 98 key points of the face.
From the above studies, it can be seen that there are abundant studies on face keypoint localization techniques and many algorithms are able to achieve better results. In the task of this paper, we are more concerned with the real time of face keypoint localization and the accuracy of face keypoint localization under different postures and expressions.
2.2. Data Transmission and Sound-Image Synchronization. Currently, data transmission is moving in two directions: first, to pursue higher transmission performance at lower transmission rates, that is, to reduce the transmission BER as much as possible; second, to increase the transmission rate as much as possible while the BER meets the requirements. Reference [11] proposes a new method for synchronizing audio and video pre-synchronization: by designing a pre-synchronization module based on the RTP/RTCP timestamp in the receive buffer and a new working mechanism, a fast synchronization within the media is achieved, eliminating the intermediate layer bias and adding no additional end-to-end delay before unpacking the RTP packets. Reference [12] proposes a method that uses timestamps to store audio and video data with correlation in acquisition time into a fixed synchronization data structure and always synchronize and control them during acquisition, encoding, transmission, reception, decoding, and playback, which can well meet the demand of audio and video synchronization in application scenarios and has good engineering practice. Reference [15] implemented a virtual reality-based gaze sensitive social communication system for autistic patients, which can measure the gaze-related index of patients during their interaction with virtual companions, and this index can be mapped to their corresponding anxiety level. At the same time, the system can influence the patient’s task performance and gaze-related index in response to the virtual companion’s emotions.
Technologies such as speech coding and decoding, data transmission, and audio and video synchronization are the basis of research in instant messaging. In the task of this paper, more attention is paid to the effect of special environment on speech, such as external playback under mobile devices and the synchronization of speech with 3D animation models.
3. Animation Design Model Based on Two-Layer RBM
Aiming at the problem that there is often a semantic gap between the underlying features and the high-level semantics of animation capture data, a semantic recognition algorithm for animation capture data that incorporates a restricted Boltzmann machine generative model and a discriminative model is proposed by combining deep
learning ideas. The algorithm adopts a two-layer restricted Boltzmann machine to perform discriminative feature extraction (feature extraction layer) and style recognition (semantic discriminative layer) on animation capture data, respectively. Firstly, considering that the autoregressive model has excellent ability to express temporal information, a conditional restricted Boltzmann machine generative model based on single-channel ternary factor interaction is constructed for extracting temporal feature information of animation capture data; then, the extracted features are then coupled with the corresponding style labels as the input of the current frame data layer of the restricted Boltzmann machine discriminative model in the semantic discriminative layer for the training of single-frame style recognition; finally, on the basis of obtaining the parameters of each frame, the voting space is added to the top of the model to achieve the effective recognition of the style semantics of the frame. The experimental results show that the algorithm has good robustness and scalability, can meet the needs of diverse animation sequence recognition, and facilitate the effective reuse of data.
3.1. Introduction to Recognition Models and Processes. As one of the representative models of deep learning, the RBM model has the ability to extract static frame features and build a CRBM model by adding autoregressive model constraints to the input layer, which in turn can obtain temporal feature information with contextual semantic scenarios. Reference [19] proposes a nonlinear mapping threshold CRBM binary hidden variable probabilistic model, which uses an unsupervised learning algorithm to extract not only the highly structured feature information that is available when transitions are transferred between video frame images, but also to portray the spatial relationships between each frame’s own pixels. In this paper, a voting space layer is added on top of the label layer for animation design, and a segmentation layer with the ability to identify transition frames can also be added. The animation design process using the two-layer RBM model is shown in Figure 1.
3.2. Bottom Feature Extraction Layer. The generative model fully considers the distribution of data and can use joint probability to get the conditional probability from input data to output data. Therefore, the RBM based on the generative model can reflect the generation process of the target object and the similarity between similar objects through the energy function and the activation state of the hidden layer neurons. The layer 1 generative RBM model developed in this paper takes advantage of the second property.
According to the autoregressive model algorithm, this paper splits the animation into 2 parts and constructs the bottom spatio-temporal feature layer: one part represents the previous $n$ frames of the current animation frame, which is called the history frame; the other part has only one frame, which represents the current animation frame, which is called the current frame. In addition, the interaction factor layer is added to realize the information interaction control between the 2 input layers and the feature layer, aiming to map the latent information and spatio-temporal feature information in the animation data to the feature representation layer through the factor layer so as to obtain more accurate probability distribution of the data in the process of reverse estimation; meanwhile, the factor layer also has the function of reducing the model space complexity from $o(n^3)$ to $o(n^2)$, which is described as follows.
The representation of each neuron in the history frame based on the RBM feature learning is $p = (p_1, p_2, ..., p_m)$, where $m = (f_r - 1)d$ is the total number of neurons, $f_r$ denotes the length of the historical frame, and $d$ denotes the frame data dimension. The neurons of the current frame are represented as $n = d$, with $v = (v_1, v_2, ..., v_m)$ representing the total number of neurons of the current frame. The hidden layer neurons are represented as $h = (h_1, h_2, ..., h_t)$, where $t$ is the total number of hidden layer neurons set. For the convenience of description, $p_i$ is the $i$th neuron of the history frame, $v_j$ is the $j$th neuron of the current frame, $b_j$ represents the bias of the $j$th neuron, $h_k$ represents the $k$th neuron of the hidden layer, and $c_k$ represents the bias of the $k$th neuron. $c_k$ is the connection weight from the interaction factor layer to the history frame (directed connection), $W_{ij}^f$ is the connection weight from the interaction factor layer to the current frame (directed connection), and $W_{ij}^r$ is the connection weight from the interaction factor layer to the hidden layer (undirected connection). $W_{ij/k}^r$ is the connection weight from the interaction factor layer to the hidden layer (undirected connection), which determines the model parameters and is denoted as $\theta = (W_{ij/k}^r, W_{ij/k}^d, W_{ij/k}^c, b, c)$. Note
that the history frame and the current frame are both real-parameter visible neurons, while the hidden layer is a binary random hidden unit.
3.3. High-Level Semantic Discriminant Layer. The DRBM model can be considered as a two-layer model, where both the visible layer and the label layer are the input sample data, and the hidden layer can be used to sample the joint probability distribution and conditional probability distribution of the visible and label data. Since an animation belongs to only one style, the label layer can be coded as “single heat”; that is, the label layer is set as a binary neuron, and only the neuron corresponding to the label has a value of 1 and is active [21, 22].
The parameters are defined as follows: the label layer neuron is \( L(L_1, L_2, \ldots, L_o) \), where \( o \) represents the number of all styles of training samples, and the bias is \( T = (t_1, t_2, \ldots, t_o) \); the visible layer is the feature information extracted from the first layer, which is a real unit, denoted as \( X = (x_1, x_2, \ldots, x_k) \), and the bias is \( Q = (q_1, q_2, \ldots, q_k) \); the hidden layer is the unit that can represent the correspondence between the label layer and the visible layer, denoted as \( Y = (y_1, y_2, \ldots, y_n) \), and the bias is \( R = (r_1, r_2, \ldots, r_n) \). The connection weights of the visible and labeled layers to the hidden layer are \( W_{xy}, W_{yf} \). Since this layer is used for classification rather than prediction of the probability distribution of the animated features, a hybrid discriminant method is used to train the second layer of the RBM, which is a linear combination of the optimal discriminant model \( p(l|x) \) and the generative model \( p(l, x) \). The training algorithm is still a comparative scattering algorithm. The log-likelihood function of the function to be optimized takes the form
\[
L_{\theta_2} = \sum_{i=1}^{s} \log P(l_i|x_i) - \alpha \sum_{i=1}^{s} \log P(l_i, x_i),
\]
where \( s \) denotes the total number of categories. For the 2nd term, i.e., the generative model part, the parameters are updated according to the steps of the 1st level [23, 24]. For the first discriminant model, the conditional distribution can be calculated as proposed by Larochelle et al.
\[
P(l|x) = \frac{e^{(l \cdot \Sigma_j (\log 1 + e^{W_{ji}x_i + W_{yj}r_j}))}}{\sum_i e^{(t_i \cdot \Sigma_j (\log 1 + e^{W_{ji}x_i + W_{yj}r_j}))}}.
\]
In a sequence of frames, equation (3) represents the magnitude of the probability that each frame belongs to each label, where \( l \) is the category label notation to which the training frame belongs, \( l \in (1, 2, \ldots, 0) \). Therefore, the conditional probability \( p(l|x) \) can be solved by an optimization function using the gradient descent method such that the probability that the animation feature \( x \) belongs to the correct label \( l \) is maximized. Then, for a single frame of animation \( x^{(t)} \) and the corresponding style label \( l^{(t)} \), there are
\[
\frac{\partial \log P(l^{(t)}|x^{(t)})}{\partial \theta_2} = \sum_j \text{sigmod}(S(x^{(t)})) \frac{\partial S(x^{(t)})}{\partial \theta_2} - \sum_{j, l} \text{sigmod}(S(x)) P(l|x^{(t)}) \frac{\partial S(x)}{\partial \theta_2}.
\]
Among them, \( S(x) = \sum_{j=1}^{k} W_{ji}x_i + U_{ij} + r_j, x_i \in x \). For label layer, bias update method is
\[
\frac{\partial \log P(l^{(t)}|x^{(t)})}{\partial t} = 1_{y = y^{(t)}} - P(l|x^{(t)}),
\]
where \( 1_{y = y^{(t)}} \) is the label layer neuron activated by the current label after the “single heat” encoding. The model parameters can be updated iteratively at each step by bringing equation (4) into the expression of the hybrid discriminant model in equation (3). The final DRBM model with classification function at layer 2 is trained [25, 26].
4. Experiment and Result Analysis
In order to verify the effectiveness of the two-layer model in animation design, the experiments are conducted on a PC with 3.30 GHz CPU and 8G memory, and the programming test environment is python3.7. In the generated model, the number of neurons in the historical and current frames as input data in the CRBM model is directly determined by the dimensionality of the input data. In the preprocessing, 53 dimensions of data were extracted for each frame, including 48 joint angular degrees of freedom, 3 animation directions, and 2 geodesic velocity data. The first 25 frames are used as the input vector of the history frame, and the 26th frame is used as the input data of the current frame so that the number of neurons of the history frame is 1325 and the number of neurons of the current frame is 53. The number of iterative updates is 250–500, and good feature information can be extracted.
4.1. Two-Layer Model Training. In this paper, we first eliminate the influence of spatial location of animation nodes on recognition and then retain the advantage of autoregressive model to build the first layer of ternary factor CRBM to extract temporal features and finally use the second layer of discriminative Boltzmann machine for classification. The two-layer model is trained to obtain a set of model parameters, including weights and biases, for each layer.
Since the layer 1 RBM uses a generative model, it contains reconstruction errors for the current frame animation data description. Using the reconstruction error, we
can roughly determine how well the model fits the current 26-frame data distribution. If the error is too large, the parameters are not set properly and the number of neurons in the feature layer needs to be increased or the number of training sessions needs to be increased. Of course, the reconstruction error should not be too small, as overfitting will
occur if it is too small. In the later tuning process, the appropriate number of hidden neurons and other techniques can reduce the occurrence of overfitting. In general, the reconstruction error will be stabilized within a certain range after a certain number of training sessions, which is verified by relevant experiments.
Figure 2 shows the reconstruction errors of layer 1 of the model for the 2 data sets. It can be seen that the reconstruction error obtained from the RBM model based on layer 1 will gradually stabilize after a certain number of iterations. For example, after 200 iterations, the reconstruction error basically tends to a stable level, and the total error of 53 Euler angles per frame does not exceed 0.9. Therefore, it can be judged that the layer 1 model does not change the original characteristics of the animation, and the fitting effect is relatively good.
To verify the reconstruction effect of the model on the animation style, Figure 3 shows the reconstructed effect of the 1st layer generating model part on the 4 end effectors (left and right hands, left and right feet) of the 1st animation style JO (jogging) of data set 1. Analyzing the fluctuation magnitude, we can see that the degree of change of the reconstructed data is similar to that of the original data animation style, which indicates that the data obtained by reconstructing using the first 25 frames and the model parameters are consistent with the style type of the current animation; that is, the hidden layer can effectively portray the style characteristics of the current animation.
The second semantic discriminative layer uses the RBM discriminative model to construct the mapping relationship between labels and each style animation feature, and the model parameters are updated according to the reconstruction errors of the input data in the label and feature layers. At the same time, a small number of samples are extracted from the training samples as the validation set to verify the accuracy of the model classification in each training cycle. Figure 4 shows the variation of the free energy of the RBM model at layer 2 and the recognition rate of the validation set in Dataset 1 and Dataset 2 as the number of training cycles increases. The free energy is closely related to the probability distribution of the model, and the trend is inversely proportional to the change in the probability distribution, as the energy decreases, the probability distribution becomes closer to the feature distribution, which
also validates the theory that the system is most stable at the lowest energy. The effect of model energy release on the recognition rate can be clearly observed in Figure 4(b): as the system stabilizes, the frame classification error of the validation set is in a decreasing state and gradually tends to be smooth.
4.2. Comparison and Analysis of Experimental Results. In order to further verify the recognition effect of the two-layer RBM model on animation style, the recognition results of this paper’s algorithm are compared with the Adaptive Motion Codebook Classifier (AMCC) algorithm of [12] and the SVM recognition algorithm based on radial basis function, and the spatial locations of 23 nodes are selected as the data preprocessing method. The spatial position information of 23 nodes was selected as the data preprocessing method. From the experimental results of the three recognition algorithms in Figure 5, it can be seen that for simple animations, the two-layer RBM algorithm can also achieve good style determination results, such as JO, KF, and KS simple sequences, and its test discrimination rate reaches 100%. The main reason is that the AMCC and SVM algorithms mainly consider the spatial information of the body joints, which has the greatest influence on the animation style, for classification, and ignore the timing information. The two-layer RBM algorithm proposed in this paper can achieve better semantic discriminative effect, mainly because the first layer extracts discriminative spatio-temporal features for effective pose portrayal; the second layer of DRBM model can effectively sample the conditional probability distribution of feature layer and class label data for semantic discriminative effect.
In terms of space storage efficiency, the AMCC algorithm needs to store the entire training set and build codeword templates for different classes of animation sequences, so the space occupation rate is large. In contrast, the depth model built in this paper only needs 2 sets of finite
parameters (1 set for each layer) to represent the sequence pose, and only some training samples are needed to learn the model parameters, so the storage space is relatively small. Therefore, the algorithm in this paper is suitable for the learning and modeling work of large data volume animation sequences. In terms of time efficiency, although the deep learning model established in this paper takes some time to learn the underlying features, once trained, the corresponding hidden units can be activated directly according to the model parameters and visible layer data, and the feature distribution of the current animation style can be obtained effectively. Therefore, the algorithm in this paper does not require additional similarity calculation, and in the MATLAB simulation environment, although the training time is long for 13 styles of animation, the recognition time is only 2.6 s. The speed of style recognition is comparable with existing algorithms, as shown in Figure 6.
5. Interactive Animation Design
In interactive animation design, the meaning of fast and slow rhythm is mostly reflected in the process of interactive experience. A fast rhythm can give immediate feedback to younger children. When children select options through the interactive buttons, as shown in Figure 7, the interactive buttons should change color and play corresponding music in an instant; for example, the button turns green with a celebratory tone when correct, and the mobile device vibrates and the button turns red when wrong. The immediate error feedback will provide a kind of error warning to the
younger children so that they can form a psychological gap and pay attention to the subsequent case explanation.
From Figure 8, it can be seen that Dynamic algorithm and this paper’s algorithm each have advantages in different styles of animation design. Dyneme vector-based recognition algorithm is weaker in the four animation styles of jump, lie, sit, and stand, because the algorithm does not sufficiently consider the backward and forward timing relationship, such as sitting on the ground and standing up from the ground are inverse animations, but their forward difference vectors are similar to each other. The algorithm in this paper overcomes this drawback by using the past frame cell layer and the current frame cell layer in the visible layer, but the shortcoming is that RBM has transfer invariance, which leads to interference in recognizing animation styles like deposit (picking something up from the ground), jog (running in place), rotate (rotating both arms), and so on, where the animation joint changes are similar but the joint positions are different. Interactive animation design should also anticipate in advance, using the platform’s error record to analyze the error-prone content of younger children and insert.
6. Conclusion
In order to meet the demand for spatio-temporal feature representation in human animation design, this paper adopts the two-layer RBM algorithm for animation feature representation and style recognition. The experimental results show that RBM has very good advantages in feature extraction and can extract more discriminative spatio-temporal features of animation sequences after adding autoregressive model constraints; meanwhile, it can achieve very good style recognition effect after introducing Boltzmann machine discriminative model, but the algorithm also has certain shortcomings, mainly because the number of neurons of its deep learning model is difficult to be determined well. Animators can create a moderate risky situation in the interactive animation design. Young children are under the care and attention of parents and lack of emotional catharsis, which leads them to subconsciously like to take risks. Therefore, moderate increase of adventure elements can stimulate their interest and let their playful emotional needs be satisfied put.
Data Availability
The experimental data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest regarding the publication of this work.
Acknowledgments
This study was supported by Research on Art Design Education under the Interaction of Art and Technology (no. JAS21104).
References
[1] J. Zhao, “Research on 3D animation processing technology in modern art design system,” in Journal of Physics: Conference Series, vol. 1856, no. 1, IOP Publishing, Article ID 01205, 2021.
[2] J. M. Bern, K.-H. Chang, and S. Coros, “Interactive design of animated plushies,” ACM Transactions on Graphics, vol. 36, no. 4, pp. 1–11, 2017.
[3] S. Izuza, Y. Endo, J. Mitani, Y. Kanamori, and Y. Fukui, “An interactive design system for pop-up cards with a physical simulation,” The Visual Computer, vol. 27, no. 6-8, pp. 605–612, 2011.
[4] Z. B. Wang, S. K. Ong, and A. Y. C. Nee, “Augmented reality aided interactive manual assembly design,” International Journal of Advanced Manufacturing Technology, vol. 69, no. 5-8, pp. 1311–1321, 2013.
[5] V. Meccaro, B. Thomaszewski, M. Nitti, O. Hilliges, M. Gross, and S. Coros, “Interactive design of 3d-printable robotic creatures,” ACM Transactions on Graphics, vol. 34, no. 6, pp. 1–9, 2015.
[6] S. Gibet, N. Courty, K. Duarte, and T. L. Naour, “The SignCom system for data-driven animation of interactive virtual signers,” ACM Transactions on Interactive Intelligent Systems, vol. 1, no. 1, pp. 1–23, 2011.
[7] Y. Meng, P. Y. Mok, and X. Jin, “Interactive virtual try-on clothing design systems,” Computer-Aided Design, vol. 42, no. 4, pp. 310–321, 2010.
[8] S. Coros, B. Thomaszewski, G. Noris et al., “Computational design of mechanical characters,” ACM Transactions on Graphics, vol. 32, no. 4, pp. 1–12, 2013.
[9] M. G. Violante and E. Vezzetti, “Virtual interactive e-learning application: an evaluation of the student satisfaction,” Computer Applications in Engineering Education, vol. 23, no. 1, pp. 72–91, 2015.
[10] X. I. E. Tao, C. Zhang, and Y. Xu, “Collaborative parameter update based on average variance reduction of historical gradients[,]” Journal of Electronics and Information Technology, vol. 43, no. 4, pp. 956–964, 2021.
[11] Z. Zhengwan, Z. Chunjiang, L. Hongbing, and X. Tao, “Multipath transmission selection algorithm based on immune connectivity model[,]” Journal of Computer Applications, vol. 40, no. 12, p. 3571, 2020.
[12] G. P. Lu, G. H. Xue, and Z. Chen, “Design and implementation of virtual interactive scene based on unity 3D[,]” Advanced Materials Research, vol. 317-319, pp. 2162–2167, 2011.
[13] J. Goedert, Y. Cho, M. Subramaniam, H. Guo, and L. Xiao, “A framework for virtual interactive construction education (VICE),” Automation in Construction, vol. 20, no. 1, pp. 76–87, 2011.
[14] O. Wu, P. Boulanger, M. Kazakevich, and R. Taylor, “A real-time performance system for virtual theater,” in Proceedings of the 2010 ACM Workshop on Surreal media and Virtual Cloning, pp. 3–8, 2010 October.
[15] J. Li, Z. Zhou, J. Wu et al., “Decentralized on-demand energy supply for blockchain in internet of things: a microgrids approach[,]” IEEE Transactions on Computational Social Systems, vol. 6, no. 6, pp. 1395–1406, 2019.
[16] W. Duan, J. Gu, M. Wen, G. Zhang, Y. Ji, and S. Mumtaz, “Emerging Technologies for 5G-IoV Networks: Applications, Trends and Opportunities[,]” IEEE Network, vol. 34.
[17] R. Ali, M. Hameed Siddiqi, and S. Lee, “Rough set-based approaches for discretization: a compact review[,]” Artificial Intelligence Review, vol. 44, no. 2, pp. 235–263, 2015.
[18] R. Li, K. Zou, X. Xu, Y. Li, and Z. Li, “Research of interactive 3D virtual fitting room on web environment,” in *Fourth International Symposium on Computational Intelligence and Design*, vol. 1, pp. 32–35, IEEE, 2011, October.
[19] A. Pedro, Q. T. Le, and C. S. Park, “Framework for integrating safety into construction methods education through interactive virtual reality,” *Journal of Professional Issues in Engineering Education & Practice*, vol. 142, no. 2, Article ID 04015011, 2016.
[20] C. A. Cohen and M. Hegarty, “Visualizing cross sections: training spatial thinking using interactive animations and virtual objects,” *Learning and Individual Differences*, vol. 33, pp. 63–71, 2014.
[21] D. Wu, Y. Lei, M. He, C. Zhang, and L. Ji, “Deep reinforcement learning-based path control and optimization for unmanned ships,” *Wireless Communications and Mobile Computing*, vol. 2022, Article ID 04015011, 8 pages, 2022.
[22] P. An, Z. Wang, and C. Zhang, “Ensemble unsupervised autoencoders and Gaussian mixture model for cyberattack detection,” *Information Processing & Management*, vol. 59, no. 2, Article ID 102844, 2022.
[23] U. Lahiri, Z. Warren, and N. Sarkar, “Design of a gaze-sensitive virtual social interactive system for children with autism,” *IEEE Transactions on Neural Systems and Rehabilitation Engineering*, vol. 19, no. 4, pp. 443–452, 2011.
[24] S. Marcos, J. Gómez-García-Bermejo, and E. Zalama, “A realistic, virtual head for human-computer interaction,” *Interacting with Computers*, vol. 22, no. 3, pp. 176–192, 2010.
[25] Y. Meng, P. Y. Mok, and X. Jin, “Computer aided clothing pattern design with 3D editing and pattern alteration,” *Computer-Aided Design*, vol. 44, no. 8, pp. 721–734, 2012.
[26] A. Ayala García, I. Galván Bobadilla, G. Arroyo Figueroa, M. Pérez Ramírez, and J. Muñoz Román, “Virtual reality training system for maintenance and operation of high-voltage overhead power lines,” *Virtual Reality*, vol. 20, no. 1, pp. 27–40, 2016.
[27] J. Liu, Q. Chen, and X. Tian, “3D virtual animation instant network communication system design,” *Wireless Communications and Mobile Computing*, vol. 2021, Article ID 9999113, 11 pages, 2021. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4086,
1
],
[
4086,
10018,
2
],
[
10018,
15082,
3
],
[
15082,
20478,
4
],
[
20478,
20835,
5
],
[
20835,
23387,
6
],
[
23387,
25413,
7
],
[
25413,
27018,
8
],
[
27018,
33006,
9
],
[
33006,
35197,
10
]
]
} |
b61366669ec0a179f2e0c9dd7c063fd923e55f01 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 12,
"total-fallback-pages": 0,
"total-input-tokens": 38386,
"total-output-tokens": 14406,
"fieldofstudy": [
"Agricultural And Food Sciences",
"Environmental Science"
]
} | Climate Variability Rather Than Livestock Grazing Dominates Changes in Alpine Grassland Productivity Across Tibet
Meng Li¹, Jianshuang Wu²-³*, Yunfei Feng⁴, Ben Niu⁵, Yongtao He⁵ and Xianzhou Zhang⁵
¹ School of Geographic Sciences, Nantong University, Nantong, China, ² Institute of Environment and Sustainable Development in Agriculture, Chinese Academy of Agricultural Sciences, Beijing, China, ³ Theoretical Ecology, Institute of Biology, Free Universität Berlin, Berlin, Germany, ⁴ Department of Resource Management, Tangshan Normal University, Tangshan, China, ⁵ Lhasa National Ecological Research Station, Key Laboratory of Ecosystem Network Observation and Modelling, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, China
Alpine grasslands on the Tibetan Plateau, being vulnerable to environmental and anthropogenic changes, have experienced dramatic climate change and intensive livestock grazing during the last half-century. Climate change, coupled with grazing activities, has profoundly altered alpine grassland function and structure and resulted in vast grassland degradation. To restore degraded grasslands, the Central Government of China has implemented the Ecological Security Barrier Protection and Construction Project since 2008 across the Tibetan Autonomous Region. However, the relative effect of climate change and grazing activities on the variation in alpine grassland productivity is still under debate. In this study, we quantified how aboveground net primary production (ANPP) varied before (2000–2008) and after (2009–2017) starting the project across different alpine grasslands and how much variance in ANPP could be attributed to climate change and grazing disturbance, in terms of temperature, precipitation, solar radiation, and grazing intensity. Our results revealed that Tibet's climate got warmer and wetter, and grazing intensity decreased after starting the project. Mean ANPP increased at approximately 81% of the sites, on average from 27.0 g C m⁻² during 2000–2008 to 28.4 g C m⁻² during 2009–2017. The ANPP positively correlated with annual temperature and precipitation, but negatively with grazing intensity for both periods. Random forest modeling indicated that grazing intensity (14.5%) had a much lower influence in controlling the dynamics of grassland ANPP than precipitation (29.0%), suggesting that precipitation variability was the key factor for alpine grassland ANPP increase across Tibet.
Keywords: climate change, grassland degradation, human activities, NPP, Tibetan Plateau
INTRODUCTION
Climate change and human activities are primary drivers for changes in terrestrial ecosystems globally (Haberl et al., 2007; Chen et al., 2013; Tong et al., 2018), especially for unprecedented changes in ecosystem service and function (Knight and Harrison, 2012; Seiferling et al., 2014; Erb et al., 2018). A meta-analysis by Lin et al. (2010) found that climate warming can promote global
vegetation productivity. Precipitation can also accelerate or decelerate vegetation growth in most terrestrial ecosystems, depending on its frequency and timing (Wu et al., 2011). Meanwhile, human activities can affect ecosystem response and feedback to climate change, via biomass utilization, biofuel consumption, land use, and land cover change (Haberl et al., 2007; Kröel-Dulay et al., 2015). For example, human disturbances might push an intact ecosystem away from its successional trajectory, alter species assembly, and turnover, and make it much more vulnerable to climate change than before (Kröel-Dulay et al., 2015).
Aboveground net primary production (ANPP) is a critical ecosystem service in maintaining global carbon balance (Ruimy et al., 1999; Zhang et al., 2009), often used to forecast ecological consequences under anthropogenic and climatic perturbations. A better understanding of how ecosystem ANPP responds to climate change and human activities can help mitigate environmental damages and optimize ecosystem management (Zhou et al., 2018). A considerable volume of literature tried to identify and quantify the relative influences of climate change and human activities on ecosystem productivity with various methods (Paudel and Andersen, 2010; Erb et al., 2018; Li L. et al., 2018), such as manipulative experiments, traditional statistical analysis, and residuals-trend modeling (Li L. et al., 2018). Recently, random forest modeling, with high accuracy and robust efficiency, is increasingly being used to quantify predictors’ relative importance (Gill et al., 2017; Huang and Xia, 2019). The random forest modeling can also account for interactions and non-linear relationships between predictors, obstacles (the overfitting problems) and deal with data noises (Heung et al., 2014). Therefore, scientists often recommended random forest models for processing high-dimensional and -correlated datasets (Breiman, 2001).
Due to high elevations, alpine grasslands widely distributed on the Tibetan Plateau are susceptible to climate change and human activities, as vegetation in Arctic and Antarctic (Yao et al., 2012; Yang et al., 2017; Li et al., 2020). Climate change, combined with human activities, has significantly reshaped the structure and function of the Tibetan alpine grasslands (Wang et al., 2005), and resulted in about $0.4 \times 10^6$ km$^2$ grassland degradation in the 1990s, which accounted for 33% of total grassland area on this plateau (Long et al., 2009). Therefore, rational utilization, restoration, and conservation of alpine grasslands under changing climate and anthropogenic disturbances have attracted increasing attention since 2000 (Harris, 2010; Yu et al., 2012; Dong et al., 2020). The central government of China initiated several ecological projects, like the “Ecological Security Barrier Protection and Construction Project” started since 2008, and the “Compensation and Rewards to Herders for Natural Grassland Conservation” since 2010, to promote the recovery and restoration of degraded alpine grasslands on the Tibetan Plateau (Wang et al., 2017). The implementation of these projects has eased the pressure of human disturbances (mainly referring to livestock grazing hereafter) (Fan et al., 2015) and also increased the alpine grassland productivity (Chen et al., 2014; Xu et al., 2016). However, the relative contributions of climate change and human activities to alpine grassland productivity are still unclear. Moreover, it is pertinent to examine the extent to which ecological projects and policies can affect alpine grassland productivity.
To fill these gaps in current research, we collected historical records of climatic variables and the Normalized difference vegetation index (NDVI) data before (2000–2008) and after (2009–2017) the starting of the “Ecological Security Barrier Protection and Construction Project.” These data were mainly used to simulate the changes in alpine grassland productivity during the two subperiods. We also conducted field measurements of aboveground biomass between fenced and grazed pastures in different alpine grassland types to validate the models’ outputs. By comparing the difference in alpine grassland productivity, it is possible to clarify the effects of the “Ecological Security Barrier Protection and Construction Project.” We also collected the livestock numbers from statistic yearbooks of 2000–2017 to quantify grazing intensity over time and across space. Thus, it is also possible to quantify how much the variance in alpine grassland productivity can be explained by the corresponding climatic (refers to temperature, precipitation, and solar radiation) and anthropogenic (refers to grazing intensity) factors.
**MATERIALS AND METHODS**
**Study Area**
The Tibetan Autonomous Region (hereafter Tibet) is located in the southwest of China (Figure 1), covering about 1.22 million km$^2$. With an average elevation of over 4,000 m above sea level, Tibet has a cold (mean annual temperature from 2000 to 2017 was $-1.1 ^\circ$C) and dry (mean annual precipitation from 2000 to 2017 was 307.8 mm) climate. This climate shaped various sensitive and vulnerable ecosystems. Alpine grasslands mainly distribute in northwestern places at high elevations, covary, and coevolve well with zonal climates (Wu et al., 2013). From southeast to northwest, grassland types vary from humid alpine meadow (AM) dominated by *Kobresia pygmaea* to semiarid alpine steppe...
(AS) dominated by *Stipa purpurea*, and to arid alpine desert-steppe (ADS) co-dominated by *S. purpurea* and *S. glareosa*.
**Data Collection**
Normalized difference vegetation index (NDVI) is a remote sensing technique widely used in the regional ecosystem monitoring and evaluation. This study used the moderate-resolution imaging spectroradiometer (MODIS) Version 6 NDVI (MOD13A3) from 2000 to 2017, with 1 km spatial resolution and 1 month time interval. NDVI data were downloaded from the National Aeronautics and Space Administration administration. The monthly NDVI data were developed using the Maximum Value Composition method (MVC) and calibrated for geometrical and atmospheric effects and cloud contamination. Grassland distribution referred to the China Vegetation Atlas with a scale of 1:1,000,000 (Chinese Academy of Sciences, 2001), from the Resource and Environment Data Cloud Platform.
Daily meteorological data from 2000 and 2017 were collected from the National Meteorological Information Center (NMIC), China Meteorological Administration (CMA). Daily meteorological records were aggregated at the monthly level. Then, we interpolated monthly precipitation, temperature, and sunshine duration into raster surfaces with a 1 km spatial resolution using the ANUSPLIN 4.3 (Hutchinson, 2004). According to Allen et al. (1998), solar radiation was calculated based on geographical position and sunshine duration. It has been examined that the grid climatic surfaces match well with field observations (Chen et al., 2014; Tao et al., 2015).
In 2009, a 1,200 km transect was established across the northern Tibetan Plateau. This transect crosses exceptionally arid, semi-arid, to semi-humid alpine continental climates from west to east, encompassing three primary grassland type: alpine meadow, alpine steppe and alpine desert-steppe. From 2009 to 2015, we collected aboveground biomass (AGB, g/m²) field-measured during peak growing season (late July to early August) along with this transect, between fenced and open (grazed) alpine grasslands. In total, we measured AGB at 224 sites in open alpine grasslands and 138 sites in fenced ones (Figure 1). At each sampling site, 5.0 m × 0.5 m quadrats were laid at 20 m intervals along a 100 m random transect line. Plant aboveground materials were dried at 65°C for 48 h and then weighed for AGB measurements. For grassland in Tibet, the most sampled species sprout annually in early May and senesce in late September with peak biomass generally between late July and early August. Thus, the field-measured AGB can surrogate for yearly ANPP. Finally, the dry matter was converted to carbon, assuming a carbon content of 45% (Lieth and Whittaker, 1978).
The livestock number for each county was collected from the "Statistical Yearbooks" of 2000–2017. The numbers of sheep, goats, and large herbivore animals (mainly referring to yaks, donkeys, and horses) were finally calculated as standardized sheep units (SSU), by following the algorithms of Fan et al. (2010) that one sheep equals to one SSU and one large herbivore to four SSUs.
**Calculation of Grassland ANPP**
The Carnegie-Ames-Stanford Approach (CASA) model was driven by satellite-observed NDVI and climate (e.g., temperature, precipitation, and radiation) and other factors, such as land-use change. The NDVI changes can reflect human harvest from plant material. NPP is mainly determined by two variables, absorbed photosynthetically active radiation (APAR) and the light-use efficiency (LUE) in the CASA model,
\[ NPP(x, t) = \text{APAR}(x, t) \times \varepsilon(x, t) \]
\[ \text{APAR}(x, t) = \text{PAR}(x, t) \times \text{FPAR}(x, t) \times 0.5 \]
\[ \varepsilon(x, t) = T_{x1}(x, t) \times T_{x2}(x, t) \times \text{W}_e(x, t) \times \varepsilon^* \]
\[ \text{ANPP}(x, t) = NPP(x, t) \times (1 - R) \]
where ANPP(x,t) represents plant growth at spatial location x and time t (g C m⁻²), and PAR(x,t), and FPAR(x,t) are total solar radiation (MJ m⁻²) and the fraction of the incoming PAR intercepted by plant incident at spatial location x and time. \( \varepsilon^* \) is the maximum possible light energy conversion efficiency and was set uniformly at 0.56 g C MJ⁻¹ (Zhang et al., 2013). \( T_{x1}(x, t) \) and \( T_{x2}(x, t) \) are the effects of temperature to \( \varepsilon \), and \( \text{W}_e(x, t) \) accounts for effects of water stress, also at location x and time t. ANPP can be inferred by the ratio between BNPP and ANPP (R), around 0.587 for alpine grasslands on the Tibetan Plateau predicted by Wu et al. (2010).
**Calculation of Grazing Intensity**
Grazing intensity (GI) was quantified by the ratio between actual livestock carrying capacity (\( C_a \)) and theoretical livestock carrying capacity (\( C_t \)):
\[ GI = C_a/C_t \]
The actual livestock carrying capacity for each county was determined as follows:
\[ C_a = (C_n + C_h)/A \]
where \( C_n \) is the number of livestock inventory in a given year, \( C_h \) is the number of livestock sold in a given year. A is the available grassland area (ha).
The theoretical livestock carrying capacity for each grassland pixel was calculated as follows:
\[ C_t = (Y \times U \times C \times H)/(S \times G) \]
where Y is grassland yield; U is the utilization rate of herbage (%), estimated as 70%; C is the proportion of the area available for pasture (%), estimated as 0.84 (Fan et al., 2010; Cao et al., 2020); H is the proportion of edible forage (%), estimated as 0.76, 0.69, and 0.76 for alpine meadow, alpine steppe and alpine desert-steppe, respectively, according to observed data in North Tibet; S is the daily feed intake per SSU, set as 1.33 kg (Fan et al., 2010); G is grazing days (d), set as 365.
In our study, we regarded yield (Y) as equivalent to the potential aboveground biomass (AGBp), which was not grazed by herbivores. Grassland ANPPp can be estimated according to the terrestrial ecosystem model (TEM).
\[
AGB_p = \frac{ANPP_p}{0.45}
\]
\[
ANPP_p = NPP_p(1 - R)
\]
TEM is one of the process-based ecosystem models driven by spatially referenced information on vegetation type, climate, elevation, soils, and water availability to calculate the monthly carbon and nitrogen fluxes and pool sizes of terrestrial ecosystems. TEM can only be applied in a mature and undisturbed ecosystem without considering the effects of land use. TEM NPP (NPPp) was calculated by the difference between gross primary productivity (GPP) and autotrophic respiration (Ra) in the monthly time step. Ra is considered as the sum of maintenance respiration (Rm) and growth respiration (Rg). Monthly GPP is driven by several factors and is calculated as:
\[
GPP = C_{\text{max}}(\text{PAR})f(\text{LEAF})f(T)f(CO_2, H_2O)f(NA)
\]
\[
NPP_p = GPP - R_a = GPP - R_m - R_g
\]
where C_{\text{max}} represents the maximum rate of C assimilation by plants in 1 month (g C m^{-2} month^{-1}). The function of f(PAR), f(T), and f(NA) accounts for the effects of photosynthetically active radiation, temperature, and relative nutrient availability, respectively, on GPP. f(LEAF) is the leaf area relative to the maximum annual leaf area and depends on monthly estimated evapotranspiration. f(CO_2, H_2O) is the interactive effects of atmospheric CO2 concentrations and moisture availability to GPP. In this study, the value of C_{\text{max}} was set as 949.6 g C m^{-2} month^{-1} for alpine meadow, 617.9 g C m^{-2} month^{-1} for alpine steppe and 251.2 g C m^{-2} month^{-1} for desert steppe (Chen et al., 2014).
**Statistical Analysis**
The differences in climatic variables, grazing intensity, and alpine grassland ANPP before and after the implementation of the "Ecological Security Barrier Protection and Construction Project in Tibet" were calculated by the following formula:
\[
\Delta V = \Delta V_{\text{after-project}} - \Delta V_{\text{before-project}}
\]
where V represents each of mean annual temperature (MAT), annual total precipitation (AP), annual total radiation (AR), GI, and ANPP, respectively. We first calculated the zonal mean of each variable at each county in Tibet. Then, we employed a random forest (RF) regression analysis to identify the relative importance of the four variables on the variation in grassland ANPP (Huang and Xia, 2019). In the RF model, the response variable was the differences in the mean ANPP between the two periods, and the predictors were the differences in the mean values of MAT, AP, AR, and GI. The importance of each predictor variable is defined as the percentage increase in the mean square error (%IncMSE) between observations and predictions, and the decrease is averaged over all the trees to produce the final estimation for importance (Delgado-Baquerizo et al., 2017; Huang and Xia, 2019). High %IncMSE values represent high importance for each predictor. The RF model was run using R 4.0.2 with randomForest_4.6-12⁴.
**RESULTS**
**Validation of Grassland ANPP and Potential Aboveground Biomass**
To assure the accuracy of the ANPP and AGBp, observed ANPP data in open grazed grasslands and observed AGB data in fenced grasslands were used to validate the simulated ANPP and AGBp, respectively. The results showed that both simulated ANPP and AGBp matched well with observed records. The simulated ANPP can explain 80% of the variance in observed ANPP of open alpine grasslands (Figure 2A), and the simulated AGBp can explain 78% of the variance in observed AGBp of fenced alpine grasslands (Figure 2B).
**Dynamics of Climatic Variables and Grazing Intensity Between Two Subperiods**
Both MAT and AP showed a non-significant increasing trend in the period of before (2000–2008) and after the implementation (2009–2017) of the "Ecological Security Barrier Protection and Construction Project." MAT trend was faster, but AP trend was slower in 2000–2008, compared to those in 2009–2017 (Figures 3A,B). AR trend was similar to the GI trend in the two periods, showing an initial non-significant increasing trend and then a significant decreasing trend (Figures 3C,D).
The changes in climatic variables and grazing intensity in Tibet were non-uniform across space (Figure 4). Warming was evident across the whole plateau, especially in northern Tibet, where MAT increased by 0.6°C (Figure 4A). Considerable increase and decrease in AP also occurred in northern and western Tibet (AAP > 20 mm) and in central and eastern regions, respectively (Figure 4B). In contrast, AR was dimming (negative ΔAR) in northern and western Tibet but lighting (positive ΔAR) in eastern areas (Figure 4C). Regarding grazing intensity, it increased in the middle Tibet after the implementation of the "Ecological Security Barrier Protection and Construction Project" and decreased in the edge counties of the Tibetan Autonomous Region (Figure 4D).
**Dynamics of Grassland Productivity Between Two Subperiods**
Grassland ANPP in Tibet decreased from southeast to northwest with grassland types, from alpine meadow, alpine steppe to alpine desert steppe (Figures 5A,B). Mean ANPP for all grassland types (28.4 g C m^{-2}) during 2009–2017 increased
⁴https://cran.rproject.org/web/packages/randomForest
FIGURE 2 | Comparisons (A) between simulated and observed ANPP and (B) between simulated and observed AGBₚ.
FIGURE 3 | Inter-annual dynamics of (A) MAT, (B) AP, (C) AR, and (D) GI before and after the implementation of the “Ecological Security Barrier Protection and Construction Project.”
by 5.2%, compared to 27.0 g C m⁻² during 2000–2008. ANPP increased at approximately 81% of grassland pixels (Figure 5C). Mean ANPP significantly increased by 2.41 g C m⁻² (ΔMean ANPP) in alpine meadows, followed by alpine desert steppes (ΔMean ANPP = 0.93 g C m⁻²) and alpine steppes (ΔMean ANPP = 0.88 g C m⁻²), respectively (Figure 6A). ANPP
FIGURE 4 | Distribution of the mean-difference in (A) MAT, (B) AP, (C) AR, and (D) GI between before and after the implementation of the "Ecological Security Barrier Protection and Construction Project."
decreased in the remaining 19% of grassland pixels, mainly in central Tibet (Figure 5C).
ANPP decreased during 2000–2008 for 54.2% of grasslands in central Tibet (Figure 5D). However, ANPP mainly increased during 2009–2017 in western and southern Tibet (Figure 5E). The ANPP trend during 2009–2017 (0.26 g C m^{-2} year^{-1}) for all grasslands increased by 13.0% (Figures 5F, 6B), compared with that during 2000–2008 (0.23 g C m^{-2} year^{-1}). Especially, alpine desert steppes increased most evidently (1.03 g C m^{-2} year^{-1}), followed by alpine steppes (0.50 g C m^{-2} year^{-1}). The ANPP of alpine meadows reversed from an increasing trend (0.50 g C m^{-2} year^{-1}) during 2000–2008 to a decreasing trend (-0.31 g C m^{-2} year^{-1}) during 2009–2017 (Figure 6B).
Effects of Climate and Grazing Intensity on Grassland ANPP Changes
The correlation coefficients between ANPP and three climatic variables (MAT, AP, and AR) and grazing intensity (GI) were presented in Figure 7. The ANPP had weak positive correlation with MAT (r = 0.20), AP (r = 0.13), and AR (r = 0.06) and weak negative correlation with GI (r = -0.12) during 2000–2008. The four variables had only explained 32% of the variance in ANPP during 2000–2008 (Table 1). The correlation coefficients between ANPP and the four variables changed during 2009–2017. MAT (r = 0.23) and AP (r = 0.42) had more positive effects on ANPP while AR (r = -0.12) and GI (r = -0.39) had more negative effects during 2009–2017, compared to 2000–2008. The four variables explained 72% of the variance in ANPP during 2009–2017, among which AP became the dominant factor and explained 60% of the variance in ANPP (Table 1).
RF model was used to quantify the relative contributions of the four responsible variables (ΔMeanMAT, ΔMeanAP, ΔMeanAR, and ΔMeanGI) with respect to the differences in mean ANPP (ΔMeanANPP) between the two subperiods. ΔMeanAP was the primary driver of ΔMeanANPP with % IncMSE of 29.0%, followed by ΔMeanMAT (%IncMSE = 19.9%), ΔMeanAR (%IncMSE = 16.2%) and ΔMeanGI (%IncMSE = 14.5%), respectively (Figure 8).
DISCUSSION
Quantifying the key ecosystems’ dynamics controlling factors is crucial for ecological management and adaptation (Li L. et al., 2018; Wei et al., 2020). Alpine grasslands in Tibet are one of the most vulnerable biomes to human activities and
climate change in the world. However, it is still a question of debate how and at what extent different drivers contribute to grassland productivity change on this plateau. In this study, we first used the CASA model to quantify the alpine grassland ANPP in Tibet from 2000 to 2017. Then, we investigated the changes in grassland ANPP before (2000–2008) and after (2009–2017) the implementation of the “Ecological Security Barrier Protection and Construction Project.” Finally, an RF model was used to quantify the relative importance of temperature, precipitation, radiation, and grazing intensity to the dynamics of grassland ANPP.
**Increased ANPP Due to More Favorable Climate**
We found that ANPP after the implementation of the project increased to approximately 81% of alpine grasslands in Tibet. The mean values of grassland ANPP increased from 27.0 g C m$^{-2}$ before to 28.4 g C m$^{-2}$ after the...
FIGURE 6 | The (A) mean and (B) trend of grassland ANPP in the two subperiods, before (2000–2008) and after (2009–2017) starting the “Ecological Security Barrier Protection and Construction Project” for each grassland type in Tibet.
FIGURE 7 | Spatial patterns of the correlation coefficients ($R$) of grassland ANPP with MAT, AP, AR, and GI during (A–D) 2000–2008, (E–H) 2009–2017, and (I–L) the difference in the corresponding correlation coefficients ($\Delta R$) between the two subperiods, before and after the starting “Ecological Security Barrier Protection and Construction Project.”
This finding was consistent with Wang et al. (2017) and Huang et al. (2018) who also examined that vegetation coverage and forage supply capacity in Tibet increased slightly after the start of the project. Correlation analysis revealed that this increase in ANPP might be attributed to more favorable climatic conditions and the decrease in the grazing intensity after the project. Further, the climate in Tibet became warmer and wetter after the project’s start, which positively affected the grassland ANPP. We also found that the increased precipitation had a higher effect on the f grassland ANPP than temperature. Nonetheless, this finding is not in agreement with Zhu et al. (2016) who concluded that alpine plants are sensitive to temperature as the average growing season temperature is lower than the optimum air temperature of vegetation productivity in global alpine regions (Huang et al., 2019). However, the finding is in line with long-term in situ monitoring, manipulative experiments, satellite remote sensing, and model simulations on this plateau.
For example, Wu et al. (2016) found that growing season precipitation explained the most variance of alpine grassland species richness and aboveground biomass across the northern Tibetan Plateau. Fu et al. (2018) reported that increased precipitation has more strong effects on plant production in alpine meadows than experimental warming in Tibet. A potential explanation is that colder habitats have long shaped alpine vegetation’s functional traits to adapt to the low temperatures and large diurnal temperature ranges (Elmendorf et al., 2012; Shi et al., 2014). This might be due to the reason that arctic and alpine plants have excellent resistance to short-term temperature fluctuations (Theurillat and Guisan, 2001; Elmendorf et al., 2012).
### Increased ANPP Due to Weakening Grazing Intensity
Human activities were significantly intense across the Tibetan Plateau before the implementation of the project. For example, the population reached up to 3.12 million in the Tibetan Autonomous Region of China, in 2013, which is twice as in 1965; meanwhile, the livestock number also increased from 9.74 million in 1958 to 23 million in the early twenty-first century (Fan et al., 2015). This study found that grazing intensity was negatively correlated with ANPP, suggesting that grazing activities can...
### Table 1
Summary of general linear models (GLMs) that included MAT, AP, AR, and GI as predictors for grassland ANPP in the two periods, before and after starting the “Ecological Security Barrier Protection and Construction Project” in Tibet.
| GLM for ANPP | Predicators | Df | SS | MS | F | P | %SS | R² |
|-------------|-------------|----|-----|-----|-----|-----|-----|-----|
| (2000–2008) | MAT | 1 | 1.43| 1.43| 1.06| 0.36| 17.89| 0.32|
| | AP | 1 | 0.85| 0.85| 0.63| 0.47| 10.68| |
| | AR | 1 | 0.27| 0.27| 0.20| 0.68| 3.43 | |
| | GI | 1 | 0.02| 0.02| 0.01| 0.91| 0.24 | |
| (2009–2017) | MAT | 1 | 0.90| 0.90| 1.64| 0.27| 11.22| 0.73|
| | AP | 1 | 4.80| 4.80| 8.78| 0.04| 60.01| |
| | AR | 1 | 0.01| 0.01| 0.02| 0.89| 0.14 | |
| | GI | 1 | 0.10| 0.10| 0.19| 0.69| 1.28 | |
Df, degree of freedom; SS, sum squares; MS, mean squares; F, variance ratio; P, significance; %SS, percentage of the total sum of squares explained.
### Figure 8
Relative contribution of the differences in means of the four variables (ΔMeanMAT, ΔMeanAP, ΔMeanAR, and ΔMeanGI) to the differences in mean ANPP (ΔMeanANPP) between before and after starting the “Ecological Security Barrier Protection and Construction Project” in RF model. The values were denoted by the percentage increase of mean squared error (%IncMSE).
mediate the interannual ANPP change. After the start of the project, grazing intensity decreased significantly (Figure 3D), owing to the increase in the potential grassland productivity and the reduction in the livestock (Supplementary Figure S1). This significant decrease in the grazing intensity had a positive effect on grassland ANPP. Grazing and human-induced land use/cover change are the two most significant human disturbances for alpine grassland ANPP in Tibet, and the former is supposed to be the dominant one (Arthur et al., 2008; Harris, 2010; Chen et al., 2014). The complicated process of grazing, such as forage selection, herbivores and their trampling (Parsons and Dumont, 2003; Paruelo et al., 2008), directly and indirectly, can modify grassland productivity (Chen et al., 2007; Xiong et al., 2014; Wang and Wesche, 2016). Meanwhile, grassland productivity is highly dependent on grazing and its intensity. The prevailing view is that moderate grazing promotes plant growth due to compensatory growth while overgrazing reduces vegetation productivity (de Mazancourt et al., 1998; Schuman et al., 1999; Luo et al., 2012). At the end of the twentieth century, the stocking rates of livestock in Tibet were high in most of its counties (Fan et al., 2015). Overgrazing affected the native species diversity and ecosystem stability in Tibet and altered the structure and function of grassland ecosystems, induced C losses and grassland degradation (Zhou et al., 2017; Zhang et al., 2019). The Chinese government continuously formulates policies to limit grazing throughout the project, such as grazing exclusion, conversion of grazing land to grass and grazing withdrawal programs. This decline in grazing intensity after the start of the project elevated grassland productivity. Thus, we concluded that the check on the livestock numbers was a useful tool for the restoration of grassland in Tibet.
Climate Variability Dominated the ANPP Dynamic
The RF model revealed that the grazing intensity is far less critical than climatic variables in controlling grassland ANPP. This signifies that climate change is the primary driver for the sustainability of alpine grassland ecosystems on the Tibetan Plateau (Huang et al., 2016; Lehner et al., 2016; Xu et al., 2016). Although the intensity of human activities on the Tibetan Plateau is increasing rapidly, however, the impact of human activities on ecosystems is less than other regions of the world (Venter et al., 2016; Li S. et al., 2018). Grazing activities have not altered the dominant role of climate change for grassland variation in Tibet. However, we must highlight that, as suggested by previous studies, the biochemical cycle and their feedbacks to climate change would get more complicated under human disturbance (Kröel-Dulay et al., 2015; Peters et al., 2019). For example, in our study, we found that the relationships between climatic variables and grassland ANPP were more robust before the project’s start. Those changes in correlation coefficients might cause by the changes in grazing intensity. Thus, the mechanisms of how plants respond to the coupled effects of climatic and anthropogenic stresses should be explored in the future.
CONCLUSION
This study used 9 years of datasets before and after the implementation of Ecological Security Barrier Protection and Construction Project, including meteorological conditions, grazing intensity, to explore the combined effects of climate change and grazing activities on the dynamics of grassland ANPP in Tibet. We found an increase in grassland ANPP after the project’s start. Precipitation was the dominant factor in controlling the observed alpine grassland changes during the study period. Furthermore, the weak grazing intensity after the project promoted grassland productivity. Thus, we suggested that the check on the livestock numbers has a positive effect on the restoration of degraded grasslands in Tibet.
DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author/s.
AUTHOR CONTRIBUTIONS
JW and ML conceptualized this study and led the writing. ML collected and analyzed the data. YF, BN, YH, and XZ interpreted the results and revised the text. All authors contributed to this work and approved the final manuscript before submission.
FUNDING
The study was supported by the Second Tibetan Plateau Scientific Expedition and Research (STEP) program (2019QZKK1002) and the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA19050502). JW was funded by a 2 years scholarship from the Alexander von Humboldt Foundation from 2017 to 2019 and supported by the Young Talent Scientist Program of the Chinese Academy of Agricultural Sciences since December 2019.
ACKNOWLEDGMENTS
We acknowledge the support of all co-authors for their constructive and helpful comments and organization of this study.
SUPPLEMENTARY MATERIAL
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fevo.2021.631024/full#supplementary-material
Supplementary Figure 1 | The dynamics of livestock number and potential grassland net primary production (NPP<sub>3</sub>) in Tibet from 2000 to 2017.
REFERENCES
Allen, R., Pereira, L., Raes, D., and Smith, M. (1998). Crop Evapotranspiration—Guidelines for Computing Crop Water Requirements—FAO Irrigation and Drainage Paper 56. Rome: FAO.
Arthur, A. D., Pech, R. P., Davey, C., Jiebu, O., Yanming, Z., and Hui, L. (2008). Livestock grazing, plateau pikas and the conservation of avian biodiversity on the Tibetan plateau. Biol. Conserv. 141, 1971–1981. doi: 10.1016/j.biocon.2008.05.010
Breiman, L. (2001). Random forests. Mach. Learn. 45, 5–32. doi: 10.1023/a:1010935043024
Cao, Y., Wu, J., Zhang, X., Niu, B., and He, Y. (2020). Comparison of methods for evaluating the forage-livestock balance of alpine grasslands on the Northern Tibetan Plateau. J. Resour. Ecol. 11:272. doi: 10.16741/j.jicen.2020.03.004s
Chen, B., Zhang, X., Tao, J., Wu, J., Wang, J., Shi, P., et al. (2014). The impact of climate change and anthropogenic activities on alpine grassland over the Qinghai-Tibetan Plateau. Agric. For. Meteorol. 181, 11–18. doi: 10.1016/j.agrformet.2014.01.002
Chen, H., Zhu, Q., Peng, C., Wu, N., Wang, Y., Fang, X., et al. (2013). The impacts of climate change and human activities on biogeochemical cycles on the Qinghai-Tibetan Plateau. Glob. Chang. Biol. 19, 2940–2955. doi: 10.1111/gcb.12277
Chen, Y., Lee, G., Lee, P., and Oikawa, T. (2007). Model analysis of grazing impact on plant production of an alpine meadow than does experimental warming in the Northern Tibetan Plateau. Sci. Adv. 2242ñ2252. doi: 10.1890/0012-96581998079
Dong, S., Shang, Z., Gao, J., and Boone, R. (2020). Enhancing sustainability of grassland ecosystems through ecological restoration and grazing management in an era of climate change on Qinghai-Tibetan Plateau. Agric. Ecosyst. Environ. 287:106684. doi: 10.1016/j.agee.2019.106684
Elmendorf, S. C., Henry, G. H. R., Hollister, R. D., Bjork, R. G., Boulanger-Delgado-Baquerizo, M., Eldridge, D. J., Maestre, F. T., Karunaratne, S. B., Trivedi, P., Reich, P. B., et al. (2017). Climate legacies drive global soil carbon stocks in terrestrial ecosystems. Sci. Adv. 3:7. doi: 10.1126/sciadv.1602008
Gong, J., Li, S., and Li, S. (2018). Human footprint in Tibet: assessing the spatial layout and effectiveness of nature reserves. Ecol. Appl. 52, 161ñ179. doi: 10.1051/animres:2003013
Heung, B., Bulmer, C. E., and Schmidt, M. G. (2014). Predictive soil parent material mapping at a regional-scale: a random forest approach. Geoderma 214–215, 141–154. doi: 10.1016/j.geoderma.2013.09.016
Huang, K., and Xia, J. (2019). High ecosystem stability of evergreen broadleaf forests under severe droughts. Glob. Chang. Biol. 25, 3494–3503. doi: 10.1111/gcb.14748
Huang, K., Zhang, Y., Zhu, J., Liu, Y., Zu, J., and Zhang, J. (2016). The influences of climate change and human activities on vegetation dynamics in the Qinghai-Tibet Plateau. Remote Sens. 8:876. doi: 10.3390/rs8100876
Huang, L., Cao, W., Xu, X., Fan, J., and Wang, J. (2018). The ecological effects of ecological security barrier protection and construction project in Tibet Plateau (in Chinese). J. Nat. Resour. 33, 398–411. doi: 10.1016/j.jnr.201701016
Huang, M., Piao, S., Ciais, P., Peñuelas, J., Wang, X., Keenan, T. F., et al. (2019). Air temperature optima of vegetation productivity across global biomes. Nat. Ecol. Evol. 3, 772–779. doi: 10.1038/s41477-019-0838-x
Hutchinson, M. (2004). Anupslin Version 4.3 Centre for Resource and Environmental Studies. Canberra: The Australian National University.
Knight, J., and Harrison, S. (2012). The impacts of climate change on terrestrial Earth systems. Nat. Clim. Chang. 3:24. doi: 10.1038/nclimate1660
Kroel-Dulay, G., Ransijn, J., Schmidt, I. K., Beier, C., De Angelis, P., De Gato, D., et al. (2015). Increased sensitivity to climate change in disturbed ecosystems. Nat. Commun. 6:6682. doi: 10.1038/ncomms6682
Lehnert, L. W., Wescbe, K., Trachte, K., Reudenbach, C., and Bendix, J. (2016). Climate variability rather than overstocking causes recent large scale cover changes of Tibetan pastures. Sci. Rep. 6:24367. doi: 10.1038/srep24367
Li, L., Zhang, X., Liu, L., Wu, J., Li, S., Zhang, H., et al. (2018). Current challenges in distinguishing climatic and anthropogenic contributions to alpine grassland variation on the Tibetan Plateau. Ecol. Evol. 8, 5949–5963. doi: 10.1002/ece3.4099
Li, S., Wu, J., Gong, J., and Li, S. (2018). Human footprint in Tibet: assessing the spatial layout and effectiveness of nature reserves. Sci. Total Environ. 621, 18–29. doi: 10.1016/j.scitotenv.2017.11.216
Li, M., Zhang, X., He, Y., Niu, B., and Wu, J. (2020). Assessment of the vulnerability of alpine grasslands on the Qinghai-Tibetan Plateau. PeerJ 8:e8513. doi: 10.7717/peerj.8513
Lithi, H., and Whittaker, R. H. (1978). Primary Productivity of the Biosphere. New York, NY: Springer.
Lin, D., Xia, J., and Wan, S. (2010). Climate warming and biomass accumulation of terrestrial plants: a meta-analysis. New Phytol. 188, 187–198. doi: 10.1111/j.1469-4141.2010.03347.x
Long, R., Shang, Z., Guo, X., and Ding, L. (2009). “Qinghai—Tibetan plateau rangelands,” in Rangeland Degradation and Recovery in China’s Pastoral Lands, eds V. R. Squires, X. Lu, Q. Lu, T. Wang, and Y. Yang (Wallingford: CABI), 184–196.
Luo, G., Han, Q., Zhou, D., Li, L., Chen, X., Li, Y., et al. (2012). Moderate grazing can promote aboveground primary production of grassland under water stress. Ecol. Complex. 11, 126–136. doi: 10.1016/j.ecocom.2012.04.004
Parsons, A. J., and Dumont, B. (2003). Spatial heterogeneity and grazing processes. Anim. Res. 52, 161–179. doi: 10.1015/anirex.20030013
Parsuelo, J. M., Pütz, S., Weber, G., Bertiller, M., Golluscio, R. A., Aguilar, M. R., et al. (2008). Long-term dynamics of a semiarid grass steppe under stochastic climate and different grazing regimes: a simulation analysis. J. Arid Environ. 72, 2211–2231. doi: 10.1016/j.jaridenv.2008.07.010
Paudel, K. P., and Andersen, P. (2010). Assessing rangeland degradation using multi temporal satellite images and grazing pressure surface model in Upper Mustang, Trans Himalaya, Nepal. Remote Sens. Environ. 114, 1845–1855. doi: 10.1016/j.rse.2010.03.011
Peters, M. K., Hemp, A., Appélhans, T., Becker, J. N., Behler, C., Classen, A., et al. (2019). Climate—land–use interactions shape tropical mountain biodiversity and ecosystem functions. Nature 568, 88–92. doi: 10.1038/s41586-019-1048-z
Riutiny, A., Kergoat, L., Bonneau, A., and Intercomparaison, T. P. O. T. P. N. M. (1999). Comparing global models of terrestrial net primary productivity (NPP), analysis of differences in light absorption and light–use efficiency. Glob. Chang. Biol. 5, 56–64. doi: 10.1046/j.1354-2087.1999.00007.x
Schuman, G. E., Reeder, J. D., Manley, J. T., Hart, R. H., and Manley, W. A. (1999). Impact of grazing management on the carbon and nitrogen balance of a mixed-grass Rangeland. Ecol. Appl. 9, 65–71. doi: 10.2307/2641168
Seiferling, I., Proulx, R., and Wirth, C. (2014). Disentangling the environmental-heterogeneity–species-diversity relationship along a gradient of human footprint. *Ecology* 95, 2084–2095. doi: 10.1890/13-1344.1
Shi, Y., Wang, Y., Ma, Y., Ma, W., Liang, C., Flynn, D. F. B., et al. (2014). Field-based observations of regional-scale, temporal variation in net primary production in Tibetan alpine grasslands. *Biogeosciences* 11, 16843–16878. doi: 10.5194/bg-11-2003-2014
Tao, J., Zhang, Y., Dong, J., Fu, Y., Zhu, J., Zhang, G., et al. (2015). Elevation-dependent relationships between climate change and grassland vegetation variation across the Qinghai-Xizang Plateau. *Int. J. Climatol.* 35, 1638–1647. doi: 10.1002/joc.4082
Theurillat, J. P., and Guisan, A. (2001). Potential impact of climate change on vegetation in the european alps: a review. *Clim. Chang.* 50, 77–109. doi: 10.1023/A:1010652015752
Tong, X., Brandt, M., Yue, Y., Horion, S., Wang, K., Keersmaecker, W. D., et al. (2014). Field-based observations of regional-scale, temporal variation in net primary production in Tibetan alpine grasslands. *Biotropica* 46, 1979–1980. doi: 10.1111/btp.12018
Venter, O., Sanderson, E. W., Magrach, A., Allan, J. R., Beher, J., Jones, K. R., et al. (2016). Sixteen years of change in the global terrestrial human footprint and implications for biodiversity conservation. *Nat. Commun.* 7:12558. doi: 10.1038/ncomms12558
Wang, X., Cheng, G., Zhao, T., Zhang, X., Zhu, L., and Huang, L. (2017). Assessment on protection and construction of ecological safety shelter for Tibet (in Chinese). *Bull. Chin. Acad. Sci.* 32, 29–34. doi: 10.16418/j.isss.1000-3045.2017.01.004
Wang, Y., and Wesche, K. (2016). Vegetation and soil responses to livestock grazing in Central Asian grasslands: a review of Chinese literature. *Biodivers. Conserv.* 25, 2401–2420. doi: 10.1007/s10531-015-1034-1
Wang, Y. B., Wang, G. X., Shen, Y. P., and Wang, Y. L. (2005). Degradation of the eco-environmental system in alpine meadow on the Tibetan Plateau. *J. Glaciol. Geocryol.* 37, 517–522.
Wei, D., Zhao, H., Zhang, J., Qi, Y., and Wang, X. (2020). Human activities alter response of alpine grasslands on Tibetan Plateau to climate change. *J. Environ. Manag.* 262:110335. doi: 10.1016/j.jenvman.2020.110335
Wu, J., Wurst, S., and Zhang, X. (2016). Plant functional trait diversity regulates the nonlinear response of productivity to regional climate change in Tibetan alpine grasslands. *Sci. Rep.* 6:35649. doi: 10.1038/srep35649
Wu, J., Zhang, X., Shen, Z., Shi, P., Xu, X., and Li, X. (2013). Grazing-exclusion effects on aboveground biomass and water-use efficiency of alpine Grasslands on the Northern Tibetan Plateau. *Rangeland Ecol. Manag.* 66, 454–461. doi: 10.2111/REM-D-12-00051.1
Xiong, D., Shi, P., Sun, Y., Wu, J., and Zhang, X. (2014). Effects of grazing exclusion on plant productivity and soil carbon, nitrogen storage in alpine meadows in northern Tibet, China. *Chin. Geogr. Sci.* 24, 488–498. doi: 10.1007/s11769-014-0897-y
Xu, H., Wang, X., and Zhang, X. (2016). Alpine grasslands response to climatic factors and anthropogenic activities on the Tibetan Plateau from 2000 to 2012. *Ecol. Eng.* 92, 251–259. doi: 10.1016/j.ecoleng.2016.04.005
Yang, G., Peng, C., Chen, H., Dong, F., Wu, N., Yang, Y., et al. (2017). Qinghai–Tibetan Plateau peatland sustainable utilization under anthropogenic disturbances and climate change. *Ecosyst. Health Sust.* 3:e01263. doi: 10.1002/ehs2.1263
Yao, T., Thompson, L. G., Mosbrugger, V., Zhang, F., Ma, Y., Luo, T., et al. (2012). Third Pole Environment (TPE). *Environ. Dev.* 3, 52–64. doi: 10.1016/j.envdev.2012.04.002
Yu, C., Zhang, Y., Claus, H., Zeng, R., Zhang, X., and Wang, J. (2012). Ecological and environmental issues faced by a developing Tibet. *Environ. Sci. Technol.* 46, 1197–1211. doi: 10.1021/es2047188
Zhang, Y., Qi, W., Zhou, C., Ding, M., Liu, L., Gao, J., et al. (2013). Spatial and temporal variability in the net primary production (NPP) of alpine grassland on Tibetan Plateau from 1982 to 2009 (in Chinese). *Acta Geogr. Sin.* 68, 1197–1211. doi: 10.11821/dlxbx201309004
Zhang, Y., Xu, M., Chen, H., and Adams, J. (2009). Global pattern of NPP to GPP ratio derived from MODIS data: effects of ecosystem type, geographical location and climate. *Glob. Ecol. Biogeogr.* 18, 280–290. doi: 10.1111/j.1466-8238.2008.00442.x
Zhang, Y., Zhu, Y., Li, J., and Chen, Y. (2019). Current status and future directions of the Tibetan Plateau ecosystem research. *Sci. Bull.* 64:428. doi: 10.1016/j.scib.2019.03.009
Zhou, G., Zhou, X., He, Y., Shao, J., Hu, Z., Liu, R., et al. (2017). Grazing intensity significantly affects belowground carbon and nitrogen cycling in grassland ecosystems: a meta-analysis. *Glob. Chang. Biol.* 23, 1167–1179. doi: 10.1111/gcb.13431
Zhou, X., Yamaguchi, Y., and Arjasakusuma, S. (2018). Distinguishing the vegetation dynamics induced by anthropogenic factors using vegetation optical depth and AVHRR NDVI: a cross-border study on the Mongolian Plateau. *Sci. Total Environ.* 616–617, 730–743. doi: 10.1016/j.scitotenv.2017.10.253
Zhu, Z., Piao, S., Myneni, R. B., Huang, M., Zeng, Z., Canadell, J. G., et al. (2016). Greening of the Earth and its drivers. *Nat. Clim. Chang.* 6, 791–795. doi: 10.1038/nclimate3004
**Conflict of Interest:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Copyright © 2021 Li, Wu, Feng, Niu, He and Zhang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3000,
1
],
[
3000,
8484,
2
],
[
8484,
14213,
3
],
[
14213,
19650,
4
],
[
19650,
20286,
5
],
[
20286,
22837,
6
],
[
22837,
23751,
7
],
[
23751,
25411,
8
],
[
25411,
28215,
9
],
[
28215,
33556,
10
],
[
33556,
40453,
11
],
[
40453,
46472,
12
]
]
} |
4845042731ff9c5bba5821879fb139c71ccd4b15 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 29870,
"total-output-tokens": 12391,
"fieldofstudy": [
"Psychology"
]
} | Facial threat affects trust more strongly than facial attractiveness in women than it does in men
Johanna Brustkern¹, Markus Heinrichs¹, Mirella Walker² & Bastian Schiller¹
Trust is essential in initiating social relationships. Due to the differential evolution of sex hormones as well as the fitness burdens of producing offspring, evaluations of a potential mating partner’s trustworthiness likely differ across sexes. Here, we explore unknown sex-specific effects of facial attractiveness and threat on trusting other-sex individuals. Ninety-three participants (singles; 46 women) attracted by the other sex performed an incentivized trust game. They had to decide whether to trust individuals of the other sex represented by a priori-created face stimuli gradually varying in the intensities of both attractiveness and threat. Male and female participants trusted attractive and unthreatening-looking individuals more often. However, whereas male participants’ trust behavior was affected equally by attractiveness and threat, female participants’ trust behavior was more strongly affected by threat than by attractiveness. This indicates that a partner’s high facial attractiveness might compensate for high facial threat in male but not female participants. Our findings suggest that men and women prioritize attractiveness and threat differentially, with women paying relatively more attention to threat cues inversely signaling parental investment than to attractiveness cues signaling reproductive fitness. This difference might be attributable to an evolutionary, biologically sex-specific decision regarding parental investment and reproduction behavior.
Trust is a prerequisite for initiating any kind of social relationship, especially those with potential mating partners¹–³. Besides its obvious benefits for our personal well-being⁴, this particularly intimate sort of human social bond involves significant risks and interpersonal dependency, as the partner might choose to disappoint expectations or abuse one’s own investments in the relationship (e.g., emotions, time, resources⁵,⁶). To minimize such risks, it is necessary that we accurately and quickly infer another’s trustworthiness. In doing so, humans have evolved brain modules specialized in processing facial features, which are one of the richest sources of information in signaling social intentions⁷,⁸. Two facial features crucially affecting the decision whether or not to trust other-sex individuals are attractiveness and threat⁹–¹³. As sexual-selection forces operate differentially across sexes¹⁴–¹⁸, trust behavior in a mating context might likewise be differentially impacted by attractiveness and threat in men and women. We find the shortage of empirical research on investigating sex-specific effects in actual social behavior involving financial consequences to participants (e.g.,¹⁹–²⁶) surprising (for examples from other domains, see²⁷–³¹). We therefore decided in this study to systematically investigate the influence of attractiveness and threat in single men and women by applying a refined, incentivized trust paradigm with facially manipulated trustees of the other sex.
Attractiveness is one of the most important factors when it comes to selecting a potential mating partner³²,³³. Across sexes, people exhibit more prosocial behavior towards attractive than unattractive individuals (e.g., trust³⁴; cooperation³⁵; cooperation and punishment³⁶). However, there is also evidence of sex-specific effects, with stronger attractiveness effects in other- than same-sex interactions, and in males than females³⁷; but see also³⁸. Evolutionary accounts like the “mate selection theory” state that men are particularly apt to approach attractive women, as attractiveness signals information about youth and good reproductive fitness, while women pay more attention to other “mating characteristics” signaling the potential ability to provide resources for future offspring³⁸,³⁹. So far, however, there is no evidence whether such sex-specific effects of attractiveness extend to the trust behavior domain within a potential mating context. In the present study, we try to close this gap by investigating whether the facial attractiveness of other-sex individuals may modulate trust behavior displayed towards them.
¹Laboratory for Biological and Personality Psychology, Department of Psychology, University of Freiburg, Stefan-Meier-Str. 8, 79104 Freiburg, Germany. ²Faculty of Psychology, University of Basel, Missionsstrasse 60/62, 4055 Basel, Switzerland. ³email: [email protected]
Another facial feature that is key to assessing a potential partner's trustworthiness is threat. Both men and women demonstrate lower trust levels towards individuals possessing threatening facial features, probably because threatening faces signal both harmful intentions and the capability of causing harm (i.e., dominance\textsuperscript{41,42}). Research on the neurobiological foundations of trust further corroborates the key role of threat cues in trust behavior. Brain regions involved in detecting threat (e.g., amygdala, insula) are crucially involved in assessing another person's trustworthiness\textsuperscript{41,42}, and intranasal administration of the hormone oxytocin increases trust in men by inhibiting threat-related brain activity\textsuperscript{43-45}. There seem to be interesting sex differences in these neuro-hormonal effects\textsuperscript{46-48} as well as in the general sensitivity to threat cues. Women display greater attentional bias towards threat cues, which may contribute to their higher risk for developing an anxiety disorder\textsuperscript{49-52}. From an evolutionary perspective, abusing trust is accompanied by even higher relative costs for women due to their significantly higher parenting investments (i.e., women possess relatively few oocytes and invest more time in gestation and lactation\textsuperscript{53} and their weaker physical strength makes them potential victims of male aggressive behavior\textsuperscript{54-57}). Consequently, threat cues might be relatively more important for women than for men. In sum, whereas both sexes seem to lose trust in response to threatening faces, we lack empirical research on potential sex differences in these effects in other-sex interactions.
In this study, we investigated potential sex-specific effects of both attractiveness and threat on trust behavior in 93 heterosexual participants (46 women). To control for confounding changes in females' preferences for male faces' characteristics across the menstrual cycle\textsuperscript{58,59}, we tested all women during their luteal phase and excluded women taking oral contraceptives. In addition to the solid evidence that women in the luteal phase are most similar to men in their stress response\textsuperscript{60}, there is evidence for the similar processing of emotional faces of men and women during the luteal phase\textsuperscript{61}. Participants took part in an incentivized trust game with individuals of the other sex represented by photos revealing the low- or high-intensity facial features attractiveness and threat, respectively. By using these face stimuli, our research approach aims to expand upon previous research studying incentivized social behavior in interactions between anonymous individuals (e.g.\textsuperscript{62-64}, and also see\textsuperscript{65}). In line with previous findings, we hypothesized that both female and male participants would transfer more money to attractive than to unattractive individuals (= more trust), and to unthreatening compared to threatening individuals. Moreover, we aimed to examine unexplained sex differences in the relative importance of facial attractiveness and facial threat with regard to trust behavior. On the basis of the evolutionary biological assumption that sexual selection has shaped distinct strategies for assessing attractiveness and threat in males and females, we further hypothesized that threat cues would carry higher relative importance than attractiveness cues in women compared to men.
**Results**
**Facial phenotypes and trust.** First, we analyzed whether female and male participants trusted attractive other-sex trustees more often than unattractive ones. As expected, we detected a significant main effect of facial attractiveness ($F_{1, 91} = 75.854, p < 0.001, \eta^2_p = 0.455$), indicating that participants generally trusted attractive faces more often. Second, we tested whether female and male participants trusted threatening faces less often than unthreatening faces. The significant main effect of facial threat ($F_{1, 91} = 128.810, p < 0.001, \eta^2_p = 0.586$) confirmed this hypothesis. There was no significant interaction between facial threat and facial attractiveness ($F_{1, 91} = 2.636, p = 0.108, \eta^2_p = 0.028$). Thus, both facial features, attractiveness and threat, revealed a significant influence on trusting behavior towards potential other-sex partners in men and women.
**Sex, facial phenotypes, and trust.** There was no significant main effect of sex on either trust across phenotypes ($F_{1, 91} = 0.276, p = 0.601, \eta^2_p = 0.003$), or on trust for the four different phenotypes (high facial attractiveness and low facial threat: $t_{45} = 1.415, p = 0.161$; low facial attractiveness and low facial threat: $t_{45} = 0.955, p = 0.342$; high facial attractiveness and high facial threat: $t_{45} = -0.706, p = 0.482$; low facial attractiveness and high facial threat: $t_{45} = 0.456, p = 0.649$; see Fig. 1). To analyze sex differences in the effects of attractiveness and threat on trust behavior, we next looked at those factors' interaction effects, and found no significant interactions between participants’ sex and facial attractiveness ($F_{1, 91} = 1.133, p = 0.290, \eta^2_p = 0.012$), or between participants’ sex and facial threat ($F_{1, 91} = 3.878, p = 0.052, \eta^2_p = 0.041$). However, we observed a significant interaction between facial attractiveness × facial threat × participants’ sex ($F_{1, 91} = 4.562, p = 0.035, \eta^2_p = 0.048$). Separate ANOVAs for men and women showed that the interaction effect of facial attractiveness × facial threat was significant in women ($F_{1, 45} = 6.097, p = 0.017, \eta^2_p = 0.119$), but not in men ($F_{1, 46} = 0.155, p = 0.696, \eta^2_p = 0.003$). Following up on this interaction, we found that the difference in trust decisions between the dimensions low and high facial attractiveness was greater for low threat ($\Delta M = 0.142, SD = 0.176, p < 0.001$), than high threat ($\Delta M = 0.064, SD = 0.164, p = 0.011$). Comparing the main effects in both ANOVAS in women, we found that the influence (i.e., the effect size) of facial threat ($F_{1, 45} = 79.695, p < 0.001, \eta^2_p = 0.639$) was stronger than that of facial attractiveness ($F_{1, 45} = 28.124, p < 0.001, \eta^2_p = 0.385$). Statistical comparison of effect sizes: Cohen's $d = 0.371$; medium effect). In men, on the other hand, we found that there was no difference between the influence of facial threat ($F_{1, 46} = 0.649, p < 0.001, \eta^2_p = 0.519$; statistical comparison of effect sizes: Cohen's $d = 0.176$; no effect). Hence, in men, attractiveness and threat equally affected trust, while in women, threat had a stronger effect on trust than attractiveness.
**Sex, facial phenotypes, and stimulus perception.** To ensure that the sex difference in the trust decisions between the phenotypes was not caused by different stimulus perceptions across female and male participants, we analyzed the ratings of attractiveness perception and threat perception. As the stimuli were rated separately for attractiveness and threat, we conducted two separate ANOVAs: one with the mean ratings for attractiveness perception as dependent variable, and the other with the mean ratings for threat perception as...
dependent variable. We identified no interaction between participants’ sex × facial attractiveness × facial threat in either ANOVA (ANOVA for rating attractiveness: $F_{1, 91} = 1.804, p = 0.183, \eta^2_p = 0.019$; ANOVA for rating threat: $F_{1, 91} = 0.421, p = 0.518, \eta^2_p = 0.005$; for details see Supplementary Material). In sum, there was no interaction effect of attractiveness, threat, and sex in stimulus perception, suggesting that the observed difference in trust behavior between female and male participants was not caused by different attractiveness or threat perceptions in the two groups.
**Discussion**
In this study, we investigated the sex-specific effects of the facial features attractiveness and threat on trusting individuals of the other sex. Using a trust game with actual financial consequences for participants, we systematically varied the intensities of facial attractiveness and facial threat of other-sex trustees. We found that both male and female participants exhibited more trust towards attractive and unthreatening-looking potential partners. However, the relative importance of these two facial features differed in men and women: compared to men’s behavior, women’s trust behavior was more strongly influenced by a threatening-looking than by an attractive-looking individual. Importantly, this difference in social behavior was not driven by a sex difference in social perception, suggesting that women value threat more than attractiveness in their trust decisions than do men, even though their perception of these features is similar.
By experimentally modulating both facial attractiveness and threat, our results expand upon earlier studies that investigated the effects of these features in social interactions separately from one another. In line with previous research, we detected main effects of attractiveness (e.g.,16) and threat (e.g.,11) on trust in both sexes. We failed to observe that these effects differed in strength across sexes (as some empirical and theoretical research has suggested, e.g.,24,25). However, a sex difference did emerge in the relative importance of both features, with women in their luteal phase placing more emphasis on threat than on attractiveness, and men valuing both features equally. More specifically, women trusted attractive but threatening-looking partners less than unattractive but unthreatening ones, whereas men demonstrated indistinguishable levels of trust towards both phenotypes. In other words, a partner’s high attractiveness could “compensate for” high threat in male but not female participants. From an evolutionary perspective, being relatively more wary of potential threat than vulnerable to attractiveness cues in a mating context might be a highly adaptive mechanism for women, because having one’s trust abused is more costly, and approaching attractive men of “good health” is less beneficial for them66–68.
Moreover, empirically, men (but not women) given face cues related to threat (i.e., greater facial width) abuse trust more often3 and (young) men perceived as more attractive by women reveal lower degrees of prosocial behavior69,70. Although the accuracy of social inferences from facial cues remains equivocal and people certainly refine their quick facial assessments of another’s trustworthiness on the basis of other cues and experiences
during an interaction\textsuperscript{71}, these findings suggest that it benefits women to prioritize threat over attractiveness in trust decisions that rely on the partner’s facial appearance.
When searching for explanations for this sex difference we identified in the relative importance of attractiveness and threat on trust, it is important to keep in mind that none of the women in this study were taking hormonal contraceptives, and that they were participating in this experiment during their menstrual cycle’s luteal phase. This phase, which starts after ovulation, is characterized by high levels of progesterone and to a lesser extent estradiol\textsuperscript{72,73}. Interestingly, high levels of both hormones are known to be associated with enhanced sensitivity to threat-related facial cues in women\textsuperscript{74,75}. As the highest levels of these hormones are observed during the mid-luteal phase when, potentially, conception has already taken place, and during pregnancy\textsuperscript{76}, one could speculate that these steroids trigger behavior that protects fetal development (for a similar argument; see\textsuperscript{88}). In a similar vein, the “dual sexuality” hypothesis argues that women may prefer sexually attractive men on days before ovulation when they are looking for conception partners, whereas they prefer men who appear unthreatening during their luteal phase when they are seeking high-investing partners with father qualities\textsuperscript{77–79}. Indeed, our study provides evidence that women in their luteal phase are more cautious than men, or less willing, to trust potentially threatening but attractive partners, perhaps because the price of having one’s trust abused is particularly high during this phase of the menstrual cycle when pregnancy is possible. Following the dual sexuality hypothesis, one could speculate that facial attractiveness might become more important for women when making trust decisions during the days before ovulation. Future research could systematically test this hypothesis (see\textsuperscript{86}, for example).
So far, we have interpreted the present study’s findings as evidence demonstrating that male and female participants evaluate attractiveness and threat differently in trusting other-sex individuals (= participant’s sex effect). However, one could also argue that our findings demonstrate that male and female faces are evaluated differently (= face stimulus’s sex effect). As the present study investigated approach behavior in other-sex interactions, female participants always interacted with male-face stimuli, and male participants always interacted with female-face stimuli, rendering it difficult to disentangle the participant’s sex from the stimulus’ sex effect. Interestingly, research on trait judgments from faces has revealed that judgments of female in comparison to male faces are less differentiated with regard to the effects of distinct facial characteristics and more based on a general impression of the face’s valence\textsuperscript{41}. Transferring these findings to the present study, male participants did not distinguish between faces signaling ambiguous information about trustworthiness (trust level: unattractive and unthreatening = attractive and threatening), because they might evaluate ambiguous female faces less differentially and assign intermediate valence to such faces. In contrast, female participants, who distinguished between faces offering ambiguous information (trust level: unattractive and unthreatening > attractive and threatening), might evaluate facial attractiveness and threat independently from one another, leading to a more differentiated assessment of trustworthiness towards ambiguous faces. To better distinguish the effects of participants’ and stimulus’ sex, future studies could investigate both same-sex and other-sex interactions.
In sum, the present study provides first evidence of a sex-specific interacting effect of a potential partner’s facial attractiveness and threat on trust behavior. From an evolutionary perspective, the fact that women in their luteal phase prioritize threat over attractiveness might be explained by their higher parental investment and the high price of being abused when they might get pregnant\textsuperscript{82}. Future studies might include women in their pre-ovulatory phase (validated by blood assays to measure gonadal steroid) to observe whether women do indeed prioritize attractiveness over threat during this menstrual phase, thereby contributing to the ongoing debate about whether women’s preferences for their partner’s attractiveness and threat change across the menstrual cycle\textsuperscript{83,84}. Furthermore, we expect our findings to stimulate research refining such explanations by illuminating the possible role of non-evolutionary explanations for sex differences (e.g., sex stereotypes\textsuperscript{85}, societal influences\textsuperscript{86}), or by revealing the role of individual differences in traits (e.g., general dispositional trust\textsuperscript{87}; attachment styles\textsuperscript{88}) or states (e.g., recent trust-related experiences such as trust violations\textsuperscript{89}) and their interaction with sex effects in affecting trust in other-sex interactions. It could also prove fascinating to investigate the effects of attractiveness and threat in couples in both intra- and extra-couple interactions and in homosexual male and female couples (e.g.,\textsuperscript{90}), as well as non-mating contexts like approaching new potential friends. Overall, this research may help us better understand which factors impact trust as a fundamental ingredient in intimate social relationships.
### Methods
**Participants.** We recruited a sample of 93 healthy participants (47 men, 46 women; age: $M = 22.44$, $SD = 3.85$, range: 18–34). All participants were single (i.e., not in a couple relationship\textsuperscript{91}) and attracted to the other sex (rated five or higher on a 7-point Likert scale from ‘not at all’ [1] to ‘absolutely’ [7]). Exclusion criteria were alcohol, nicotine or drug abuse, studying or having a degree in psychology or economics, current or previous history of psychiatric disorders, or insufficient fluency in the German language. All female participants took part in the experiment during their menstrual cycle’s luteal phase\textsuperscript{90,96} and were free of hormonal contraceptives. The luteal phase was determined by self-report: the earliest testing day was determined by adding half of the maximum cycle length duration, plus a 2-day buffer to the first day of menstruation, and to determine the latest testing day we added the minimal cycle length duration to the first day of menstruation (see Supplementary Material for further details). The Ethics Committee of the University of Freiburg approved this study, which was conducted according to the principles expressed in the Declaration of Helsinki.
**Procedure.** We recruited participants using flyers and bulletins. Participants had to fill out an online screening to assess exclusion criteria\textsuperscript{92}. We telephoned eligible participants to offer appointments for the experimental session, which took place in a group laboratory with up to 12 participants taking part simultaneously. Participants provided written informed consent to participate in the study and have their photo taken. For the picture
We created two sets of stimuli: one with female faces that were presented to male participants, and one with male faces presented to female participants. We strictly used neutral faces not demonstrating any emotional states. Faces were manipulated to reveal two features of low or high intensity, namely attractiveness and threat (e.g., 'high threat and low attractiveness'), resulting in four phenotypes (see Fig. 2). Faces were taken from the Basel Face Database93, as well as from pictures shot by our own photographer. Face stimuli were generated by applying a data-driven, computational approach that captured the variance in facial structure that signals specific social attributions42,94. This approach enabled us to parametrically manipulate the values of facial attractiveness and threat based on previously collected other-sex ratings. Based on those ratings, vectors were created and applied to the photographed faces with a neutral facial expression, which caused faces to have high or low values on attractiveness and high or low values threat (e.g., 'high threat' and 'low attractiveness'; also see95,96). These newly-created faces were then rated by 53 participants (20 women, 33 men, age: $M = 24.17, SD = 3.57$) in a pilot study. Afterwards, we selected the 22 distinct faces most characteristic of each phenotype, resulting in 88 faces with subtle attractiveness and threat manipulations per stimulus set so that the phenotype should not have been apparent to the participants. As required for the purpose of this experiment, all $t$-tests comparing threat and attractiveness ratings of faces with the same intensity (i.e., low vs. low or high vs. high) were not significant ($p > 0.078$), whereas all $t$-tests comparing threat and attractiveness ratings of faces with different intensity (i.e., low vs. high) were significant ($p < 0.001$; for details, see Supplementary Material).
**Trust game paradigm.** Participants took part in a slightly modified version of the trust game97,98 (for details on screen presentation durations, see Fig. 3). Participants were assigned the role of the investor, and, in each round, saw a face from the other sex's stimulus set representing the trustee. Both investor and trustee received an initial endowment to ensure that no social preference other than trust (e.g., inequality aversion, altruism) would influence the participant's decision about whether to transfer money to the trustee. Participants could then decide whether to keep their endowment, in which case both the investor and trustee received 14 MU, or to transfer their endowment. If they transferred their endowment, the trustee could either keep everything for
**Figure 2.** Drawings of representative male (left) and female stimulus set (right). There were four different phenotypes with 22 faces each revealing either low- or high-intensity ‘attractiveness’ and ‘threat’. In total, every set contained 88 faces, each generated from a unique face identity. The symbolic faces in this figure represent prototypes by which to illustrate the face phenotypes, facial symmetry codes attractiveness (asymmetric = low attractiveness), and mouth codes threat (showing teeth = high threat). Please note that this figure illustrates schematic representations of the stimulus categories for visualization purposes, and that the actual stimuli were derived from photos of real human faces exhibiting neutral expressions (i.e., displaying no teeth or other emotionally-loaded expressions; see Fig. 3B for a stimulus example).
him/herself (‘not trustworthy’), in which case the investor received 0 MU and the trustee received 60 MU, or transfer back half of it (‘trustworthy’), in which case both the investor and trustee received 30 MU. We chose a payoff structure (see Fig. 3) which triggered trust-decision rates of approximately 50% in previous studies without face stimuli99, thus enabling both the up- and down-modulation of trust decision rates by varying facial features. At the end of the study, participants received their payoff according to the following exchange ratio: 100 MU = 0.50€. Participants were told that a subgroup of participants had been randomly selected as trustees who had already made their decision whether to return money. In fact, to determine payments, we randomly drew trustee decisions from a distribution of decisions collected during our laboratory’s previous studies43. Participants learned about trustees’ decisions at the end of the experiment to avoid any influence of reciprocal or reputational considerations of previous interactions on trust behavior. This paradigm was programmed using Presentation software (Version 18.0, Neurobehavioral Systems, Inc., Berkeley, CA).
Stimuli perception paradigm. Participants rated all 88 faces for attractiveness and threat, respectively, on a 7-point Likert scale from ‘very unattractive’/’very unthreatening’ to ‘very attractive’/’very threatening’. The presentation order of the photos was randomized. In total, there were four blocks with 44 photos, respectively. At the beginning of each block, participants learned which facial feature they should rate (attractiveness or threat). Whether participants rated attractiveness or threat in block one and three was also randomized, and followed by the other feature in the subsequent block (i.e., block two and four, respectively).
Statistical analysis. All analyses were conducted with the software SPSS (27th edition). We first calculated the mean trust for each phenotype by dividing the number of decisions to trust a specific phenotype by 22, i.e., the total number of trust decisions for each phenotype. To test the influence of the facial features attractiveness and threat on mean trust, and whether there were any differences between men and women in the trust decisions, we conducted a repeated-measures ANOVA with participants’ sex (women and men) as a between-subject factor, and facial attractiveness (low vs. high) and facial threat (low vs. high) as within-subject factor. We then compared the effect sizes of the main effects facial attractiveness and facial threat to investigate any sex differences in the importance of both features. For that purpose, we transformed the $\eta^2$ effect size of each main effect to the effect size $r$ and then compared those within the sexes100,101.
The Stimuli Perception Paradigm was used to show that any differences in the trust game decisions between sexes were not due to differing attractiveness or threat perceptions of the distinct other-sex stimulus sets. We first calculated mean ratings for facial attractiveness perception and facial threat perception by averaging the ratings of the 22 faces of each phenotype. Then, we conducted two repeated-measures ANOVAs, one for the mean ratings of attractiveness perception and one for the mean ratings of threat perception as dependent variable. We included participants’ sex (women and men) as a between-subject factor, and facial attractiveness (low vs. high) and facial threat (low vs. high) as within-subject factors.
Figure 3. Modified version of the trust game. (A) Payoff structure. Participants were assigned the role of the investor. If the investor decided not to trust the trustee, both investor and trustee received 14 MUs. If the investor decided to trust, the trustee could either keep everything for him/herself (0/60) or transfer half of the points back to the investor (30/30). (B) Example trial with screen durations in milliseconds (ms). First, participants saw a blank screen for 400–600 ms, followed by fixation cross for 1000–1500 ms. Then, participants saw a photo of the trustee until they made their decision, which was then displayed for 1000–1250 ms.
References
1. Ballet, D. & Van Lange, P. A. M. Trust, conflict, and cooperation: A meta-analysis. Psychol. Bull. 139, 1090–1112 (2013).
2. Fletcher, G. I. O., Simpson, J. A. & Thomas, G. The measurement of perceived relationship quality components: A confirmatory factor analytic approach. Pers. Soc. Psychol. Bull. 26, 340–354 (2000).
3. Stirrat, M. & Perrett, D. I. Valid facial cues to cooperation and trust: Male facial width and trustworthiness. Psychol. Sci. 21, 349–354 (2010).
4. Holt-Lunstad, J., Smith, T. B. & Layton, J. B. Social relationships and mortality risk: A meta-analytic review. PLoS Med. 7, e1000316 (2010).
5. Kleinert, T. et al. The Trust Game for Couples (TGC): A new standardized paradigm to assess trust in romantic relationships. PLoS ONE 15, e0230776 (2020).
6. Rempel, J. K., Holmes, J. G. & Zanna, M. P. Trust in close relationships. J. Pers. Soc. Psychol. 89, 95–112 (1985).
7. Frith, C. D. Interacting minds—A biological basis. Science 266, 1692–1695 (1999).
8. van Wout, M. & Sanfey, A. G. Friend or foe: The effect of implicit trustworthiness judgments in social decision-making. Cognition 108, 796–803 (2008).
9. Little, A. C., Jones, B. C. & DeBruine, L. M. Facial attractiveness: Evolutionary based research. Philos. Trans. R. Soc. B Biol. Sci. 366, 1638–1659 (2011).
10. Maner, J. K. et al. Sexually selective cognition: Beauty captures the mind of the beholder. J. Pers. Soc. Psychol. 85, 1107–1120 (2003).
11. Oosterhof, N. N. & Todorov, A. The functional basis of face evaluation. Proc. Natl. Acad. Sci. 105, 11087–11092 (2008).
12. Puts, D. A., Jones, B. C. & DeBruine, L. M. Sexual selection on human faces and voices. J. Sex Res. 49, 227–243 (2012).
13. Thornhill, R. & Gangestad, S. W. Human facial beauty: Averageness, symmetry, and parasite resistance. Hum. Nat. 4, 237–269 (1993).
14. Buss, D. M. Evolutionary Psychology: The New Science of the Mind. Vol. 22, 456 (Allyn & Bacon, 1999).
15. Zuckerman, M. et al. Oxytocin changes behavior, spatio-temporal brain dynamics underlying inter-group conflict in humans. Eur. Neuropsychopharmacol. 31, 119–130 (2020).
16. Schiller, B., Baumgartner, T. & Knoch, D. Neurobiological influences of trust in romantic relationships. Front. Behav. Neurosci. 8, 458 (2015).
17. McCarty, M. M., Woolley, C. S. & Arnold, A. P. Incorporating sex as a biological variable in neuroscience: What do we gain? Nat. Rev. Neurosci. 18, 707–708 (2017).
18. Wu, Y. et al. Exogenous testosterone increases the audience effect in healthy males: Evidence for sex-specific effects on social perception. Proc. Biol. Sci. 285, 20181520 (2018).
19. Wilson, R. K. & Eckel, C. C. A social cognitive theory of altruistic giving: Behavioral experiments with children aged 3 to 8. Evol. Hum. Behav. 33, 291–308 (2012).
20. Wuttke-Linnemann, A., Nater, U. M., Ehrt, U. & Ditzen, B. Sex-specific effects of music on romantic relationships. PLoS ONE 10, e0230776 (2015).
21. Eastwick, P. W., Luchies, L. B., Finkel, E. J. & Hunt, L. L. The predictive validity of ideal partner preferences: A review and meta-analysis. Psychol. Bull. 140, 623–665 (2014).
22. Lobmaier, J. S., Schibback, U., Wirthmüller, U. & Knoch, D. The scent of attractiveness: Levels of reproductive hormones explain individual differences in women’s body odour. Proc. Biol. Sci. 285, 20181520 (2018).
23. Lucas, M. & Koff, E. How conception risk affects competition and cooperation with attractive women and men. Evol. Hum. Behav. 34, 16–22 (2013).
24. Hart, T. R., Harkness, D. D., Macintosh, A. & Williams, R. D. The evolution of the female brain: The role of sexual selection. Cons. Pol. Biol. Sci. 27, 663–620 (2013).
25. Declerck, C., Boone, C. & Emonds, G. When do people cooperate? The neuroeconomics of prosocial decision making. Brain Cogn. 81, 95–117 (2011).
26. Todorov, A., Baron, S. G. & Oosterhof, N. N. Evaluating face trustworthiness: A model based approach. Soc. Cogn. Affect. Neurosci. 3, 119–127 (2008).
27. Baumgartner, T., Heinrichs, M., Vonlanthen, A., Fischbacher, U. & Fehr, E. Oxytocin shapes the neural circuitry of trust and trust adaptation in humans. Neuron 58, 639–650 (2008).
28. Kosfeld, M., Heinrichs, M., Zak, P. J., Fischbacher, U. & Fehr, E. Oxytocin increases trust in humans. Nature 435, 673–676 (2005).
45. Schiller, B., Heinrichs, M. & Heinrichs, M. The neuroendocrinological basis of human affiliation: How oxytocin coordinates affiliation-related cognition and behavior via changing underlying brain activity. In *Routledge International Handbook of Social Neuroendocrinology* (eds Schultheiss, O. C. & Mehta, P. H.) 193–204 (Routledge, 2018).
46. Domes, G. *et al.* Effects of intranasal oxytocin on emotional face processing in women. *Psychoneuroendocrinology* **35**, 83–93 (2010).
47. Spengler, F. B. *et al.* Kinetics and dose dependency of intranasal oxytocin effects on amygdala reactivity. *Biol. Psychiatry* **82**, 885–894 (2017).
48. Ditzen, B. *et al.* Sex-specific effects of intranasal oxytocin on autonomic nervous system and emotional responses to couple conflict. *Soc. Cogn. Affect. Neurosci.* **8**, 897–902 (2013).
49. Catutti, J. E. & Beck, K. D. Anxiety vulnerability in women: a two-hit hypothesis. *Exp. Neurol.* **259**, 75–80 (2014).
50. Hampson, E., van Anders, S. M. & Mullin, L. I. A female advantage in the recognition of emotional facial expressions: Test of an evolutionary hypothesis. *Evol. Hum. Behav.* **27**, 401–416 (2006).
51. McClure, E. B. *et al.* A developmental examination of gender differences in brain engagement during evaluation of threat. *Biol. Psychiatry* **55**, 1047–1055 (2004).
52. Remes, O., Brayne, C., van der Linde, R. & Lafortune, L. A systematic review of reviews on the prevalence of anxiety disorders in adult populations. *Brain Behav.* **6**, e00497 (2016).
53. Trivers, R. L. *Parental Investment and Sexual Selection* Vol. 838 (University of Chicago Press, 1996).
54. Benenson, J. F. The development of human female competition: Allies and adversaries. *Philos. Trans. R. Soc. Lond. B. Biol. Sci.* **368**, 20130079 (2013).
55. Ein-Dor, T., Perry-Paldi, A., Hirschberger, G., Birnbaum, G. E. & Deutsch, D. Coping with mate poaching: Gender differences in detection of infidelity-related threats. *Evol. Hum. Behav.* **36**, 17–24 (2015).
56. Lindenfors, P. & Tullberg, B. S. Evolutionary aspects of aggression the importance of sexual selection. *Adv. Genet.* **75**, 7–22 (2011).
57. Nivette, A., Sutherland, A., Eissner, M. & Murray, J. Sex differences in adolescent physical aggression: Evidence from sixty-three low- and middle-income countries. *Agress. Behav.* **45**, 82–92 (2019).
58. Penton-Voak, I. S. *et al.* Menstrual cycle alters face preference. *Nature* **399**, 741–742 (1999).
59. Penton-Voak, I. S. & Perrett, D. I. Female preference for male faces changes cyclically: Further evidence. *Evol. Hum. Behav.* **21**, 39–48 (2000).
60. Kirschbaum, C., Kudi, K. M., Gaab, J., Schommer, N. C. & Hellhammer, D. H. Impact of gender, menstrual cycle phase, and oral contraceptives on the activity of the hypothalamus-pituitary-adrenal axis. *Psychosom. Med.* **61**, 154–162 (1999).
61. Guapo, V. G. *et al.* Effects of sex hormonal levels and phases of the menstrual cycle in the processing of emotional faces. *Psychoneuroendocrinology* **34**, 1087–1094 (2009).
62. Camerer, C. F. *Behavioral Game Theory: Experiments in Strategic Interaction* (Princeton University Press, 2011).
63. Manski, C. F. Economic analysis of social interactions. *J. Econ. Perspect.* **14**, 115–136 (2000).
64. Camerer, C. F. & Fehr, E. When does ‘economic man’ dominate social behavior? *Science* **311**, 47–52 (2006).
65. Vick, S.-J., Waller, B. M., Parr, L. A., Smith Pasqualini, M. C. & Bard, K. A. A cross-species comparison of facial morphology and movement in humans and chimpanzees using the facial action coding system (FACS). *J. Nonverbal Behav.* **31**, 1–20 (2007).
66. Bjorklund, D. F. & Shackelford, T. K. Differences in parental investment contribute to important differences between men and women. *Carr. Dir. Psychol. Sci.* **8**, 86–89 (1999).
67. Buss, D. M. The evolution of human mating. *Acta Psychol. Sin.* **39**, 502–512 (2007).
68. Todd, P. M., Penke, L., Fosso, B. & Lenton, A. D. Different cognitive processes underlie human mate choices and mate preferences. *Proc. Natl. Acad. Sci.* **104**, 15011–15016 (2007).
69. Price, M. E., Brown, S., Dukes, A. & Kang, J. Bodily attractiveness and egalitarianism are negatively related in males. *Evol. Psychol.* **13**, 147470491501300100 (2015).
70. Shinada, M. & Yamagishi, T. Physical attractiveness and cooperation in a prisoner's dilemma game. *Evol. Hum. Behav.* **35**, 451–455 (2014).
71. Todorov, A., Olova, C. Y., Dotsch, R. & Mende-Siedlecki, P. Social attributions from faces: Determinants, consequences, accuracy, and functional significance. *Annu. Rev. Psychol.* **66**, 519–545 (2015).
72. Hawkins, S. M. & Matzuk, M. M. The menstrual cycle: Basic biology. *Annu. N. Y. Acad. Sci.* **1135**, 10–18 (2008).
73. Mihm, M., Gangody, S. & Muttukrishna, S. The normal menstrual cycle in women. *Anim. Reprod. Sci.* **124**, 229–236 (2011).
74. Conway, C. A. *et al.* Salience of emotional displays of danger and contagion in faces is enhanced when progesterone levels are raised. *Horm. Behav.* **51**, 202–206 (2007).
75. Pearson, R. & Lewis, M. R. Fear recognition across the menstrual cycle. *Horm. Behav.* **47**, 267–271 (2005).
76. Hahn-Holbrook, J. & Holbrook, C. The social neuroendocrinology of pregnancy and breastfeeding in mothers (and others). In *Routledge International Handbook of Social Neuroendocrinology* (eds Schultheiss, O. C. & Mehta, P. H.) (Routledge, 2018).
77. Grebe, N. M., Emery Thompson, P. & Gangestad, S. W. Hormonal predictors of women’s extra-pair vs in-pair sexual attraction in natural cycles: Implications for extended sexuality. *Horm. Behav.* **78**, 211–219 (2016).
78. Roney, J. R. Functional roles of gonadal hormones in human pair bonding and sexuality. In *Routledge Int. Handbk. Soc. Neuroen- drocrinol.* 239–255 (Routledge, 2018).
79. Thornhill, R. & Gangestad, S. G. *The Evolutionary Biology of Human Female Sexuality* Vol. 38 (Oxford University Press, 2008).
80. Ball, A. *et al.* Variability in ratings of trustworthyworthiness across the menstrual cycle. *Biol. Psychol.* **93**, 52–57 (2013).
81. Oh, D., Dotsch, R., Porter, J. & Todorov, A. Gender biases in impressions from faces: Empirical studies and computational models. *J. Exp. Psychol. Gen.* **149**, 323–342 (2020).
82. McNamara, J. M. & Wolf, M. Sexual conflict over parental care promotes the evolution of sex differences in care and the ability to care. *Proc. Biol. Sci.* **282**, 20142752 (2015).
83. Gildersleeve, K., Haselton, M. G. & Fales, M. R. Do women's mate preferences change across the ovulatory cycle? A meta-analytic review. *Psychol. Bull.* **140**, 1205–1259 (2014).
84. Wood, W., Kressel, L., Joshi, P. D. & Louie, B. Meta-analysis of menstrual cycle effects on women's mate preferences. *Emot. Rev.* **6**, 229–249 (2014).
85. Spencer, S. I., Steele, C. M. & Quinn, D. M. Stereotype threat and women's math performance. *J. Exp. Soc. Psychol.* **35**, 4–28 (1999).
86. Ridgeway, C. L. & Correll, S. J. Unpacking the gender system: A theoretical perspective on gender beliefs and social relations. *Gend. Soc.* **18**, 510–531 (2004).
87. Evans, A. Interpersonal trust scale. In *Encyclopedia of Personality and Individual Differences* (eds Zeigler-Hill, V. & Shackelford, T. K.) 1–2 (Springer, 2016).
88. Ainsworth, M. S. & Bowlby, J. An ethological approach to personality development. *Am. Psychol.* **46**, 333–341 (1991).
89. Mikulincer, M. Attachment working models and the sense of trust: An exploration of interaction goals and affect regulation. *J. Pers. Soc. Psychol.* **74**, 1209–1224 (1998).
90. Appleby, P. R., Miller, L. C. & Rothsman, S. The paradox of trust for male couples: When risking is a part of loving. *Pers. Relatsh.* **6**, 81–93 (1999).
91. Little, A. C., Jones, B. C., Penton-Voak, I. S., Burt, D. M. & Perrett, D. I. Partnership status and the temporal context of relationships influence human female preferences for sexual dimorphism in male face shape. *Proc. R. Soc. Lond. B Biol. Sci.* **269**, 1095–1100 (2002).
92. Schiller, B., Tönsing, D., Kleintert, T., Böhm, R. & Heinrichs, M. Effects of the COVID-19 pandemic nationwide lockdown on mental health, environmental concern, and prejudice against other social groups. *Environ. Behav.*, 1–12. https://doi.org/10.1177/001391652110365211036991 (2018).
93. Walker, M., Schönborn, S., Greifeneder, R. & Vetter, T. The Basel face database: A validated set of photographs reflecting systematic differences in big two and big five personality dimensions. *PLoS ONE* **13**, e0193190 (2018).
94. Walker, M. & Vetter, T. Changing the personality of a face: Perceived big two and big five personality factors modeled in real photographs. *J. Pers. Soc. Psychol.* **108**, 609–624 (2016).
95. Rudert, S. C., Reutner, L., Greifeneder, R. & Walker, M. Faced with exclusion: Perceived facial warmth and competence influence moral judgments of social exclusion. *J. Exp. Soc. Psychol.* **68**, 101–112 (2017).
96. Todorov, A., Dotsch, R., Porter, J. M., Oosterhof, N. N. & Falvello, V. R. Validation of data-driven computational models of social perception of faces. *Emotion* **13**, 724–738 (2013).
97. Berg, J., Dickhaut, J. & McCabe, K. Trust, reciprocity, and social history. *Games Econ. Behav.* **10**, 122–142 (1995).
98. Kumar, A., Capraro, V. & Perc, M. The evolution of trust and trustworthiness. *J. R. Soc. Interface* **17**, 20200491 (2020).
99. von Dawans, B., Fischbacher, U., Kirschbaum, C., Fehr, E. & Heinrichs, M. The social dimension of stress reactivity: Acute stress increases prosocial behavior in humans. *Psychol. Sci.* **23**, 651–660 (2012).
100. Cohen, J. *Statistical Power Analysis for the Behavioral Sciences* (Academic Press, 2013).
101. Lenhard, W. & Lenhard, A. *Computation of Effect Sizes* (Psychometrica, 2016).
**Acknowledgements**
This study was supported by the German Research Foundation (Grant "Effects of oxytocin on socio-cognitive processes: new insights from spatio-temporal EEG analyses", SCHI 1311/3-1, to Bastian Schiller and Markus Heinrichs).
**Author contributions**
B.S., J.B., M.H., and M.W. conceived and designed the study. B.S. and J.B. performed research. B.S., J.B., M.H., and M.W. analyzed the data and wrote the manuscript.
**Funding**
Open Access funding enabled and organized by Projekt DEAL.
**Competing interests**
The authors declare no competing interests.
**Additional information**
**Supplementary Information** The online version contains supplementary material available at https://doi.org/10.1038/s41598-021-01775-5.
**Correspondence** and requests for materials should be addressed to B.S.
**Reprints and permissions information** is available at www.nature.com/reprints.
**Publisher’s note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
© The Author(s) 2021 | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4602,
1
],
[
4602,
11947,
2
],
[
11947,
15317,
3
],
[
15317,
22787,
4
],
[
22787,
26326,
5
],
[
26326,
30521,
6
],
[
30521,
34791,
7
],
[
34791,
42577,
8
],
[
42577,
45714,
9
]
]
} |
78141e6a1e5f265de38ebd6611c8e1afe0acfab9 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 15,
"total-fallback-pages": 0,
"total-input-tokens": 47815,
"total-output-tokens": 17245,
"fieldofstudy": [
"Business"
]
} | “Earnings management and impression management: European evidence”
AUTHORS
Tiago Goncalves
Cristina Gaio
Pedro Ramos
ARTICLE INFO
Tiago Goncalves, Cristina Gaio and Pedro Ramos (2022). Earnings management and impression management: European evidence. Problems and Perspectives in Management, 20(1), 459-472. doi:10.21511/ppm.20(1).2022.37
DOI
http://dx.doi.org/10.21511/ppm.20(1).2022.37
RELEASED ON
Friday, 01 April 2022
RECEIVED ON
Wednesday, 29 December 2021
ACCEPTED ON
Thursday, 24 March 2022
LICENSE
This work is licensed under a Creative Commons Attribution 4.0 International License
JOURNAL
"Problems and Perspectives in Management"
ISSN PRINT
1727-7051
ISSN ONLINE
1810-5467
PUBLISHER
LLC “Consulting Publishing Company “Business Perspectives”
FOUNDER
LLC “Consulting Publishing Company “Business Perspectives”
NUMBER OF REFERENCES
56
NUMBER OF FIGURES
2
NUMBER OF TABLES
4
© The author(s) 2022. This publication is an open access article.
**Abstract**
This study explores the relationship between Earnings Management and Impression Management in the context of some European listed companies. The analysis focuses on the readability of annual reports, measured by the file size. Earnings management is assessed using the modified Jones model. The sample consists of 2,953 listed companies from 17 industries of 24 European countries between 2012 and 2018 resulting in 13,020 firm-year observations. It has been found that one standard deviation increase in financial reports file size increases discretionary accruals in around 4%. These results are robust across different sample specifications in terms of firms’ size, industry and country. The findings show that increased intensity in the use of discretionary accruals is obfuscated by the disclosure of less readable annual reports, implying that Earnings Management and Impression Management are used complementarily. The conclusions have impact both for investment management and for policy, preventing inefficient allocation of capital budgeting and providing additional information that improves regulation on financial reporting transparency.
**Keywords**
discretionary accruals, financial reporting quality, obfuscation hypothesis, readability of annual reports
**JEL Classification**
G30, M21, M41, O52
**INTRODUCTION**
The need for information and transparent communication gives corporate media the status of potential vehicle of Impression Management (IM) that managers can use to manage the perceptions that the public builds about the company (Clatworthy & Jones, 2006). In fact, the literature has studied managers’ communications from the perspective of IM as an attempt to obfuscate or reinforce information (Merkl-Davies & Brennan, 2007).
Empirical research on information obfuscation in financial reports has focused on the readability of the narratives disclosed by managers. Bloomfield (2008) suggests two alternative explanations for a positive relationship between the readability of annual reports and the level of reported earnings. The first is that the decreased readability of annual reports is an attempt by managers to obfuscate results, a practice included in the concept of IM (Merkl-Davies & Brennan, 2007). The second one is that bad news is just inherently more difficult to communicate and is contextualized as ontological theory. Ajina et al. (2016) and Lo et al. (2017) present evidence of management opportunism and they report a negative relationship between earnings management (EM) practice and narrative readability.
As vehicles of communication to external users, annual reports are subject to both IM and EM. However, the literature that explores the association between EM and IM is recent and, therefore, still scarce. Thus, this study evaluates the association between EM practices and the readability of annual reports in the context of European listed companies.
1. LITERATURE REVIEW
Every year (or more frequently), managers release financial reports presenting the economic and financial performance of the companies. The report consists of the Financial Statements and discretionary information that is intended to explain and provide additional information regarding the Financial Statements. The Financial Statements encompass quantitative information and are presented in accordance with mandatory guidelines and standards, but discretionary information may be presented in the form of narratives, photographs, and graphs and is susceptible to being used as a tool to obfuscate a company’s economic reality (Courtis, 1995). However, both Financial Statements and discretionary information are subject to judgement by managers, which gives them a margin to manage information for their own benefit despite the various levels of regulation (Gonçalves, 2022; Godfrey et al., 2003; Healy & Wahlen, 1999). In fact, although annual reports are considered to be a means of conveying information that enhances the decision-making process of their users, a more skeptical perspective has emerged that considers them to be potential vehicles for the disclosure of biased information (Gonçalves et al., 2022; Merkl-Davies & Brennan, 2007).
Research on discretionary information presents two schools of thought: The first is the incremental information school that fits into an informational perspective, i.e., it assumes that the disclosure of discretionary information aims to overcome the barrier of information asymmetries providing complementary and additional information and having as ultimate consequence the reduction of the cost of capital (Baginski et al., 2000). The second is the IM school that considers the disclosure of discretionary information to be a way of practicing opportunistic acts to satisfy the interests of the managers thus increasing information asymmetry between internal and external agents to the company (Aerts, 2005; Godfrey et al., 2003).
Research on EM also presents two perspectives similar to those of discretionary information. The first one is the information perspective equivalent to the incremental information approach whereby managers use accounting discretion to provide private and useful information that reveals their future expectations about the company (Hollhausen & Leftwich, 1983). The second is an opportunistic perspective that assumes the use of accounting discretion as a mean for managers to pursue their own interests (Gonçalves et al., 2022; Healy, 1985).
Opportunistic EM is well-documented in the literature. EM occurs when managers use judgment in Financial Statements and in structuring operations to alter Financial Statements to “fool” some stakeholders about the economic performance of the company, influence the contractual results (Healy & Wahlen, 1999), or to obtain some private gain (Schipper, 1989).
1.1. Impression management
The term “Impression Management” has emerged in the psychology literature (Schlenker, 1980). Later, it was defined as the process through which an individual seeks to obtain control over the impression that others have about himself (Leary & Kowalski, 1990). In the context of accounting disclosure, IM is effective through the selection of the content and the form of the disclosed information to influence the interpretation of the results by the users of the information (Neu, 1991). The study of IM has been approached via four perspectives: psychological, economic, sociological, and critical. In the literature, the psychological (based on attribution theory) and the economic perspectives (explored in the context of the agency theory (Merkl-Davies & Brennan, 2007) predominate.
Under attribution theory, IM is considered to be an opportunistic practice resulting from a cognitive process in which an individual tries to collect
credit for success and denies responsibility for failure (self-serving bias) (Knee & Zuckerman, 1996). In the context of financial reporting, attribution is approached from an egocentric perspective that has been consistently observed (Bettman & Weitz, 1983; Clapham & Schwenk, 1991; Salancik & Meindl, 1984; Wagner & Gooding, 1997). This means that managers tend to attribute responsibility for good results to themselves or to internal factors (e.g., strategy, management decisions, human resources, know-how, product/service quality) and responsibility for bad results to external factors (e.g., economic environment, inflation, political action, exchange rate fluctuation, natural disasters) (Aerts, 2001; Aerts & Cheng, 2011; Clatworthy & Jones, 2003). Attribution theory focuses on the analysis of the actions and events presented as justification for financial performance (Brennan & Merkl-Davies, 2013) assuming that managers adopt attribution behavior consciously, although research in this area is not conclusive (Clatworthy & Jones, 2006; Leary & Kowalski, 1990; Schlenker, 1980).
Under agency theory, IM aims to intentionally bias information reporting (reporting bias) (Bowen et al., 2005) and may have several purposes, including maximization of the managers’ remuneration package with special relevance in scenarios that include stock options (Rutherford, 2003; Courtis, 2004a). The agency cost associated with IM consists of the inefficient allocation of capital as observed in most situations that fall under this theory (Davidson et al., 2004; Jensen & Meckling, 1976; Merkl-Davies & Brennan, 2007).
From the IM perspective, analysis in the context of agency theory focuses on the obfuscation of results either by covering up the results that did not meet expectations or by emphasizing the results that did meet or exceeded expectations (Gioia et al., 2000).
### 1.2. Obfuscation hypothesis
Obfuscation is a form of writing or presenting information that masks the content of a message. Information can be obfuscated by deliberately disseminating an opaque message or concealing undesirable facts and events that seek to mitigate negative reactions (Courtis, 2004a). Various techniques can be used to obfuscate information. Li (2008) reported that companies with lower earnings results tend to issue annual reports with longer and more complex narratives. Aerts and Zhang (2014) found a causal relationship between accruals earnings management and intensity of performance explanation. Hyland (1998) argued that the section of the annual reports that contain a Chief Executive Officer (CEO) message can be the subject of rhetorical discourse using specific linguistic terms that convey an idea of competence, reliability, authority, and honesty about the CEO. Clatworthy and Jones (2001) found that the introduction to the CEO’s communication (which includes a reference to the year’s results) tends to be easier to read than the rest of the communication (which presents passages about the problems facing the company). Bowen et al. (2005) published evidence for the intention to present good news before bad news. The connotation attributed to the narrative as offering additional information to assist in forecasting future cash flows has also been shown to be an element of obfuscation (Feldman et al., 2010; Schleicher & Walker, 2010). Other ways of obfuscation include managing the visual impression, e.g., by highlighting parts of the text (Brennan et al., 2009) through the choice of color in reports and releases (Courtis, 2004b) or even by using linguistic morphology techniques such as the use of repetition to reinforce certain contents (Davison, 2008).
### 1.3. Impression management and earnings management
As vehicles of communication to external users, annual reports are subject to both IM and EM. EM arises in the preparation of the Financial Statements, while IM occurs in the preparation of the remaining components of the annual reports (Neu et al., 1998). IM and EM are different processes of perception management and are determined by different factors and directed to different audiences but are likely to occur simultaneously (Guillamón-Saorin & Osma, 2010). Thus, IM can integrate the perception management strategy as a complement or a substitute for the EM. In the context of graphs, Godfrey et al. (2003) found that one year after the change of CEO, companies
http://dx.doi.org/10.21511/ppm.20(1).2022.37
tend to practice upward EM and complement this practice with a presentation in the annual report of graphs with the key indicators that are most favorable to the company’s performance. Aerts and Cheng (2011) also verified a complementary relationship but this time with EM being practiced through attribution behavior to attract subscribers for IPOs.
As far as the readability of financial documents is concerned, the obfuscation hypothesis suggests that when there is bad news to disclose, the preparers of financial information tend to reduce the clarity of reports making them less transparent (Rutherford, 2003). At the level of annual reports, Li (2008) found a positive and significant association between the persistence of results and the readability of narratives presenting statistical evidence that managers resort to a greater number of words and more complex words when they have less persistent results to disclose.
In terms of EM, Ajina et al. (2016) found a negative association between narrative readability and EM intensity. Lo et al. (2017) observed that companies that more likely managed earnings have a more complex Management Discussion and Analysis (M.D.&A.) section. Importantly, Ajina et al. (2016) investigated the entire annual report, and Lo et al. (2017) focused on the M.D.&A. section; Li (2008) presented results for both and found a strong positive and significant correlation between the readability of the M.D.&A. and the readability of the entire annual report.
Since the literature that studies the association between EM and IM is recent and, therefore, still relatively unexplored, this study evaluates the association between EM practices, through discretionary accruals, and the readability of annual reports in a context less studied in the literature: European listed companies.
Thus, based on previous literature and on the Obfuscation Hypothesis, this study aims to analyze the complementary relationship between EM and IM and test if the readability of the annual report is associated with the level of discretionary accruals presented by a company.
2. METHOD
2.1. Data and sample
Data were extracted from Bureau Van Dijk’s Amadeus database. All listed companies in the Eurozone (EU28) were selected, excluding companies belonging to the financial and public administration sectors due to accounting and regulatory specificities (Ajina et al., 2016; Lo et al., 2017; Gonçalves et al., 2020). All companies with insufficient data availability for the calculation of the EM measure and/or no submission of the annual report in the database were excluded, as well as companies from countries and industries with fewer than 8 observations. Finally, variables are winsorized at 1% and 99% to control for outliers.
The final sample is composed of 2,953 listed companies from 17 industries of 24 European countries. The period of analysis corresponds to 7 years, between 2012 and 2018, resulting in 13,020 firm-year observations. More than half of the sample are companies based in the United Kingdom and France with a representativeness of 29.99% and 18.92%, respectively, followed by Germany (12.51%) (results not tabulated). Two industries predominate: M. Professional, scientific, and technical activities (27.56%) and C. Manufacturing (24.85%) (results not tabulated).
2.2. Measuring the readability of annual reports
The Fog Index is a widely used indicator to quantify the readability of annual report narratives. However, it has been subject to several criticisms. The Fog Index is an indicator composed of a linear combination of average sentence length and proportion of complex words built to assess any type of prose. Loughran and McDonald (2014), among others, argue that the Fog Index is not appropriate for measuring the readability of financial documents. In fact, the identification of sentences is not very effective, given that financial documents present lists, epigraphs, peculiar narrative structures, abbreviations, and a set of other particularities that make it difficult to identify (by computer) the punctuation that identifies the beginning and the end of each sentence. Complex words
are frequently used in accounting narratives, and the Fog Index considers complex words to be all English words composed of three or more syllables. Loughran and McDonald (2014) note that words such as company, corporation, operations, and management are common in financial reports and do not test the ability of the readership. Therefore, Loughran and McDonald (2014) suggest using the size of the electronic file as an alternative to the Fog Index to quantify the readability of financial documents.
Dale and Chall’s (1948) definition of readability includes all the elements in a printed document that affect its understanding. This definition is considered by Tekfi (2007) as the classic definition, as well as by DuBay (2007) as the most comprehensive. This definition allows the use of electronic file size as a metric of financial report readability to be extended to annual reports as elements such as charts and images.
Discretionary information is voluntary and will be disclosed under two scenarios. The first is if it is demanded a priori by investors, a scenario in which companies will be incentivized to disclose the same amount of information. It is expected that annual reports will not have significantly different electronic file sizes. The second is because managers intend to hide or obscure any reality, a scenario in which significant differences in electronic file sizes will be expected because the content and form of annual reports will have to be selected with a different purpose than serving investors with the information that they want.
Thus, the additional content voluntarily disclosed in annual reports will also have a role to play in obfuscating bad news as argued by Loughran and McDonald (2014). This helps determine the readability of annual reports.
This study focuses on the readability of annual reports considering not only the accounting narratives but all disclosed elements as potential obfuscation factors. The amount of information disclosed is analyzed following the line of Guay et al. (2016) who suggest that the costs associated with processing long and complex documents are assumed to be high, i.e., they might be more difficult to read and understand. Thus, following Loughran and McDonald (2014) and Guay et al. (2016), this study uses electronic file size as a measure of annual report readability.
2.3. Measuring earnings management
To capture the practice of EM, the model of Jones (1991) modified by Dechow et al. (1995) and by Kothari et al. (2005) is used as follows:
\[
\frac{TAcc_{i,t}}{TA_{i,t-1}} = \beta_0 + \beta_1 \frac{1}{TA_{i,t-1}} +
\beta_2 \frac{\Delta REV_{i,t} - \Delta AR_{i,t}}{TA_{i,t-1}} +
\beta_3 \frac{PPE_{i,t}}{TA_{i,t-1}} + \beta_4 ROA_{i,t} + \epsilon_{i,t},
\]
where, \(TAcc_{i,t}\) is total accruals of firm \(i\) in year \(t\); \(\Delta REV_{i,t}\) is change in sales of firm \(i\) from year \(t-1\) to year \(t\); \(\Delta AR_{i,t}\) is change in accounts receivable of firm \(i\) from year \(t-1\) to year \(t\); \(PPE_{i,t}\) is property, plant and equipment of firm \(i\) in year \(t\); \(ROA_{i,t}\) is return on assets of firm \(i\) in year \(t\) as the ratio of net income to assets; and \(TA_{i,t}\) is total assets of firm \(i\) in year \(t - 1\). All variables are divided by total assets at the beginning of the year to reduce the presence of heteroscedasticity in the residuals. These metrics are estimated for each industry (Gonçalves et al., 2021).
Total accruals are computed using the balance sheet approach as follows:
\[
TA_{i,t} = \Delta CA_{i,t} - \Delta CL_{i,t} -
-\Delta Cash_{i,t} + \Delta Debtst_{i,t} - Dep_{i,t},
\]
where, \(\Delta CA_{i,t}\) is change in current assets of company \(i\) from year \(t - 1\) to year \(t\); \(\Delta CL_{i,t}\) is change in current liabilities of company \(i\) from year \(t - 1\) to year \(t\); \(\Delta Cash_{i,t}\) is change in cash and cash equivalents of firm \(i\) from year \(t - 1\) to year \(t\); \(\Delta Debtst_{i,t}\) is change in short-term debt of firm \(i\) from year \(t - 1\) to year \(t\); and \(Dep_{i,t}\) is depreciation and amortization of firm \(i\) in year \(t\).
The direction of EM (upward or downward) is given by the value of the errors \(\epsilon_{i,t}\) from equation (1), and the intensity of EM is revealed by the absolute value of these errors \(|\epsilon_{i,t}|\).
2.4. Empirical model
To study the association between IM ad EM, the following model was developed:
\[
\ln \text{FileSize}_{it} = \beta_0 + \beta_1 \text{EM}_{it} + \\
+ \beta_2 \ln \text{Size}_{it} + \beta_3 \text{MTB}_{it} + \beta_4 \text{FirmAge}_{it} + \\
+ \beta_5 \text{SpecItems}_{it} + \beta_6 \text{EarnVol}_{it} + \\
+ \beta_7 \text{RetVol}_{it} + \beta_8 \ln \text{Nitems}_{it} + \\
+ \Sigma \text{Industry}_{it} + \Sigma \text{Country}_{it} + \Sigma \text{Year}_{it} + \epsilon_{it},
\]
where, \(\ln \text{FileSize}_{it}\) represents the natural logarithm of the size of the electronic file of the annual report corresponding to each firm-year observation in kilobytes (KB). Whenever a company has submitted more than one annual report per reporting period, then the electronic file size for that reporting period was assumed to be the value corresponding to the largest amongst the annual reports submitted during that same period. This choice does not ignore any element that has been disclosed and is consistent with Dale and Chal’s (1948) theorization arguing that all elements included in the annual report increase the readability of its understanding. A higher value of \(\ln \text{FileSize}\) implies a lower readability.
The independent variable of interest \(\text{EM}_{it}\) represents EM by discretionary accruals and takes the designation \(\text{ABS_DACC}_{it}\) when the focus of the analysis is on the intensity of EM, and the designation \(\text{DACC}_{it}\) when the focus is on the direction of EM (upward or downward).
Based on prior literature (Li, 2008; Lo et al., 2017; Gonçalves et al., 2019), the following control variables are used: firm size (\(\ln \text{Size}\)), growth opportunities (\(\text{MTB}\)), firm age (\(\text{FirmAge}\)), special items (\(\text{SpecItems}\)), earnings volatility (\(\text{EarnVol}\)), stock returns volatility (\(\text{RetVol}\)), and firm complexity (\(\ln \text{Nitems}\)) (see the Appendix A for more details). The model also controls for industry, country, and year fixed effects to account for sector-specific reporting requirements, institutional factors differences, and year-specific effects on the electronic file size of annual reports, respectively. The regression model was estimated by the pooled least squares method (Pooled OLS). Like Li (2008) and Lo et al. (2017), errors are clustered robust by industry in order to estimate the standard deviations, because the readability of annual reports may be correlated across industries.
3. RESULTS
3.1. Descriptive statistics
Table 1 reports descriptive statistics. The average electronic file size of the annual reports is 3,573.85 KB (\(e^{8.1814}\)). The electronic files considered in the sample present a coefficient of variation for their size of 1.03 with the largest electronic file being 17.36 times larger than the average electronic file and the smallest electronic file being 32.19 times smaller than the average electronic file.
The average of discretionary accruals is positive suggesting that, on average, the companies in the sample manage earnings upwards. The average company in the sample has a market value of equity of 145,509,987 thousand euros (\(e^{11.888}\)), a market-to-book ratio of 1.6377, and an age of approximately 35 years. Extraordinary events occurred in 28.49% of the observations of the sample. The average
average volatility of earnings and stock returns are 4.21% and 10.07%, respectively. Finally, companies, on average, disclose 33 items (e^{3.4944}) out of the 37 items listed by the Global Standard Format corresponding to the Statement of Financial Position and the Income Statement.
The average electronic file size by country and by industry are presented in Figure 1 and Figure 2, respectively. Countries from Central Eastern Europe and Southern Europe are predominant among the countries with the largest average electronic file. The countries of Northern Europe and Western Europe are the ones with the lowest average electronic file. The exceptions are Luxembourg and Latvia, which are among the countries with the lowest representation in the sample along with Greece and Slovenia. These are possibly due to factors inherent to the country itself.
In terms of industries, the categories D. Electricity, gas, steam, and air conditioning supply and F. Construction have the largest average electronic file sizes, and categories P. Education and A.
Agriculture, forestry, and fishing have the lowest (the industry classification is based on NACERev.2.).
Correlation results show a negative and significant correlation between the IM measure and the absolute value of discretionary accruals, as well as a positive and significant correlation with discretionary accruals. The highest correlation coefficient is 0.5104 between \( \ln \text{Nitems} \) and \( \text{SpecItems} \), suggesting that there are no multicollinearity issues, which is confirmed by the Variance Inflation Factors (VIF) below 10 for all variables (not tabulated).
### 3.2. Regression results
Table 2, Panel A, presents the results of the regression model considering as independent variable \( \text{ABS}_{\text{DACC}} \) (Column (1)) or \( \text{DACC} \) (Column (2)), in order to study the association between IM and both intensity and direction of EM.
Results show a positive and statistically significant coefficient (p-value < 0.05) of the \( \text{ABS}_{\text{DACC}} \) variable, indicating that lower levels of EM are associated with greater readability of annual reports, supporting the study hypothesis.
In terms of EM direction (upward and downward), the results do not provide any evidence of an association between \( \ln \text{FileSize} \) and the \( \text{DACC} \). Indeed, the coefficient, although negative, does not reveal statistical significance. To extend the analysis and to circumvent the suspicion of a non-linear relationship, two additional models were estimated: the association between upward and downward EM and the readability of annual reports separately. Table 2, Panel B, presents the results for the sample of companies with \( \text{DACC} > 0 \) in column (3), and for the sample of companies with \( \text{DACC} < 0 \) in column (4).
The coefficient on \( \text{DACC} \) is positive in both regressions although not statistically significant. Since the non-linearity of the relationship between the variables may be at the origin of this result, a test was carried out for the equality of means of the size of the electronic file of annual reports between the two subsamples. The result of the test (not tabulated) shows a significant difference (p-value < 0.01) between the averages of the two groups, suggesting that upwardly oriented companies present a higher average and disclose less readable annual reports than downwardly oriented companies.
### Table 2. Relationship between earnings management and impression management
| Variables | Panel A | Panel B |
|---------------|---------|---------|
| | (1) | (2) | (3) | (4) |
| \( \text{ABS}_{\text{DACC}} \) | 0.0380** | – | – | – |
| | (2.487) | – | – | – |
| \( \text{DACC} \) | – | –0.0340 | 0.0093 | 0.0734 |
| | – | (–1.127)| (0.248) | (1.171) |
| \( \ln \text{Size} \) | 0.1513***| 0.0000***| 0.1572***| 0.1458***|
| | (21.935)| (21.534)| (18.227)| (35.247)|
| \( \text{MTB} \) | –0.0368***| –0.0356***| –0.0414***| –0.0309***|
| | (–3.836)| (–3.765)| (–3.056)| (–3.622)|
| \( \text{FirmAge} \) | 0.0001 | 0.0001 | 0.0000 | 0.0004 |
| | (0.304) | (0.306) | (0.028) | (0.669) |
| \( \text{SpecItems} \) | 0.0179 | 0.0173 | 0.0085 | 0.0368 |
| | (0.652) | (0.633) | (0.330) | (0.819) |
| \( \text{EarnVol} \) | –0.3613***| –0.3310***| –0.1724 | –0.5795 |
| | (–5.015)| (–4.343)| (–1.477)| (–3.957)|
| \( \text{RetVol} \) | 0.1833* | 0.1845* | 0.3277**| 0.0350 |
| | (1.929) | (1.926) | (2.277) | (0.373) |
| \( \ln \text{Nitems} \) | 0.5578 | 0.5533 | 0.6977 | 0.3054 |
| | (1.597) | (1.588) | (1.534) | (0.628) |
| \( \text{Observations} \) | 13.020 | 13.020 | 8.072 | 4.948 |
| \( \text{Adjusted } R^2 \) | 0.2416 | 0.2416 | 0.2494 | 0.2374 |
Note: Panel A shows the results for the full sample. Panel B shows the results for companies with \( \text{DACC} > 0 \) (column (3)) and \( \text{DACC} < 0 \) (column (4)). t-statistics are in parentheses, *** p < 0.01, ** p < 0.05, * p < 0.1.
3.3. Robustness analysis
To test the robustness of the main results, several analyses were performed: alternative sample composition; the influence of company size; and the influence of reporting an operating profit or loss.
Indeed, more than half of the sample is composed by firms from only three countries (United Kingdom, France and Germany) concentrated in three industries (M. Professional, scientific and technical activities; C. Manufacturing; and J. Information and communication). Table 3, Panels A and B, presents the results obtained without firms from these countries (columns (1) and (2)) and these industries (columns (3) and (4)).
Results for both EM intensity and EM direction are similar to those obtained in the main analysis. The exclusion of the three most representative countries and the three most represented industries does not alter the statistical significance of the complementary relationship between EM and IM in terms of intensity, suggesting that higher levels of earnings management are associated with less readable annual reports.
Prior results suggest an important role of a company’s size in explaining the readability of annual reports. Since the sample comprises companies with significantly different sizes, the sample was split into two subsamples: small and medium entities (SMEs) and large entities (LEs). Companies with total assets below and above 43,000,000 euros (European Commission Recommendation, 2003) are considered SMEs and LEs, respectively. Table 3, Panel C, reports the results for SMEs in columns (5) and (6) and for LEs in columns (7) and (8).
Positive coefficients of $\text{ABS}_\text{DACC}$ suggest a decrease in the readability of annual reports as the intensity in the use of discretionary accruals increases. However, only the SMEs group has a significant coefficient. The absence of statistical significance in the LEs sample may be due to
Table 3. Influence of predominant countries and industries, company size and reporting operating profit or loss
| Variables | Panel A | Panel B | Panel C | Panel D |
|--------------------|---------------|---------------|---------------|---------------|
| | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
| $\text{ABS}_\text{DACC}$ | 0.1021** | – | 0.0635** | – | 0.1108** | – | 0.0040 | – | 0.0301* | – |
| | (2.407) | – | (2.422) | – | (2.805) | – | (0.108) | – | (2.027) | – |
| $\text{DACC}$ | – | –0.0512 | – | –0.0611 | – | –0.0691 | – | –0.0206 | – | –0.0132 |
| | – | (–0.513) | – | (–1.115) | – | (–1.226) | – | (–0.784) | – | (–0.512) |
| Loss | – | – | – | – | – | – | – | – | 0.0472* | 0.0457** |
| $\ln\text{Size}$ | 0.1069*** | 0.1062*** | 0.1510*** | 0.1512*** | 0.1164*** | 0.1156*** | 0.1347*** | 0.1348*** | 0.1539*** | 0.1537*** |
| | (13.892) | (13.162) | (12.695) | (12.780) | (3.870) | (3.996) | (14.536) | (14.419) | (20.638) | (20.713) |
| $\text{MTB}$ | 0.0250*** | –0.0209*** | –0.0402* | –0.0385* | 0.0082 | 0.0113 | –0.0545* | –0.0539*** | –0.0378*** | –0.0368*** |
| | (–3.807) | (–3.410) | (–1.908) | (–1.802) | (0.557) | (0.713) | (–4.556) | (–4.428) | (–4.042) | (–3.920) |
| $\text{FirmAge}$ | 0.0001 | 0.0001 | –0.0002 | –0.0002 | –0.0021** | –0.0021* | 0.0005* | 0.0005* | –0.0001 | 0.0005 |
| | (0.161) | (0.165) | (–0.282) | (–0.319) | (–2.184) | (–2.107) | (1.996) | (2.016) | (0.381) | (0.371) |
| $\text{SpecItems}$| 0.0901** | 0.0888* | 0.0576 | 0.0563 | 0.1185* | 0.1162* | –0.0126 | –0.0127 | 0.0174 | 0.0170 |
| | (2.146) | (2.058) | (1.557) | (1.508) | (2.054) | (2.020) | (–0.408) | (–0.412) | (0.648) | (0.635) |
| $\text{EarnVol}$ | –0.3122 | –0.2382 | –0.4966** | –0.4256* | –0.2172* | –0.1521 | –0.3713* | –0.3649* | –0.4101*** | –0.3774*** |
| | (–1.564) | (–1.454) | (–2.614) | (–2.002) | (–1.893) | (–1.137) | (–2.050) | (–1.867) | (–5.673) | (–5.061) |
| $\text{RetVol}$ | 0.1269* | 0.1263 | 0.0451 | 0.0453 | 0.2583 | 0.2571* | 0.1706* | 0.1704* | 0.1694* | 0.1722* |
| | (1.882) | (1.710) | (0.388) | (0.410) | (1.538) | (1.479) | (1.759) | (1.803) | (1.865) | (1.881) |
| $\text{InNitems}$ | 1.1578* | 1.1645* | 1.1831 | 1.1833 | 1.9684** | 1.9370** | –0.3004 | –0.3056 | 0.5650 | 0.5611 |
| | (2.121) | (2.058) | (1.563) | (1.577) | (2.869) | (2.814) | (–0.865) | (–0.892) | (1.624) | (1.619) |
| Observations | 5.022 | 5.022 | 4.569 | 4.569 | 3.565 | 3.565 | 9.455 | 9.455 | 13.020 | 13.020 |
| Adjusted $R^2$ | 0.2194 | 0.2192 | 0.2501 | 0.2502 | 0.2277 | 0.2277 | 0.1863 | 0.1864 | 0.2419 | 0.2419 |
Note: Panel A shows results for the influence of predominant countries (columns (1) and (2)). Panel B shows results for the influence of predominant industries (columns (3) and (4)). Panel C shows results for the subsamples of SMEs (columns (5) and (6)) and LEs (columns (7) and (8)). Panel D shows results for the influence of reporting operating profit or loss (columns (9) and (10)). *t-statistics are in parentheses. *** p < 0.01. ** p < 0.05. * p < 0.1.
the greater scrutiny that this group of firms is subjected compared to SMEs. Again, the coefficients of DACC are positive but without statistical significance.
Finally, to analyze the effect of operating performance on the association between EM and IM, a dummy variable, Loss, was included in the model. Loss takes the value 1 if a firm reported operating loss and 0 otherwise. Table 3, Panel D, presents the results in columns (9) and (10).
There is evidence that companies disclose less readable annual reports when they report operating losses rather than operating profits. The results of the main analysis remain unchanged with the ABS_DACC showing a positive and statistically significant coefficient and DACC having a positive but not significant coefficient.
4. DISCUSSION
This study documents a positive association between EM intensity and IM practices in the context of annual reports. The results suggest that managers seek to obfuscate the intensity with which they manage earnings by disclosing more complex, meaning less readable annual reports, reinforcing the conclusions of Ajina (2016), Li (2008), and Lo (2017).
Thus, there is evidence of a complementary relationship between the practice of EM through accruals and IM through managing the readability of annual reports, suggesting that firms present annual reports with more content as an attempt to obfuscate discretionary accounting choices. This evidence is consistent with the results from Aerts and Cheng (2011) and Godfrey et al. (2003). In terms of narrative readability, Ajina et al. (2016) and Lo et al. (2017) also found that companies that practice EM tend to make their annual report less readable.
No evidence was found in terms of the association between the direction of EM and the practice of IM, but further analysis suggests that companies that practice income-increasing EM have on average higher file size of annual reports than companies that practice income-decreasing EM.
Finally, the robustness of the results was confirmed by using a different sample composition, without the influence of the three countries and three industries more representative and by analyzing the role of firm size and financial performance on the relationship between EM and IM.
Additional results suggest that, although large firms tend to present annual reports more complex, it is in the context of small and medium enterprises that the practice of obfuscating EM is more significant. There is also evidence that companies that report operating losses are more likely to disclose more complex annual reports than those that report an operating profit, consistent with prior research (Li, 2008; Lo et al., 2017).
This study contributes to the literature in several ways. First, it extends a rare stream of research on the association between EM practices and annual report readability by providing evidence of the complementarity of EM and IM under managerial discretion. Second, it provides a better understanding of these relationship by analyzing a broad sample of European companies. Third, it uses an alternative and novel measure of readability (the size of the electronic file) that mitigates the criticism associated with the measures used in previous literature. Fourth, it provides evidence that the association is stronger in the context of small and medium sized firms revealing the scrutiny effect to which large companies are subjected.
The results have economic and practical implications. Understanding the relationship between EM and IM is relevant to avoid inefficient allocation of capital, which can harm investment profitability and therefore negatively affect value creation. It is also relevant to regulators who, by understanding the strategies for managing information and communication, obtain guidelines for establishing a standardization that is more effective in eliminating information asymmetries.
CONCLUSION
This study analyzes the association between EM and IM practices in the context of annual reports. EM is measured using discretionary accruals using the modified Jones model. The measure of IM is the size of firms’ annual reports. The sample consists of 2,953 listed firms in 24 European countries, with data between 2012 and 2018, corresponding to 13,020 firm-year observations.
A positive and significant association is found between EM (discretionary accruals) and IM (report file size). The results are robust across different robustness tests. The same positive and significant association is obtained after controlling for the most representative countries or industries and controlling for year, country and sector fixed effects.
The results support that the increased intensity in the use of discretionary accruals leads managers to obfuscate these accounting choices with the disclosure of less readable annual reports, suggesting a complementary relationship between EM and IM.
AUTHOR CONTRIBUTIONS
Conceptualization: Tiago Goncalves, Cristina Gaio, Pedro Ramos.
Data curation: Tiago Goncalves, Pedro Ramos.
Formal analysis: Tiago Goncalves, Pedro Ramos.
Funding acquisition: Tiago Goncalves, Cristina Gaio.
Investigation: Tiago Goncalves, Cristina Gaio, Pedro Ramos.
Methodology: Tiago Goncalves, Pedro Ramos.
Project administration: Tiago Goncalves, Cristina Gaio.
Resources: Tiago Goncalves, Cristina Gaio.
Software: Pedro Ramos.
Supervision: Tiago Goncalves, Cristina Gaio.
Validation: Tiago Goncalves, Cristina Gaio, Pedro Ramos.
Visualization: Tiago Goncalves, Cristina Gaio, Pedro Ramos.
Writing – original draft: Cristina Gaio, Pedro Ramos.
Writing – review & editing: Tiago Goncalves.
ACKNOWLEDGMENT
The authors are grateful to financial support from FCT – Fundação para a Ciência e Tecnologia (Portugal), national funding through research grant (UID/SOC/04521/2020).
REFERENCES
1. Aerts, W. (2001). Inertia in the attributional content of annual accounting narratives. The European Accounting Review, 10(1), 3-32. https://doi.org/10.1080/09638180122562
2. Aerts, W. (2005). Picking up the pieces: Impression management in the retrospective attributional framing of accounting outcomes. Accounting, Organizations and Society, 30(6), 493-517. https://doi.org/10.1016/j.aos.2004.07.001
3. Aerts, W., & Cheng, P. (2011). Causal disclosures on earnings and earnings management in an IPO setting. Journal of Accounting and Public Policy, 30(5), 431-459. https://doi.org/10.1016/j.jaccpubpol.2011.03.006
4. Aerts, W., & Zhang, S. (2014). Management’s causal reasoning on performance and earnings management. European Management Journal, 32(5), 770-783. https://doi.org/10.1016/j.emj.2013.12.006
5. Ajina, A., Laouiti, M., & Msolli, B. (2016). Guiding through the Fog: Does annual report readability reveal earnings management? Research in International Business and Finance, 38, 509-516. https://doi.org/10.1016/j.ribaf.2016.07.021
6. Ali, A., & Zhang, W. (2015). CEO tenure and earnings management.
7. Baginski, S., Hassell, J., & Hillison, W. (2000). Voluntary causal disclosures: Tendencies and capital market reaction. *Review of Quantitative Finance and Accounting, 15*(4), 371-389. Retrieved from https://citeeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.454.1358&rep=rep1&type=pdf
8. Bettman, J. R., & Weitz, B. A. (1983). Attributes in the Board Room: Causal Reasoning in Corporate Annual Reports. *Administrative Science Quarterly, 28*(2), 165-183. Retrieved from https://psycnet.apa.org/doi/10.2307/2392616
9. Bloomfield, R. (2008). Discussion. *Auditing & Accountability Journal, 22*(2), 267-275. Retrieved from http://dx.doi.org/10.1016/j.aacco.2004.07.003
10. Bowen, R. M., Davis, A. K., & Matsumoto, D. A. (2005). Emphasis on Pro Forma versus GAAP Earnings in Quarterly Press Releases: Determinants, SEC intervention, and Market Reactions. *The Accounting Review, 80*(4), 1011-1038. Retrieved from https://depts.washington.edu/cfoforum/Matsumoto03.pdf
11. Brennen, N., & Merkl-Davies, D. M. (2013). Accounting Narratives and Impression Management, In L. Jack, J. Davison, & R. Craig (Eds.), *The Routledge Companion to Communication in Accounting* (pp. 109-132). London: Routledge.
12. Brennen, N., Guillamon-Saorin, E., & Pierce, A. (2009). Impression management: developing and illustrating a scheme of analysis for narrative disclosures – a methodological note. *Accounting, Auditing & Accountability Journal, 22*(5), 789-832. https://doi.org/10.1108/09535790910966379
13. Clapham, S. E., & Schwenk, C. R. (1991). Self-serving attributions, managerial cognition, and company performance. *Strategic Management Journal, 12*(3), 219-229. https://doi.org/10.1002/smj.4250120305
14. Clatworthy, M. A., & Jones, M. J. (2006). Differential patterns of textual characteristics and company performance in the chairman’s statement. *Accounting, Auditing & Accountability Journal, 19*(4), 493-511. https://doi.org/10.1108/095357061079100
15. Clatworthy, M., & Jones, M. J. (2001). The effect of thematic structure on the variability of annual report readability. *Accounting, Auditing & Accountability Journal, 14*(3), 311-326. https://doi.org/10.1108/0953570103199890
16. Clatworthy, M., & Jones, M. J. (2003). Financial reporting of good news and bad news: evidence from accounting narratives. *Accounting and Business Research, 33*(3), 171-185. https://doi.org/10.1080/00014788.2003.9729645
17. Courits, J. K. (1995). Readability of annual reports: Western versus Asian evidence. *Accounting, Auditing & Accountability Journal, 8*(2), 4-17. https://doi.org/10.1108/09535799510086795
18. Courtis, J. K. (2004a). Corporate report obfuscation: artefact or phenomenon? *The British Accounting Review, 36*(3), 291-312. https://dx.doi.org/10.1016%2Fj.bar.2004.03.005
19. Courtis, J. K. (2004b). Colour as visual rhetoric in financial reporting. *Accounting Forum, 28*(3), 265-281. https://doi.org/10.1016/j.accfor.2004.07.003
20. Dale, E., & Chall, J. S. (1948). A formula for predicting readability. *Education Research Bulletin, 27*(1), 37-54. Retrieved from https://www.jstor.org/stable/1473169
21. Davidson, W. N., Jiraporn, P., Kim, Y. S., & Nemec, C. (2004). Earnings management following duality-creating Successions: Ethnostatistics, impression management, and agency theory. *Academy of Management Journal, 47*(2), 267-275. https://doi.org/10.2307/20159577
22. Davison, J. (2008). Rhetoric, repetition, reporting and the “dot.com” era: words, pictures, intangibles. *Accounting, Auditing & Accountability Journal, 21*(6), 791-826. https://doi.org/10.1108/0953570810893254
23. Dechow, P. M., Sloan, R., & Sweeney, A. P. (1995). Detecting Earnings Management. *The Accounting Review, 70*(2), 193-225. Retrieved from https://www.jstor.org/stable/2483030
24. DuBay, W. (2007). *Unlocking Language*. Charleston, South Carolina: BookSurge Publishing.
25. Feldman, R., Govindaraj, S., Livnat, J., & Segal, B. (2010). Management’s tone change, post earnings announcement drift and accruals. *Review of Accounting Studies, 15*(4), 915-953.
26. Gioia, D. A., Schultz, M., & Corley, K. G. (2000). Organizational identity, image, and adaptive instability. *Academy of Management Review, 25*(1), 63-81. https://doi.org/10.5465/AMR.2000.2791603
27. Godfrey, J., Mather, P., & Ramsay, A. (2003). Earnings and Impression Management in Financial Reports: The Case of CEO Changes. *Abacus, 30*(1), 95-123. https://doi.org/10.1111/1467-6281.00122
28. Gonçalves, T. (2022). The Impact of Discretionary Measurement Criteria on Investors’ Judgement and Decisions. *Games, 13*(1), 3. https://doi.org/10.3390/g13010003
29. Gonçalves, T., Barros, V., & Serra, G. (2022). Political elections uncertainty and earnings management: Does firm size really matter? *Economics Letters, 110438. https://doi.org/10.1016/j.econlet.2022.110438
30. Gonçalves, T., Gaio, C., & Ferro, A. (2021). Corporate Social Responsibility and Earnings Management: Moderating Impact of Economic Cycles and Financial Performance. *Sustainability, 13*(17), 1-15. https://doi.org/10.3390/su13179969
31. Gonçalves, T., Gaio, C., & Lélis, C. (2020). Accrual mispricing:
Evidence from European sovereign debt crisis. *Research in International Business and Finance*, 52, 101-111. https://doi.org/10.1016/j.rbif.2019.10111
32. Gonçalves, T., Gaio, C., & Santos, T. (2019). Women on the board: Do they manage earnings? Empirical evidence from European listed firms. *Review of Business Management*, 21, 582-597. https://doi.org/10.7819/rgbv.v21i3.4010
33. Guay, W., Samuels, D., & Taylor, D. (2016). Guiding through the fog: Financial statement complexity and voluntary disclosure. *Journal of Accounting and Economics*, 62(2-3), 234-269. https://doi.org/10.1016/j.jaceco.2016.09.001
34. Guillamón-Saorín, E., & Osma, B. (2019). Women on the board: Self-serving financial reporting communication: A study of the association between earnings management and impression management. Universidad Carlos III de Madrid. Retrieved from https://citeservex.ist.psu.edu/viewdoc/download?doi=10.1146.30038&rep=rep1&type=pdf
35. Healy, P. M. (1985). The effect of bonus schemes on accounting decisions. *Journal of Accounting and Economics*, 7(1-3), 85-107. https://doi.org/10.1016/0165-4101(85)90029-1
36. Healy, P. M., & Wahlen, J. M. (1999). A review of the earnings management literature and its implications for standard setting. *Accounting Horizons*, 13(4), 365-383. Retrieved from https://papers.ssrn.com/sol3/papers.cfm?abstract_id=156445
37. Holthausen, R. W., & Leftwich, R. W. (1983). The economics consequences of accounting choice: Implications of Costly Contracting and Monitoring. *Journal of Accounting and Economics*, 5, 77-117. https://doi.org/10.1016/0165-4101(83)90007-1
38. Hyland, K. (1998). Exploring Corporate Rhetoric: Metadiscourse in the CEO’s Letter. *Journal of Business Communication*, 35(2), 224-244. https://doi.org/10.1177%2F002194369803500203
39. Jensen, M. C., & Meckling, W. H. (1976). Theory of the Firm: Managerial Behaviour, Agency Costs and Ownership Structure. *Journal of Financial Economics*, 3(4), 305-360. https://doi.org/10.1016/0304-405X(76)90026-X
40. Jones, J. J. (1991). Earnings Management During Import Relief Investigations. *Journal of Accounting Research*, 29(2), 193-228. https://doi.org/10.2307/2491047
41. Knee, C. R., & Zuckerman, M. (1996). Causality orientations and the disappearance of the self-serving bias. *Journal of Research in Personality*, 30(1), 76-87. Retrieved from https://s3.amazonaws.com/SDT/doc/discretionary%20accrual%20measures%20Knee%26Zuckerman%20IRP.pdf
42. Kothari, S. P., Leone, A. J., & Wasley, C. E. (2005). Performance matched discretionary accrual measures. *Journal of Accounting and Economics*, 39(1), 163-197. https://doi.org/10.1016/j.jacceco.2004.11.002
43. Leary, M. R., & Kowalski, R. M. (1990). Impression management: a literature review and two-component model. *Psychological Bulletin*, 107(1), 34-47. https://doi.org/10.1037/0033-2909.107.1.34
44. Li, F. (2008). Annual Report Readability, Current Earnings, and Earnings Persistence. *Journal of Accounting and Economics*, 45(2-3), 221-247. https://doi.org/10.1016/j.jacceco.2008.02.003
45. Lo, K., Ramos, F., & Rogo, R. (2017). Earnings management and annual report readability. *Journal of Accounting and Economics*, 63(1), 1-25. https://doi.org/10.1016/j.jacceco.2016.09.002
46. Loughran, T., & McDonald, B. (2014). Measuring Readability in Financial Disclosures. *The Journal of Finance*, 69(4), 1643-1671. https://doi.org/10.1111/jofi.12162
47. Merkl-Davies, D. M., & Brennan, N. M. (2007). Discretionary disclosure strategies in corporate narratives: incremental information or impression management. *Journal of Accounting Literature*, 26, 116-196. Retrieved from http://hdl.handle.net/10197/2907
48. Neu, D. (1991). Trust, impression management and the public accounting profession. *Critical Perspectives on Accounting*, 2(3), 295-313. https://doi.org/10.1016/1045-2354(91)90015-6
49. Neu, D., Warsame, H., & Pedwell, K. (1998). Managing public impressions: Environmental disclosures in annual reports. *Accounting Organizations and Society*, 23(3), 263-282. https://doi.org/10.1016/S0361-3682(97)00008-1
50. Rutherford, B. A. (2003). Obfuscation, textual complexity and the role of regulated narrative accounting disclosure in corporate governance. *Journal of Management and Governance*, 7(2), 187-210. https://doi.org/10.1023/A:1023647615279
51. Salancik, G. R., & Meindl, J. R. (1984). Corporate Attributions as Strategic Illusions of Management Control. *Administrative Science Quarterly*, 29(2), 238-254. https://doi.org/10.2307/2393176
52. Schipper, K. (1989). Commentary: earnings management. *Accounting Horizons*, 3(4), 91-102.
53. Schleicher, T., & Walker, M. (2010). Bias in the tone of forward-looking narratives. *Accounting and Business Research*, 40(4), 371-390. https://doi.org/10.1080/00014788.2010.995318
54. Schlenker, B. R. (1980). Impression management: The self-concept, social identity, and interpersonal relations. Monte: Brooks/Cole.
55. Tekfi, C. (1987). Readability formulas: an overview. *Journal of Documentation*, 43(3), 261-273. https://doi.org/10.1177/002136928704300305
56. Wagner, J. A., & Gooding, R. Z. (1997). Equivocal information and attribution: an investigation of patterns of managerial sensemaking. *Strategic Management Journal*, 18(4), 175-286. https://doi.org/10.1002/(SICI)1097-0266(199704)18:4%3C175::AID-SMJ880%3E3.0.CO;2-V
### APPENDIX A
**Table A1. Variables description**
| Variables | Description |
|--------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| LnFileSize | Is the natural logarithm of the size of the electronic file of the annual report corresponding in kilobytes (KB) |
| | A higher value implies a lower readability |
| ABS_DACC | Is the absolute value of the errors from Jones Model (1991) modified by Dechow et al. (1995) and Kothari et al. (2005) |
| | The intensity of EM. A higher value implies a higher level of EM |
| DACC | Is the value of the errors of the errors from Jones Model (1991) modified by Dechow et al. (1995) and Kothari et al. (2005) |
| | The direction of EM (upward or downward) |
| LnSize | Is the natural logarithm of the market value |
| | Larger firms are expected to have more complex operations and higher political costs leading managers to disclose more information and, consequently, annual reports with a larger size of the respective electronic file |
| MTB | Is the market value of equity plus book value of liabilities divided by total assets |
| | Controls for the impact of the firm’s growth opportunities assuming that firms with more growth opportunities will disclose annual reports with more information in order to bridge the uncertainty associated with their business models |
| FirmAge | Is the difference between the year of observation and the year of incorporation of the firm |
| | Controls for the effect of firm seniority on the readability of the annual report. On one hand, companies with greater seniority may present greater diversity or investment in their activities leading to the disclosure of less readable annual reports. On the other hand, if information users are familiar with and have more accurate information about the business model of older firms, then one would expect these firms to release more readable annual reports |
| SpecItems | Is a dummy variable that takes a value of 1 if the company reported Extraordinary and other P/L Items and 0, otherwise |
| | Controls for the effect of the occurrence of extraordinary events that lack explanation in the annual report. It is expected that, when they occur, they will contribute to the increase in the size of the electronic file |
| EarnVol | Is the standard deviation of operating income over the last 3 reporting years divided by assets |
| | Control for the effect of the volatility of the business and operations that may make reporting more complex and extensive because a decrease in predictability of the results is associated with increased volatility and, users demand for additional explanations in order to reduce uncertainty |
| RetVol | Is the standard deviation of monthly stock returns over the last 12 months |
| | |
| lnNitems | is the natural logarithm of the number of items disclosed according to the Global Standard Format and is available in Bureau Van Dijk’s Amadeus database |
| | Controls for the complexity of the firm. Companies that disclose more items in the Financial Statements should present more complex and extensive annual reports | | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
965,
1
],
[
965,
3547,
2
],
[
3547,
7778,
3
],
[
7778,
12239,
4
],
[
12239,
16401,
5
],
[
16401,
20765,
6
],
[
20765,
24147,
7
],
[
24147,
25202,
8
],
[
25202,
29339,
9
],
[
29339,
36022,
10
],
[
36022,
39935,
11
],
[
39935,
42967,
12
],
[
42967,
48118,
13
],
[
48118,
53490,
14
],
[
53490,
58836,
15
]
]
} |
bd09a9938047408d5df66708c1b1907c9db0c3eb | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 10,
"total-fallback-pages": 0,
"total-input-tokens": 32289,
"total-output-tokens": 10277,
"fieldofstudy": [
"Biology"
]
} | Mini Review
Biochemical functional predictions for protein structures of unknown or uncertain function
Caitlyn L. Mills, Penny J. Beuning, Mary Jo Ondrechen *
Department of Chemistry and Chemical Biology, Northeastern University, Boston, MA 02115, United States
A R T I C L E I N F O
Article history:
Received 3 December 2014
Received in revised form 6 February 2015
Accepted 11 February 2015
Available online 18 February 2015
Keywords:
Structural genomics
Protein function prediction
Local structure methods
Computational chemistry
A B S T R A C T
With the exponential growth in the determination of protein sequences and structures via genome sequencing and structural genomics efforts, there is a growing need for reliable computational methods to determine the biochemical function of these proteins. This paper reviews the efforts to address the challenge of annotating the function at the molecular level of uncharacterized proteins. While sequence- and three-dimensional-structure-based methods for protein function prediction have been reviewed previously, the recent trends in local structure-based methods have received less attention. These local structure-based methods are the primary focus of this review. Computational methods have been developed to predict the residues important for catalysis and the local spatial arrangements of these residues can be used to identify protein function. In addition, the combination of different types of methods can help obtain more information and better predictions of function for proteins of unknown function. Global initiatives, including the Enzyme Function Initiative (EFI), COMPUTational BRidges to EXperiments (COMBREX), and the Critical Assessment of Function Annotation (CAFA), are evaluating and testing the different approaches to predicting the function of proteins of unknown function. These initiatives and global collaborations will increase the capability and reliability of methods to predict biochemical function computationally and will add substantial value to the current volume of structural genomics data by reducing the number of absent or inaccurate functional annotations.
© 2015 Mills et al. Published by Elsevier B.V. on behalf of the Research Network of Computational and Structural Biotechnology. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Contents
1. Introduction .............................................................. 183
2. Functional site prediction methods .................................................... 183
2.1. Sequence-based methods ..................................................... 183
2.2. Structure-based methods ..................................................... 183
2.3. Combined methods ....................................................... 184
3. Annotating protein function ....................................................... 186
3.1. Local active site prediction methods .......................................... 186
3.1.1. ProFunc ........................................................ 186
3.1.2. Structurally Aligned Local Sites of Activity (SALSA) ......... 186
3.2. Community initiatives and projects .......................................... 187
3.2.1. The Enzyme Function Initiative (EFI) ......................... 187
3.2.2. Critical Assessment of Function Annotation (CAFA) experiment 188
3.2.3. COMPUTational BRidges to EXperiments (COMBREX) .... 189
4. Summary and outlook ......................................................... 189
Acknowledgments ........................................................................ 189
References .............................................................................. 189
* Corresponding author at: 360 Huntington Ave., Boston, MA 02115, United States.
E-mail addresses: [email protected] (P.J. Beuning), [email protected] (M.J. Ondrechen).
http://dx.doi.org/10.1016/j.csbj.2015.02.003
2001-0370/© 2015 Mills et al. Published by Elsevier B.V. on behalf of the Research Network of Computational and Structural Biotechnology. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
1. Introduction
The number of protein sequences and structures in databases such as UniProt [1] and the Protein Data Bank (PDB) [2] has grown significantly since the inception of genome sequencing and high-throughput structure determination. As of January 2015, the UniProt/TrEMBL database contains over 89 million protein sequence entries, an increase of more than six-fold since January of 2011; only a very small fraction of these proteins is assigned a reliable function [3]. Additionally, the PDB now includes more than 13,000 structural genomics (SG) protein structures as a result of structural genomics projects, notably the Protein Structure Initiative (PSI). At the turn of the millennium, the National Institute of General Medical Sciences (NIGMS) of the National Institutes of Health (NIH) in the United States launched the PSI with the goal to determine three-dimensional structures of proteins representing every family [4,5]. At that time, the human genome project and the sequencing of the genomes of many other organisms were completed [6,7]. The high throughput techniques developed by the PSI and other SG programs have increased the number of known protein structures. Since the PSI has been primarily concerned with high volume structure determination and prompt public availability of protein structures, most of these protein structures lack reliable accompanying information regarding their biochemical function; in some cases, no functional annotation is given. Thus, most of these proteins are assigned a putative or possible function based on the closest sequence or structure match; however, these assignments are often incorrect [8–10], and these incorrect functional labels can propagate within databases [11,12].
In 2010, the NIGMS launched a new phase of the PSI named PSI-Biology. This phase was implemented to determine the biological roles of the SG proteins under structural study. However, large numbers of functional annotations remain missing or incorrect. Better computational methods and verification through biochemical experimentation are clearly needed. Reliable and accurate computational methods for predicting the function of proteins can add significant value to genomics data and also improve efficiency of experimental verification of function. While there have been a number of review articles on sequence-based and three-dimensional-structure-based methods for function prediction [13–19], this article focuses on newer, local-structure-based computational methods to predict protein function at the molecular level; these methods are in turn based on prediction of the local spatial regions that are biochemically active in the structure. Finally, efforts within the broader scientific community to contribute to the testing and verification of functional predictions are explored.
When the function of a protein is not known, a putative function is sometimes assigned. These assignments are often the result of simple bioinformatics analyses including sequence and three-dimensional structure comparisons using programs such as BLAST [20,21] and Dali [22,23]. SG proteins can be assigned a putative function based on simple transfer of function from the closest sequence or structure match. However, sequence or structural similarities can be misleading. For instance, less than 30% of pairs of proteins with greater than 50% sequence identity have identical E.C. numbers [9]. Even a BLAST E value of 10−50 or less does not guarantee that two proteins have the same function [9]. Sequence identities of 60% or greater will transfer function incorrectly in 10% of cases [10]. Furthermore, structural superfamilies, such as the enolase, amidohydrolase, and Clp/crotonase [24] superfamilies, can consist of several, or even dozens, of different biochemical functions [25–28]. The TIM barrel and the Rossmann fold each represent over 50 different types of biochemical function; the TIM barrel has been observed in five out of the six major E.C. categories and the Rossmann fold occurs in all six [29–32]. Thus, the practice of assigning function using simple transfer of function based on sequence or structure similarity has caused misannotations. In one study, the GenBank NR [33], UniProtKB/TrEMBL [1], and Kyoto Encyclopedia of Genes and Genomes (KEGG) [34] databases were shown to have up to 63% misannotation across six superfamilies [8].
For many SG proteins, possible functional assignments obtained from informatics-based approaches can provide too many options with insufficient discrimination of the most likely functions to be able to assign function with confidence or test function experimentally with reasonable efficiency. The development and implementation of new, reliable computational methods is an important aspect of a solution to the challenge of assignment of function to proteins.
2. Functional site prediction methods
Many computational programs have been developed to help predict the active sites and biochemical functions of proteins [16,18,19,35–39], although there remains much yet to be done to improve and to verify predictive capability for biochemical function.
2.1. Sequence-based methods
Sequence-based approaches are the more commonly used method of computational analysis [18]; these methods primarily utilize sequence alignments but sometimes also incorporate 3D structures [40,41]. Evolutionary Trace [42] and INformation-theoretic TREe traversal for Protein functional site IDentification (INTREPID) [43,44], examine a protein in its phylogenetic context and the evolutionary history of each amino acid in a protein sequence to assign a score to each amino acid. Evolutionary Trace analyzes the conservation of residues between proteins of similar function and evaluates amino acid variations that are known to be associated with changes in function. This information then suggests which residues are important for specific functions and which residues can be altered in order to change the function of a protein. This method exploits the similarities and differences between groups of homologous proteins and includes functional resolution, which involves analyzing the different functional clusters that are generated within a given family. Similar to Evolutionary Trace, INTREPID computes scores depending on the degree of conservation within a set of proteins with known functions. This score examines information over an entire family tree instead of just analyzing certain branches, or subfamilies. INTREPID is also able to identify residues important for catalysis that are not necessarily conserved across an entire family [44]. Both methods compute a score for each residue that is a measure of its importance to the function.
2.2. Structure-based methods
Structure-based methods of predicting protein function involve analyzing the structure and shape of a protein. This analysis helps determine where a ligand may bind by transferring the function of another similar protein of known function. Identification of the local site of biochemical activity in a protein can serve as a first step toward the prediction of the function. Geometric-based computational programs like Surfnet [45], CASTp [46], Ligsite [47], PocketFinder [48], and geometric potential [49] are structure-based approaches that examine the different properties of a protein surface or active site pocket to gain insight into the identity and location of binding pockets. Surfnet generates many protein surfaces, such as pockets within a protein, gaps between molecules, and van der Waals interactions, based on PDB coordinate data. The different surface output data are shown as a grid depicting the densities. These grids are created by applying a Gaussian function to the atoms within the protein. The residues that are specified as important are determined from the intensity of the densities. CASTp locates voids within a protein structure using the PDB, Swiss-Prot, and Online Mendelian Inheritance in Man (OMIM) to determine active site residues. Similarly, Ligsite uses a set of ligand–receptor complexes to locate pockets on a protein surface and can analyze a large set of proteins rather quickly [50]. PocketFinder and geometric potential also analyze the topological and geometric features of the protein surface. However, PocketFinder locates ligand binding envelopes instead of scanning the
surface of a protein to find different sized pockets. Geometric potential adds local structural analysis in parallel with global structural analysis to analyze the residues within the pockets.
In addition to geometry-based methodologies, docking methods are another type of structure-based approach. Docking approaches such as Q-SiteFinder [51] and computational solvent mapping [52] identify the position and properties of the catalytic site regions within proteins through the use of small molecule probes. Q-SiteFinder exploits the energy differences between spaces in a protein and van der Waals probes. This helps find the locations in a protein that are energetically favorable for ligand binding. Similarly, solvent mapping uses small organic molecule probes to analyze a protein surface, locates favorable areas where the probes may bind, and then ranks the positions based on their free energies. These methods help locate both catalytic sites and non-catalytic, small molecule binding sites, such as allosteric sites within a given protein structure.
Theoretical Microscopic Anomalous Titration Curve Shapes (or THEMATICS) [53–55], a functional site prediction method, is able to predict accurately the ionizable active site residues within a given protein using only the 3D structure of the query protein. THEMATICS identifies ionizable amino acid residues (Arg, Asp, Cys, Glu, His, Lys, and Tyr, plus the N- and C-terminals) that participate in catalysis or ligand recognition. The ionizable side chains of amino acid residues in protein active sites exhibit unusual electrostatic properties, specifically theoretical titration curves as shown in Fig. 1. These curves are obtained by approximate calculation of the electrostatic potential function, followed by a calculation of the average charge of each ionizable residue as a function of pH. These theoretical titration curves of active site residues are perturbed from the normal sigmoidal shape that is characteristic of the Brönsted acid-base chemistry of the free amino acid [53]. In a normal titration curve, the proton occupation is one at low pH and as the pH is increased, the proton occupation suddenly drops sharply around the pK_a, approaching zero at higher pH. Normally this transition, where both the protonated and deprotonated forms exist in appreciable population, occurs in a narrow pH range. However, the residues within the active site tend to be partially protonated over a larger pH range and in this manner the shape of the titration curve is perturbed [53]. This method has been described previously as based on computed pK_a shifts [38,56]; however, this is incorrect. Only metrics that characterize the shape of the titration curves, and not the pK_a shifts, are used in the THEMATICS predictions.
The degree of deviation of a catalytic ionizable residue from the typical Henderson–Haselbalch titration curve can be quantified by the moments of the first derivative of the curve [57]. This method has been tested on the Catalytic Site Atlas (CSA) 100, and THEMATICS-predicted residues have been shown to constitute good predictions of the active site for proteins in the benchmark set [55]; they have also been shown to be generally well conserved [58].
2.3. Combined methods
In order to take advantage of the strengths of each approach to improve the performance of active site predictors, many current methods utilize structure and sequence-based properties in parallel [59–67]. ConCavity [68] is one method that utilizes both sequence and structure information to predict the functionally active residues of a protein. It uses algorithms that analyze not only the surface of a protein for binding pockets, but also uses evolutionary conservation to help locate these pockets. First, ConCavity scores areas on the surface of a protein according to the topology, using methods such as Ligsite or Surfnet (mentioned above). It then combines the conservation scores of residues within these pocket areas. Next, pocket structures are constructed based on the analysis and the structure of the protein. Finally, the potential pockets are mapped on the surface and the residues are analyzed and scored based on their position with respect to the pockets. With this information, ConCavity is able to predict spaces within a protein structure where a ligand is most likely to bind. The creators of ConCavity have shown that combining structure and sequence analyses significantly improves the ability to identify active site pockets and the residues responsible for catalysis [68].
Since THEMATICS can only predict the seven ionizable amino acids, machine learning methods were developed that can extract more information from the computed electrostatic and chemical properties and can predict all 20 amino acid types. The ionizable residues arginine, aspartate, cysteine, glutamate, histidine, lysine, and tyrosine make up about 76% of active site residues within functionally annotated proteins in databases [69]. To predict all 20 amino acid residue types, a new machine learning method was developed that can analyze the non-ionizable residues as well. This led to the development of Partial Order Optimum Likelihood, or POOL. POOL, a machine learning method, is a maximum likelihood, monotonocity-constrained multidimensional isotonic regression method that has the ability to identify both ionizable and non-ionizable active site residues [70]. POOL accepts THEMATICS metrics for the ionizable residues as one of its input features. However, it also calculates environment variables for all residues based on the THEMATICS metrics for the ionizable residues in the neighborhood of each residue. POOL can accept other input features, including scores from INTREPID [43,44] and the structure-only version of ConCavity [68]. Using structure-based geometric features, ConCavity supplies a score for each residue based on its likelihood of binding to a ligand.
Fig. 1. Three histidine residues from histidinol phosphate phosphatase (HPP) (PDB 2yz5) were analyzed by THEMATICS to produce theoretical titration curves (A), which plot the mean net charge of a given residue of a large ensemble of protein molecules as a function of pH, and first derivative plots (B). The titration curves of two non-catalytic residues, H84 and H150, show sigmoidal curve shapes with a small buffer range, while the catalytic H226 displays a curve with an anomalous shape, shallow slope, and larger buffer range. When analyzing the first derivatives of the titration curves, non-catalytic residues display symmetrical, highly peaked plots. However, active site residues such as H226 shown here display broad, asymmetric derivative plots and may have multiple peaks.
Together, these three input types from THEMATICS, INTREPID, and structure-only ConCavity generate POOL rankings that yield predictions of the residues that are important for catalysis.
For instance, THEMATICS and POOL were used to analyze the Structural Genomics protein *Bifidobacterium adolescentis* YP_910028.1 of unknown function and predicted that it is a metal-dependent phosphoesterase [71]. Sequence and structure comparisons with BLAST and Dali were inconclusive and suggested multiple different functions. The closest structure match was to a DNA polymerase catalytic domain. Initial phylogenetic analysis suggested that this protein could function to repair DNA or function as a DNA polymerase.
The crystal structure of YP_910028.1 contains a PHP domain, but PHP domains are present in multiple functional types, including X-family DNA polymerases [72], DNA polymerase III [73], and a histidinol phosphate phosphatase [74]. The location of the iron and zinc metals can suggest a general location for the active site, but cannot be used to determine a specific function since these trinuclear metal-binding sites are seen in a range of diverse proteins including endonucleases, phosphatases, and phospholipases [75–78]. Other analyses [79,80] were unable to provide a definitive functional annotation.
THEMATICS and POOL analysis of YP_910028.1 predicted sets of residues that closely match those predicted for histidinol phosphate phosphatase (HPP, PDB ID 2yz5) in a local structure alignment, with weaker matches to the other proteins of known function with similar folds, suggesting phosphoesterase activity for the enzyme. DNA polymerase III (PDB: 2hpi) has a similar metal-binding motif, but key cysteine and tyrosine residues are replaced by histidine and threonine residues in YP_910028.1, respectively. When YP_910028.1 is superimposed with both DNA polymerase III and HPP, the predicted active site residues align better with HPP (Fig. 2). This indicates that YP_910028.1 possesses phosphoesterase activity and not DNA polymerase activity. Phosphoesterase activity was detected by observation of the hydrolysis of the phosphate group of para-nitrophenyl phosphate (pNPP) to form p-nitrophenol and was shown to be dependent on the concentration of YP_910028.1. However, the tests for DNA polymerase activity resulted in no detectable activity regardless of the conditions used [71].
(A) The metal binding pocket of YP_910028.1, containing a PHP (Polymerase and Histidinol Phosphatase) domain (PDB ID 3e0f, shown in dark blue) aligns well with that of DNA Pol III alpha subunit (PDB ID 2hpi, shown in magenta). However, C145 and Y74 of DNA Pol III are mismatched with a histidine and threonine, respectively in YP_910028.1. (B) On the other hand, the metal binding pocket of YP_910028.1 (PDB 3e0f) aligns perfectly with the pocket of histidinol phosphate phosphatase (HPP) (PDB 2yz5), shown in green.
3. Annotating protein function
3.1. Local active site prediction methods
In comparison to global sequence- and structure-based methods that analyze an entire protein, local active site prediction methods find the biochemically active local region of the structure and then focus on the residues within the pocket and in the immediate surroundings. These methods are useful when analyzing entire families of proteins for which a specific signature is observed within the local active site.
For example, ProBiS [81] is a web server that utilizes an algorithm to detect similarities within protein binding pockets through local structural alignments of multiple proteins. ProBiS provides access to a database of 420 million pairwise local structure alignments and will perform pairwise local alignments for structures that are not in its database.
3.1.1. ProFunc
ProFunc [82] is a metaserver that combines sequence, global structure, and local structure-based methods to obtain a set of function predictions from which one might seek consensus. First, the protein of unknown function is analyzed by numerous sequence searches, shown on the left-hand side in Fig. 3. BLAST [20,21] analysis scans both the PDB and UniProt and uses multiple sequence alignment to determine sequence similarities and detect sequence motifs [83]. Gene neighbors are also examined based on the query protein’s predicted location within the genome. The genes located near each other are often functionally related or functionally similar [82]. Next, structure-based analyses are performed on the protein of interest. This involves searching a number of databases for global folds or local structures that are similar to the query protein. Surfnet, mentioned in the above section, is one of these databases. Another database, secondary structure matching (SSM) [84] evaluates the secondary structure elements (SSEs) of the query protein of unknown function and compares them to the SSEs of protein structures within its database. The algorithm retrieves high, strong matches and superimposes the structures with the query protein to give a root mean square deviation (RMSD) so that a common number can be used to compare the results. Finally, ProFunc utilizes other servers to search for 3D templates of proteins with known binding sites. These binding sites may be simple active sites with the residues important for catalysis known [85], or ligand binding sites wherein residues important for catalysis are known and also the natural ligand/substrate is known. In some cases, the databases can also compare DNA-binding sites and motifs known to be associated with binding DNA.
3.1.2. Structurally Aligned Local Sites of Activity (SALSA)
The computational method Structurally Aligned Local Sites of Activity, or SALSA [86] utilizes a combination of functional residue prediction from POOL with local three-dimensional structural alignments. The characteristic spatial patterns of predicted residues at the local active site are used to identify biochemical functions. For example, a superfamily can consist of a number of functional families, each with a biochemical function that is different from the other members of that superfamily. SALSA tables can be constructed using the locally aligned residues at the predicted active sites across the entire superfamily. Proteins with the same function generally possess a particular spatial pattern or signature of predicted functional residues, while proteins of different functions possess different signatures. This consensus signature for each functional family is established using POOL predictions for a set of proteins with known common function; this defines the signature for each of the known functional types within a superfamily. If the superfamily contains SG proteins, the predicted sets of functional residues for the SG proteins can be compared with the consensus signatures for the known functional families. Thus, SALSA defines the different kinds of active sites, and therefore different functional types, within a superfamily. The general method is illustrated in the workflow shown in Fig. 4.
Fig. 3. Schematic diagram outlining the different methods utilized in ProFunc. HMM: Hidden Markov Model; SSM: Secondary Structure Matching; HTH: Helix–Turn–Helix.
3.2. Community initiatives and projects
In an effort to tackle the growing challenges of protein function prediction and the correction of enzyme function misannotations within databases, the community has come together to take on the challenge. These global projects involve collaboration between numerous groups, employing theory, computation, and experiment, and have started to make significant progress toward the confirmation of protein function, thus adding a substantial value to the information on structural genomics proteins currently available.
3.2.1. The Enzyme Function Initiative (EFI)
The Enzyme Function Initiative (EFI) [3], funded by NIGMS, began 10 years after the start of the PSI. This initiative combines bioinformatics with experimental enzymology to help determine the substrate specificity of proteins of unknown function. Each aspect of the EFI can be divided into whether or not the work can be done in a high throughput, moderate throughput, or low throughput manner. Generally, the first steps of the project, computational and bioinformatics analysis, fall under high throughput methods that help focus the experimental work in the final stages of this project, which involve lower throughput methods. The initial bioinformatics analyses, including database searches for sequences and structures of unknown function, preliminary molecular ligand docking, and clustering of pathways, can be executed on a high throughput basis [87]. Experimental enzymology, including preliminary homology modeling, expression and purification of enzymes of interest, and screening enzymes for different activities can be done at a rate of a few enzymes per month and falls under moderate throughput. The limiting factors of this project, however, are the experiments that fall under the low throughput category, including obtaining higher resolution homology models and docking studies, determining structure–function relationships, in vivo studies of functional predictions, and identification of enzymes with functional promiscuity [88,89], each of which can be highly demanding of time and labor. However, the preliminary work helps refine the experimental analysis, which highlights the necessity of reliable computational prediction methods to be used in parallel with experimental validation methods.
The project focuses these methods on five superfamilies with diverse functions that have been selected as test cases for developing the strategy outlined above: (1) amidohydrolase (AH), (2) enolase (EN), (3) glutathione transferase (GST), (4) haloalkanoic acid dehalogenase (HAD), and (5) isoprenoid synthase (IS). These Bridging Projects help determine target enzymes as well as information about the enzymes of known function in each superfamily.
In order to be successful, the EFI strategy must be able to assign a novel function for enzymes that are functionally diverse from enzymes of known function. However, molecular docking of a ligand into an enzyme is not always a reliable way to determine substrate specificities. In particular, substrates can cause conformational changes in vitro that are not observed in silico and the scoring algorithms may not be accurate [3]. At the end of its term, the EFI proposes that it will have a working strategy consisting of a set of databases and programs that the scientific community can utilize in expanding this analysis to every protein superfamily.
Fig. 4. Schematic diagram outlining the SALSA method of annotating protein function.
This method has been successfully tested on numerous proteins of unknown function. Specifically, the in silico docking method of the EFI described above has been successfully applied to the entire dipeptide epimerase family within the EN superfamily. Within this superfamily, a member of the cis,cis-muconate lactonizing enzyme (MLE) family encoded by the Bacillus cereus ATCC 14579 genome with previously unknown function was predicted to have N-succinyl arginine racemase function based on docking approaches [90]. A virtual library consisting of N-succinyl amino acids and dipeptides was virtually docked into a homology model of this enzyme. The homology model was created using a series of template structures from the PDB. The structure of L-Ala-D/L-Glu epimerase from Bacillus subtilis (PDB ID 1TKK) was the template that contributed the most to the homology model. This template was also prominent in many subsequent homology models for members of the dipeptide epimerase family and was useful in the docking studies of nearly 700 enzymes.
Another successful docking study, performed by one of the Bridging Projects, aided in assigning function to Thermotoga maritima Tm0936, a member of the AH superfamily whose function was previously unknown. Tm0936 was predicted to have a novel function as an S-adenosylhomocysteine deaminase [91]. This study involved docking thousands of metabolites into Tm0936 and creating a target list comprising adenine analogues. Five potential substrates were chosen based on availability and rank within the docking study; of these, the enzyme had significant activity with three: adenosine, 5-methylthioadenosine (MTA), and S-adenosylhomocysteine (SAH) (Fig. 5). It was concluded that this enzyme is involved in the deamination of metabolites within the MTA/SAH pathway.
3.2.2. Critical Assessment of Function Annotation (CAFA) experiment
Until recently, there was no way to compare the performance of different automated function prediction methods. Over the past few years, Iddo Friedberg and Predrag Radiovjacić, through collaboration with many computational research groups, have designed an experiment to test multiple automated function prediction tools and programs. This Critical Assessment of Function Annotation (CAFA) [92] experiment is a large-scale community-wide collaboration designed to evaluate the performance of the many diverse methodologies [60,82,93–99] developed by research groups over the years. These methods range from studying protein–protein interactions [100–103] to analyzing sequences [104–108] to examining evolutionary features of proteins [109–113]. The main focus is to evaluate the quality of current sequence-based automated function prediction methods and to identify the computational methods that perform the best in predicting correct or novel functions.
So far, the CAFA experiment has gone through two experimental periods, with the second experiment recently completed. In both instances, the protocols, or “rules,” are similar. The classification system used by the CAFA experiments was developed based on the definition of protein function classification by the Gene Ontology (GO) Consortium [114]. The GO project utilizes many different databases [115–142] to help provide a solution to the problem of automated function prediction. The main goal of the GO Consortium is to develop a uniform vocabulary to use when describing the functions of all eukaryotic proteins. The first CAFA project lasted 15 months and consisted of 30 teams of researchers from around the globe, who tested over 50 algorithms designed to annotate protein function. The different methods were tested on a set of over 860 protein sequences spanning 11 species, including Escherichia coli, B. subtilis, and Homo sapiens [92].
From the GO Consortium categories, this project involves information from the “Biological Process” and “Molecular Function” sections. These sections are two of the three structured vocabularies that the GO project utilizes many different databases (Fig. 5). It was concluded that this enzyme is involved in the deamination of metabolites within the MTA/SAH pathway.
This large-scale CAFA experiment and others to follow like CAFA2 are designed to help researchers evaluate their methods in comparison to other methods in existence. They also provide the community with a set of predictions for a number of proteins of unknown or uncertain function. Overall, the results of the first experiment showed accurate performances when predicting the “Molecular Function” of the target proteins. However, the same could not be said for predicting the “Biological Processes” of the target proteins, which shows room for improvement in all methods.
The two top performing methods for predicting both “Molecular Function” and “Biological Process” ontologies were Jones—UCL [143] and Argot2 [144]. The Jones—UCL method uses known protein–protein interactions, gene expression, and sequence similarity to assign protein functions [143]. The Argot2 method analyzes a given protein sequence by BLAST [20,21] and a Naïve baseline method [92], were used to compare the test methods. In the BLAST method, the GO terms that define any protein sequences for which a function has been experimentally determined are assigned to the sequence being analyzed. In the naïve method, the GO terms used to describe the target sequences are scored based on how frequently the term occurs in the Swiss-Prot database overall.
This large-scale CAFA experiment and others to follow like CAFA2 are designed to help researchers evaluate their methods in comparison to other methods in existence. They also provide the community with a set of predictions for a number of proteins of unknown or uncertain function. Overall, the results of the first experiment showed accurate performances when predicting the “Molecular Function” of the target proteins. However, the same could not be said for predicting the “Biological Processes” of the target proteins, which shows room for improvement in all methods.
In the first CAFA global project (CAFA1), an analysis of human mitochondrial polynucleotide phosphorylase 1 (hPNGase) from a family of exonuclease Iases was reported. This large protein works in complex with other portions of the mitochondrial degradome and is characterized by a number of diverse functions for which experimental data exist.
---
Fig. 5. The metabolites above dock in silico into Tm0936 and are substrates of the enzyme Tm0936. The general structure of these three metabolites is the same with the exception of the moieties shown in the boxes.
These functions include hydrolyzing single-stranded RNA [147], facilitating the import of RNAs into the mitochondrial matrix [148], and responding to oxidative stress [149]. A number of methods under examination in the CAFA project made predictions for hPNPase. In the “Molecular Function” GO terms category, most methods were able to predict correctly two functions for hPNPase: single-stranded RNA hydrolysis and import of small RNAs. Other functions are more uncommon within the family of hPNPase, which may contribute to the lack of methods able to predict these functions [92]. The most well-known biological function of hPNPase is the import of RNA into the mitochondria. Within the “Biological Process” GO terms category, this major function as well as others were not predicted.
3.2.3. Combinatorial Bridges to Experiments (COMBREX)
The COMBREX Project’s main goal is to understand and annotate the function of microbial proteins [150]. As its name implies, this project brings theorists and experimentalists together in order to increase the rate at which proteins from archaeal and bacterial genomes are functionally annotated [151]. There are three main components to this project: the COMBREX Community, the COMBREX Database, and the COMBREX grants. The grants are used to fund community members working on the efforts described above, while the database serves as a universal place to house the list of functionally annotated proteins. Currently, this database contains more than 3.3 million proteins spanning over 1000 microbial genomes [150]. Of the genes in the database, less than 0.5% have experimental data regarding the function of the gene. However, over 75% of the genes contain a computationally predicted function, but lack experimental validation. In general, the COMBREX project is working toward creating a Gold Standard Database to serve as the basis for training algorithms for future protein annotation methods. During the beginning of the COMBREX-funded projects, experimentalists were assigned 140 proteins on which to perform experiments. Of these 140 proteins, 37 contain 28 unique domains that are similar to human proteins, which potentially can lead to new information about human health and diseases. Also within this group of proteins are eight domains of unknown function defined by Pfam, which allows for some novel predictions of function to be made. Of these 140 proteins, about half have a successfully validated functional prediction [152–156]. In one instance [155], bacterial YbbB is identified in twelve archaeal genomes and its function is determined to be a tRNA 2-selenouridine synthase. In order to confirm this functional classification, first preliminary computational analysis, including BLAST [20,21] searches, was performed on the protein of uncertain function. Next, structure-based alignments and neighboring genes were analyzed using CLUSTAL W [157] and a neighbor-joining method [158]. To validate the results of the computational methods, in vitro activity assays were performed by gene complementation/replacement [159,160] and tRNA selenation [155] experiments. In the end, the computational predictions were successfully validated by the experimental methods, and the function of this protein was determined.
4. Summary and outlook
The process of annotating proteins of unknown and uncertain function continues to be challenging yet critical for understanding the enormous amount of information generated by genome sequencing and structural genomics projects. Function prediction methods that focus on the local spatial region of biochemical activity show promise for improving predictive capability. Proteins that contain high sequence similarity on a global level do not always have that same sequence similarity at the local active site. Conversely, proteins with low overall sequence similarity can have high similarity in the spatial region of the active site. Too often, the function of a protein that has high global sequence similarity with a protein of unknown function is transferred to the target protein without analyzing the local active site sequence similarities.
In an effort to provide useful information about enzymes of unknown function, many research groups have developed methods to predict protein function. However, the probability of misannotation is higher when only one type of analysis, sequence- or structure-based, is used when making predictions. As methods continue to be optimized and used in parallel with other methods, the information obtained though the genome projects can become more useful and complete. With the help of these breakthrough computational methods listed above and others to come in the future, the challenges of assigning functions to proteins can begin to be resolved. Even with the number of methods available today to predict the function of proteins, it is clear that the field of protein function prediction will continue to grow, especially as the quality and quantity of data continue to increase. While these computational methods are being optimized, biochemical studies can be used to validate the predictions made. Such experimental verification is a major current need in the field. In the future, as computational methods improve and are subjected to experimental verification, biochemical studies can be more focused and less time consuming. Future automation of the computational methods will enable fast, high-throughput functional annotation of these proteins and thus add significant value to the vast, growing store of genomics data.
Acknowledgments
Support of the National Science Foundation under grant number CHE-1305655, a grant from MathWorks, an American Cancer Society Research Scholar Grant, RSG–12–161-01-DMC (PJB), and a PhRMA Foundation Fellowship (CLM) are gratefully acknowledged.
References
[1] The UniProt Consortium. Activities at the universal protein resource (UniProt), Nucleic Acids Res 2014;42:D191–8.
[2] Westbrook J, Feng Z, Chen L, Yang H, Berman HM. The Protein Data Bank and structural genomics. Nucleic Acids Res 2003;31:489–91.
[3] Gerlt JA, et al. The enzyme function initiative. Biochemistry 2011;50:9950–62.
[4] Stevens RC. Design of high-throughput methods of protein production for structural biology. Structure 2000;8:R77–85.
[5] Burley SK, Joachimiak A, Montelione GT, Wilson IA. Contributions to the NIH–NIGMS Protein Structure Initiative from the PSI production centers. Structure 2008;16:5–11.
[6] Venter JC, et al. The sequence of the human genome. Science 2001;291:1304–51.
[7] Lander ES, et al. Initial sequencing and analysis of the human genome. Nature 2001:409:860–921.
[8] Schnoes AM, Brown SD, Dedovski L, Babbitt PC. Annotation error in public databases: misannotation of molecular function in enzyme superfamilies. PLoS Comput Biol 2009;5:e1000625.
[9] Rost B. Enzyme function less conserved than anticipated. J Mol Biol 2002;318: 695–608.
[10] Tian W, Skolnick J. How well is enzyme function conserved as a function of pairwise sequence identity? J Mol Biol 2003;333:863–82.
[11] Gultis WR, Audit B, de Angelis D, Tissot S, Duzouinis CA. Percolation of annotation errors through hierarchically structured protein sequence databases. Math Biosci 2005;193:223–34.
[12] Lewellyn R, Eisenberg DS. Annotating proteins with generalized functional linkages. Proc Natl Acad Sci U S A 2008;105:17700–5.
[13] Cabaldon T. Computational approaches for the prediction of protein function in the mitochondrion. Am J Physiol Cell Physiol 2006;291:C1121–8.
[14] Pandey G, Kumar V, Steinbach M. Computational approaches for protein function prediction: a survey, TR 06-028. Twin Cities: Department of Computer Science.
[15] Hu P, Bader G, Wigle DA, Emili A. Computational prediction of cancer-gene function. Nat Rev Cancer 2007;7:23–34.
[16] Lee D, Redfern O, Oregno C. Predicting protein function from sequence and structure. Nat Rev Mol Cell Biol 2007;8:995–1005.
[17] Sharan R, Uludag I, Shamir R. Network-based prediction of protein function. Mol Syst Biol 2007;3:88.
[18] Loewenstein Y, et al. Protein function annotation by homology-based inference, Genome Biology 2009;10:207.
[19] Sharan R, Uludag I, Shamir R. Network-based prediction of protein function. Mol Syst Biol 2007;3:88.
[20] Altschul SF, et al. Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res 1997;25:3389–402.
[21] Camerone M, Williams HE, Campan A. Improved gapmed alignment in BLAST. IEEE/ACM Trans Comput Biol Bioinformatics 2004;1:116–29.
[22] Holm L, Karajainen S, Wilton C, Plewczyński D. Using DALI for structural comparison of proteins. Curr Protoc Bioinformatics 2006;514:5.3.1–5.5.24 [Chapter 5: Unit 5.5].
| 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4244,
1
],
[
4244,
12630,
2
],
[
12630,
19368,
3
],
[
19368,
22312,
4
],
[
22312,
26616,
5
],
[
26616,
30131,
6
],
[
30131,
36757,
7
],
[
36757,
45476,
8
],
[
45476,
45476,
9
],
[
45476,
45476,
10
]
]
} |
32693150b714c79bd17e045b4d60c14551bebd33 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 12,
"total-fallback-pages": 0,
"total-input-tokens": 37609,
"total-output-tokens": 12242,
"fieldofstudy": [
"Biology"
]
} | SGC-CK2-1 Is an Efficient Inducer of Insulin Production and Secretion in Pancreatic β-Cells
Mandy Pack 1, Claudia Götz 1,*, Selina Wrublewsky 2 and Mathias Montenarh 1
1 Medical Biochemistry and Molecular Biology, Saarland University, Building 44, D-66421 Homburg, Germany; [email protected] (M.P.); [email protected] (M.M.)
2 Institute for Clinical & Experimental Surgery, Saarland University, D-66421 Homburg, Germany; [email protected]
* Correspondence: [email protected]
Abstract: The pyrazolopyrimidine based compound SGC-CK2-1 is a potent and highly specific CK2 inhibitor and a new tool to study the biological functions of protein kinase CK2 irrespective from off-target effects. We used this compound in comparison with the well-established CK2 inhibitor CX-4945 to analyze the importance of CK2 for insulin production and secretion from pancreatic β-cells. Both inhibitors affected the proliferation and viability of MIN6 cells only marginally and downregulated the endogenous CK2 activity to a similar level. Furthermore, both inhibitors increased the message for insulin and boosted the secretion of insulin from storage vesicles. Thus, regarding the high specificity of SGC-CK2-1, we can clearly attribute the observed effects to biological functions of protein kinase CK2.
Keywords: protein kinase CK2; SGC-CK2-1; CX-4945; pancreatic β-cells; insulin
1. Introduction
The human kinome encompasses more than 500 kinases [1]. One of these kinases, namely CK2 (formerly known as casein kinase 2) phosphorylates a great number of proteins which are implicated in central biological processes leading to the difference between life and death of a cell, cell proliferation, DNA damage response, differentiation of cells, controlling of angiogenesis, and ion channel activation [2–7]. In addition, metabolic pathways including the glucose metabolism are regulated by CK2 [8]. CK2 phosphorylates and controls a number of different transcription factors that regulate the expression of various genes. Over the last 20 years, it has been shown that the kinase activity of CK2 is elevated in rapidly proliferating cells, such as tumor cells (for review see: [9,10]). Furthermore, it was shown that CK2 is a potent suppressor of apoptosis, which is a hallmark of cancer [11]. Due to this particular property of CK2, there are many attempts to inhibit the kinase activity in order to stop cell proliferation and tumor growth [10,12,13]. Meanwhile, there is a still growing list of CK2 inhibitors, most of which are ATP competitive inhibitors [14].
It has been shown that the CK2 kinase inhibitors DRB and DMAT lowered glucose-induced insulin secretion [15]. In contrast to these results, over the last more than ten years, we and others [16] have shown that CK2 is strongly implicated in the regulation of the expression of insulin in pancreatic β-cells. We have demonstrated that inhibition of CK2 led to an increased transcription of the gene encoding insulin in pancreatic β-cells [17]. The elevated level of insulin production is due to an increased transport of the transcription factor Pdx1 into the nucleus and an elevated transcription factor activity after CK2 inhibition [18–20]. Moreover, the stability of Pdx1 is enhanced, presumably, by disturbing the interaction with PCIF, a ubiquitin ligase adapter protein [18]. The transcription factor USF1 is also a substrate for CK2, and inhibition of CK2 leads to an elevated transcription of the gene encoding insulin [21,22]. The level of intracellular concentration of Ca2+ is critical for the synthesis and secretion of insulin from pancreatic β-cells. Two Ca2+ channels, Cav2.1 and TRMPM3, are substrates for CK2 and inhibition
of CK2 leads to an elevated intracellular Ca^{2+} concentration [23,24]. For these studies, we have used tetrabromobenzotriazol (TBB) [25,26], quinalizarin [27,28], or CX-4945 [29,30] as inhibitors. As TBB was shown to inhibit protein kinases other than CK2, we switched to CX-4945, which was used as a CK2 specific inhibitor to treat various cancers mostly in combination with other drugs [31,32]. Recently however, CX-4945 was identified as a splicing regulator [33] and a selective inhibitor of cdc2-like kinases [34]. Furthermore, about 10 kinases other than CK2 were shown to also be inhibited at low nanomolar concentrations. Thus, according to these results, off-target effects are most likely. Recently, Wells and co-workers published a new compound named SGC-CK2-1, which exhibited a remarkable selectivity for CK2 [35]. Furthermore, proliferation of cells was inhibited in just one analyzed cell line. On the other hand, protein kinase activity of CK2 was strongly inhibited as shown by an impaired Akt S129 phosphorylation. As disruption of the Akt signaling has also been reported for other CK2 inhibitors, these results demonstrated an influence on the down-stream signaling of CK2. As SGC-CK2-1 inhibited CK2 kinase activity ten times more than CX-4945, but seems to have no influence on cell proliferation, we decided to treat pancreatic β-cells with SGC-CK2-1 and, for comparison, with CX-4945. We analyzed the effect on insulin production and secretion from these cells in order to exclude off-target effects more efficiently. We found that both inhibitors had only marginal effects on cell proliferation and cell viability. Both efficiently inhibited CK2 kinase activity, which was determined by Akt Ser129 phosphorylation as well as by phosphorylation of a synthetic CK2 substrate peptide. However, inhibition of CK2 by both inhibitors led to the stimulation of insulin production and secretion. Thus, SGC-CK2-1 turned out to be an appropriate inhibitor to interrogate the biological significance of CK2 for pancreatic β-cells. Due to the high efficiency and specificity of SGC-CK2-1 and the limited influence on cell proliferation, this new inhibitor seems to be highly qualified for further use as potential therapeutic drug in diabetes therapy.
2. Materials and Methods
2.1. Cell Culture and Treatment
The mouse cell line MIN6 [36,37] was maintained in Dulbecco’s modified Eagle’s medium DMEM supplemented with 10% (v/v) fetal bovine serum in a humidified atmosphere with 5% CO\textsubscript{2} at 37 °C. Cells were passaged at a split ratio of 1:3.
The CK2 inhibitors SGC-CK2-1 (Sigma-Aldrich, Taufkirchen, Germany) and CX-4945 (SelleckChem, Munich, Germany) were dissolved in dimethyl sulfoxide (DMSO). A 10 mM stock solution was prepared to treat the cells with the corresponding final concentration. In any case, smaller volumes of stock solution were filled up with pure DMSO to have equal volumes of the solvent in the cell culture dishes. In control experiments, we used an equal volume of the solvent DMSO alone in order to exclude any solvent effects. The final concentration of DMSO in the medium did not exceed 1% (v/v).
2.2. Extraction of Cells and Western Blot Analysis
Cells were harvested by scraping off the plate with a rubber spatula. They were centrifuged (7 min, 4 °C, 400 × g) and subsequently washed with cold phosphate-buffered saline (PBS). Cells were lysed for 30 min at 4 °C with lysis buffer (10 mM Tris-HCl, pH 7.5, 10 mM NaCl, 0.1 mM EDTA, 0.5% (v/v) Triton X-100, 0.02% NaN\textsubscript{3} (w/v) supplemented with 0.5 mM phenylmethylsulfonyl fluoride (PMSF) and a protease and phosphatase inhibitor cocktail (1:75 v/v, Sigma-Aldrich, Taufkirchen, Germany). After lysis, cell debris was removed by centrifugation. The protein content was determined using the BioRad protein assay dye reagent (BioRad, Munich, Germany). SDS polyacrylamide gel electrophoresis and Western Blot analysis was performed essentially as described [38]. Equal amounts of protein extracts were loaded onto 12.5% polyacrylamide gels (5 μg for the detection of proinsulin, 15 μg for the detection of CK2 subunits and 25 μg for the detection of total and phosphorylated Akt). Electrophoresis was performed with a Tris based running buffer (25 mM Tris-HCl, pH 8.3, 190 mM glycine, 0.1% sodium dodecyl sulfate) for 1 h at 100 V.
After electrophoresis, proteins were blotted onto PVDF membranes by a semi-dry blot procedure using 48 mM Tris, pH 9.2, 39 mM glycine, 20% (v/v) methanol as blot buffer in a BioRad Trans-Blot-Turbo transfer system (BioRad, Munich Germany) for 7 min at 25 V and 1.3 A. After blotting, the membranes were incubated with the primary antibodies (anti-proinsulin (abcam, Berlin, Germany, ab181542), a polyclonal serum against CK2α, anti-CK2β (Santa Cruz Biotechnologies, Heidelberg, Germany, sc-46666), or anti-α-tubulin (clone DM1A, Sigma-Aldrich, Taufkirchen, Germany)) in TBS (20 mM Tris-HCl, pH 7.5, 150 mM NaCl) supplemented with 0.1% Tween20 (TBS-T) and 1% BSA overnight at 4 °C. Subsequently, membranes were washed twice with TBS-T, and then incubated with the horseradish peroxidase (HRP)-conjugated secondary antibodies (anti-rabbit (HAF-008)) and anti-mouse antibody (HAF-007) from R&D Systems, Abingdon, UK) for 1 h at room temperature. After two further washing steps, the expression of the corresponding proteins was visualized by enhanced chemoluminescence.
2.3. In Vitro Phosphorylation
For the determination of the protein kinase activity of CK2 in extracts of treated or untreated cells, we used the synthetic CK2 specific substrate peptide with the sequence RRRDDDSDDD [39]. The enzymatic reaction was performed using radio-labelled $^{32}$Pγ ATP in an appropriate kinase buffer (50 mM Tris/HCl, pH 7.5, 100 mM NaCl, 10 mM MgCl$_2$, 1 mM dithiotreitol (DTT)) containing 20 µg protein/20 µL, which was mixed with 30 µL CK2 mix (25 mM Tris/HCl, pH 8.5, 150 mM NaCl, 5 mM MgCl$_2$, 1 mM DTT, 50 µM ATP, 0.19 mM substrate peptide) containing 10 µCi/500 µL $^{32}$Pγ ATP (Hartmann Analytic, Braunschweig, Germany). The mixture was spotted onto a P81 ion exchange paper. After washing three times with 85 mM H$_3$PO$_4$ and once with ethanol, the paper was dried and the Čerenkov-radiation was determined in a scintillation counter.
2.4. Detection of Insulin Secreted from MIN6 Cells
The determination of secreted insulin was essentially performed as described by Kelly et al. [40]. MIN6 cells were seeded at 3 \times 10^4 cells/well in a 24-well plate. After 24 h, cells were treated with vehicle, SGC-CK2-1 or CX-4945 for 24 h. The medium was removed and after washing with Krebs Ringer buffer KRB (115 mM NaCl, 4.7 mM KCl, 1.28 mM CaCl$_2$, 1.2 mM MgSO$_4$, 0.1% BSA), the cells were incubated with KRB supplemented with 25 mM glucose for 1 h to induce insulin secretion. After this treatment, insulin was determined in the collected supernatants with the insulin ELISA kit from Invitrogen according to the recommendation of the provider.
2.5. RNA Extraction
Cells were harvested by trypsinizing and were subsequently spun down by centrifugation (7 min, 4 °C, 400 \times g). RNA was extracted from treated and control cells using the QIAzol lysis reagent (Qiagen, Hilden, Germany) according to the manufacturer’s instructions. For qRT-PCR, RNA was subsequently washed with 75% ethanol. After drying, RNA was resuspended in RNase-free water and the concentration was determined using a NanoDrop UV-Vis Spectrophotometer. mRNA was reverse transcribed to cDNA with a qScriber cDNA Synthesis Kit (HighQu, Kraichtal, Germany) according to the manufacturer’s protocol.
2.6. Quantitative Real-Time PCR (qRT-PCR)
For amplification of the proinsulin cDNA, we applied the ORA SEE qPCR Green ROX L Mix Kit (HighQu). We strictly followed the recommendations of the manual of the producer. Briefly, 100 ng of total RNA per reaction were reverse transcribed and analyzed in a one-step reaction using the primer combinations shown in Table 1. GAPDH served as an endogenous control for mRNA detection.
Table 1. Primer pairs applied in qRT-PCR.
| Target | Direction | Sequence |
|-----------|-----------|---------------------------|
| Proinsulin| forward | 5′-GGG GAG CGT GGC TTC TTC TA-3′ |
| Proinsulin| reverse | 5′-GGG GAC AGA ATT CAG TGG CA-3′ |
| GAPDH | forward | 5′-CGG TGC TGA GTA TGT C-3′ |
| GAPDH | reverse | 5′-TTT GGC TCC ACC CTT C-3′ |
2.7. Viability Assays
A WST-1 (water-soluble tetrazolium salt-1) assay (cell proliferation reagent Cellpro-Ro from Roche, Rotkreuz, Switzerland) was used to determine the viability of MIN6 cells according to the protocol described in [41]. In brief, 10 µL of WST-1 solution was added to each well of a 96 well plate and mixed with the culture medium. After 30 min the absorbance of the formed dye was determined in a plate reader at 450 nm.
MIN6 cells were seeded in a 24-well plate and cultivated for 24 h. Cells were treated with vehicle, SGC-CK2-1, or CX-4945 (1 µM or 10 µM) for 24 h. The adherent cells were detached with Cell Dissociation Buffer (GIBCO by Fisher Scientific GmbH, Schwerte, Germany), centrifuged, and resuspended with PBS. For the determination of the viability, 10 µL of the cell suspension was stained with a trypan blue solution (0.4%) and counted by a LUNA™ Automated Cell Counter (logos Biosystems, Villeneuve D’Ascq, France) according to the manufacturer’s protocol.
2.8. Statistical Analysis
After testing the data of the in vitro experiments for normal distribution and equal variance, differences between the groups were assessed by the one-way analysis of variance (One-way ANOVA). This was followed by the Tukey post hoc test by means of Prism software 8 (GraphPad). Results were expressed as mean ± standard deviation (SD) of at least three or four independent experiments. Statistical significance was accepted as p < 0.05.
3. Results
3.1. Impact of SGC-CK2-1 on Cell Viability
In recent years, different CK2 inhibitors were used as potential tumor therapeutics as they more or less compromised the growth of many tumor cells. The recently published highly specific CK2 inhibitor SGC-CK2-1, however, did not elicit an antiproliferative activity towards most of the tested 140 tumor cell lines, although it inhibited intracellular CK2 activity with a high efficiency [35]. Due to these results, we asked whether the published effects on functions of pancreatic β-cells after inhibition with different CK2 inhibitors are also true for the treatment with SGC-CK2-1.
For our experiments we used the mouse insulinoma cell line MIN6 [36,37], which has morphological characteristics of pancreatic β-cells and shows glucose-inducible insulin secretion comparable to cultured normal mouse islet cells. There are numerous reports showing that inhibition of CK2 may have an impact on the viability of cells (for review see: [42–45]). Therefore, we treated MIN6 cells with the recently published inhibitor SGC-CK2-1 (1 and 10 µM) or with the well-established inhibitor CX-4945 (1 and 10 µM). After 24 h, we performed a dye exclusion test using trypan blue and determined the ratio of viable cells. As shown in Figure 1a, we observed essentially no reduction in viability after treatment with 1 µM CX-4945 compared to the DMSO control. Upon application of 10 µM CX-4959, the viability was reduced to 90%. Treatment with 1 µM SGC-CK2-1 caused a drop of viability to 85% which was no further exceeded by the higher concentration.
We treated the cells as described above and subsequently analyzed the expression of the viability of the cells was determined in a WST-1 assay. The results shown in Figure 1b confirmed the data of the previous experiment. Treatment with CX-4945 had no influence on the viability of cells, whereas treatment with SGC-CK2-1 led to a reduction in viability to about 85% when using 10 µM SGC-CK2-1. Thus, with both assays, we found no influence of CX-4945 and a weak influence of SGC-CK2-1 on the viability of MIN6 cells.
Viability of cells can also be tested by analyzing the metabolic activity of dehydrogenases. Cells were treated with the inhibitors as described for the dye exclusion test; the viability of the cells was determined in a WST-1 assay. The results shown in Figure 1b confirmed the data of the previous experiment. Treatment with CX-4945 had no influence on the viability of cells, whereas treatment with SGC-CK2-1 led to a reduction in viability to about 85% when using 10 µM SGC-CK2-1. Thus, with both assays, we found no influence of CX-4945 and a weak influence of SGC-CK2-1 on the viability of MIN6 cells.
3.2. Impact of SGC-CK2-1 on Endogenous CK2 Activity
In the next step, we asked whether treatment of MIN6 cells with SGC-CK2-1 would influence the expression of CK2α and CK2β. Cells were treated with 1 or 10 µM SGC-CK2-1 and, for comparison, with the same concentration of CX-4945. After 24 h cells were harvested and lysed. Total cellular proteins were analyzed by SDS gel electrophoresis followed by Western blot analysis with CK2α or CK2β specific antibodies. As shown in Figure 2a, neither SGC-CK2-1 nor CX-4945 had an influence on the expression of CK2α or CK2β. Next, we asked whether the inhibitors also inhibit the intracellular CK2 activity. We treated the cells as described above and subsequently analyzed the expression of the endogenous CK2 substrate Akt and the phosphorylation of Akt S129 with a phospho-specific antibody. Furthermore, we also analyzed the ability of CK2 to phosphorylate the synthetic CK2-specific peptide substrate RRRDDSDDDD [46].
Figure 1. Impact of the treatment of MIN6 cells with SGC-CK2-1 or CX-4945 on cell viability. MIN6 cells were treated with 1 or 10 µM SGC-CK2-1 (SGC) or 1 or 10 µM CX-4945 (CX) for 24 h. (a) Viability of cells was determined by counting living cells after trypan blue exclusion. Living cells in the control culture (vehicle) were set 100% and living cells in the treated culture were calculated in reference to it. (b) After 24 h treatment, the metabolic activity of MIN6 cells was analyzed by a WST-1 viability assay. Experiments were undertaken at least in quadruplicate and statistical analysis was performed as described in “Material and Methods”.
Viability of cells can also be tested by analyzing the metabolic activity of dehydrogenases. Cells were treated with the inhibitors as described for the dye exclusion test; the viability of the cells was determined in a WST-1 assay. The results shown in Figure 1b confirmed the data of the previous experiment. Treatment with CX-4945 had no influence on the viability of cells, whereas treatment with SGC-CK2-1 led to a reduction in viability to about 85% when using 10 µM SGC-CK2-1. Thus, with both assays, we found no influence of CX-4945 and a weak influence of SGC-CK2-1 on the viability of MIN6 cells.
3.2. Impact of SGC-CK2-1 on Endogenous CK2 Activity
In the next step, we asked whether treatment of MIN6 cells with SGC-CK2-1 would influence the expression of CK2α and CK2β. Cells were treated with 1 or 10 µM SGC-CK2-1 and, for comparison, with the same concentration of CX-4945. After 24 h cells were harvested and lysed. Total cellular proteins were analyzed by SDS gel electrophoresis followed by Western blot analysis with CK2α or CK2β specific antibodies. As shown in Figure 2a, neither SGC-CK2-1 nor CX-4945 had an influence on the expression of CK2α or CK2β. Next, we asked whether the inhibitors also inhibit the intracellular CK2 activity. We treated the cells as described above and subsequently analyzed the expression of the endogenous CK2 substrate Akt and the phosphorylation of Akt S129 with a phospho-specific antibody. Furthermore, we also analyzed the ability of CK2 to phosphorylate the synthetic CK2-specific peptide substrate RRRDDSDDDD [46].
Figure 2. Influence of CK2 inhibitors SGC-CK2-1 and CX-4945 on CK2 expression and CK2 kinase activity. MIN6 cells were treated with 1 or 10 µM CX-4945 (CX) or 1 or 10 µM SGC-CK2-1 (SGC) for 24 h. Control cells were incubated with an equal volume of the vehicle DMSO. Proteins were extracted and equal amounts were either loaded on a 12.5% SDS polyacrylamide gel and blotted onto a PVDF membrane or subjected to an in vitro phosphorylation assay. (a) Representative immunoblot analysis of MIN6 cell extracts for the detection of the catalytic subunit CK2α and the non-catalytic CK2β subunit; the detection of α-tubulin served as loading control. (b) Representative immunoblot analysis for the detection of total Akt and Akt phosphorylated at the CK2 site serine 129 (pAkt). α-tubulin served as loading control. (c) Cell extracts were incubated with [32P]γATP and the synthetic CK2 substrate peptide RRRDDDSDDD. After the kinase reaction, labelled phosphate incorporated into the peptide was determined by Čerenkov counting. Activity measured in control extracts was set 100% and the activity of treated extracts calculated in reference to it. Statistical analysis was performed as described in “Material and Methods”. * Statistical significance was accepted with a p-value of at least p < 0.05.
The Western blot analysis of the known CK2 phosphorylation site S129 in Akt (pAkt) compared with the amount of total Akt demonstrated the inhibiting impact of SGC-CK2-1 or CX-4945 on intracellular CK2 activity (Figure 2b). By using CX-4945, phosphorylation at Akt S129 was efficiently reduced with a 10 µM concentration. Treating the cells with 1 µM SGC-CK2-1 prevented the Akt S129 phosphorylation already nearly completely.
To verify the inhibitory activity with another substrate, we used the synthetic CK2 substrate peptide RRRDDDSDDD. We performed an in vitro phosphorylation assay with extracts of SGC-CK2-1 or CX-4945 treated cells and radiolabeled ATP as phosphate donor. The phosphate incorporation into the peptide was determined by Čerenkov counting. Activity in extracts of DMSO treated control cells was set 100% and residual activity in extracts of SGC-CK2-1 or CX-4945 treated cells was referred to it. As shown in Figure 2c CK2 activity was efficiently reduced with both inhibitors to a level of roughly 20% residual activity using 10 µM CX-4945 or both concentrations of SGC-CK2-1.
Thus, both CK2 inhibitors efficiently inhibited endogenous CK2 without exerting any influence on the expression of the protein and without significantly impairing the viability and proliferation of cells.
3.3. Impact of SGC-CK2-1 on Insulin Production and Secretion
In recent years, we intensively studied the importance of protein kinase CK2 for functions of pancreatic β-cells. The most obvious effects were an enhancement of insulin transcription—presumably by stabilization of PDX-1—and insulin secretion after inhibiting protein kinase CK2 by different CK2 inhibitors. We now wanted to know whether SGC-CK2-1 might also induce insulin production and secretion.
In the first instance, we checked the effect of CK2 inhibition on insulin transcription by qRT-PCR. MIN6 were treated with 1 and 10 µM SGC-CK2-1 and, for comparison, also with 1 and 10 µM CX-4945 or with the solvent DMSO for control. mRNA was isolated, reverse transcribed and subjected to a qPCR analysis with insulin specific primers. The message was normalized to the housekeeping gene GAPDH. The bar graphs in Figure 3a show that upon addition of both CK2 inhibitors the message for insulin increased up to two-fold compared to the DMSO control.
We next asked whether the increase in insulin transcription was also mirrored in protein expression. We treated the cells as described above and analyzed the expression of the precursor form proinsulin in a Western blot analysis and presented the relative amount after normalization to the loading control α-tubulin (Figure 3b). We repeatedly found an elevated level of proinsulin protein in treated cells. The increase was, however, lower than expected from the qRT-PCR analysis.
To cope with glucose concentrations about the physiological level of 5 mM, it is important that insulin is secreted from the β-cell to induce processes which lower high glucose amounts after feeding. As we observed in former experiments an enhanced secretion of insulin after inhibition of CK2, we now asked whether the treatment of MIN6 with SGC-CK2-1 might lead to the same result. Again, we treated the cells with SGC-CK2-1 and, for comparison, also with CX-4945, and determined the secreted insulin. With both inhibitors, we observed a significant increase in insulin secretion by 1.5-fold. Thus, we could demonstrate that by inhibiting endogenous protein kinase CK2 in pancreatic β-cells with the recently published inhibitor SGC-CK2-1 led to the same effects on β-cell specific functions than with the long established CK2 inhibitor CX-4945.
Figure 3. Influence of CK2 inhibition on insulin expression and secretion. MIN6 cells were treated with 1 or 10 µM SGC-CK2-1 (SGC) or 1 or 10 µM CX-4945 (CX) for 24 h. Control cells were incubated with an equal volume of the vehicle DMSO. (a) Cells were harvested, and total RNA was isolated using the QiAziol lysis reagent. The mRNA amount of insulin was determined using qRT-PCR. After normalization to GAPDH, the amount of insulin mRNA of control-treated cells was set 100% and the amount of treated mRNA cells calculated in reference to it. (b) Cells were harvested, proteins were extracted, and equal amounts were loaded on a 12.5% SDS polyacrylamide gel and blotted onto a PVDF membrane. A representative immunoblot analysis of MIN6 cell extracts for the detection of proinsulin is shown; the detection of α-tubulin served as loading control. Signals for proinsulin from three independent experiments were analyzed by a densitometric scan and normalized to the arbitrary amount of the loading control α-tubulin. The relative mean amount of proinsulin +/− SD for the different treatments is shown as bar graphs. (c) After a glucose stimulus, secreted insulin was determined in the cell culture supernatant with the insulin ELISA kit. Statistical analysis in all experiments was performed as described in “Material and Methods”. * Statistical significance was accepted with a p-value of at least p < 0.05.
4. Discussion
The observation that CK2 expression and CK2 protein kinase activity is elevated in rapidly proliferating cells has stimulated the search for inhibitors of the kinase activity with the goal to use inhibitors as anti-cancer agents. Modifying existing chemical structures and substitutions led to an increase in the specificity of these inhibitors. By using larger panels of different kinases as well as the use of the inhibitors in different biological systems, it turned out that at least the class of ATP competitive CK2 inhibitors have off target effects [29,33,35,47,48]. These observations did not considerably influence the use of these inhibitors, often in combination with other drugs, for the treatment of cancer, where growth arrest and eventually apoptosis was intended [12,49]. Beside cancer cells, we have used several CK2 inhibitors in pancreatic β-cells where we could show an elevated production and subsequent secretion of insulin after CK2 inhibition [17,22,23]. Additionally, in pancreatic β-cells we have faced the problem with possible off-target effects of the used inhibitors. Recently, a new CK2 inhibitor, namely SGC-CK2-1, was published [31], which had no anti-proliferative activity against 140 different cancer cell lines. Wells et al. [35] further found that SGC-CK2-1 inhibited CK2 kinase activity more efficiently than the commonly used CX-4945 inhibitor at the same concentrations. Recently, Licciardello and Workman [50] encouraged the scientific community to embrace SGC-CK2-1 as the new gold standard to interrogate the biological significance of CK2. The observations described by Wells et al. [35], together with the paper by Licciardello and Workman, stimulated us to compare both SGC-CK2-1 and CX-4945 in pancreatic β-cells with regard to their influence on cell viability, kinase activity, protein expression and production, and secretion of insulin. It turned out that both inhibitors have only a minor effect on cell viability, with a reduction of around 10–15%, compared to the untreated cells. There might be a slightly greater reduction for SGC-CK2-1 treated cells than for CX-4945 treated cells. The results obtained here for CX-4945 treated MIN6 cells are in agreement with earlier observations with non-cancer ARPE-19 cells, where CX-4945 efficiently inhibited CK2 kinase activity without an influence on cell viability [51].
CK2 kinase activity is often determined by measuring the phosphorylation of one of the down-stream signaling molecules, namely Akt, which is phosphorylated by CK2 at serine129 [52]. Phosphorylation of Akt is detected by a phospho-specific antibody directed against the CK2 phosphorylation site serine 129. As shown here, Akt 129 phosphorylation is inhibited by both inhibitors where SGC-CK2-1 is effective already at 1 µM, whereas CX-4945 strongly inhibits Akt 129 phosphorylation at a concentration of 10 µM. A very similar result was obtained when a peptide with the CK2 consensus sequence RRRDDDSDDD [39] was used as substrate. Both inhibitors do not have an influence on the expression of CK2α and CK2β as shown by a Western blot analysis. Thus, the reduction in the CK2 kinase activity is not due to reduction in the level of CK2 proteins. We have shown that inhibition of CK2 kinase activity leads to an elevated level of the transcription factor Pdx-1 in the nucleus, which acts there as a transcription factor increasing the expression of insulin [20]. As shown here, both inhibitors stimulated the expression of proinsulin, which was detected by qRT-PCR and Western blots. We observed that the mRNA expression for insulin was considerably enhanced after CK2 inhibition by both inhibitors. The proinsulin protein expression was only slightly increased in the presence of the inhibitors; SGC-CK2-1 seems to be more efficient than CX-4945 when a 10 µM concentration was used. We have previously shown that not only the synthesis of insulin was enhanced after CK2 inhibition, but also the secretion of insulin [23]. Here, we have shown that both inhibitors forced the secretion of insulin from pancreatic β-cells as measured by an insulin ELISA. This result might also explain that the level of proinsulin is only slightly elevated after CK2 inhibition as the secretion is elevated simultaneously. In summary, our results strongly suggest that the elevated production and secretion of insulin from pancreatic β-cells is not due to off-target effects, but specific for the inhibition of the CK2 kinase activity. These results suggest SGC-CK2-1 as a new tool to target CK2 in pancreatic β-cells in order to improve the treatment of diabetes.
References
1. Manning, G.; Whyte, D.B.; Martinez, R.; Hunter, T.; Sudarsanam, S. The protein kinase complement of the human genome. *Science* **2002**, *298*, 1912–1934. [CrossRef]
2. Montenarh, M. Protein kinase CK2 in DNA damage and repair. *Transl. Cancer Res.* **2016**, *5*, 49–63.
3. Montenarh, M. Protein kinase CK2 and angiogenesis. *Adv. Clin. Exp. Med.* **2014**, *23*, 153–158. [CrossRef]
4. Montenarh, M.; Götz, C. Protein kinase CK2 and ion channels. *Biomed. Rep.* **2020**, *13*, 55. [CrossRef]
5. Götz, C.; Montenarh, M. Protein kinase CK2 in development and differentiation. *Biomed. Rep.* **2016**, *6*, 127–133. [CrossRef] [PubMed]
6. Guerra, B.; Issinger, O.G. Protein kinase CK2 and its role in cellular proliferation, development and pathology. *Electrophoresis* **1999**, *20*, 391–408. [CrossRef]
7. Pinna, L.A.; Meggio, F. Protein kinase CK2 (“casein kinase-2”) and its implication in cell division and proliferation. *Prog. Cell Cycle Res.* **1997**, *3*, 77–97. [PubMed]
8. Al-Quobaili, F.; Montenarh, M. CK2 and the regulation of the carbohydrate metabolism. *Metabolism* **2012**, *61*, 1512–1517. [CrossRef]
9. Trembley, J.H.; Wang, G.; Unger, G.; Slaton, J.; Ahmed, K. CK2: A key player in cancer biology. *Cell. Mol. Life Sci.* **2009**, *66*, 1838–1867. [CrossRef] [PubMed]
10. Trembley, J.H.; Chen, Z.; Unger, G.; Slaton, J.; Kren, B.T.; Van, W.C.; Ahmed, K. Emergence of protein kinase CK2 as a key target in cancer therapy. *Biofactors* **2010**, *36*, 187–195. [CrossRef]
11. Ahmad, K.A.; Wang, G.; Unger, G.; Slaton, J.; Ahmed, K. Protein kinase CK2—A key suppressor of apoptosis. *Adv. Enzyme Regul.* **2008**, *48*, 179–187. [CrossRef]
12. Cozza, G.; Pinna, L.A. Casein kinases as potential therapeutic targets. *Expert Opin. Ther. Targets* **2016**, *20*, 319–340. [CrossRef] [PubMed]
13. Wang, G.; Unger, G.; Ahmed, K.A.; Slaton, J.W.; Ahmed, K. Downregulation of CK2 induces apoptosis in cancer cells—A potential approach to cancer therapy. *Mol. Cell. Biochem.* **2005**, *274*, 77–84. [CrossRef]
14. Sarno, S.; Salvi, M.; Battistutta, R.; Zanotti, G.; Pinna, L.A. Features and potentials of ATP-site directed CK2 inhibitors. *Biochim. Biophys. Acta* **2005**, *1754*, 263–270. [CrossRef] [PubMed]
15. Jaksch, C.; Thams, P. A critical role for CK2 in cytokine-induced activation of NFkappaB in pancreatic beta cell death. *Endocrine* **2013**, *47*, 117–128. [CrossRef]
16. Rossi, M.; Ruiz de Azua, I.; Barella, L.F.; Sakamoto, W.; Zhu, L.; Cui, Y.; Lu, H.; Rehbolz, H.; Matschinsky, F.M.; Doliba, N.M.; et al. CK2 acts as a potent negative regulator of receptor-mediated insulin release in vitro and in vivo. *Proc. Natl. Acad. Sci. USA* **2015**, *112*, E6818–E6824. [CrossRef]
17. Meng, R.; Götz, C.; Montenarh, M. The role of receptor kinase CK2 in the regulation of the insulin production of pancreatic islets. *Biochem. Biophys. Res. Commun.* **2010**, *401*, 203–206. [CrossRef]
18. Klein, S.; Meng, R.; Montenarh, M.; Götz, C. The phosphorylation of PDX-1 by protein kinase CK2 is crucial for its stability. *Pharmaceutics* **2016**, *8*, 2. [CrossRef] [PubMed]
19. Meng, R.; Al-Quobaili, F.; Müller, I.; Götz, C.; Thiel, G.; Montenarh, M. CK2 phosphorylation of Pdx-1 regulates its transcription factor activity. *Cell. Mol. Life Sci.* **2010**, *67*, 2481–2489. [CrossRef]
20. Welker, S.; Götz, C.; Servas, C.; Laschke, M.W.; Menger, M.D.; Montenarh, M. Glucose regulates protein kinase CK2 in pancreatic β-cells and its interaction with PDX-1. *Int. J. Biochem. Cell Biol.* **2013**, *45*, 2786–2795. [CrossRef] [PubMed]
21. Lupp, S.; Götz, C.; Khadouma, S.; Horbach, T.; Dimova, E.Y.; Bohrer, A.-M.; Kietzmann, T.; Montenarh, M. The upstream stimulatory factor USF1 is regulated by protein kinase CK2 phosphorylation. *Cell. Signal.* **2014**, *26*, 2809–2817. [CrossRef] [PubMed]
22. Spoehr, S.; Gross, R.; Nalbach, L.; Schwind, L.; Stumpf, H.; Menger, M.D.; Amipofo, E.; Montenarh, M.; Götz, C. Functional interplay between the transcription factors USF1 and PDX-1 and protein kinase CK2 in pancreatic b-cells. *Sci. Rep.* **2017**, *7*, 16367. [CrossRef] [PubMed]
23. Scheuer, R.; Philipp, S.E.; Becker, A.; Nalbach, L.; Amipofo, E.; Montenarh, M.; Götz, C. Protein Kinase CK2 Controls CaV2.1-Dependent Calcium Currents and Insulin Release in Pancreatic b-Cells. *Int. J. Mol. Sci.* **2020**, *21*, 4668. [CrossRef]
24. Becker, A.; Götz, C.; Montenarh, M.; Philipp, S.E. Control of TRPM3 ion channels by protein kinase CK2-mediated phosphorylation in pancreatic b-cells of the line INS-1. *Int. J. Mol. Sci.* 2021, 22, 13133. [CrossRef]
25. Zien, P.; Duncan, J.S.; Skierski, J.; Bretner, M.; Litchfield, D.W.; Shugar, D. Tetramobromobenzotriazole (TBBt) and tetramobromobenzimidazoles (TBBz) as selective inhibitors of protein kinase CK2: Evaluation of their effects on cells and different molecular forms of human CK2. *Biochim. Biophys. Acta* 2005, 1754, 271–280. [CrossRef] [PubMed]
26. Szyszka, R.; Grankowski, N.; Felczak, K.; Shugar, D. Halogenated benzimidazoles and benzotriazoles as selective inhibitors of protein kinases CK I and CK II from Saccharomyces cerevisiae and other sources. *Biochim. Biophys. Res. Commun.* 1993, 208, 418–424. [CrossRef]
27. Battistutta, R. Structural bases of protein kinase CK2 inhibition. *Cell. Mol. Life Sci.* 2014, 71, 1889. [CrossRef] [PubMed]
28. Schwind, L.; Nalbach, L.; Zimmer, A.D.; Kostelnik, K.B.; Menegatti, J.; Grasser, F.; Gotz, C.; Montenarh, M. Quinalizarin inhibits a potent, selective and cell-permeable inhibitor of protein kinase CK2. *Biochem. J.* 2009, 421, 387–395. [CrossRef] [PubMed]
29. Schneider, J.; Litchfield, D.W.; Shugar, D. Tetrabromobenzotriazole (TBBt) and tetrabromobenzimidazole (TBBz) as selective inhibitors of protein kinase CK2: Evaluation of their effects on cells and different molecular forms of human CK2. *Biochim. Biophys. Acta* 2005, 1754, 271–280. [CrossRef] [PubMed]
30. Zien, P.; Duncan, J.S.; Skierski, J.; Bretner, M.; Litchfield, D.W.; Shugar, D. Tetramobromobenzotriazole (TBBt) and tetramobromobenzimidazoles (TBBz) as selective inhibitors of protein kinase CK2: Evaluation of their effects on cells and different molecular forms of human CK2. *Biochim. Biophys. Acta* 2005, 1754, 271–280. [CrossRef] [PubMed]
31. D'Amore, C.; Borgo, C.; Sarno, S.; Salvi, M. Role of CK2 inhibitor CX-4945 in anti-cancer combination therapy-potential clinical relevance. *Cell. Oncol.* 2020, 43, 1003–1016. [CrossRef] [PubMed]
32. Pierre, F.; Chua, P .C.; O'Brien, S.E.; Siddiqui-Jain, A.; Bourbon, P.; Haddach, M.; Michaux, J.; Nagasawa, J.; Schwaebe, M.K.; Stefan, E.; et al. Discovery and SAR of 5-(3-chlorophenylamino)benzo[c][2,6]naphthyridine-8-carboxylic acid (CX-4945), the first clinical stage inhibitor of protein kinase CK2 for the treatment of cancer. *J. Med. Chem.* 2011, 54, 635–654. [CrossRef]
33. Siddiqui-Jain, A.; Drygin, D.; Streiner, N.; Chua, P.; Pierre, F.; O'Brien, S.E.; Bliesath, J.; Omori, M.; Huser, N.; Ho, C.; et al. CX-4945, an Orally Bioavailable Selective Inhibitor of Protein Kinase CK2, Inhibits Prosurvival and Angiogenic Signalling and Exhibits Antitumor Efficacy. *Cancer Res.* 2010, 70, 10288–10298. [CrossRef]
34. Miyazaki, J.; Araki, K.; Yamato, E.; Ikegami, H.; Asano, T.; Shibasaki, Y.; Oka, Y.; Yamamura, K. Establishment of a pancreatic islet cell line that retains glucose-inducible insulin secretion: Special reference to expression of glucose transporter isoforms. *Endocrinol. Metab. (Tokyo)* 1993, 36, 37–43. [CrossRef]
35. Ishihara, H.; Asano, T.; Tsukuda, K.; Katagiri, H.; Inukai, K.; Anai, M.; Kikuchi, H.; Yazaki, Y.; Miyazaki, J.I.; Oka, Y. Pancreatic islets of Langerhans reveals importance of homotypic cell interactions. *Pancreas* 2005, 30, 251–257. [CrossRef]
36. Schwind, L.; Nalbach, L.; Zimmer, A.D.; Kostelnik, K.B.; Menegatti, J.; Grasser, F.; Gotz, C.; Montenarh, M. Quinalizarin inhibits adipogenesis through down-regulation of transcription factors and microRNA modulation. *Biochim. Biophys. Acta* 2017, 1861, 3272–3281. [CrossRef] [PubMed]
37. Miyazaki, J.; Araki, K.; Yamato, E.; Ikegami, H.; Asano, T.; Shibasaki, Y.; Oka, Y.; Yamamura, K. Establishment of a pancreatic beta cell line that retains glucose-inducible insulin secretion: Special reference to expression of glucose transporter isoforms. *Endocrinol. Metab. (Tokyo)* 1993, 36, 37–43. [CrossRef]
38. Borgo, C.; Ruzzene, M. Protein kinase CK2 inhibition as a pharmacological strategy. *Adv. Protein Chem. Struct. Biol.* 2021, 124, 23–46. [CrossRef] [PubMed]
39. Cozza, G.; Meggio, F.; Moro, S. The dark side of protein kinase CK2 inhibition. *Curr. Med. Chem.* 2011, 18, 2867–2884. [CrossRef] [PubMed]
40. Duncan, J.S.; Litchfield, D.W. Too much of a good thing: The role of protein kinase CK2 in tumorigenesis and prospects for therapeutic inhibition of CK2. *Biochim. Biophys. Acta* 2008, 1784, 33–47. [CrossRef]
41. Kuenzel, E.A.; Krebs, E.G. A synthetic peptide substrate specific for casein kinase II. *Proc. Natl. Acad. Sci. USA* 1985, 82, 737–741. [CrossRef]
42. Kim, H.; Lee, K.S.; Kim, A.K.; Choi, M.; Choi, K.; Kang, M.; Chi, S.W.; Lee, M.S.; Lee, J.S.; Lee, S.Y.; et al. A chemical with proven clinical safety rescues Down-syndrome-related phenotypes in through DYRK1A inhibition. *Dis. Models Mech.* 2016, 9, 839–848. [CrossRef]
48. Cozza, G.; Sarno, S.; Ruzzene, M.; Girardi, C.; Orzeszko, A.; Kazimierczuk, Z.; Zagotto, G.; Bonaiuto, E.; Di Paolo, M.L.; Pinna, L.A. Exploiting the repertoire of CK2 inhibitors to target DYRK and PIM kinases. Biochim. Biophys. Acta 2013, 1834, 1402–1409. [CrossRef]
49. Ahmad, K.A.; Wang, G.; Slaton, J.; Unger, G.; Ahmed, K. Targeting CK2 for cancer therapy. Anti-Cancer Drugs 2005, 16, 1037–1043. [CrossRef]
50. Licciardello, M.P.; Workman, P. A New Chemical Probe Challenges the Broad Cancer Essentiality of CK2. Trends Pharmacol. Sci. 2021, 42, 313–315. [CrossRef]
51. Intemann, J.; Saidu, N.E.B.; Schwind, L.; Montenarh, M. ER stress signaling in ARPE-19 cells after inhibition of protein kinase CK2 by CX-4945. Cell. Signal. 2014, 26, 1567–1575. [CrossRef] [PubMed]
52. DiMaira, G.; Salvi, M.; Arrigoni, G.; Marin, O.; Sarno, S.; Brustolon, F.; Pinna, L.A.; Ruzzene, M. Protein kinase CK2 phosphorylates and upregulates Akt/PKB. Cell Death Differ. 2005, 12, 668–677. [CrossRef] [PubMed] | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3713,
1
],
[
3713,
8069,
2
],
[
8069,
11773,
3
],
[
11773,
15221,
4
],
[
15221,
19541,
5
],
[
19541,
21262,
6
],
[
21262,
24486,
7
],
[
24486,
25896,
8
],
[
25896,
30529,
9
],
[
30529,
34927,
10
],
[
34927,
39884,
11
],
[
39884,
40886,
12
]
]
} |
5c9694dbaa905ec2db4c55f2e57a355580cdfb37 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 24,
"total-fallback-pages": 0,
"total-input-tokens": 56999,
"total-output-tokens": 16763,
"fieldofstudy": [
"Engineering",
"Physics"
]
} | A CFD-Based Comparison of Different Positive Displacement Pumps for Application in Future Automatic Transmission Systems
Thomas Lobsinger 1,*; Timm Hieronymus 1, Hubert Schwarze 2 and Gunther Brenner 3
Abstract: The efficiency requirements for hydraulic pumps applied in automatic transmissions in future generations of automobiles will increase continuously. In addition, the pumps must be able to cope with multiphase flows to a certain extent. Given this background, a balanced vane pump (BVP), an internal gear pump (IGP) and a three-dimensional geared tumbling multi chamber (TMC) pump are analyzed and compared by a computational fluid dynamics (CFD) approach with ANSYS CFX and TwinMesh. Furthermore, test bench measurements are conducted to obtain experimental data to validate the numerical results. The obtained numerical results show a reasonable agreement with the experimental data. In the first CFD setup, the conveying characteristics of the pumps with pure oil regarding volumetric efficiencies, cavitation onset and pressure ripple are compared. Both the IGP and the BVP show high volumetric efficiencies and low pressure ripples whereas the TMC shows a weaker performance regarding these objectives. In the second CFD setup, an oil-bubbly air multiphase flow with different inlet volume fractions (IGVF) is investigated. It can be shown that free air changes the pumping characteristics significantly by increasing pressure and mass flow ripple and diminishing the volumetric efficiency as well as the required driving torque. The compression ratios of the pumps appear to be an important parameter that determines how the multiphase flow is handled regarding pressure and mass flow ripple. Overall, the BVP and the IGP show both a similar strong performance with and without free air. In the current development state, the TMC pump shows an inferior performance because of its lower compression ratio and therefore needs further optimization.
Keywords: positive displacement pumps; internal gear pump; balanced vane pump; tumbling multi-chamber pump; CFD; multiphase flow
1. Introduction
In the last few years and in the decades to come the automotive industry worldwide faces a great transformation. Classical internal combustion engine (ICE) powertrains are more and more replaced by hybrid or electrical powertrains for ecological reasons. This also influences the market of transmission systems. Looking at ICE powertrains, the market share of automatic transmission systems worldwide increased constantly for many years until now. This is because drivers favor the comfort of an automatic transmission over a manual one [1,2]. There are different types of automatic transmission systems. The most important type is the classical torque converter automatic transmission (AT), which was first invented and applied in the 1930s and 1940s in the United States. Besides that, continuous variable transmissions (CVT) and dual clutch transmissions (DCT) became
more and more popular in the last decades [2]. All these transmission systems have in common that they require a hydraulic circuit to operate. To actuate clutches, brakes and shifting elements, a pressurized hydraulic fluid is required. In addition, the systems need to be lubricated and cooled by a certain flow rate of the automatic transmission oil [3]. This also applies to modern compactly constructed electrical drivetrain systems, such as the eAxle [4,5]. Because of their compactness and functional design, they require lubrication and cooling by a hydraulic fluid. Furthermore, there are electrical powertrains that include a two-speed automatic transmission for efficiency reasons or to achieve higher top speeds and starting torques [5]. These systems likewise require a hydraulic oil circuit to operate. Overall, this means that despite the ongoing transformation towards electrical powertrains, automatic transmissions will still be present for many years and need to be further improved and developed. Moreover, there are chances that hydraulic circuits are applied in some electrical drivetrains in the future. Therefore, the respective hydraulic pumps also need to be further developed and optimized, as they are essential for the function of the systems.
The requirements, which the pumps have to fulfil, have become stricter in recent years. On the one hand, this concerns the noise emission, as the powertrains themselves became quieter. Thus, the acoustic characteristics of the pumps have to be improved in order to avoid that their noise spectrum remains the only one that can be perceived. Generally, this means that the pressure ripple caused by the pump should be as low as possible. Analog to that a low ripple of the mass flow rate and volumetric flow rate is required. In addition, the overall efficiency of the pumps is becoming increasingly important. As the required power to operate the oil pump has to be branched off from the ICE, inefficient pumps can diminish the driving range and increase fuel consumption. This also applies if a small electric motor is used to run the pump, as the required power has to be branched off the battery.
Besides that, pump operation in multiphase flow conditions is a requirement that is becoming more and more important. On the one hand, this means that the pump has to cope with high rotational speeds without being damaged by cavitation erosion. On the other hand, the pump must function reliably when priming not only pure liquid oil but also air bubbles or oil foam. Oil foam formation is a common phenomenon in transmission systems despite the usage of anti-foaming agents. Additionally, the pump has to prime the oil from a tank through a suction nozzle. In different driving situations, it happens that the fluid level inside the tank tilts and the pump is suddenly priming big chunks or bubbles of air. Furthermore, there is often a certain amount of dissolved air apparent in hydraulic oils, which can outgas suddenly at pressure drops. Consequently, the pump is required to handle high inlet gas volume fractions (IGVF) of free air of up to 40%. Of course, this changes the operational characteristic significantly. For future transmission applications, these requirements are expected to become even stricter. Because of that, the question arises, if vane pumps, which are often applied in automatic transmission systems, are the most suitable positive displacement pump (PDP) type for these systems [6]. Therefore, besides a balanced vane pump, two other positive displacement pump types are investigated and compared to each other in this work by using a computational fluid dynamics (CFD) approach.
There are a few scientific contributions, which are investigating this issue and directly compare different pump types to each other. For example, the authors in [7] theoretically and experimentally compare different pump types for application in a CVT system. They found that roller vane pumps could be a promising and fitting solution. In [3], the influence of pump selection on the fuel economy of a DCT vehicle is investigated by the use of analytical models. The authors found that the application of a variable displacement vane pump instead of a gerotor pump results in a significantly better fuel economy. However, there is no study available that compares different pump types by means of extensive three-dimensional (3D)-CFD simulations. Generally, there are many scientific publications focusing on various aspects of positive displacement pumps through different simulative
and experimental approaches. One simulative way is to use one-dimensional (1D) or zero-dimensional (0D) lumped parameter models to investigate basic operational characteristics. Examples for such studies are [8–15]. For more complex problems, 3D-CFD simulations are a way to gain a detailed insight into PDPs. As PDPs form rotating and deforming fluid volumes while they operate, the mesh generation is challenging. However, a few different ways to generate the appropriate grids were successfully applied. An overview of them can be found in [16]. Another challenge when performing CFD simulation of PDP are the inherent tight clearances, which determine the volumetric efficiency of the machines. Phenomena such as vapor cavitation and outgassing of dissolved air in PDPs are investigated in depth by CFD simulations in [17,18]. However, simulating a bubbly air–oil multiphase flow is difficult in positive displacement pumps because of the tight clearances, and therefore, there is a lack of such studies [19]. The authors presented their approach to model a bubbly oil–air multiphase flow in [20] and applied it successfully to a simplified two-dimensional (2D) case of a vane pump. In this work, this approach is transferred and applied to 3D pump geometries and validated by experimental data. The aim of this paper is to improve the understanding for the operational characteristic of the three different PDPs and compare them regarding their operation with and without free air.
2. Investigated Pump Types
2.1. Balanced Vane Pump (BVP)
As already mentioned, the vane pump is often applied as hydraulic supply in automatic transmission systems because of its high specific performance, good overall efficiency, adaptability and its beneficial acoustic characteristic. Weaknesses of the vane pump are its inferior quick start ability and a high susceptibility regarding dirt particles in the oil [6,21–24]. The inner parts of the investigated Bosch balanced vane pump with \( V_{\text{displ}} = 14.8 \text{ cm}^3/\text{rev} \) are shown in Figure 1a. Twelve vanes, which move radially in and out of the rotor in slots, slide along a cam ring and form displacement chambers for the fluid. The cam ring curve determines where the chamber volume is increasing and decreasing, and therefore, where fluid is primed into the chamber or pushed out. The investigated vane pump is a balanced vane pump, which means within one rotor revolution, two suction and two delivery ports are supplied. Both strokes are of the same height and the two delivery ports merge before the outlet. The occurring pressure forces consequently balance each other out. Further details regarding its function can be found in [20].
2.2. Internal Gear Pump (IGP)
As a second pump type, an Eckerle Technologies internal gear pump without a crescent with \( V_{\text{displ}} = 15 \text{ cm}^3/\text{rev} \) is investigated. It features a compensation ring to reduce the radial gap heights between the gear teeth in operation. Besides that, it has also a mechanism to reduce the axial gap heights. Advantages of this pump type are its high volumetric efficiency, its good quick start ability and its robustness against dirt particles. Its lower available displacement volume \( V_{\text{displ}} \) per overall installation space and its limited adaptability, as the IGP cannot be designed in such a way that it makes two strokes within one revolution, are two disadvantages of this pump type [6]. The inner parts
---
**Figure 1.** Inner parts of the BVP (a) and the IGP without a crescent (b).
of the investigated internal gear pump can be seen in Figure 1b. The pinion features 15 teeth and the ring gear 16 teeth. The suction side is located where the displacement chambers formed between the gears increase in size. The motion of the gears conveys the fluid from the suction to the delivery side, and in the delivery side, the chambers decrease in volume and the fluid is pushed out into the delivery port. Gaps between the tooth tips are kept very small in this pump by the aforementioned mechanical compensation mechanism using the pressure difference between suction and delivery side. Hence, the leakage flow through these gaps is minimized.
2.3. Tumbling Multi-Chamber Pump (TMC)
The third pump type to be investigated is the TMC pump. This is a new gear pump principle developed by Bosch in the last couple of years. The BVP and the IGP are both built up by two-dimensional shapes, whereas the TMC pump features three-dimensional shaped trochoid gears. The gears are aligned axially inside the housing. The TMC pump’s most important internal parts are displayed in Figure 2: the rotor (a), stator (b) and the hollow shaft (c). The hollow shaft is driven by a motor and transfers torque to the rotor via a slanting plate. A spring ensures that the hollow shaft and the rotor are always axially pushed against the stator to keep the existing leakage gaps coming from the manufacturing tolerances small. This preloading, furthermore, reduces the negative effects of occurring wear during the operation. Therefore, the pump parts can be molded from polymer materials, which leads to a great advantage regarding the manufacturing costs in the range of 30–50% compared to standard gear pumps at optimal annual production volumes.
Within one hollow shaft rotation, the rotor tumbles one tooth further inside the stator. The increasing and decreasing fluid volumes between rotor and stator push and pull fluid through the channels in the rotor, similar to an axial piston pump. The slanting plate acts as a valve plate and separates suction and delivery port. Further details of this pump’s function can be found in the work of Munih et al. [16].
The advantages of this pump type are low manufacturing cost, as the pump parts can be molded from a polymer material, high efficiency and its robustness against dirt particles [16]. The geometry of the teeth can be optimized for different applications. For our investigations, prototype injection molded pump parts without additional mechanical machining out of thermoset material are used due to their availability. These parts are from another application and were, therefore, optimized for a different medium and pressure range but with a suitable theoretical displacement volume of \( V_{\text{displ}} = 15.9 \text{ cm}^3/\text{rev} \). The rotor has eight gear teeth, the stator has seven. A sectional view through the pump is provided in Figure 3. Orange arrows indicate the flow path from the suction to the delivery port.
A particular feature of the TMC pump is that due to its design, the rotor channels are always connected to the displacement chambers forming between rotor and stator. They present an additional fluid volume, which is not changing in size within the rotation. Therefore, the calculated compression ratio of this pump in the current development state is much lower compared to the two other pumps. However, it would be possible to change that by adjusting the rotor design.
The key properties and dimensions of all three pumps are summarized in Table 1.
**Table 1.** Key properties and dimensions of the investigated pumps.
| | Balanced Vane Pump (BVP) | Internal Gear Pump (IGP) | Tumbling Multi-Chamber Pump (TMC) |
|------------------------|--------------------------|---------------------------|-----------------------------------|
| Manufacturer | Robert Bosch Automotive Steering GmbH | Eckerle Technologies GmbH | Robert Bosch GmbH |
| $V_{\text{displ}}$ | 14.8 cm$^3$/rev | 15.0 cm$^3$/rev | 15.9 cm$^3$/rev |
| Number of displacement elements | 12 | 15 | 7 |
| Compression ratio | 9.15 | 11.93 | 3.67 |
| $V_{\text{displ}}/V_{\text{core}}$ | 0.094 | 0.058 | 0.034 |
| External housing dimensions (axial length/diameter) | 90 mm/120 mm | 125 mm/150 mm | 185 mm/125 mm |
In Table 1, the specific displacement volume $V_{\text{displ}}/V_{\text{core}}$ is also listed. The volume $V_{\text{core}}$ does not mean the total needed installation space of the pump with the housing and the shaft but only the volume enclosing the main internal parts of the pump. A higher value means that the pump achieves a high $V_{\text{displ}}$ without using much space for the main internal parts. It can be clearly seen that the BVP has the highest value here. This is due to its design as a double stroke type.
**3. CFD Models**
**3.1. Balanced Vane Pump (BVP)**
The computational mesh of the BVP has a total of 7.8 million computational cells. The rotating and deforming displacement chambers are meshed with a structured hexahedral grid, which is generated with the commercial software TwinMesh. In radial direction,
24 cells are used to resolve the displacement chambers. In axial direction, there are 90 cells, and in circumferential direction, 1600 cells are used. The radial gaps between the vane tips and the cam ring are assumed to be 2 \( \mu \text{m} \) in height. As the grid has an O-shaped topology, all cell layers in the displacement chambers are also present in the radial gaps. The axial gaps, forming between the housing, the vanes and the rotor have a height of 8 \( \mu \text{m} \) on both sides. They are resolved by an unstructured mesh with 15 cell layers in the axial direction. The assumptions for the different gap heights result from the manufacturing tolerances of the pump parts and measurement data from earlier investigations. The spatial mesh resolution for the rotor and the gaps is derived from investigations of the authors presented in [20], where a grid convergence study on a 2D model of a BVP was performed. However, for the investigated 3D cases, a compromise between high spatial resolution and computational cost must be made. The details of the moving rotor mesh are displayed in Figure 4. The mesh nodes are kept fixed on the vane and rotor contour, while they can slide on the outer cam ring contour. Between the structured rotor mesh and the unstructured mesh of the stator parts, interfaces provide grid connections. Similar cell aspect ratios and cell volumes on both sides of the interfaces are especially important to achieve convergence. In the stator parts, all walls are refined with prism layers to ensure a \( y^+ < 30 \) value in the first cell layer near the wall. This value for the dimensionless wall distance \( y^+ \) is necessary to fulfill the mesh requirements of the wall function of the employed turbulence models in ANSYS CFX. The complete model with the corresponding boundary conditions (BC) can be seen in Figure 5a.
**Figure 4.** Mesh of the displacement chambers (a) and details of the radial gap mesh (b) of the BVP.
**Figure 5.** Full CFD model with BCs (a) and meshing details of the axial gaps and grooves (b) of the BVP.
Although a double stroke balanced vane pump is investigated, both suction and delivery ports are merging in the pumps housing, so there is just one inlet and one outlet. Further meshing details of the axial gap mesh and the different grooves and notches can be seen in Figure 5b. It is especially important to resolve the grooves with a high spatial resolution, as very high pressure gradients and velocities occur at these locations.
3.2. Internal Gear Pump (IGP)
The computational mesh of the internal gear pump has a total of 8.2 million cells. In the structured mesh of the displacement chambers forming between the gears of pinion and gear ring, which is generated by TwinMesh, the grid nodes are kept fixed both on the contours of the gear ring and the pinion. As the pinion and gear ring are both rotating with different rotation rates, the mesh is divided into two separate parts, which are connected
by an interface. The mesh nodes can slide on the interface, which is displayed in Figure 6a. Both mesh parts have 20 cells in radial direction. In axial direction, there are 50 cell layers. Circumferentially, there are about 2000 nodes on the pinion and gear ring. The topology of the two meshes is also O-shaped. The radial gaps are assumed to have a height of 5 µm, and the mesh in the gap region is displayed in Figure 6b.
Figure 6. Mesh of the displacement chambers (a) and meshing details of the radial gaps (b) of the IGP.
Besides the radial gaps, there are also axial gaps between the housing and the gears, which have to be considered in the CFD simulation. They are assumed to be 5 µm in height and resolved with 18 cell layers in axial direction. The meshing of the stator parts is done with an unstructured grid with prism layers on the walls. The complete CFD model of the IGP with the respective boundary conditions is displayed in Figure 7a. Figure 7b shows the structured mesh of the axial gap and the unstructured mesh of the delivery port stator part.
Figure 7. Full CFD model with BCs (a) and meshing details of the axial gap and the delivery port groove (b) of the IGP.
3.3. Tumbling Multi-Chamber Pump (TMC)
The computational mesh of the TMC pump has a total cell count of 9.6 million cells. As mentioned in Section 2, the hollow shaft transfers torque to the rotor by a slanting plate. This means that the respective meshes for the fluid volume in the rotor and in the hollow shaft have different motion functions. The mesh of the displacement chambers forming between rotor and stator is generated by TwinMesh. In the gaps between the teeth, which are assumed to be 10 µm in height, 23 cell layers are used in θ-direction. In r-direction, there are 60 cell layers, while in φ-direction, there are 1500 elements over the total circumference. These meshing details are displayed in Figure 8.
Besides this apparent leakage path through the gaps between the teeth, there are other leakage paths from the delivery to the suction side, which have to be considered and incorporated in the model in order to get a correct estimation of the volumetric efficiency of the pump. The two spherical gaps, which are formed between stator and rotor, as the rotor slides in the stator, are assumed to be 10 µm (inner spherical gap) and 20 µm (outer spherical gap) in height. They are displayed in Figure 9a. Both are resolved with 15 cell layers in r-direction. Between the rotor and the slanting plate of the hollow shaft, there is a gap, which is estimated to be 10 µm in height, and it is also resolved by 15 cells. The unstructured mesh of this rotor–shaft gap is displayed in Figure 9b. Finally, there is a gap between the hollow shaft and its journal bearing (see Figure 3), which is assumed to be 20 µm in height. High-pressure oil from the delivery port can flow back into the suction port through this gap. Therefore, it is incorporated in the CFD model of the TMC pump by resolving it with 15 cell layers in radial direction. The rotor channels and the hollow shaft are resolved with unstructured meshes. These can be seen in Figures 9b and 10b.
All these tight gaps contribute to a higher total cell count of the TMC pump CFD model compared to the two other pumps. In Figure 10a, the complete CFD model with
its boundary conditions and, in Figure 10b, the mesh of the fluid volume in the hollow shaft are displayed. It is clearly visible how delivery and suction ports are separated from each other by the hollow shaft geometry. At the interface to the rotor–shaft gap, the mesh needs to be especially fine in order to avoid high differences in cell volume and high aspect ratios at the interface. The suction port and the delivery port are resolved by unstructured meshes.
3.4. General CFD Setup and Boundary Conditions
For the numerical investigations, ANSYS CFX is used as CFD solver. To investigate all mentioned multiphase phenomena in one single setup is quite difficult, because a three-phase approach would be necessary. This would lead to further numerical difficulties and convergence issues. Therefore, it is decided to investigate the multiphase phenomena separately in two independent numerical setups. On the one hand, setup 1 incorporates cavitation phenomena by employing a homogeneous Euler–Euler two phase flow setting with a continuous liquid oil and a continuous oil vapor phase. The mass transfer between the two phases is modelled by the Rayleigh–Plesset Cavitation model. Setup 2 incorporates an inhomogeneous Euler–Euler multiphase flow regime with continuous liquid oil and disperse bubbles of free air. No mass transfer between the phases is considered. Both setups are explained in more details in [20]. Additionally, further investigations concerning model parameters are discussed in that article. The most important details of both numerical setups are listed in Table 2.
| Setup 1 (Cavitation) | Setup 2 (IGVF of Free Air) |
|----------------------|---------------------------|
| Simulation method | RANS, unsteady | RANS, unsteady |
| Euler–Euler approach | homogeneous | inhomogeneous |
| Phases | Liquid oil | Oil vapor |
| Phase morphology | Continuous | Continuous |
| Turbulence model | k-ω SST | k-ω SST |
| Interphase transfer | Rayleigh–Plesset, 2 μm mean bubble diameter | Particle Model, 0.1 mm mean bubble diameter |
| Mass transfer | - | - |
| Momentum transfer | - | Schiller Naumann |
| Heat transfer | - | Ranz Marshall |
| Turbulence transfer | - | SATO Enhanced Eddy Viscosity |
| Buoyancy | - | Density difference |
To spatially discretize the deforming and rotating displacement chambers of these three positive displacement pumps, a moving mesh approach is selected. As already mentioned, the commercial software TwinMesh is used for the grid generation. TwinMesh generates structured hexahedral meshes with a high cell quality, which is especially important for multiphase flow simulations [25]. The meshes are generated in advance for a certain angle step size and are then loaded into the ANSYS CFX solver by a Junction Box routine at the beginning of each time step. For most simulations, an angle step size of 0.5° is sufficient. For the simulations with an IGVF > 0, a smaller angle step size of 0.25° is required to obtain convergence. For the investigated rotational speeds from 500–6000 rpm, this leads to a time step size range from 1.61·10⁻⁵ s to 8.33·10⁻⁵ s. This ensures mean Courant numbers C < 5 at all investigated operating points for the three CFD models. As operating fluid, a typical transmission oil is used. The fluid properties of the oil are listed in Table 3.
Table 3. Fluid properties of the automatic transmission oil at 20 °C and 1 bar.
| Property | Value |
|----------------------------------|-----------|
| Density (kg/m³) | 843 |
| Dynamic Viscosity (Pa·s) | 0.07485 |
| Liquid Bulk Modulus (Pa) | 1.5·10⁹ |
| Surface Tension Oil–Air (N/m) | 2.5·10⁻² |
| Vapor Pressure (Pa) | 30 |
| Specific Heat Capacity (J/(kg·K))| 1781 |
| Thermal Conductivity (W/(m·K)) | 0.142 |
At the inlet of the fluid domain in the suction ports, a pressure BC of 1 bar is set. In addition, the IGVF is applied there when setup 2 is used. At the outlet in the delivery port, another pressure BC with the investigated pressure load is used as well as a zero gradient BC for the volume fractions of the different phases.
To investigate and compare the pressure ripple in the delivery port of the pumps, a further tubular extension of the computational domain starting at the delivery port outlet of the pumps including an orifice is added. This can be seen in Figure 11. The tubular extension is identical for all three pumps and represents the setup at the test bench, where the experimental data are obtained. The new outlet pressure boundary condition for these cases is set to 1 bar, as the pressure drop over the orifice serves as the pressure load. The intention of this long tubular extension is to minimize the influence of the outlet boundary condition on the pressure ripple induced by the pumps that are monitored at the indicated point. The orifice diameter is adjusted until the time averaged pressure at the monitor point equals the desired pressure load.
Furthermore, the rotational speed of the rotor is set as a boundary condition for the Junction Box routine that loads the grids into the solver, and all simulations are performed at an inlet oil temperature of 20 °C.
It is important to mention that in all simulations conducted with setup 2 (IGVF of free air), all incorporated clearances in the CFD models for the three pumps have to be artificially enlarged to 30 µm height in order to obtain convergence. The multiphase flow setup 2 does not converge for smaller clearances. However, for setup 1 (cavitation) the original clearance height dimensions, which were mentioned before, are used for the CFD simulations.
4. Test Bench Measurements
In order to validate the numerical results, measurements are conducted. The respective test bench setup is schematically shown in Figure 12. High-frequency pressure and temperature sensors are placed in the suction and delivery port. Furthermore, the volumetric flow rate is measured on the delivery side. On the suction side, air is injected into the oil by a compressor. The IGVF of free air $\alpha_{air}$ is determined in the suction area by a Flucon Concentration Gas System (CGS) Inline Aeration Meter, which derives the IGVF from measuring the complex fluid impedance of the mixture and comparing it to the complex fluid impedance of the pure liquid oil.
Furthermore, the required driving torque and the respective power demand of the motor are measured. Measurement data are obtained at 30 operating points with no air injection and at 27 operating points with 5–20% IGVF of free air. The pressure load is varied between 5 bar and 22.5 bar, and the rotational speed ranges from 500 rpm up to 6000 rpm. The inlet oil temperature is held constant at a value of 20 °C.
For validation purposes, an additional measurement campaign is performed with the BVP, where the displacement chamber pressure is recorded during the pump rotation by a high frequency pressure sensor, which is glued into the rotor. The experimental setup is analog to the work of Suzuki et al. [26] and Hieronymus et al. [27]. The pressure transducer in the rotor can be seen in Figure 13.
The measured pressure data are transferred to the data acquisition system by wires leading through the driving shaft and a slip ring. With this setup, measurements up to 3000 rpm and 22.5 bar pressure load can be performed.
5. Results
5.1. Setup Cavitation (IGVF = 0)
At first, the results obtained with the setup 1 (cavitation, see Table 2) are investigated. In Figure 14, the conveying characteristics and the equivalent volumetric efficiencies of the three pumps are compared. The volumetric efficiencies are calculated as stated in Equation (1).
\[
\eta_{vol} = \frac{Q_{actual}}{Q_{theo}} = \frac{Q_{theo} - Q_{leakage}}{Q_{theo}} \text{ with } Q_{theo} = V_{displ} \cdot n
\]
(1)
In Figure 14a, it is visible that for the TMC pump, cavitation starts at about 3500 rpm. The maximum volumetric flow rate is restricted to a value of slightly below 60 L/min. At 4000 rpm, the BVP is the second pump to reach the cavitation onset, and at 5000 rpm, the IGP is the last one, reaching a volumetric flow rate of approximately 80 L/min. This can be explained by the different suction port geometries and filling strategies of the displacement chambers in the pumps. In the TMC pump, the flow has to perform a 180° turn in the stator suction port area in order to reach the channels in the rotor where the oil is sucked into the displacement chambers (see Figure 3). This leads to high velocities and a high pressure drop resulting in an early cavitation onset. This could be improved by designing a new suction port geometry with a radial inlet. The BVP has two suction ports where the fluid is fed into the displacement chambers, as it is of two-stroke type. Furthermore, the chambers are fed both axially and radially, which leads to higher flow cross section area, less pressure loss and, hence, a delayed cavitation onset. The IGP, however, has the highest flow cross section area in the suction port. Although it is of one-stroke type and only axially fed, the suction port is laid out with ample flow cross section area and small pressure losses. Therefore, the cavitation onset is further delayed to higher rotational speeds.
Additionally, it can be seen in Figure 14a that the three pumps show a slightly different gradient \( \frac{dQ_{\text{actual}}}{dN} \) for rotational speeds before the cavitation onset. As \( \frac{dQ_{\text{actual}}}{dN} \approx V_{\text{disp}} \), the TMC pump has a slightly higher gradient and the BVP a slightly lower one with the gradient of the IGP staying between those two. This corresponds to the theoretical displacement volumes \( V_{\text{disp}} \) of the pumps, which are listed in Table 1.
The volumetric efficiencies of the three pumps are in a quite similar range between 1000 and 3500 rpm, which can be obtained from Figure 14b. At lower rotational speeds the BVP seems to feature slightly higher volumetric efficiencies than the IGP and the TMC pump.
To validate the CFD model of the three investigated pumps, in Figure 15, Figure 16, Figure 17, the volumetric efficiencies obtained from the CFD simulations are compared with the experimental data.
Figure 15. Volumetric efficiencies obtained from the CFD simulations and from the experiment for the IGP at 22.5 bar pressure load and 20 °C oil temperature.
As it can be observed from Figures 15 and 16, the CFD data show a good fit to the experimental data for the BVP and the IGP. By iteratively calibrating, the applied Rayleigh–Plesset cavitation model constants to $F_{vap} = 90$ and $F_{cond} = 0.01$, the cavitation onset is also captured quite well. However, the drop of the volumetric efficiency due to the onset of cavitation with increasing rotational speed is underestimated for all three pump types. This is probably because of the limitations of the Rayleigh–Plesset cavitation model. It only incorporates vapor cavitation, while in reality, we can expect vapor cavitation as well as outgassing of dissolved air from the oil limiting the suction capability of the pumps. The usage of a more sophisticated cavitation model could be a way to enhance this prediction.
For the case of the TMC pump, it can be clearly seen in Figure 17 that the CFD prediction for the volumetric efficiency does not fit as well to the experimental data, as it does for the BVP and the IGP. The volumetric efficiency is considerably overpredicted in the CFD simulations. As the volumetric efficiency is governed by the internal leakages, most possibly a difference between the clearance heights assumed in the CFD model and the real clearance heights are responsible for this deviation. Besides the deviation in absolute value of the volumetric efficiency, the qualitative characteristic while increasing the rotational speed is captured quite well. This indicates that the CFD model itself is valid, but the assumptions for the gap heights need to be improved. However, it is quite difficult to determine the actual gap heights during pump operation. Furthermore, the gap height is kept constant in the CFD simulation. In reality, the rotor–stator system with the spring can dynamically move axially depending on the pressure distributions and the spring stiffness. This effect, which then enlarges the gap heights significantly, is not incorporated in the CFD simulations and could be a further reason for the deviation, which especially becomes higher at rotational speeds above 3500 rpm, when cavitation starts. Additionally, the limits of the employed cavitation model contribute to the higher deviations here.
Considering the experimental data, the TMC pump shows lower volumetric efficiencies than the BVP and the IGP, which are both on a similar, higher level. Apparently, the gap heights in the TMC pump are larger than assumed. One possibility to improve this would be to use a spring with a higher stiffness (see Figure 3). The force pushing the rotor against the stator would increase and the leakages would decrease. However, this would presumably also lead to an increased required driving torque and wear.
Besides the volumetric efficiency and the conveying characteristic, the instantaneous pressure profile inside a displacement chamber within one shaft rotation is quite distinctive for a pump’s operational characteristic. In Figure 18, the pressure profiles gained by the CFD simulations for all three pumps are compared to each other at two different operating points. It has to be noted that for the BVP and the IGP, the shaft rotation angle equals the rotor rotation angle. For the TMC pump, because of the slanting plate, this is not the case. Within one shaft rotation of 360° the rotor undergoes a rotation of 51.42° around the tilted axis. However, to compare the pumps, in the following, all instantaneous displacement chamber profiles are plotted over the shaft rotation angle.
Figure 18. Comparison of the CFD data for the displacement chamber pressure profiles at $p_2 = 22.5$ bar pressure load and 20 °C oil temperature for 1000 rpm (a) and 3000 rpm (b).
The first obvious difference between all three pumps is that the BVP undergoes two delivery pressure plateaus within one shaft revolution. Furthermore, it is obvious that the pressure surge, when the displacement chamber connects to the delivery port, has the highest values for the BVP. Increasing the rotational speed increases the pressure surge height further. For the IGP, a pressure surge occurring when the displacement chamber disconnects from the delivery port seems to be especially distinctive, while both other pumps do not really show a pressure surge at that point. This can be quite well observed in Figure 18b and is due to the fact that the displacement chambers are still decreasing in volume when they disconnect from the pressure port. Furthermore, the pressure ripple while the displacement chamber is connected to the delivery port shows the highest amplitudes for the TMC pump in Figure 18b.
To validate the CFD model, test bench measurements are conducted with a pressure transducer placed in the rotor wall of the BVP, recording the instantaneous pressure profile (see Section 4). In Figure 19, both CFD and experimental data are compared at two different operating points.
Figure 19. Displacement chamber pressure profiles of the BVP at $p_2 = 22.5$ bar pressure load and 20 °C oil temperature for 500 rpm (a) and 2000 rpm (b).
It is clearly visible that the CFD simulations overpredict the pressure surge appearing when the displacement chamber connects to the delivery port. This is, on the one hand,
due to numerical reasons and a high sensitivity regarding the meshing of the radial gap area and has also been observed by the authors in [27] for CFD simulations with the solver STAR-CCM+. On the other hand, in the CFD simulations, the radial gap height is kept constant. In reality, the vanes can radially recede when the force balance is disturbed, and therefore, the pressure surge may be damped, while the vanes slide a bit back into the rotor. Because of these reasons, it is quite challenging to accurately predict this pressure surge in the simulations. Apart from that pressure surge, the pressure profiles obtained numerically fit quite well to the experimental data. In Figure 19a, it can be seen that especially the two minor pressure drops at 181 and 211° on the delivery port plateau are very well captured. Those pressure drops result from the two following displacement chambers connecting to the delivery port [27]. The thereby occurring pressure surges are also visible in the observed displacement chamber, as the pressure waves travel through radial and axial gaps between displacement chambers.
As the noise emission of pumps is an important aspect, in the following, the pressure ripple at the delivery port is analyzed, as it is described in Section 3.4. In Figure 20, the 30° periodicity in the pressure signal of the BVP can be easily related to the 12 vanes. In the signal of the IGP, a 24° periodicity can be obtained, which here relates to the 15 teeth of the pinion. For the TMC pump, the seven gear teeth in the stator lead to a periodicity of 51.42° in the time signal of the pressure ripple.
From the CFD simulations for this operating point follows the conclusion that the pressure ripple of the TMC pump seems to be significantly higher in amplitude compared to the BVP and the IGP. However, when comparing the pressure ripple obtained from the CFD simulations to the test bench measurement for the BVP in a FFT analysis frequency wise, Figure 21 shows a deviation of both curves over the whole frequency range. Although the first few blade passing frequencies are correctly captured, the pressure ripple amplitudes are underpredicted by the CFD simulation. This shortcoming may be due to the negligence of the dynamic vane movement of the BVP in the simulation model.
For both the IGP and the TMC pump, the deviation between CFD data and experimentally obtained data is smaller than for the BVP, which can be seen in Figures 22 and 23. Both the blade passing frequencies and the amplitudes of the pressure ripple are reasonably captured in the low- and mid-frequency range. At higher frequencies, however, an increasing deviation can be observed for all pumps. Fluid structure interactions as well
as additional vibrations in the test bench setup emerging from the driving engine and being transferred through the hydraulic circuit into the fluid, which are not incorporated in the CFD simulations, could be a reason for this.
**Figure 22.** Delivery port pressure ripple FFT analysis obtained from the CFD simulations and the experiment for the IGP at $p_2 = 22.5$ bar pressure load, 20 °C oil temperature and 2000 rpm.
**Figure 23.** Delivery port pressure ripple FFT analysis obtained from the CFD simulations and the experiment for the TMC at $p_2 = 22.5$ bar pressure load, 20 °C oil temperature and 2000 rpm.
5.2. Setup Free Air ($IGVF > 0$)
When positive displacement pumps convey a multiphase flow with a nearly incompressible phase of oil and a strongly compressible phase of air, the volumetric efficiency decreases to a value below $\eta_{vol} < 1 - IGVF$ as the IGVF of air increases. The CFD setup 2 (IGVF of free air, see Table 2) is capable of predicting this drop for all three investigated pumps. The respective curves are displayed in Figure 24.
**Figure 24.** Volumetric efficiencies obtained from the CFD simulations at $p_2 = 5$ bar pressure load, 20 °C oil temperature and 2000 rpm while increasing the IGVF.
Besides the volumetric efficiency, the displacement chamber pressure profiles also change significantly when an $IGVF > 0$ is introduced. This was observed by the authors in [20] for a simplified 2D model of a BVP. In Figure 25, the influence of increasing the IGVF on the pressure profiles is shown for the BVP. With increasing IGVF, two effects occur. On the one hand, the pressure rise is delayed to higher shaft rotation angles with an increasing IGVF. The displacement chambers need more volume decline to achieve a pressure rise in the highly compressible mixture of oil and air than they need in pure oil. For the BVP, the pressure rise is delayed by 24.75° when the IGVF is at 10% compared to the pure oil with an IGVF = 0.
Figure 25. Displacement chamber pressure profiles for the BVP obtained from the CFD simulations at $p_2 = 5$ bar pressure load, 20 °C oil temperature, 2000 rpm and different IGVF.
On the other hand, the pressure ripple while the displacement chamber is connected to the delivery port also increases with increasing IGVF. The increase in the amplitudes of the pressure ripple while the chamber is connected to the delivery port is especially strong in the BVP, as it can be seen in Figure 25 when comparing it to the other two pumps in Figures 26 and 27.
Figure 26. Displacement chamber pressure profiles for the IGP obtained from the CFD simulations at $p_2 = 5$ bar pressure load, 20 °C oil temperature, 2000 rpm and different IGVF.
Figure 27. Displacement chamber pressure profiles for the TMC pump obtained from the CFD simulations at $p_2 = 5$ bar pressure load, 20 °C oil temperature, 2000 rpm and different IGVF.
The height of the pressure surge, when the displacement chamber is connected to the delivery port seems not to be much affected by introducing an IGVF. In the 2D investigations of the authors in [20], increasing the IGVF damped this pressure surge significantly. However, due to the missing third dimension, in the 2D case, this pressure surge is much higher, reaching values of \( \frac{P_1}{P_2} \approx 16 \) with pure oil. In the currently investigated 3D case of the BVP, this pressure surge is due to the grooves that are generally much smaller with values of \( \frac{P_1}{P_2} < 3 \). Because of that, an increase in the IGVF does not lead to a significant reduction in this first pressure surge.
Looking at the pressure profiles for the IGP in Figure 26, an increase in the IGVF does not decrease the height of the pressure surge when the displacement chamber connects to the delivery port but even increases it. With pure oil, this pressure surge in the IGP is lower than in the BVP, which means that the pump has a superior design with optimized control times at this operating point. A high pressure surge is, therefore, prevented with pure oil. The increased compressibility with free air, however, leads because of the specific and optimized control times and the compression ratio to a higher pressure difference when the displacement chamber connects to the delivery port. Thus, the pressure surge is intensified with an increasing IGVF. Contrary to that effect, the appearing pressure surge when the delivery port is disconnected is not decreased in the IGP. Analog to the BVP, the pressure ripple while the displacement chamber is connected to the delivery port increases with increasing the IGVF. However, the amplitudes of the pressure ripple on the delivery port plateau are much smaller in the IGP compared to the BVP. The delay of the pressure rise with increasing IGVF can likewise be observed in the IGP. The pressure rise is delayed by 15° when the IGVF is at 10% compared to the pure oil with an IGVF = 0.
For the TMC pump, the same tendencies can be observed in Figure 27. The first pressure surge is intensified by increasing the IGVF up to 10%, but then declines when the IGVF is further increased to 20 and 40%. In addition, this first pressure surge reaches values of \( \frac{P_1}{P_2} > 2 \) for 5 and 10% IGVF, which is higher than at both other pumps.
The same trend as in the other pumps applies to the amplitudes of the pressure ripple on the delivery port plateau. However, after intensifying the amplitudes of the pressure ripple up to an IGVF of 10%, a further increase up to 20% seems to lead to a decline analogous to the pressure surge. At 40% IGVF, however, an intensification can be seen in Figure 27 quite well again, and the pressure ripple amplitudes are the highest.
The delay of the pressure rise when an IGVF of 10% is applied compared to 0% is only 8.4° for the TMC pump. This appears to be due to the lower compression ratio of the displacement chambers compared to the other pumps (see Table 1). The rotor channels, which are always connected to the displacement chambers forming between stator and rotor gear teeth, are an additional volume, which decreases the effective compression ratio. Therefore, the delay of the pressure rise with an IGVF of 10% is significantly smaller for the TMC pump than for the other pumps.
To validate the second CFD setup, experimental data for the displacement chamber pressure in the BVP are compared with data obtained from CFD simulations. Both profiles are plotted in Figure 28a,b for two different operating points. Due to limitations of the test bench measurement, it is not possible to record the displacement chamber pressure profile for an IGVF > 5%.
Both analyzed operating points show a reasonable fit of the CFD data to the experimentally obtained pressure profiles. The CFD data, however, show an earlier and slower pressure rise than in the experiment. This seems to be because the radial and axial gaps of the CFD model have to be enlarged to 30 µm for the simulations with an IGVF > 0 in order to obtain convergence. The real dimensions of the axial and radial gaps, which are used for the simulations with the CFD setup cavitation, are one order of magnitude smaller, as it is described in Section 3. Because of these artificially enlarged gaps, leakages through them are higher, and therefore, the pressure rise begins earlier and has a lower gradient as well as the pressure drop after the chamber disconnects from the delivery port begins earlier and is smoother.
The increased pressure ripple on the delivery port plateau is quite well captured by the CFD simulations, although it is a bit overpredicted. However, there are many assumptions in the multiphase flow modelling setup used in this work. This also applies to the experimental test setup. Although a precise measurement of the IGVF of air is possible by the CGS system, as described in Section 4, no information regarding the phase morphology of the disperse air phase is available. For the CFD simulations, however, a mean air bubble diameter of 0.1 mm is assumed. Bearing in mind those limitations of the numerical as well as of the experimental analysis, it can be stated that the fit of the displacement chamber pressure profile for the BVP is quite reasonable.
Another finding of the authors in [20] is that with an increasing IGVF, the required power demand of the 2D pump decreases. As it could be seen in this chapter, the increasing compressibility of the mixture with increasing IGVF leads to a significant delay of the pressure rise in the displacement chamber. The time fraction, when delivery pressure is present in the chamber within one rotation, therefore, is reduced (see Figure 25, Figure 26, Figure 27). This leads subsequently to a reduction in the mean required driving torque. This phenomenon is observed for all three investigated pumps. The required time-averaged driving torque $M$ for an IGVF > 0 is compared to the required driving torque for pure oil $M_0$ and displayed in Figure 29. Besides the CFD results, data from the test bench measurements are also displayed.
The numerical results fit quite well to the experimental data for the BVP as well as for the TMC pump. For the IGP, the deviation is a bit higher, but the CFD simulations correctly predict the tendency of the driving torque drop, which can be seen in the experimental data.
Besides the ripple in the displacement chamber pressure profile, the mass flow ripple at the delivery port outlet is another important aspect when analyzing multiphase flow pumping characteristics of a pump.
By increasing the IGVF, analog to the amplitude increase in the pressure ripple in the displacement chambers, the mass flow ripple at the delivery port outlet also increases. This can be observed in Figures 30 and 31 for the BVP and the IGP, respectively. It seems that the increase in the mass flow ripple amplitudes in the BVP is a bit higher than it is in the IGP. This could be due to the difference in compression ratio. The BVP has a slightly lower compression ratio than the IGP (see Table 1). Of course, the time-averaged mass flow decreases when the IGVF rises. This is due to the falling mixture density of the fluid.
Compared to both other pump types, the outlet mass flow ripple increase when the IGVF is raised is significantly stronger in the TMC pump. This can be clearly seen in Figure 32. At
10% IGVF, there are shaft rotation angles where the mass flow is nearly at a value of zero. A further increase in the IGVF > 10% then leads to the occurrence of intermittent backflow of the oil–air mixture. An explanation for this phenomenon could be again the much lower compression ratio of the TMC pump compared to the IGP and the BVP. Because of that lower compression ratio, the mixture in the displacement chamber does not reach as high pressure levels before the chamber is connected to the delivery port and subsequently impinged with the delivery port pressure, as it does in both other pumps with higher compression ratios. Therefore, the pressure differences at that point in time are much higher in the TMC pump. This could also be observed in Figure 25, Figure 26, Figure 27 where the TMC pump showed the highest pressure surges with IGVF > 0 when the displacement chamber connects to the delivery port. Subsequently, a stronger backflow of the mixture from the delivery port into the displacement chamber while the fluid is pushed out can be expected. This results in a higher mass flow and pressure ripple. In the BVP and the IGP, the higher compression ratios lead to lower pressure differences when the displacement chambers connect to the delivery port. Consequently, lower pressure ripple and mass flow ripple at the outlet can be observed. Nevertheless, there is the potential to enhance the design of the TMC pump to achieve a higher compression ratio comparable to the other two pumps. This needs to be further investigated.
Figure 32. Outlet mass flow ripple CFD data for the TMC at p_2 = 5 bar pressure load, 20 °C oil temperature and 2000 rpm at different IGVF.
6. Conclusions
A numerical study to compare three different positive displacement pumps regarding the application in future automatic transmission system was presented in this paper.
In a first simulation setup, the characteristics of the pumps operating with pure oil and incorporating vapor cavitation were analyzed. Validating the numerical results regarding the volumetric efficiency with experimentally obtained data from the test bench, both the IGP and the BVP showed a reasonable match. A distinctively higher deviation between numerical and experimental results could be observed for the TMC pump, as the CFD results overpredicted the volumetric efficiency. As the TMC pump has additional and more complex leakage paths compared to the IGP and the BVP, the obtained volumetric efficiencies from the CFD simulations are very sensitive regarding the assumptions for the different leakage gap dimensions. For further validation, the instantaneous displacement chamber pressure profiles were experimentally recorded in the BVP and compared to the numerical data. A generally reasonable fit of the pressure profiles could be achieved. Besides the displacement chamber pressure, the outlet pressure ripple signals were compared with experimentally recorded data frequency wise and showed a reasonable fit for the IGP and the TMC pump. The deviation for the BVP was a bit higher. Here, the omitted dynamic motion of the vanes in the CFD model could be an explanation for this shortcoming. Generally, comparing outlet pressure ripples is challenging, as the test bench measurement data include fluid–structure interactions and vibrations from the driving engine, which are transmitted through the hydraulic circuit into the fluid.
In a second simulation setup, the operational characteristics of the pumps with an IGVF of free air in the oil were investigated and compared. Validation was performed by comparing the experimentally obtained displacement chamber pressure profiles for the BVP with the numerically obtained ones. Although there are many assumptions in the numerical
models for the dispersed oil–air multiphase flow such as the mean bubble diameter as well as limitations in the experimental measurements, the data show a reasonable fit. Besides the displacement chamber pressure profiles, the drop of required driving torque and volumetric efficiency with increasing IGVF could also be predicted with a reasonable fit to the experimental data.
With both applied CFD setups, it was possible to compare the three pumps regarding the application in a future automatic transmission system for vehicles. For the operation without free air, the IGP showed the latest cavitation onset due to high flow cross sections and lower pressure losses in the suction port. Comparing the calculated volumetric efficiency of the three investigated pump types, the CFD data showed no significant difference at the most commonly used rotational speeds from 1000 to 3500 rpm. From the experimental data, however, it could be clearly observed that the TMC pump has a lower volumetric efficiency than both other pumps. Looking at the displacement chamber profiles of the three pumps, it became clear that the pressure ripple is highest for the TMC pump. This was also visible in the outlet pressure ripple signal in the delivery port, where the TMC pump showed the highest amplitudes as well.
Regarding the operation with an IGVF of free air, all three pumps showed the same phenomena in the displacement chamber pressure profiles when the IGVF was raised. The degree of these effects, however, varied for the different pumps. The BVP and the TMC showed a greater amplification of the pressure ripple on the delivery port plateau with rising IGVF than the IGP. Furthermore, the TMC pump showed the highest intensification of the pressure surge when the displacement chamber was connected to the delivery port. This was also the case for the outlet mass flow ripple. The TMC pump showed much higher amplitudes and at an IGVF > 10%, even intermittent backflow was observed. Both the IGP and the BVP showed a superior characteristic with a much smaller intensification of the mass flow ripple. The disadvantage of the TMC pump compared to the BVP and the IGP appeared to be due to the difference in compression ratio. Whereas the BVP and the IGP feature a compression ratio of 9.15 and 11.93, respectively, the TMC due to its design with rotor channels has a much lower compression ratio of 3.67. This fact leads to an inferior performance regarding mass flow and pressure ripple with an IGVF > 0.
Summarizing all numerical and experimental results, all three pumps showed a potential for future applications in automatic transmission systems. However, the BVP and the IGP showed the best performance both with and without free air in the transmission oil. The volumetric efficiencies were for both pumps on a high level. The BVP, furthermore, features a slightly more compact design, as it is a double stroke pump. The TMC pump showed inferior volumetric efficiencies and the earliest cavitation onset of all three pumps. Comparing the delivery port outlet pressure ripple, the TMC pump likewise showed an inferior performance with higher amplitudes than both other pump types for the cases with and without free air. This subsequently also leads to an inferior acoustic characteristic of the pump. Due to the lower compression ratio of the TMC pump, a higher outlet mass flow ripple could also be observed with free air. A further optimization of the TMC pump is necessary to achieve a similar performance such as the other two pumps in the investigated operating points. Adding grooves for pressure ripple reduction and increasing the compression ratio by adjusting the rotor design could be two possible measures to attain this goal. However, the promising potential of the TMC pump is the possibility to mold its parts from polymer materials, which can lead to lower total manufacturing costs.
Author Contributions: Conceptualization, T.L.; formal analysis, T.L.; investigation, T.L.; methodology, T.L.; project administration, T.L.; supervision, H.S. and G.B.; visualization, T.L.; writing—original draft, T.L.; writing—review and editing, T.L., T.H., H.S. and G.B. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The data presented in this study are available on request from the corresponding author.
Acknowledgments: Marian Kacmar is acknowledged for assistance with the TMC pump design and the procurements of the test samples, as well as for assistance with the test bench measurements. Furthermore, Stephan Beitler and his team from the ITR at the TU Clausthal are acknowledged for their great support at the test bench with all measurements. Artur Bohr from Eckerle Technologies is acknowledged for providing the internal gear pump test samples and for assistance with interpreting measurement data.
Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature
| Symbol | Description | Unit |
|--------|-------------|------|
| C | Courant number | (-) |
| $F_{vap}$ | Vaporization calibration constant | (-) |
| $F_{cond}$ | Condensation calibration constant | (-) |
| M | Torque | (Nm) |
| $M_0$ | Torque at IGVF=0 | (Nm) |
| n | Rotational speed | (L/min) |
| p | Pressure | (Pa) |
| $p_2$ | Mean pressure at the delivery port | (Pa) |
| $Q_{leakage}$ | Leakage volumetric flow rate | (L/min) |
| $Q_{actual}$ | Actual volumetric flow rate | (L/min) |
| $Q_{theo}$ | Theoretical volume flow rate | (L/min) |
| r | Radial coordinate | (m) |
| $V_{displ}$ | Theoretical displacement volume | (L) |
| $V_{core}$ | Volume enclosing main internal pump parts | (L) |
| $y^+$ | Dimensionless wall distance | (-) |
| x, y, z | Cartesian coordinates | (m) |
Greek Letters
| Symbol | Description | Unit |
|--------|-------------|------|
| $\alpha_{air}$ | Inlet gas volume fraction of free air | (-) |
| $\eta_{vol}$ | Volumetric efficiency | (-) |
| $\theta$ | Spherical coordinate | (rad) |
| $\phi$ | Spherical coordinate | (rad) |
| $\omega$ | Angular velocity | (rad/s) |
Abbreviations
| Abbreviation | Description |
|--------------|-------------|
| 0D | Zero-dimensional |
| 1D | One-dimensional |
| 2D | Two-dimensional |
| 3D | Three-dimensional |
| AT | Torque converter automatic transmission |
| BC | Boundary condition |
| BVP | Balanced vane pump |
| CFD | Computational fluid dynamics |
| CFT | Continuous variable transmission |
| DCT | Dual clutch transmission |
| Exp | Experiment |
| FFT | Fast Fourier transform |
| ICE | Internal combustion engine |
| IGP | Internal gear pump |
| IGVF | Inlet gas volume fraction |
| PDP | Positive displacement pump |
| RANS | Reynolds-averaged Navier–Stokes |
rev Revolution
RPM Rounds per minute (L/min)
SST Shear stress transport
TMC Tumbling multi-chamber pump
References
1. Xu, X.; Dong, P.; Liu, Y.; Hui, Z. Progress in Automotive Transmission Technology. Automat. Innov. 2018, 1, 87–210. [CrossRef]
2. Naunheimer, H.; Fietkau, P.; Lechner, G. Automotive Transmissions: Fundamentals, Selection, Design, and Application, 2nd ed.; Springer: New York, NY, USA, 2011.
3. Ablawat, R.; Lee, B.; Fathy, H.K.; Stei, J.L.; Jung, D.; Guo, C. Effect of pump selection on fuel economy in a dual clutch transmission vehicle. In Proceedings of the 2009 American Control Conference, St. Louis, MO, USA, 10–12 June 2009; pp. 1371–1378.
4. Höfer, A.; Herbel, M.; Schierle, D.; Peschcow, W.; Hamon, P. eAxle development and optimization regarding NVH, efficiency and power density. In 20. Internationales Stuttgart Symposium; Springer: Berlin/Heidelberg, Germany, 2020; pp. 185–196.
5. Güth, D.; Haupt, J.; Gassmann, T. Seamless-Shift Two-Speed eAxle with Torque Vectoring. VDI-Ber. 2018, 2328, 255–268.
6. Ivantsyn, J.; Ivantsynova, M. Hydrostatische Pumpen und Motoren, 1st ed.; Vogel Verlag: Wuerzburg, Germany, 1993; pp. 358–361.
7. Van der Sluis, F. A new pump for CVT applications. SAE Tech. Pap. 2003, 2003-01-3207.
8. Battarra, M.; Blum, A.; Micchi, E. Kinematics of a balanced vane pump with circular tip vanes. Mech. Mach. Theory 2019, 137, 355–373. [CrossRef]
9. Battarra, M.; Micchi, E. On the relation between vane geometry and theoretical flow ripple in balanced vane pumps. Mech. Mach. Theory 2020, 146, 103736. [CrossRef]
10. Lu, Y.; Zhang, W.; Zhao, Y-Y.; Wang, Z.-Z.; Shu, P-C. Studies on several key problems of water hydraulic vane pump. Ind. Lubr. Tribol. 2011, 63, 134–141. [CrossRef]
11. Fornarelli, F.; Lippolis, A.; Oresta, P.; Posa, A. Investigation of a pressure compensated vane pump. Energy Procedia 2018, 148, 194–201. [CrossRef]
12. Truong, B.N.; Quang Truong, D.; Thanh Trung, N.; Kwan, A.K. Mathematical modeling of a variable displacement vane pump for engine lubrication. Int. Conf. Control Autom. Syst. 2015, 15, 1946–1951.
13. Bianchi, G.; Fatigati, F.; Murgia, S.; Cipollone, R. Design and analysis of a sliding vane pump for waste heat to power conversion systems using organic fluids. Appl. Eng. 2017, 124, 1038–1048. [CrossRef]
14. Neyrat, S.; Orand, N.; Jonquet, D. Modeling and Analysis of an Automatic Transmission Internal Gear Oil Pump with Cavitation. SAE Tech. Pap. 2005, 2005-01-2448.
15. Zhao, X.; Vacca, A. Theoretical Investigation into the Ripple Source of External Gear Pumps. Energies 2019, 12, 353. [CrossRef]
16. Munih, J.; Hocevar, M.; Petrič, K.; Dular, M. Development of CFD-based procedure for 3d gear pump analysis. Eng. Appl. Comput. Fluid Mech. 2020, 14, 1023–1034. [CrossRef]
17. Rundo, M.; Altare, G.; Casoli, P. Simulation of the Filling Capability in Vane Pumps. Energies 2019, 10, 283. [CrossRef]
18. Iannetti, A.; Hocevar, M.; Posa, A. An experimental investigation into the filling capability of vane pumps. Eng. Appl. Comput. Fluid Mech. 2016, 10, 57–71. [CrossRef]
19. Patil, A. Performance Evaluation and CFD Simulation of Multiphase Twin-Screw Pumps. Ph.D. Thesis, Texas A & M University, College Station, TX, USA, 2013.
20. Lobsinger, T.; Hieronymus, T.; Brenner, G. A CFD Investigation of a 2D Balanced Vane Pump Focusing on Leakage Flows and Multiphase Flow Characteristics. Energies 2020, 13, 3314. [CrossRef]
21. Will, D.; Gebhardt, N. Hydraulik: Grundlagen, Komponenten, Systeme, 6th ed.; Springer: Berlin/Heidelberg, Germany, 2014; pp. 132–134.
22. Giuffrida, A.; Lanzafame, R. Cam shape and flow rate in balanced vane pumps. Mech. Mach. Theory 2005, 40, 353–369. [CrossRef]
23. Inaguma, Y. Theoretical Analysis of Mechanical Efficiency in Vane Pump. JTEKT Eng. J. 2010, 1007E, 28–35.
24. Zouani, A.; Dzibpinschi, G.; Marri, V. Optimal Vanes Spacing for Improved NVH Performance of Variable Displacement Oil Pumps. SAE Tech. Pap. 2017, 2017-01-1062.
25. Hesse, J.; Spille-Kohoff, A.; Hauser, J.; Schulze-Beckinghausen, P. Structured meshes and reliable CFD simulations: TwinMesh for positive displacement machines. VDI-Ber. 2014, 2228, 297–308.
26. Suzuki, K.; Nakamura, Y.; Yakabe, S.; Watanabe, H.; Nakamura, K. Characteristics Prediction of Vane Pump by CFD Analysis. KYB Tech. Rev. Technol. 2016, 53, 8–15.
27. Hieronymus, T.; Lobsinger, T.; Brenner, G. Investigation of the Internal Displacement Chamber Pressure of a Rotary Vane Pump. Energies 2020, 13, 3341. [CrossRef] | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2983,
1
],
[
2983,
7554,
2
],
[
7554,
11125,
3
],
[
11125,
14184,
4
],
[
14184,
16639,
5
],
[
16639,
19632,
6
],
[
19632,
21549,
7
],
[
21549,
22962,
8
],
[
22962,
26668,
9
],
[
26668,
29729,
10
],
[
29729,
31225,
11
],
[
31225,
33798,
12
],
[
33798,
36554,
13
],
[
36554,
39054,
14
],
[
39054,
42145,
15
],
[
42145,
44179,
16
],
[
44179,
45101,
17
],
[
45101,
48855,
18
],
[
48855,
51274,
19
],
[
51274,
52568,
20
],
[
52568,
56481,
21
],
[
56481,
60896,
22
],
[
60896,
63542,
23
],
[
63542,
68032,
24
]
]
} |
cefdaa9007f4e30c0baafef0a20589896246b503 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 11,
"total-fallback-pages": 0,
"total-input-tokens": 39896,
"total-output-tokens": 14676,
"fieldofstudy": [
"Medicine"
]
} | Higher serum soluble receptor for advanced glycation end product levels and lower prevalence of metabolic syndrome among Japanese adult men: a cross-sectional study
Haruki Momma¹, Kaijun Niu², Yoritoshi Kobayashi³, Cong Huang³, Masahiko Chujo³, Atsushi Otomo³, Hiroko Tadaura⁴, Toshio Miyata⁵ and Ryoichi Nagatomi¹,³*
Abstract
Background: Although several studies showed that decreased soluble receptor for advanced glycation end products (sRAGE) is associated with metabolic syndrome (MetS), inflammation level has not been considered, even though ligand–RAGE interaction induces inflammation. The objective of the study was to determine the association between sRAGE and MetS among Japanese adult in a cross-sectional survey, taking the level of low grade inflammation into consideration.
Methods: Serum soluble RAGE (sRAGE) were measured in 712 men and 176 women aged 30–83 years with serum C-reactive protein (hsCRP) concentration below 3 mg/L. MetS was defined using the criteria of the American Heart Association Scientific Statements of 2009.
Results: After multivariable adjustment, among men, higher sRAGE levels were associated with lower odds of MetS as well as central obesity and elevated blood pressure. Comparing the extreme tertiles of sRAGE, odds ratios (95% confidence interval) were 0.58 (0.36–0.95; \(P\) for trend = 0.001) for MetS; 0.41 (0.25–0.52; \(P\) for trend < 0.001) for central obesity; and 0.45 (0.29–0.70; \(P\) for trend < 0.001) for elevated blood pressure. Moreover, participants were categorized according to their median hsCRP and sRAGE values. Men in the higher hsCRP/higher sRAGE category had a 40% lower odds ratio for MetS than those in the higher hsCRP/lower sRAGE category (\(P = 0.031\)). Among women, there was no association between sRAGE levels and the prevalence of MetS.
Conclusions: Higher circulating RAGE concentrations were associated with lower prevalence of MetS and its components among Japanese men.
Keywords: Endogenous secretory RAGE, Low grade inflammation, CRP
Introduction
The receptor for advanced glycation end products (RAGE) is a cell surface molecule belonging to the immunoglobulin superfamily that binds many ligands including advanced glycation end products (AGEs) [1]. Circulating forms of RAGE, arising from receptor ectodomain shedding [soluble RAGE (sRAGE)] and secretion of its splice variant [endogenous secretory RAGE (esRAGE)], may competitively inhibit binding of the ligand to membrane-bound RAGE by acting as an endogenous decoy [2]. Indeed, in animal models, recombinant sRAGE administration suppressed the development of atherosclerosis and stabilized established atherosclerosis [3,4]. Thus, circulating RAGE (sRAGE and esRAGE) levels may inversely reflect ligand–RAGE interaction evoked pathogenesis.
Several studies have reported that decreased circulating RAGE concentrations are associated with metabolic syndrome (MetS) risk factors [5-9]. Moreover, participants...
with MetS showed significantly lower plasma esRAGE concentration than those without MetS [7], and plasma sRAGE levels decreased with increasing number of MetS risk factors [10]. Proinflammatory state [e.g., high concentration of C-reactive protein (CRP)] is considered to have a significant impact on the pathogenesis of MetS and its components [11]. Under low grade chronic inflammation circumstances, higher sRAGE level may attenuate the deteriorating effect of inflammation on MetS and its components. However, such association has not been investigated.
Thus, the purpose of this study was to examine the association between circulating RAGE (sRAGE and esRAGE) concentrations and the prevalence of MetS in Japanese adult in a population-based cross-sectional study, with particular regard to systemic inflammatory level measured by circulating CRP.
Methods
Study population
The study participants comprised adult employees enrolled in a prospective study of risk factors for lifestyle-related illnesses or health status at the Sendai Oroshisho Center in Sendai, Japan. The participants received annual health examinations in 2009. This study was conducted during the first week (from Monday to Friday) of August. The details of this study have been described previously [12]. The sample selection process is described in Figure 1. In 2009, 1,263 participants had undergone health examinations for lifestyle-related illnesses. Of these, 1,215 participated in our survey and provided informed consent for data analysis (response rate, 96.2%). The following participants were excluded: those for whom sRAGE or esRAGE measurements were unavailable (n = 5); those with a history of cardiovascular disease (n = 8); those whose serum CRP concentration was ≥ 3.0 mg/L (n = 64), because people with above 3 mg/L of CRP are considered as being in high risk for cardiovascular disease [13]; and those for whom complete data was not available (n = 250). Thus, 712 men and 176 women were included in the present study. The protocol of this study was approved by the Institutional Review Board of the Tohoku University Graduate School of Medicine.
Assessment of MetS
Fasting blood samples were drawn from the antecubital vein with minimal tourniquet use, with the participants in a seated position. Samples were collected in siliconized vacuum glass tubes containing sodium fluoride for fasting blood glucose (FBG) analysis, and with no additives for lipid analysis. The FBG concentration was measured enzymatically (Eerotec Co., Ltd., Tokyo, Japan). The concentrations of triglycerides (TG), low-density lipoprotein cholesterol (LDL-C), and high-density lipoprotein cholesterol (HDL-C) were also measured by enzymatic methods using appropriate kits (Sekisui Medical Co., Ltd., Tokyo, Japan). Blood pressure (BP) was measured twice from the upper left arm by means of an automatic device (Yamasu 605P; Kenzmedico, Saitama, Japan) after the participants had rested for 5 min in a sitting position and the mean of the 2 measurements was taken as the BP value. Waist circumference (WC) was measured at the umbilical level with the participants in a standing position and breathing normally. The criteria of the American Heart Association Scientific Statements of 2009 were used to define MetS [14].
participants were considered to have MetS if they presented ≥3 of the following risk factors: (1) central obesity (≥ 90 cm for men and ≥ 80 cm for women) (2) elevated TG (≥150 mg/dL); (3) reduced HDL-C (< 40 mg/dL for men and < 50 mg/dL for women); (4) elevated BP [systolic BP (SBP) ≥130 mm Hg or diastolic BP (DBP) ≥85 mm Hg]); and (5) elevated FBG (≥100 mg/dL). Those participants who were receiving drug treatment for a given risk factor were considered as having that risk factor.
**Measurements of sRAGE and esRAGE**
Serum sRAGE and esRAGE were measured using a commercially available Quantikine ELISA kit (R&D System, Inc., Minneapolis, MN) and the ELISA kit from B-Bridge International (Sunnyvale, CA), respectively. The intra- and interassay coefficients of variation were 2.8% and 6.4%, respectively, for sRAGE and 6.8% and 6.0%, respectively, for esRAGE. Although our hypothesis was that higher serum sRAGE and esRAGE levels were associated with lower prevalence of MetS, previous studies reported conflicting findings for the role of circulating soluble forms of RAGE. Thus, because we postulated the possibility that too high or too low serum sRAGE and esRAGE might have an unfavorable influence on the prevalence of MetS and its components resulting in an U or J curve relationship, serum sRAGE and esRAGE concentrations were divided into low, middle, and high tertiles in this study.
**Assessment of other variables**
High sensitivity CRP (hsCRP) concentration was determined using N-latex CRP-2 (Siemens Healthcare Japan, Tokyo, Japan). The measurement limit of hsCRP was 0.02 mg/L, and an hsCRP value less than the measurement limit was considered to be 0.01 mg/L. Estimated glomerular filtration rate (eGFR) was calculated using the following equation established by the Japanese Society of Nephrology for Japanese subjects: eGFR (mL/min/1.73 m²) = 194 × [serum creatinine (mg/dL)]⁻¹.094 × (age)⁻₀.287 [15].
Anthropometric parameters (height and body weight) were recorded using a standard protocol. Body mass index (BMI) was calculated as weight (kg) divided by height squared (m²).
Age, educational level (<college or ≥ college), occupation (desk-based or not), marital status (married or unmarried), smoking status (never, former, or current) and sleep duration (6–8 h or <6 and >8 h) were obtained through a self-reported questionnaire survey. Daily physical activity (PA) levels were estimated using the International Physical Activity Questionnaire (Japanese version) [16] and divided into three categories [<1.0, 1–22.9, or ≥23.0 metabolic equivalent of tasks (METs) × hours/week] [17]. Total energy intake and alcohol drinking were estimated using a brief self-administered dietary history questionnaire [18]. Alcohol drinking status was categorized into 4 groups (never, ≤3 day(s)/week, 4–6 days/week, or every day). Depressive symptoms were assessed according to the Japanese version of the Self-Rating Depression Scale (SDS) [19]. The participants were considered as depressed when the SDS score was ≥40 [20].
**Statistical analysis**
All statistical analyses were performed using SPSS 17.0 for Windows (SPSS, Inc., Chicago, IL, USA).
The distributions of all continuous variables in this study were skewed positively; therefore, we normalized by log-transforming the data in our analyses. Spearman’s rank correlation coefficient was calculated to examine the relationship between sRAGE and esRAGE. To compare the participants’ characteristics, we used the chi-square test and ANOVA for categorical and continuous variables, respectively. Descriptive data are represented as the median (interquartile range) for non-adjusted continuous variables and as percentages for categorical variables. Multiple logistic regression analysis was used to analyze the association of circulating sRAGE or esRAGE concentration with MetS and its components. For analysis, MetS and its components were used as dependent variables, and tertiles of sRAGE or esRAGE were used as independent variables. Analysis was performed after adjustment for potential confounding factors including age, smoking status, drinking status, educational level, occupation, depressive symptoms, PA, total energy consumption, sleeping time, and eGFR (model 1); all parameters in model 1 plus serum hsCRP concentration were used in model 2; all parameters in model 2 plus mutual MetS components were included in model 3 for analysis of MetS components. Moreover, because sex differences existed in the circulating levels of RAGE and hsCRP, and in the prevalence of MetS, we performed separate analyses for men and women. All P values for linear trends were calculated using the median values of sRAGE or esRAGE tertiles.
To examine the influence of inflammatory levels on the association between sRAGE and MetS, participants were categorized into higher hsCRP/lower sRAGE, higher hsCRP/higher sRAGE, lower hsCRP/lower sRAGE, or lower hsCRP/higher sRAGE categories according to the median values. Using these categories as independent variables, multiple logistic regression analysis was performed, adjusted for the model 1 and model 4 including all parameters in model 3 except for serum hsCRP concentration. All tests for statistical significance were two-sided and P < 0.05 was defined as statistically significant.
**Results**
Of the 712 men, 179 (25.1%) had ≥3 MetS components. The median (interquartile range) values were 1259.0 (946.4–1609.1) pg/mL for serum sRAGE, 319.0 (235.7–432.2) pg/mL for serum esRAGE, and 0.38 (0.22–0.77)
Higher percentage of current smokers (P prevalence of central obesity and elevated BP (P respectively associated with the number of MetS components. Moreover, higher serum sRAGE concentration was negatively associated with BMI, WC, SBP, and DBP (P for trend < 0.001) among men. The characteristics according to the tertiles of serum sRAGE in men are presented in Table 1. Serum sRAGE concentration was negatively associated with age, BMI, WC, SBP, DBP, hsCRP (P for trend < 0.001), and TG (P for trend = 0.036). Moreover, higher tertiles of serum sRAGE had a lower percentage of participants with ≥23 METs × hours/week (P for trend = 0.011) and those who drank ≥7 days/week (P for trend < 0.001), and they also had a higher percentage of current smokers (P for trend = 0.020). No other significant associations were observed between the groups. Among women, serum sRAGE concentration was negatively associated with BMI, WC, SBP, and hsCRP (Additional file 1: Table S1).
The prevalence of MetS was 30.7% in the lowest tertile of serum sRAGE, 27.4% in the middle tertile, and 17.3% in highest tertile (P for trend = 0.001, Table 1) among men. Moreover, higher serum sRAGE concentration was negatively associated with the number of MetS components (P for trend < 0.001), and negatively associated with the prevalence of central obesity and elevated BP (P for trend < 0.001). Similar results were obtained for women (Additional file 1: Table S1).
Table 2 shows the relationship of tertiles of serum sRAGE with the prevalence of MetS and its components after adjustment for potential confounders in men. The adjusted odds ratio (95% confidence interval) for MetS in the middle and highest tertiles of serum sRAGE were 0.89 (0.59–1.35) and 0.45 (0.28–0.71) (P for trend = 0.001), respectively. Even after adjustment for serum hsCRP concentration, participants with higher serum sRAGE concentration had a lower prevalence of MetS [1.04 (0.67–1.61) for middle tertile, and 0.58 (0.36–0.95) for highest tertile, P for trend = 0.038]. Furthermore, participants with higher serum sRAGE concentration had a lower prevalence of central obesity [0.86 (0.58–1.27) for middle tertile, 0.33 (0.21–0.52) for highest tertile, P for trend < 0.001], elevated BP [0.61 (0.40–0.93) for middle tertile, 0.38 (0.25–0.57) for highest tertile, P for trend < 0.001], and elevated TG [1.00 (0.68–1.48) for middle tertile, and 0.62 (0.41–0.93) for highest tertile, P for trend = 0.024], after adjustment for potential confounders. With central obesity and elevated BP, even after adjustment for serum hsCRP concentration (model 2) and mutual MetS components (model 3), the association remained. Moreover, similar results were obtained for the relationships of serum esRAGE concentration with MetS and its components, except for reduced HDL-C in model 1 [0.98 (0.58–1.65) for middle tertile, and 0.44 (0.24–0.79) for highest tertile, P for trend = 0.006]. Among women, serum sRAGE level was associated with only elevated BP after adjustment for confounding factors (Additional file 1: Table S2).
We examined the interrelationship between sRAGE, MetS, and hsCRP. Table 3 shows the adjusted odds ratio (95% confidence intervals) for MetS in the higher hsCRP/higher sRAGE, lower hsCRP/lower sRAGE, and lower hsCRP/higher sRAGE categories in men. Participants in the higher hsCRP/higher sRAGE category had a 40% lower odds ratio for MetS than those in the higher hsCRP/lower sRAGE category (P = 0.031). Moreover, after adjustment for mutual MetS components (model 2), participants in the higher hsCRP/higher sRAGE category had a 46% lower odds ratio for central obesity (P = 0.020) and a 51% lower odds ratio for elevated BP (P = 0.007) than those in the higher hsCRP/lower sRAGE category. Among women, there was no difference between higher hsCRP/higher sRAGE and hsCRP/lower sRAGE category after adjustment for confounders (Additional file 1: Table S3).
To examine the influence of those excluded because of incomplete data, we examined the associations between circulating sRAGE or esRAGE levels and the prevalence of MetS including those who had incomplete data by complementing the incomplete data. For example, the educational
Table 1 Characteristics of the participants according to the tertiles of serum sRAGE in men (n = 712)\(^1\)
| Characteristics | Low (n = 238) | Middle (n = 237) | High (n = 237) | P for trend\(^d\) |
|----------------------------------------|-----------------------------------|------------------------------------|------------------------------------|-------------------|
| Median, interquartile range (pg/mL) | (847.6, 710.0–950.0) | (1259.1, 1152.8–1377.2) | (1835.0, 1608.9–2107.8) | |
| Age (years) | 51.0 (41.0–57.0) | 46.0 (38.0–56.0) | 44.0 (38.0–54.0) | <0.001 |
| BMI (kg/m\(^2\)) | 24.5 (22.3–26.1) | 23.7 (21.7–26.1) | 22.7 (20.9–24.4) | <0.001 |
| WC (cm) | 86.0 (81.0–92.0) | 85.0 (79.0–92.0) | 82.0 (77.0–87.0) | <0.001 |
| SBP (mmHg) | 133.0 (122.0–143.0) | 130.0 (118.0–140.0) | 122.0 (114.0–134.0) | <0.001 |
| DBP (mmHg) | 84.5 (76.8–91.3) | 82.0 (76.0–90.0) | 78.0 (70.0–86.0) | <0.001 |
| TG (mg/dL) | 125.5 (83.0–174.3) | 115.0 (78.0–180.0) | 100.0 (73.0–160.0) | 0.036 |
| LDL-C (mg/dL) | 118.5 (101.8–146.0) | 120.0 (101.5–139.5) | 118.0 (100.0–137.0) | 0.28 |
| HDL-C (mg/dL) | 52.0 (43.0–60.3) | 51.0 (43.5–61.0) | 51.0 (43.0–60.0) | 0.34 |
| eGFR (ml/min/1.73 m\(^2\)) | 81.3 (73.7–90.4) | 81.8 (73.6–90.6) | 80.8 (72.4–89.1) | 0.16 |
| hsCRP (mg/L) | 0.46 (0.27–0.93) | 0.40 (0.21–0.78) | 0.33 (0.19–0.58) | <0.001 |
| esRAGE (pg/mL) | 208.1 (170.3–260.9) | 320.4 (278.3–374.6) | 480.9 (411.9–573.9) | <0.001 |
| Total energy intake (kcal/day) | 1882.0 (1553.8–2309.5) | 1866.6 (1523.5–2315.3) | 1854.6 (1450.2–2196.5) | 0.063 |
| PA | | | | |
| <1.0 METs · hours/week (%) | 20.6 | 20.7 | 26.6 | 0.011 |
| 1.0–22.0 METs · hours/week (%) | 38.7 | 42.6 | 44.3 | |
| ≥23.0 METs · hours/week (%) | 40.7 | 36.7 | 29.1 | |
| Smoking status | | | | |
| Never smoker (%) | 39.5 | 38.4 | 32.1 | 0.020 |
| Former smoker (%) | 15.5 | 10.1 | 10.5 | |
| Current smoker (%) | 45.0 | 51.5 | 57.4 | |
| Drinking status | | | | |
| Non-drinker (%) | 12.2 | 15.6 | 21.1 | <0.001 |
| ≤ 3 day(s)/week (%) | 29.0 | 35.4 | 35.4 | |
| 4–6 days/week (%) | 21.8 | 18.2 | 18.6 | |
| Every day (%) | 37.0 | 30.8 | 24.9 | |
| Sleep time, ≥6 and ≤8 hours/day (%) | 80.3 | 81.0 | 76.8 | 0.35 |
| Education (≥college, %) | 34.0 | 32.9 | 35.4 | 0.75 |
| Desk work (%) | 80.3 | 79.3 | 76.4 | 0.30 |
| Being married (%) | 83.6 | 78.5 | 79.3 | 0.24 |
| Depressive symptoms (SDS ≥40, %) | 33.6 | 28.7 | 32.1 | 0.72 |
| Number of MetS components (%) | | | | |
| No | 11.3 | 20.7 | 30.4 | <0.001 |
| 1 component | 31.1 | 26.2 | 34.2 | |
| 2 components | 26.9 | 25.7 | 18.1 | |
| ≥3 components | 30.7 | 27.4 | 17.3 | |
| Central obesity (%) | 33.6 | 30.8 | 15.6 | <0.001 |
| Elevated BP (%) | 71.0 | 57.4 | 44.3 | <0.001 |
Table 1 Characteristics of the participants according to the tertiles of serum sRAGE in men (n = 712)
| Characteristic | Low (n = 238) | Middle (n = 237) | High (n = 237) | P for trend |
|---------------------------|--------------|------------------|---------------|------------|
| Elevated FBG (%) | 32.8 | 32.9 | 25.3 | 0.078 |
| Elevated TG (%) | 35.3 | 35.4 | 27.0 | 0.054 |
| Reduced HDL-C (%) | 14.7 | 13.5 | 13.9 | 0.81 |
aData are medians (interquartile range) or proportions. sRAGE, soluble receptor of advanced glycation end-products; BMI, body mass index; WC, Waist circumference; SBP, systolic blood pressure; DBP, diastolic blood pressure; TG, triglyceride; LDL-C, low density lipoprotein cholesterol; HDL-C, high density lipoprotein cholesterol; FBG, fasting blood glucose; eGFR, estimated glomerular filtration rate; hsCRP, high sensitivity C-reactive protein; esRAGE, endogenous secretory RAGE; PA, physical activity; SDS, Self-rating Depression Scale; MetS, metabolic syndrome.
Table 2 Relationship of the tertile of serum sRAGE with the prevalence of MetS in men (n = 712)
| Median, interquartile range (pg/mL) | Low (n = 238) | Middle (n = 237) | High (n = 237) | P for trend |
|-------------------------------------|--------------|------------------|---------------|------------|
| MetS | Crude | 1.00 | 0.85 (0.57–1.27) | 0.47 (0.31–0.73) | <0.001 |
| | Model 1a | 1.00 | 0.89 (0.59–1.35) | 0.45 (0.28–0.71) | 0.001 |
| | Model 2b | 1.00 | 1.04 (0.67–1.61) | 0.58 (0.36–0.95) | 0.038 |
| Central obesity | Crude | 1.00 | 0.88 (0.60–1.29) | 0.37 (0.24–0.57) | <0.001 |
| | Model 1b | 1.00 | 0.86 (0.58–1.27) | 0.33 (0.21–0.52) | <0.001 |
| | Model 2b | 1.00 | 0.96 (0.64–1.45) | 0.41 (0.25–0.66) | <0.001 |
| | Model 3c | 1.00 | 0.99 (0.65–1.52) | 0.46 (0.28–0.75) | 0.003 |
| Elevated BP | Crude | 1.00 | 0.55 (0.38–0.80) | 0.33 (0.22–0.48) | <0.001 |
| | Model 1b | 1.00 | 0.61 (0.40–0.93) | 0.38 (0.25–0.57) | <0.001 |
| | Model 2b | 1.00 | 0.66 (0.43–1.02) | 0.45 (0.29–0.70) | <0.001 |
| | Model 3c | 1.00 | 0.65 (0.42–1.01) | 0.49 (0.31–0.77) | 0.002 |
| Elevated FBG | Crude | 1.00 | 1.01 (0.69–1.48) | 0.70 (0.47–1.04) | 0.078 |
| | Model 1b | 1.00 | 1.17 (0.78–1.75) | 0.89 (0.58–1.37) | 0.64 |
| | Model 2b | 1.00 | 1.21 (0.81–1.84) | 0.97 (0.63–1.51) | 0.95 |
| | Model 3c | 1.00 | 1.29 (0.85–1.96) | 1.20 (0.76–1.89) | 0.40 |
| Elevated TG | Crude | 1.00 | 1.01 (0.69–1.47) | 0.68 (0.46–1.03) | 0.054 |
| | Model 1b | 1.00 | 1.00 (0.68–1.48) | 0.62 (0.41–0.93) | 0.024 |
| | Model 2b | 1.00 | 1.11 (0.74–1.65) | 0.75 (0.49–1.65) | 0.19 |
| | Model 3c | 1.00 | 1.17 (0.77–1.77) | 0.85 (0.54–1.33) | 0.50 |
| Reduced HDL-C | Crude | 1.00 | 0.91 (0.54–1.52) | 0.94 (0.56–1.57) | 0.81 |
| | Model 1b | 1.00 | 0.77 (0.44–1.33) | 0.63 (0.36–1.11) | 0.11 |
| | Model 2b | 1.00 | 0.88 (0.45–1.56) | 0.87 (0.46–1.56) | 0.65 |
| | Model 3c | 1.00 | 0.85 (0.47–1.53) | 0.90 (0.48–1.68) | 0.74 |
aData are odds (95% confidence interval). sRAGE, soluble receptor of advanced glycation end-products; MetS, metabolic syndrome.
Multiple logistic regression analysis.
Adjusted for age (continuous variable), smoking status (never, former, or current), drinking status (never, ≤3 day(s)/week, 4–6 days/week, or every day), educational level (≥college or not), occupation (desk work or non-desk work), depressive symptoms (Self-Rating Depression Scale ≥40 or not), physical activity (<1.0 METs · hour/week, 1.0–22.9 METs · hour/week, or ≥23.0 METs · hour/week), total energy intake (continuous variable), sleep time (≥6 and ≤8 hours/day or not), and eGFR (continuous variable).
Additionally adjusted for serum high sensitivity C-reactive protein concentration (continuous variable).
Additionally adjusted for mutual metabolic syndrome components.
### Table 3 Odds ratios of MetS risk factors by hsCRP and sRAGE categories in men (n = 712)
| MetS | Crude | Model 1<sup>a</sup> | Model 1' | Model 4<sup>d</sup> | Model 4<sup>d</sup> |
|------|-------|------------------|-----------|------------------|------------------|
| | Odds ratio (95% CI) | Odds ratio (95% CI) | Odds ratio (95% CI) | Odds ratio (95% CI) |
| | | | | | |
| Higher hsCRP/lower sRAGE (n = 192) & Higher hCRP/higer sRAGE (n = 161) | 1 | 1 | 1 | 1 |
| Lower hsCRP/lower sRAGE (n = 164) | 0.26 | 0.16 | 0.16 | 0.16 |
| Lower hsCRP/higer sRAGE (n = 195) | 0.16 | 0.09 | 0.16 | 0.09 |
| Elevated BP | Odds ratio (95% CI) | Odds ratio (95% CI) | Odds ratio (95% CI) |
| Higher hsCRP/lower sRAGE (n = 192) | 1 | 1 | 1 |
| Higher hCRP/higer sRAGE (n = 161) | 0.40 | 0.26 | 0.40 | 0.40 |
| Lower hsCRP/lower sRAGE (n = 164) | 0.47 | 0.30 | 0.47 | 0.47 |
| Lower hsCRP/higer sRAGE (n = 195) | 0.24 | 0.16 | 0.24 | 0.24 |
| Elevated FBG | Odds ratio (95% CI) | Odds ratio (95% CI) | Odds ratio (95% CI) |
| Higher hsCRP/lower sRAGE (n = 192) | 1 | 1 | 1 |
| Higher hCRP/higer sRAGE (n = 161) | 0.75 | 0.48 | 0.75 | 0.75 |
| Lower hsCRP/lower sRAGE (n = 164) | 0.51 | 0.32 | 0.51 | 0.51 |
| Lower hsCRP/higer sRAGE (n = 195) | 0.47 | 0.30 | 0.47 | 0.47 |
| Elevated TG | Odds ratio (95% CI) | Odds ratio (95% CI) | Odds ratio (95% CI) |
| Higher hsCRP/lower sRAGE (n = 192) | 1 | 1 | 1 |
| Higher hCRP/higer sRAGE (n = 161) | 0.91 | 0.59 | 0.91 | 0.91 |
| Lower hsCRP/lower sRAGE (n = 164) | 0.52 | 0.34 | 0.52 | 0.52 |
| Lower hsCRP/higer sRAGE (n = 195) | 0.34 | 0.21 | 0.34 | 0.34 |
| Reduced HDL-C | Odds ratio (95% CI) | Odds ratio (95% CI) | Odds ratio (95% CI) |
| Higher hsCRP/lower sRAGE (n = 192) | 1 | 1 | 1 |
| Higher hCRP/higer sRAGE (n = 161) | 1.09 | 0.65 | 1.09 | 1.09 |
| Lower hsCRP/lower sRAGE (n = 164) | 0.35 | 0.18 | 0.35 | 0.35 |
| Lower hsCRP/higer sRAGE (n = 195) | 0.34 | 0.18 | 0.34 | 0.34 |
<sup>a</sup>Participants were categorized by the median values (1259.0 pg/mL for sRAGE; 0.38 mg/L for hsCRP). CI, confidential interval; sRAGE, soluble receptor of advanced glycation end-products; BP, blood pressure; FBG, fasting blood glucose; TG, triglyceride; HDL-C, high density lipoprotein cholesterol.
<sup>b</sup>Multiple logistic regression analysis.
<sup>c</sup>Adjusted for age (continuous variable), smoking status (never, former, or current), drinking status (never, < 6 days/week, or every day), educational level (< college, college, or missing value group), and physical activity was categorized into <1.0, 1–22.9, ≥23.0 METs · hours/week, or missing value group. For continuous variables including eGFR and energy intake, missing values were assigned to their medians. In model 2, for men, the adjusted odds ratio (95% confidence interval) for MetS in the middle and highest tertiles of serum sRAGE were 0.83 (0.56–1.26) and 0.46 (0.29–0.72) (P for trend < 0.001), respectively. Among women, even inclusion of participants with incomplete data, there was no
significant association between serum sRAGE and esRAGE, and MetS. Moreover, for the interrelationship between sRAGE, MetS, and hsCRP among men, participants in the higher hsCRP/higher sRAGE category had a 40% lower odds for MetS than those in the higher hsCRP/lower sRAGE category (0.59 [0.38–0.92], \( P = 0.021 \)).
Discussion
The present study examined the association between the levels of circulating RAGE (sRAGE and esRAGE) and prevalence of MetS and its component among adult with low grade inflammatory level, through a population-based cross-sectional study. Our results suggested that, among men, after adjustment for serum hsCRP concentration higher circulating RAGE levels were associated with lower prevalence of MetS, central obesity, and elevated BP. Moreover, participants in the higher hsCRP/higher sRAGE category had lower odds ratio of MetS than those in the higher hsCRP/lower sRAGE category. Thus, higher levels of circulating RAGE were associated with lower prevalence of MetS and its components including central obesity and elevated BP among adult men with low grade inflammation.
Previous studies have reported a relationship between circulating RAGE level and MetS [7,10]. For example, Koyama et al. reported that participants with MetS had lower circulating esRAGE concentration than those without it, using a univariate model among type 2 diabetic patients and healthy controls [7]. Recently, in young to middle-aged medication-free non-diabetic subjects, plasma sRAGE concentration was found to decrease as the number of MetS risk factors increased [10]. In the present study, we focused on the relationship between circulating RAGE level and the prevalence of MetS because (i) a proinflammatory state, such as high concentration of circulating CRP, was reported to significantly influence the pathogenesis of MetS and its components [11], and (ii) circulating soluble forms of RAGE may attenuate inflammatory responses via competitive inhibition of ligand-RAGE interaction [2]. However, our finding showed that the significant negative association between serum sRAGE level and the prevalence of MetS remained after adjusting for serum hsCRP level. Therefore, circulating sRAGE as an anti-inflammatory decoy may not be sufficient to explain the contributions of circulating sRAGE to the lower prevalence of MetS. In addition, in the present study, the mean (SD) serum sRAGE concentration was 1344.8 (563.9) pg/ml. Although the concentrations of circulating ligands for RAGE were not measured in this study, a previous study of Japanese adult men reported that the concentration of circulating high mobility group box 1, a RAGE ligand, was 1.69 (0.04) ng/ml [21]. As RAGE is known to be a multi-ligand receptor, the potential ligand concentration likely exceeds the sRAGE concentration. Therefore, it remains unknown whether the concentration of circulating soluble forms of RAGE is sufficient to scavenge accumulating ligands [22].
One of the potential mechanisms explaining the contribution of sRAGE to the decreased incidence of MetS is polymorphisms in RAGE. Kankova et al. [23] demonstrated that subjects bearing the 1704 T allele of the RAGE gene had significantly lower plasma levels of antioxidants, including carotenoids, tocopherol, lutein, and lycopene, than those with the 1704G allele. These results suggest that G1704T is involved in oxidative stress. A recent meta-analysis indicated that the frequency of the 1704 T allele in East Asian populations was 7.76–20.6%, which is substantially higher than that in Caucasians (4.82–9.92%); moreover, the ORs associating the 1704 T allele with diabetes and its complications are higher in East Asian populations [24]. Moreover, RAGE single-nucleotide polymorphism rs2060700 (Gly82Ser) is strongly associated with circulating sRAGE levels [25]. Furthermore, the RAGE Gly82Ser polymorphism is associated with a risk of coronary artery disease [26]. In addition, another RAGE polymorphism might be linked with insulin resistance [27]. Given these results, further comprehensive studies including the evaluation of RAGE polymorphisms are required to clarify the association between circulating soluble forms of RAGE and MetS.
Recently, the role of circulating sRAGE is conflicting. Colhoun et al. investigated the relationship of sRAGE to incident coronary heart disease (CHD) in patients with type 2 diabetes [28]. The patients were followed for 3.9 years, and it was demonstrated that sRAGE concentration were positively associated with incident CHD in type 2 diabetes [28]. Similar results have been obtained among type 1 diabetes [29,30] and elderly women [31]. These results suggest that serum sRAGE concentration has a bivalent role. In conditions of elevated inflammatory level, such as diabetes or aging, serum sRAGE may be a marker of inflammation rather than a decoy, because there is emerging evidence that proteolytic cleavage, through which the component is formed, is part of a regulatory process and may reflect ongoing inflammation [32]. One would, therefore, expect higher concentration to be associated with more vascular disease. In contrast, among our participants, higher sRAGE concentration was associated with a lower prevalence of MetS even if they were in the higher hsCRP category. Consistent with our results, Selvin et al. have demonstrated a negative relationship between low concentration of circulating sRAGE and the risks of diabetes, CHD, and mortality in a community-based prospective cohort of middle-aged adults [33]. Thus, these results suggested that serum sRAGE concentration may be a marker of inflammation in conditions of elevated CRP, whereas they may be negatively associated with a risk of cardiovascular diseases and its risk factors, such as MetS, in conditions of low grade inflammation.
Although the details of regulation of soluble forms of RAGE have not been revealed, it is possible that the risk factors of MetS or cardiovascular diseases might influence the amount of circulating soluble forms of RAGE. Previous studies have reported the relationships between higher serum sRAGE concentration and lower BMI and WC in general population [5] and non-diabetic Japanese populations [6], and consistent with these findings, there was a positive correlation with adiponectin [28]. We also showed that higher sRAGE concentration was associated with lower prevalence of central obesity in this study. Thus, although the mechanism of the association between lower level of circulating soluble forms of RAGE and obesity is not still clear, the impaired function of adipocyte might be contributing to lower level of circulating soluble forms of RAGE. An alternative possibility is an up-regulation of full-length RAGE shedding by treatment of statin. A recent in vitro study showed that reduction of cellular cholesterol by statins significantly increases the levels of soluble RAGE by enhancement of full-length RAGE shedding [34]. This result was supported by clinical studies with hypercholesterolemic [35]. Further experimental studies are necessary to elucidate the regulation of soluble forms of RAGE.
In addition to central obesity, there was a negative association between the prevalence of elevated BP and serum sRAGE levels. Geroldi et al. showed that the plasma concentration of sRAGE was lower in hypertensive subjects than in normotensive controls [9]. Because crosslinking between collagen molecules and AGE could be implicated in the pathogenesis of arterial stiffening and hypertension [36], the secreted form of RAGE could prevent hypertension by binding to circulating AGE, thus preventing them from forming protein–protein crosslinks. A significantly elevated AGE concentration was found in the vascular smooth muscle cells of spontaneously hypertensive rats [37]. Taken together, higher circulating sRAGE concentrations may be associated with lower the prevalence of MetS by lowering the prevalence of central obesity and elevated BP.
There are some limitations in this study. First, because the sample size of our female participants was relatively small, statistical power may not have been sufficient to obtain a statistical significance. Whether the abovementioned relationship is present in women populations remains unknown. Second, because this study used a cross-sectional design, we cannot conclude the causal relationship between sRAGE and esRAGE and the prevalence of MetS and its components. A larger population-based prospective study needs to be performed to further confirm the causal relationship between sRAGE and esRAGE and the prevalence of MetS and its components.
Conclusion
In conclusion, higher concentrations of circulating RAGE were associated with lower prevalence of MetS and its components including central obesity and elevated BP among Japanese adult men with low grade inflammation.
Additional file
Additional file 1: Table S1. Characteristics of the participants according to the tertiles of serum sRAGE in women (n = 176)
Additional file 2: Relationship of the tertile of serum sRAGE with the prevalence of MetS risk factors in women (n = 176)
Additional file 3: Odds ratios of MetS risk factors by hsCRP and sRAGE categories in women (n = 176)
Abbreviations
sRAGE: Soluble receptor for advanced glycation end products; esRAGE: Endogenous secretory receptor for advanced glycation end products; MetS: Metabolic syndrome; hsCRP: High sensitivity C-reactive protein; AGEs: Advanced glycation end products; FBG: Fasting blood glucose; TG: Triglycerides; LDL-C: Low-density lipoprotein cholesterol; HDL-C: High-density lipoprotein cholesterol; WC: Waist circumference; BP: Blood pressure; SBP: Systolic blood pressure; DBP: Diastolic blood pressure; eGFR: Estimated glomerular filtration rate; BMI: Body mass index; PA: Physical activity; METs: Metabolic equivalent of tasks; SDS: Self-rating depression scale; ANOVA: Analysis of variance; ANCOVA: Analysis of covariance; CHD: Coronary heart disease.
Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
HM and RN conceived the study. HM, RN, KN, and YK designed the study. HM, KN, YK, AO, MC, CH, and HT did the data collection and processing. HM, KN, YK, AO, MC, and CH did the statistical analysis. HM and RN wrote the manuscript. HM, TM and RN contributed substantially to the interpretation of results and provided critical revisions to the manuscript. RN took overall responsibility for the integrity of the study. All authors read and approved the final manuscript.
Acknowledgments
This study was supported by “Knowledge Cluster Initiative” from the Ministry of Education, Culture, Sports, Science and Technology of Japan. We gratefully acknowledge all the participants in our study and the Sendai Orishicho Center for allowing us to perform the study. We also appreciate the Morinomiyako Occupational Health Association. We thank Lei Guan, Hui Guo, Yufei Cui, Eriko Ouchi, Tatsunori Saito for their valuable contributions to this study.
Author details
1Division of Biomedical Engineering for Health & Welfare, Tohoku University Graduate School of Biomedical Engineering, 2-1 Seiyo-machi, Aoba-ku, 980-8575 Sendai, Japan 2Department of Epidemiology, School of Public Health, Tianjin Medical University, Tianjin 300070, People’s Republic of China 3Department of Medicine and Science in Sports and Exercise, Tohoku University Graduate School of Medicine, Sendai 980-8575, Japan. 4Department of Medicine and Science in Sports and Exercise, Tohoku University Graduate School of Medicine, Sendai 980-8575, Japan. 5Department of Medicine and Science in Sports and Exercise, Tohoku University Graduate School of Medicine, Sendai 980-8575, Japan. 6United Centers for Advanced Research and Translational Medicine, Tohoku University Graduate School of Medicine, Sendai 980-8575, Japan. 7United Centers for Advanced Research and Translational Medicine, Tohoku University Graduate School of Medicine, Sendai 980-8575, Japan. 8United Centers for Advanced Research and Translational Medicine, Tohoku University Graduate School of Medicine, Sendai 980-8575, Japan.
Received: 8 August 2013 Accepted: 13 February 2014
Published: 6 March 2014
References
1. Yan SF, Ramasamy R, Schmidt AM: The RAGE axis: a fundamental mechanism signaling danger to the vulnerable vasculature. Circ Res 2010, 106:842–853.
2. Schmidt AM, Vianna M, Gerlach M, Brett J, Ryan J, Kao J, Esposito C, Hegarty H, Hufey W, Claus M: Isolation and characterization of two binding proteins for advanced glycosylation end products from bovine lung which are present on the endothelial cell surface. J Biol Chem 1992, 267:14987–14997.
1. Bucciacelli LG, Wendt T, Qu W, Lu Y, Lella E, Rong LL, Goova MT, Moser B, Kislinger T, Lee DC, Kashyap Y, Stem DM, Schmidt AM. RAGE blockade stabilizes established atherosclerosis in diabetic apolipoprotein E-null mice. Circulation 2002, 106:S287–S285.
2. Park L, Raman KG, Lee KJ, Lu Y, Ferran L, Schalkwijk CG, Schalkwijk CJ, Zimmet PZ, Cleeman JI, Donato KA, Ishikawa-Takata K, Tabata I: Exercise and Physical Activity Reference for healthcare professionals from the centers for disease control and prevention; American Heart Association; National Heart, Lung, and Blood Institute; American heart association; world heart federation; international atherosclerosis society; and international association for the study of obesity. Circulation 2009, 120:1640–1645.
3. Matsuura S, Imai E, Horio M, Yasuda Y, Tomita K, Nitta K, Yamagata K, Tomino Y, Yokoyama H, Hishida A: Revised equations for estimated GFR from serum creatinine in Japan. Am J Kidney Dis 2006, 48:1025–1031.
4. Nata J, Gasparrini F, Girao L, Tibolla G, Rassell S, Redaelli L, Buccianni G, Catapano AL: Circulating soluble receptor for advanced glycation end-products is inversely associated with body mass index and waist/hip ratio in the general population. Nutr Metab Cardiovasc Dis 2009, 19:129–134.
5. Yamagishi S, Adachi H, Nakamura K, Matsu T, Jinnoyuchi Y, Takenaka K, Takeuchi M, Emomoto M, Furuki H, Asteo Y, Ishimatsu T: Positive association between serum levels of advanced glycation end products and the soluble form of receptor for advanced glycation end products in nondiabetic subjects. Metabolism 2006, 55:S227–S231.
6. Yoshi O, Nishigori C, Watanabe T, Yamamoto H, Nishizawa Y: Suppression of accelerated diabetic atherosclerosis by the soluble receptor for advanced glycation end products in mice. J Clin Endocrinol Metab 2002, 87:2675–2679.
7. Koyama H, Shoji T, Yokoyama H, Motoyama K, Mori K, Fukumoto S, Watanabe T, Yamamoto H, Nishizawa Y: Plasma level of endogenous secretory RAGE is associated with components of the metabolic syndrome and atherosclerosis. Arterioscler Thromb Vasc Biol 2005, 23:2587–2593.
8. Basta G, Sironi AM, Lazzerini G, Del Turco S, Buzzigoli E, Casolari A, Natali P, Ferrannini E, Garattini A: Circulating soluble receptor for advanced glycation end products is inversely associated with glycemic control and S100A12 protein. J Clin Endocrinol Metab 2006, 91:4628–4634.
9. Geroldi D, Falcone C, Emmanuelle E, D’Angelo A, Calaginino M, Buza MP, Scioli GA, Fogari R: Decreased plasma levels of soluble receptor for advanced glycation end-products in patients with essential hypertension. J Hypertens 2005, 23:1725–1729.
10. Sebekova K, Krivosikova Z, Gajdos M: Total plasma Nepsilon-(carboxymethyl)lysine and sRAGE levels are inversely associated with a number of metabolic syndrome risk factors in non-diabetic young-to-middle-aged medication-free subjects. Clin Chem Lab Med 2013, 53:139–149.
11. Grundy SM, Cleeman JI, Daniels SR, Donato KA, Eckel RH, Franklin BA, Gordon DJ, Krauss RM, Savage PJ, Smith SC Jr, Speruto JA, Costa F: Diagnosis and management of the metabolic syndrome: an American Heart Association/National Heart, Lung, and Blood Institute Scientific Statement. Circulation 2005, 112:727–752.
12. Momma H, Nii K, Kobayashi Y, Guan L, Sato M, Guo H, Chuo J, Ottoo A, Yufei C, Tadaura H, Saito T, Mori T, Miyata T, Nagatomi R: Skin advanced glycation end-product accumulation is negatively associated with calcaneal osteo-sono assessment index among non-diabetic adult Japanese men. Jpn J Physiol 2011, 61:1673–1681.
13. Pearson TA, Menish GA, Alexander RW, Anderson JL, Cannon RO 3rd, Criqui M, Fadl YF, Fortmann SP, Hong Y, Myers GL, Rifai N, Smith SC Jr, Taubert K, Tracy RP, Vincor F, Centers for Disease Control and Prevention, American Heart Association: Markers of inflammation and cardiovascular disease: application to clinical and public health practice: a statement for healthcare professionals from the centers for disease control and prevention and the american heart association. Circulation 2003, 107:499–511.
14. Alberti KG, Eckel RH, Grundy SM, Zimmerman PZ, Cleeman JI, Donato KA, Fruchtman J, James WP, Loria CM, Smith SC Jr: Metabolic syndrome: a joint interim statement of the international diabetes federation task force on epidemiology and prevention; national heart, lung, and blood institute; american heart association; world heart federation; international atherosclerosis society; and international association for the study of obesity. Circulation 2009, 120:1640–1645.
15. Matsuura S, Imai E, Horio M, Yasuda Y, Tomita K, Nitta K, Yamagata K, Tomino Y, Yokoyama H, Hishida A: Revised equations for estimated GFR from serum creatinine in Japan. Am J Kidney Dis 2006, 48:1025–1031.
16. Craig CL, Marshall AL, Stompier M, Bauman AE, Booth ML, Ainsworth BE, Pratt M, Ekelund U, Yngve A, Sallis JF, Oja P: International physical activity questionnaire: 12-country reliability and validity. Med Sci Sports Exerc 2003, 35:1381–1395.
17. Ishikawa-Takata K, Tabata I: Exercise and Physical Activity Reference for Health Promotion 2006 (EPAR2006). J Epidemiol 2007, 17:177.
patients with hypercholesterolemia: effects of statins. Free Radic Biol Med 2007, 43:1255–1262.
36. Aronson D: Cross-linking of glycated collagen in the pathogenesis of arterial and myocardial stiffening of aging and diabetes. J Hypertens 2003, 21:3–12.
37. Wu L, Juurlink Bt: Increased methylglyoxal and oxidative stress in hypertensive rat vascular smooth muscle cells. Hypertension 2002, 39:609–614.
doi:10.1186/1758-5996-6-33
Cite this article as: Momma et al: Higher serum soluble receptor for advanced glycation end product levels and lower prevalence of metabolic syndrome among Japanese adult men: a cross-sectional study. Diabetology & Metabolic Syndrome 2014 6:33.
Submit your next manuscript to BioMed Central and take full advantage of:
- Convenient online submission
- Thorough peer review
- No space constraints or color figure charges
- Immediate publication on acceptance
- Inclusion in PubMed, CAS, Scopus and Google Scholar
- Research which is freely available for redistribution
Submit your manuscript at www.biomedcentral.com/submit | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2965,
1
],
[
2965,
6496,
2
],
[
6496,
12032,
3
],
[
12032,
16258,
4
],
[
16258,
23200,
5
],
[
23200,
28252,
6
],
[
28252,
31298,
7
],
[
31298,
37122,
8
],
[
37122,
43983,
9
],
[
43983,
49126,
10
],
[
49126,
50185,
11
]
]
} |
2b3d346bc7ec6f7cd17625f30e0b61f20a8e7f01 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 6,
"total-fallback-pages": 0,
"total-input-tokens": 20145,
"total-output-tokens": 3973,
"fieldofstudy": [
"Mathematics"
]
} | Title
Jacobians and branch points of real analytic open maps
Permalink
https://escholarship.org/uc/item/96j8z7mz
Journal
Aequationes Mathematicae, 63(1-2)
ISSN
0001-9054
Author
Hirsch, MW
Publication Date
2002
DOI
10.1007/s00010-002-8006-8
Peer reviewed
Jacobians and branch points of real analytic open maps
MORRIS W. HIRSCH*
Summary. The main result is that the Jacobian determinant of an analytic open map \( f: \mathbb{R}^n \to \mathbb{R}^n \) does not change sign. A corollary of the proof is that the set of branch points of \( f \) has dimension \( \leq n - 2 \).
Mathematics Subject Classification (2000). Primary 26E05, 26B10; Secondary 54C10.
Keywords. Real analytic map, open map, branch points.
Introduction
The main object of this paper is to prove the following result:
**Theorem 1.** The Jacobian of a real analytic open map \( f: \mathbb{R}^n \to \mathbb{R}^n \) does not change sign.
One of the referees kindly pointed out that the special case of polynomial maps was proved by Gamboa and Ronga [3]:
**Theorem 2** (Gamboa and Ronga). A polynomial map in \( \mathbb{R}^n \) is open if and only if point inverses are finite and the Jacobian does not change sign.
The proof of Theorem 1 is very similar to methods in [3], which are easily adapted to analytic maps; but as Theorem 1 does not seem to be known, a direct proof may be useful.
\( f: \mathbb{R}^n \to \mathbb{R}^n \) denotes a (real) analytic map in Euclidean \( n \)-space. We always assume \( f \) is open, that is, \( f \) maps open sets onto open sets. Denote the Jacobian matrix of \( f \) at \( p \in \mathbb{R}^n \) by \( df_p = \left[ \frac{\partial f_i}{\partial x_j} (p) \right] \). The rank of \( df_p \) is called the rank of \( f \) at \( p \), denoted by \( \text{rk}_p f \); the determinant of \( df_p \) is the Jacobian of \( f \) at \( p \), denoted by \( Jf(p) \). When the analytic function \( Jf: \mathbb{R}^n \to \mathbb{R} \) is everywhere non-negative or everywhere non-positive (in a set \( X \)), we say \( Jf \) does not change sign (in \( X \)).
*This research was partially supported by a grant from the National Science Foundation.
The following sets are defined for any $C^1$ map $g: M \to N$ between $n$-manifolds (without boundary):
- the set $R_k = \{ p \in M : \text{rk}_p g \leq k \}$
- the critical set, $C = R_{n-1}$
- the branch set, $B = \{ p \in U : g$ is not a local homeomorphism at $p \}$
Note that $B \subset C$ by the inverse function theorem. When $g$ is analytic, we also define:
- the critical analytic hypersurface $H \subset C$, comprising those points having a neighborhood in $C$ that is an analytic submanifold of dimension $n - 1$
- the constant rank analytic hypersurface $V \subset H$, at which $g | H$ has locally constant rank
The following results are byproducts of the proof of Theorem 1:
**Theorem 3.**
(i) The restricted map $f | V$ has rank $n - 1$,
(ii) $f$ is a local homeomorphism at every point of $V$,
(iii) $B \subset R_{n-2}$,
(iv) $\text{dim } R_{n-2} \leq n - 2$.
When $n = 2$, conclusions (iii) and (iv) imply $B$ is a closed discrete set; thus in this case $f$ is light, i.e., point inverses are 0-dimensional. From Stolow [4], which topologically characterizes germs of light open surface maps, we obtain:
**Corollary 4.** When $n = 2$, the germ of $f$ at any point is topologically equivalent to the germ at 0 of the complex function $z^d$ for some integer $d \neq 0$.
A key role in our proofs is played by the following result, Theorem 1.4 of Church [2]:
**Theorem 5 (Church).** If $g: \mathbb{R}^n \to \mathbb{R}^n$ is $C^n$ and open with rank $\geq n - 1$ at every point, then $g$ is a local homeomorphism.
Our results are close to some of those obtained by Church for $C^n$ maps. It is interesting to compare Theorem 3 (iii) and Corollary 4 to the following results from paragraphs 1.5 to 1.8 of his paper [2]:
**Theorem 6 (Church).** Let $g: M \to N$ be a $C^n$ map between $n$-manifolds.
(i) If $M = N = \mathbb{R}^n$ and $g$ is light, the following conditions are equivalent:
(a) $g$ is open,
(b) $Jg$ does not change sign,
(c) $B \subset R_{n-2}$.
(ii) If $M$ is compact and $g$ is open, then $g$ is light.
Lemma 7. Assume the critical set of $f$ is $C = Jf^{-1}(0) = \mathbb{R}^{n-1} \times \{0\}$, and $f|C$ has constant rank $k$, $0 \leq k \leq n - 1$. Then $f$ is a local homeomorphism, $k = n - 1$, and $Jf$ does not change sign in $\mathbb{R}^n$.
Proof. It suffices to prove that the conclusion holds in some neighborhood of each point, which we may take to be the origin.
It is convenient to denote points of $\mathbb{R}^n$ as $(y, t) \in \mathbb{R}^{n-1} \times \mathbb{R}$.
By the rank theorem we assume that in some open cubical neighborhood $N$ of the origin,
$$f_i(y, 0) \equiv 0, \quad i = k + 1, \ldots, n. \quad (1)$$
Identifying $N$ with $\mathbb{R}^n$ by an analytic diffeomorphism, we assume this holds for all $y \in \mathbb{R}^n$.
Because $f$ is analytic and open, there is a dense open set $\Lambda \subset \mathbb{R}^{n-1}$ such that for every $y \in \Lambda$, the map $t \mapsto f_n(y, t)$ is not constant on any interval. For each $y \in \Lambda$ there exists a maximal integer $\mu(y) \geq 0$ such that
$$0 < j < \mu(y) \implies \left(\frac{\partial}{\partial t}\right)^j f_n(y, 0) = 0,$$
Fix $y_* \in \Lambda$ such that the function $\mu: \Lambda \to \mathbb{N}$ takes its minimum value $m$ at $y_*$. Then $\mu = m$ in a precompact open neighborhood $W \subset \Lambda$ of $y_*$. By Taylor’s theorem there exists $\epsilon > 0$ such that for $(y, t)$ in the open set $N = W \times ] - \epsilon, \epsilon[ \subset \mathbb{R}^{n-1} \times \mathbb{R}$ we have
$$f_n(y, t) = t^m H(y, t), \quad H(y, t) \neq 0. \quad (2)$$
Claim. If $k \leq n - 2$ and $(y_0, t_0) \in N$ is such that $f_n(y_0, t_0) = 0$, then $f_{n-1}(y_0, t_0) = 0$. For $t_0 = 0$ by (2), and $k \leq n - 2$ implies $f_{n-1}(y_0, 0) = 0$ by (1).
Now we assume $k \leq n - 2$ and reach a contradiction. Since $f(N)$ is open and contains
$$f(y_*, 0) = (a_1, \ldots, a_{n-2}, 0, 0),$$
$f(N)$ also contains points $(a_1, \ldots, a_{n-2}, \delta, 0)$ with $\delta > 0$. But this contradicts the claim.
As $f$ has rank $n - 1$ at every point of the critical set, $f$ must be a local homeomorphism by Theorem 5. Therefore for every $p$, the induced homomorphism of homology groups
$$\mathbb{Z} = H_n(\mathbb{R}^n, \mathbb{R}^n \setminus \{p\}) \to H_n(\mathbb{R}^n, \mathbb{R}^n \setminus \{f(p)\}) = \mathbb{Z}$$
is an isomorphism, hence is multiplication by a number $\delta(p) \in \{+1, -1\}$.
Homology theory implies that each of the two level sets of \(\delta: \mathbb{R}^n \to \{+1, -1\}\) is open. As \(\mathbb{R}^n\) is connected, \(\delta(p)\) is constant. As \(\delta(p)\) is the sign of \(Jf(p)\) if \(Jf(p) \neq 0\), we have proved \(Jf\) does not change sign.
**Proof of Theorem 1.** For any set \(Y \subset \mathbb{R}^n\), we say the local theorem holds in \(Y\) if every point of \(Y\) has a neighborhood in \(Y\) in which \(Jf\) does not change sign.
**Lemma 8.** If the local theorem holds in a connected set \(Y\), then \(Jf\) does not change sign in the closure \(\overline{Y}\).
**Proof.** It suffices to prove \(Jf\) does not change sign in \(Y\), because \(Jf\) is continuous. Define \(Y_+, Y_-\) to be the subsets of \(Y\) where \(Jf\) is respectively \(\geq 0\) and \(\leq 0\). These sets are closed in \(Y\) by continuity of \(Jf\), and open in \(Y\) by hypothesis. As \(Y\) is connected, either \(Y = Y_+\) or \(Y = Y_-\).
The local theorem obviously holds in the set \(\mathbb{R}^n \setminus C\) of noncritical points. By Lemma 7, it also holds in the relatively open analytic hypersurface \(V \subset C\) defined in the introduction. It remains to prove that every point of \(C \setminus V\) has a neighborhood in which \(Jf\) does not change sign.
**Lemma 9.** Every point \(p \in C \setminus V\) has a neighborhood \(X_p \subset C \setminus V\) that is an analytic variety of dimension \(\leq n-2\).
**Proof.** Write
\[
C \setminus V = (C \setminus H) \cup (H \setminus V)
\]
Suppose \(p \in C \setminus H\). In this case we take \(X_p\) to be the union of the variety \(C_{\text{sing}}\) of singular points of \(C\) and those connected components of \(C \setminus C_{\text{sing}}\) having dimension \(\leq n-2\).
Suppose \(p \in H \setminus V\), or equivalently: \(p \in H\) and some minor determinant of \(df\) vanishes at \(p\) but not identically in any neighborhood of \(p\) in \(H\). We take \(X_p\) to be the intersection of \(C\) with the union of the zero sets of such minors.
Now consider any point \(p \in C \setminus V\). By Lemma 9, \(p\) has a neighborhood \(X_p \subset C \setminus V\) that is the union of finitely many smooth submanifolds of \(\mathbb{R}^n\) having dimensions \(\leq n-2\).
Choose a connected open neighborhood \(N_p \subset \mathbb{R}^n\) of \(p\) such that \(N_p \cap (C \setminus V) = N_p \cap X_p\). Then \(N_p \setminus X_p \subset (\mathbb{R}^n \setminus C) \cup V\). Therefore the local theorem holds in \(N_p \setminus X_p\).
Now \(N_p \setminus X_p\) is connected, by a standard general position argument. Therefore from Lemma 8, with \(Y = N_p \setminus X_p\), we infer that \(Jf\) does not change sign in \(N_p \setminus X_p\), which equals \(N_p\) because \(X_p\) is nowhere dense. This completes the proof of Theorem 1.
Proof of Theorem 3. Parts (i) and (ii) of Theorem 2 are proved by applying Lemma 7 locally. Lemma 9 implies (iii), because \( B \subset C \setminus V \) by (ii). For (iv), suppose \( \dim R_{n-2} = n - 1 \). Then the variety \( R_{n-2} \) contains an analytic hypersurface, which must meet \( V \). As \( R_{n-2} \subset C \), this implies \( R_{n-2} \cap V \neq \emptyset \), contradicting (i).
\[ \square \]
References
[1] A. Casson, personal communication, 1997.
[2] P. Church, Differentiable open maps on manifolds, Trans. Amer. Math. Soc. 109 (1963), 87–100.
[3] J. Gamboa and F. Ronga, On open real polynomial maps, J. Pure Appl. Algebra 110 (1996), 297–304.
[4] S. Stoilow, Sur les transformations continues et la topologie des fonctions analytiques, Ann. Sci. École Norm. Sup. III 45 (1928), 347–382. | 2025-03-06T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
261,
1
],
[
261,
2155,
2
],
[
2155,
4207,
3
],
[
4207,
6598,
4
],
[
6598,
9410,
5
],
[
9410,
10221,
6
]
]
} |
fd1601f6db8924ce1d8b50c1f0a76b3d70129899 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 10,
"total-fallback-pages": 0,
"total-input-tokens": 29544,
"total-output-tokens": 7398,
"fieldofstudy": []
} | Urban Planning Simulation Game and the Development of Spatial Competence
N I Pramaputi¹ and A Gamal²
¹First author, Department of Architecture, Faculty of Engineering, Universitas Indonesia, Depok 16425, Indonesia
²Corresponding author, Department of Architecture, Faculty of Engineering, Universitas Indonesia, Depok 16425, Indonesia
E-mail: ¹[email protected], ²[email protected]
Abstract. The use of simulation has proven to be helpful for many academics from various disciplines in the last decade. In the field of pedagogy, not only does simulation help in learning something new, but it also can be utilized as a learning tool for students. Today, there have been a lot of academic discourse of what kind of competence that can be harvested from the use of simulation. On the other hand, spatial intelligence is one type of intelligence whose existence is foreshadowed by the two more popular intelligence today; verbal and mathematical intelligence. To this day, only a few studies have thoroughly explored how to develop spatial intelligence, but only for children. This lack of dedicated framework and research has produced a consequential impediment for the uptake of simulation use in university-level education, particularly in spatial-oriented subjects. This paper addresses this shortcoming by reintroducing several key information regarding simulation, model, gamification, and its connection to spatial intelligence. This literature review will then be applied to an urban planning simulation game case study of SimCity. The result of this paper shows that there are several types of simulation that can train specific spatial competencies, which will further students’ spatial competence.
Keywords. Architecture, Urban planning, Simulation, Model, Education
1. Introduction
This paper tries to elaborate on the impact of urban planning simulation game in developing spatial competencies of its users. According to the previous statement, we generate two questions that we will attempt to answer with this paper, (1) What components does an urban planning simulation game has that could develop spatial competencies, and (2) how these components manage to develop spatial competence.
Simulation is commonly used in many disciplines, especially in science, technology, engineering, and mathematics (often abbreviated as STEM). Simulation is heavily used in those disciplines due to its capability to simulate a system or potential problem and allows scientist to actually test on them so that they don’t have to make a real test. With this advantage, scientists can test their new answers or strategies within a simulation, without the constraint of finance, labor, and time. One field that has implemented simulation heavily is education. A physics teacher can manage to explain a difficult concept to its students within the reach of his computer. Various educational simulations have been implemented in order to solve various problems in education, such as the now-computerized National Examination (Ujian Nasional) to educational software that help students in rural areas that lack human resources.
This paper will then attempt to find the possibility of simulation in developing one’s spatial competence. Both spatial intelligence and competence are rarely addressed in the list competencies of
Spatial intelligence consists of understanding and the development of spatial intelligence are only made possible with the use of technology. The SAMR model progression highlighted the progress through (1) substitution, (2) augmentation, and (3) simulation knowledge integration. This model is called the SAMR model that stands for Substitution, Augmentation, Modification, and Redefinition [7]. The use of simulations in education can be modelled based on degrees of classroom technology integration. This model is called the SAMR model that stands for Substitution, Augmentation, Modification, and Redefinition [7]. The SAMR model was created to generate a language that can be used to describe the system and its application in the real world. A system is described as a collection of organized components [11] including (1) entity, (2) condition, and (3) events [8]. An entity is the subject of the system, and it can be tangible or intangible. Researchers use a set of condition to differentiate between one entity and another. A condition can be further defined into an attribute (quality or characteristic that an entity may have) and activity (activity an entity may do). An entity is then put into a series of events that can trigger a change of its attribute and activity.
The use of simulation may provide several types of knowledge for its users, including; (1) contextual knowledge, (2) scientific knowledge, and (3) simulation knowledge [10]. These three knowledges can serve as answers to the original goal of the use of simulation; as a basis for individuals to be able to formulate answers, or as feedback to develop better simulations.
Contextual knowledge is the knowledge, which is gained from the use of simulations, that can be used to describe the system and its application in the real world. Scientific knowledge is contextual knowledge that is connected to each other in order to explain a bigger cause within a bigger framework. Simulation knowledge is knowledge of how to develop simulation designs, which ultimately enriches the information that can be received by simulation users. This three knowledge is obtained in stages. Contextual knowledge is obtained from the individual's understanding of the simulation as a set of models that have their own context. Scientific knowledge is derived from an individual's understanding of simulation as a set of interrelated models. Finally, simulation knowledge is obtained from the individual's understanding of the simulation as a set of interrelated models in explaining a system [10].
2. Literature review
We conducted literature reviews that can be grouped into three stages; SimCity, spatial competence, and how specifically SimCity helped to develop spatial competence. We looked at how a system of simulation (SimCity) works and its constituent components [4], types of knowledge obtained from the use of simulation [2], what are the things to identify in spatial environments [5], spatial competences [1,6], and the application of technology in pedagogy [7].
Simulation is defined as the process of imitating something tangible, together with its surroundings [8], or as a collection of artificial models that represents parts of a real system so it can be used a replacement of the real system in an experiment [9]. A system is described as a collection of organized components [11] including (1) entity, (2) condition, and (3) events. An entity is the subject of the system, and it can be tangible or intangible. Researchers use a set of condition to differentiate between one entity and another. A condition can be further defined into an attribute (quality or characteristic that an entity may have) and activity (activity an entity may do). An entity is then put into a series of events that can trigger a change of its attribute and activity.
The use of simulation may provide several types of knowledge for its users, including; (1) contextual knowledge, (2) scientific knowledge, and (3) simulation knowledge [10]. These three knowledges can serve as answers to the original goal of the use of simulation; as a basis for individuals to be able to formulate answers, or as feedback to develop better simulations.
Contextual knowledge is the knowledge, which is gained from the use of simulations, that can be used to describe the system and its application in the real world. Scientific knowledge is contextual knowledge that is connected to each other in order to explain a bigger cause within a bigger framework. Simulation knowledge is knowledge of how to develop simulation designs, which ultimately enriches the information that can be received by simulation users. This three knowledge is obtained in stages. Contextual knowledge is obtained from the individual's understanding of the simulation as a set of models that have their own context. Scientific knowledge is derived from an individual's understanding of simulation as a set of interrelated models. Finally, simulation knowledge is obtained from the individual's understanding of the simulation as a set of interrelated models in explaining a system [10].
The use of simulations in education can be modelled based on degrees of classroom technology integration. This model is called the SAMR model that stands for Substitution, Augmentation, Modification, and Redefinition [7]. The SAMR model was created to generate a language that can be used to model classroom technology integration. Regardless of the variety of subjects, they all share the common SAMR language. The SAMR model progression highlighted the progress through teaching with technology. The higher the model level, the more profound the effect it may have on students.
Substitution is the first level in the SAMR model, where technology only acts as a replacement of the same task, without any functional changes. Augmentation is where technology augments the same task and stands out as a better tool to use. Modification is where not only technology increases the ability of conventional education derivatives but can also modify the original learning objectives. Redefinition is where technology allows students to redefine tasks that were previously impossible to do without technology and it also produces new learning objectives [7].
Spatial intelligence is the intelligence used in imagining and processing a space [11]. Even though not all intelligence is made equal, spatial intelligence ranks second in education (compared to verbal intelligence and logic-mathematical intelligence which ranks first as the most tested intelligence at school) [1]. Currently, no computer simulations are associated with the development of spatial intelligence as one of the benefits of its use, and the development of spatial intelligence are only addressed almost exclusively for children only [12–15]. This research seeks to find out how urban planning simulations (with the SimCity case study) can affect a person's spatial intelligence. Spatial intelligence consists of competencies that can be used to measure whether someone is spatially intellect or not.
Spatial competence includes the ability to position two tangible or three-dimensional objects in the context of Euclidean space (x, y, and z axes). Spatial thinking competencies consists of several abilities
to imagine and interpret six visual attributes, including (1) location, (2) position, (3) distance, (4) direction, (5) relationship, and (6) movement [5]. Spatial thinking skills are not only useful to architects, artists, or other visual professions but also to ordinary individuals in their daily activities, starting from reading maps to finding an address or even to read chart tables in newspapers.
Spatial competence is composed of (1) the selection of strategy in solving spatial problems and (2) the ability to choose and use spatial representation [6]. It can then be concluded that not only does one have to be able to imagine and analyze a three-dimensional object, but he also needs to be able to choose and use the appropriate representation. Due to the advancement of technology, representation tools have then progressed to be more sophisticated, which then triggered the emergence of new spatial competencies.
Those two competencies eventually developed into four subcategories beyond Hegarty’s two spatial competence categories. These sub-categories are; (1) spatial, (2) mental rotation, (3) spatial visualization, and (4) spatiotemporal [1]. Spatial perception is the ability to be able to position an object and ignore irrelevant information. Mental rotation is the ability to visualize objects with provisions rotated, folded, or reflected. Spatial visualization competence is the ability to see and think analytically in the form of three-dimensional space. Spatiotemporal competence is the ability to read patterns and draw conclusions about the movement of a two-dimensional or three-dimensional object that moves over time.
3. SimCity Components
SimCity provides two types of views that can be utilized in accordance with its users’ needs; regional view and city view. The regional view provides an overview of the micro of a city, whereas city view provides an overview of the micro of a city. Both views are available for SimCity users to generate a comprehensive picture of what a city looks like. It will enable them to get a clear picture of how a city works and constructed and to observe the impact of their every command to the city development.
In the city view tab, there are several systems that can be identified, including; zoning, electricity, water, sewage treatment, roads, public transportation, garbage disposal, government, parks, health, fire, education, and the police. We then categorized these systems into three major systems that are crucial in urban planning namely; zoning system, utility system, and public facilities system. The zoning system consists of residential, commercial and industrial zone. Utility systems consist of electricity, water, and waste treatment systems. Finally, the system of public facilities consists of road systems, public transportation, waste disposal, government, parks, health, fire, education, and police. These systems (Table 1) have their own entities that act as their building blocks, which will be identified later.
| Zoning | Utility | Public Facilities |
|-----------------|----------|-------------------|
| Residential zone| Electricity | Road |
| Commercial zone | Water | Public transportation |
| Industrial zone | Waste treatment | Waste disposal |
| | | Government |
| | | Park |
| | | Health |
| | | Fire |
| | | Education |
| | | Police |
Table 1. Identified systems on SimCity 5
Every system represented in SimCity 5 has their own respective entities, attributes, and activities. In this paper, we selected residential zone as the chosen system for further analysis.
3.1. Simulation components
Residential zone has several identified entities, namely (1) location (zoning), (2) object (house), and (3) subject (resident). Based on these entities, we conclude that SimCity has two (2) types of entities; playable and non-playable entities. Playable entities, such as zoning and house, are entities the users can locate, position, and measure accordingly. Whereas non-playable entities such as residents are non-
An entity has attributes and activities that can be used to distinguish one entity from the others. Residential zoning doesn’t have any attributes except for its location. House has attributes that include its density level (that determines whether the house is a single, landed house or a skyscraper apartment) and its land value (that determines whether the residence falls into which economy level). Activities that occur at residential zone – as well as the rest of the system in SimCity 5 – includes the (1) construction, (2) upgrade, (3) operation, and (4) destruction when needed.
3.2. SAMR model
The simulation model is a model that directly replaces the real form of the system and the entities involved in building a city. It only substitutes the real form with a digital form that can be used in the game. But then again, this simulation model cannot provide more features than the actual system. Based on Figure 1, SimCity modeled the exact actual system and translated it into a digitalized version.
**Figure 1.** The real residential system (left) and the simulated residential system (right) on SimCity 5. Note how the simulated (right) doesn’t have any added features other than depicting the real entities.
Source: Maximillan Conacher of Unsplash (a) and illustrated by author (b).
The augmentation model is a model that directly replaces the real form of a system to simulation and adds features that don’t exist in the real world. As a result, SimCity users can learn about entities, attributes, and activities that are owned by a system by directly clicking the simulation, an action that cannot be done easily in the real life. Based on Figure 2, SimCity modeled the entity and added augmentation such as information of the entity and its condition with graphs and visual cues.
**Figure 2.** The augmentation model in SimCity 5 that provides information regarding land value and density of an apartment building (a) and giving visual cues regarding the condition of the apartment building that is abandoned (b).
Source: Illustrated by author.
The modification model is a model that can change the shape of an old model into a new one, thus enabling the users to obtain new information that previously could not be seen. This model is useful for describing complex things that are impossible to be displayed by one model. Based on Figure 3, SimCity modeled the entity and managed to modify the entity into other forms of communication (bar chart, pie chart, spectrum) to generate a more comprehensive condition to the users.
The modification model provides information regarding the total population in SimCity 5. The model provides (a) distribution of the population in a part of the city, (b) population growth in a city per time, and (c) number of needs for residential zoning per economic level.
Source: Illustrated by author.
The redefinition model is a model that can reshape an old model into a new one and associate the simulation with other simulations, therefore making it easier to observe the relationship between simulations. This model is useful for describing things that previously could not be represented with only one simulation. Based on Figure 4, SimCity modeled the entity and provided augmented maps to explain the current condition.
Figure 4. The redefinition model in SimCity 5 that describes the land value of a residential zone (a), that are influenced by (b) water availability (noted in blue), (c) availability of schools (marked green), and (d) the level of air pollution (polluting agents marked red).
Source: Illustrated by author.
4. SimCity and the Development of Spatial Competence
4.1. Visual perception
This competence requires users to be able to distinguish between one entity and another entity by comparing their attributes and activities. SimCity trains users' visual perception competencies with simulation models and augmentation models. The simulation model (Table 2) will give a clear idea of an entity to the users. If the users can recognize the entity by its attributes and activities, it will be easier for them to determine what kind of entity it is. The augmentation model will provide a more in-depth picture of entities that are not visible to the naked eye when observing the real system (Figure 5).
Table 2. SimCity 5 simulation type, identified components, and how it develops visual perception.
| Model Type | Model Description | Components Observed | Objective |
|--------------|-------------------------------------------------------------|--------------------------------------|--------------------------------------------|
| Simulation (S) | An aerial view of several residential zones with houses of various designs and sizes | Entity (house, street, park, power plant) | perceive what a city consists of |
| | | Attribute (size, location, and position of house) | perceive how city constituents distinguish from each other |
| Augmentation (A) | A zoom in view of an apartment building, with a pop-out consists of spectrums that depicts the apartment building's land value and density level | Entity (apartment building) | perceive what an apartment building looks like |
| | | Attribute (size of apartment building) | |
| | | Augmentation (spectrum of land value and density level of an apartment) | perceive the land value and density level of an apartment building |
4.2. Mental rotation
This competence requires the users to understand every part of an entity so they can determine the size of said entity before they put it on its designated place (Figure 6). SimCity trains mental rotation competencies with simulation models and augmentation models. The simulation model will give an idea of the shape of an entity that will be mentally rotated. In order to be rotated, users need to be familiar with every angle of the entity, so that they can still recognize the entity even when they see it from different perspective or point of view. SimCity also facilitates mental rotation by its augmentation model. SimCity is able to display the consequences of the wrong placement so the users might reconsider their choice and start planning their next move. SimCity is also able to help its users to tell whether the entity is proportional enough for the lot to be placed (Table 3).
| Model Type | Model Description | Components Observed | Objective |
|--------------|-----------------------------------------------------------------------------------|--------------------------------------------------------|---------------------------------------------------------------------------|
| Simulation (S) | A zoom in view of a coal power plant in operation, emitting air pollution in the | Entity (coal power plant) | perceive what a coal power plant looks like |
| | process | Attribute (size, location, and position of power | silence how a coal power plant operates (generates power and pollution) |
| | | plant) | |
| | | Activity (generating power) | |
| Augmentation (A) | An aerial view of a coal power plant placed amidst residential housing. Residential housing is highlighted green to distinguish between houses and the rest of the entities captured in the view | Entity (power plant, residential area) | perceive what a coal power plant looks like and how it operates |
| | | Attribute | |
| | | Activity (generating power) | |
| | | Augmentation (green = residential area) | highlighted the position of coal plant (which generates pollution) among residential areas |
| Modification (M) | The same aerial view as previous, but with the colors muted. The simulation can be switched interchangeably (zonation map, wind map, etc). The simulation depicts each and every map differently - in the case of wind maps, blue moving arrows were used. | Entity (city components) | generate what an overview of a city looks like |
| | | Augmentation (blue arrow = wind direction) | highlighted the direction of the wind |
Figure 6. With information generated by the model, it allows the user to simulate the consequences of placing the power plant in certain parts of the city in their mind. Users must mentally rotate the power plant (highlighted) in different scenarios (A, B, C, or D) to decide which position is the best. SimCity deems the best position is when it has the least exposure to the residential areas.
4.3. Spatial visualization
This competence requires the users’ imagination to picture how an entity looks like if a change occurred to its attributes or activities. SimCity trains users’ spatial visualization competency by showing the attributes in the form of data (Table 4). It will help the users to predict the outcome if they change the attributes or activities of an entity. SimCity trains the spatial visualization competency of its users using modification models and redefinition models. The modification model will show how the entity changes when the change occurs. If the users have a good understanding of the entity, they will have no difficulty to identify which entities will change in the new conditions. The redefinition model will provide information about how the changes will affect other entities. If the user is able to read the pattern of changes from the entity, then the users can predict the next results without needing further simulation. With the use of these two simulations, the users can visualize an entity and its attributes in under any circumstances and at any time (Figure 7).
| Table 4. SimCity 5 simulation type, identified components, and how it develops spatial visualization |
|----------------|-----------------------------------------------|
| Model Type | Model Description | Components Observed | Objective |
| Simulation (S) | An aerial view of several residential zones with houses of various designs and sizes | Entity (house, street, park, power plant) | perceive what a city consists of |
| | | Attribute (size, location, and position of house) | perceive how city constituents distinguish from each other |
| Augmentation (A) | A zoom in view of the houses with a yellow house figure blinking on top of several houses, indicating that the house is abandoned | Entity (houses) | perceive what housing zone in a city consists of |
| | | Attribute (size, location, and position of house) | perceive that the house indicated is abandoned |
| | The same zoom in view but with the colors muted except parks (tinted green) and coal power plant (tinted red), indicating its effects on the residential areas | Entity (house, street, park (in green), power plant (in red)) | perceive what a city consists of |
| | | Augmentation (yellow indicator = house is abandoned) | perceive that parks raises land value, whereas power plant lowers land value |
| Modification (M) | Bar graph of the city population, showing a significant drop from February to March. | identify sudden drop of population happening in some part of the city |
| Model Type | Model Description | Components Observed | Objective |
|------------------|-----------------------------------------------------------------------------------|-------------------------------------------------------------------------------------|--------------------------------------------------------------------------|
| Observed | The information is also supported by pie charts indicating population source (locals, visitors) and wealth (low, medium, high) | Bar chart indicating population growth in a city per month | |
| Objective | The same aerial view in simulation but with the colors muted except for the bar graph mapped in every residential entity, indicating the number of populations living in a particular house | Mapping of distribution of population in the city | perceive and identify which part of the city has higher / lower population than the others |
| Redefinition (R) | The same aerial view in simulation but with designated maps that highlights level of land value, utilities (water, electricity, sewage) and public facilities location (e.g. parks) | Mapping of distribution of land value (a), water (b), education (c), and pollutants (d) | perceive what causes the sudden population to drop (power plant), which will affect land value (a), water (b), education (c), and pollutants (d) |
**Figure 7.** With every information modified into different models, allow the population drop issue to be addressed by the user (a), locate where the population drop happens (b), and identify what city entities that causes the population drop (c). From the figure it can be deducted that the cause of the population drop is the current placement of power plant (indicated red in c1) that causes the water to be polluted (highlighted brown in c2).
### 4.4. Spatiotemporal
This competency requires the users to be able to read the visual pattern of a changing spatial entity in a certain duration of time. SimCity trains its users’ spatial-temporal competency with both simulation and augmentation models (Table 5). The simulation model will provide information about how SimCity depicted the pattern over time. The users then can inspect the visual changes that are taking place and the pattern of changes. If the users understand the pattern of changes and their reasons, they can determine how these changes can occur. With the use of a simulation model, the users can read and translate patterns that occur in an entity that goes along with time in under any conditions (Figure 8).
Table 5. SimCity 5 simulation type, identified components, and how it develops spatiotemporal
| Model Type | Model Description | Components Observed | Objective |
|---------------|------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------|---------------------------------------------------------------------------|
| Simulation (S)| A zoom in view of a commercial entity (a store) with a garbage truck picking up the store's trash | Entity (shop, garbage truck) | perceive what a city consists of |
| | | Attribute (size, location, and position of the garbage truck) | perceive the capacity and the attribute of a garbage truck |
| Augmentation (A)| An aerial view of the city with muted colors except for brown bar graphs mapped in every entity, indicating the volume of trash they have | Entity (city components) | perceive how trash collecting system works inside a city |
| | The same aerial view as the previous description, but as the time goes by, the brown bar graphs has started to decrease, indicating the trash were picked up by the garbage trucks, providing information on garbage trucks' movement pattern throughout the city (it started in small circles, picking up from the blocks around the landfill before moving to a bigger circle) | Volume of trash per entity (highlighted brown) | |
Figure 8. Information generated by models (a) allows the users to read the garbage truck movement pattern when operating in the city (b). This information will be useful once they decide to put another garbage dump, as the garbage truck movement determines the placement of the next garbage dump. Based on (a1) through (a3), we can see that the garbage truck works in a circular motion and will deduce the movement of garbage trucks with (b). Source: Screenshot of SimCity by author.
5. Conclusion
Based on the evaluation study, we find that the simulation components that directly addresses and exercises spatial competencies are simulation, augmentation, modification, and redefinition. Each model requires and exercises specific spatial competencies. Every type of model trains different spatial competencies. All perception, mental rotation, and spatiotemporal competencies are trained with simulation and augmentation model, whereas spatial visualization requires all four of the models. We
conclude that in order to train every spatial competence, the users must be able to utilize all four of the specified models.
6. Acknowledgement
This article was presented at the 2nd International Conference on Smart City INNOVATION (ICSCI) 2019, jointly held by Universitas Indonesia and Universitas Diponegoro. ICSCI conferences have been supported by the United States Agency for International Development (USAID) through the Sustainable Higher Education Research Alliance (SHERA) Project for Universitas Indonesia’s Scientific Modelling, Application, Research, and Training for City-centered Innovation and Technology (SMART CITY) Center for Collaborative Research, administered through Grant #AID-497-A-1600004, Sub Grant #IIE-00000078-UI-1
7. References
[1] Ness D, Farenga S J and Garofalo S G 2017 *Spatial Intelligence* (Routledge)
[2] Chen J-Q 1993 Building on Children’s Strengths: Examination of a Project Spectrum Intervention Program for Students at Risk for School Failure.
[3] Reiss M, Boulter C and Tunnicliffe S D 2007 Seeing the natural world: a tension between pupils diverse conceptions as revealed by their visual representations and monolithic science lessons *Vis. Commun.* 6 99–114
[4] Bonney M C, Schmidt J W and Taylor R E 1971 *Simulation and Analysis of Industrial Systems* *Oper. Res. Q.* 22 92
[5] Sinton D S, Bednarz S W, Gersmehl P, Kolvoord R A and Uttal D H 2013 *The people’s guide to spatial thinking* (National Council for Geographic Education)
[6] Hegarty M 2010 Components of Spatial Intelligence *The Psychology of Learning and Motivation* (Elsevier) pp 265–97
[7] Puente.dura R 2014 *Learning, technology, and the SAMR model: Goals, processes, and practice Ruben R. Puente.dura’s Weblog*
[8] Morgan C B, Banks J and Carson J S 1984 *Discrete-Event System Simulation* *Technometrics* 26 195
[9] Law A M and Kelton W D 1991 *Simulation Modeling & Analysis*. New York, McGraw-Hili Inc. USA
[10] Lukosch H K, Bekebrede G, Kurapati S and Lukosch S G 2018 A Scientific Foundation of Simulation Games for the Analysis and Design of Complex Systems *Simul. Gaming* 49 279–314
[11] Gardner H 2011 *Frames of mind: The theory of multiple intelligences* (Hachette Uk)
[12] Verdi.ne B N, Golinkoff R M, Hirsh-Pasek K, Newcombe N S, Filipowicz A T and Chang A 2013 Deconstructing Building Blocks: Preschoolers Spatial Assembly Performance Relates to Early Mathematical Skills *Child Dev.* 85 1062–76
[13] Levine S C, Ratliff K R, Huttenlocher J and Cannon J 2012 Early puzzle play: A predictor of preschoolers spatial transformation skill. *Dev. Psychol.* 48 530–42
[14] Beceren B Ö 2010 Determining multiple intelligences pre-school children (4-6 age) in learning process *Procedia-Social Behav. Sci.* 2 2473–80
[15] Gumilar Y and Nandi N 2018 The Student’s Spatial Intelligence Level in Senior High School *IOP Conf. Ser. Earth Environ. Sci.* 145 12094 | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3333,
1
],
[
3333,
10628,
2
],
[
10628,
14908,
3
],
[
14908,
17511,
4
],
[
17511,
20695,
5
],
[
20695,
24718,
6
],
[
24718,
27998,
7
],
[
27998,
30862,
8
],
[
30862,
33904,
9
],
[
33904,
36805,
10
]
]
} |
65df41ce1e61ec8de40aa79da44fa0b9a398c1ae | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 22934,
"total-output-tokens": 5766,
"fieldofstudy": [
"Engineering"
]
} | Comparison of Fuel Economy between Hydraulic Hybrids and Hybrid Electric Vehicles
Chi-Jui Huang*, Ming-Siang Du, Go-Long Tsai
Graduate institute of Mechanical and Electrical Engineering, National Taipei University of Technology, Taiwan
Abstract Due to the conventional vehicles produce a lot of pollution and fuel consumption in driving. So the purpose of this study was to effectively improve emission and energy consumption, and kept the original vehicles in the better performance. Although pure electric vehicle had the good performance and low pollution features, the vehicle was limited by the distance, and the batteries were very expensive comparing to the conventional vehicle. The hybrid vehicles could achieve energy-saving purposes, but the prices of vehicles and the replaced batteries were still expensive than conventional vehicles. Hydraulic hybrid vehicles engines need to be accelerated with other dynamic alternate during work. And as the hydraulic accumulators exhausted, the accumulator would return to traditional mode. In the meantime, the engines will take the advantage of dynamic brake and pump energy recycles, and therefore fuel consumption and energy recovery function could be reached. In this study applied the feed-back simulation to establish hydraulic hybrid vehicle and hybrid electric vehicle models, and the NEDC (New European Driving cycle) was applied and simulated in this energy state. The simulation results showed the hydraulic hybrid vehicles had 56.7% better fuel economy efficiency than hybrid electric vehicles, this was the tremendous contribution on this study.
Keywords Hydraulic Hybrid Vehicle, Hybrid Electric Vehicle, Hydraulic Pump/Motor, Hydraulic Accumulators, Feed-back Simulation
1. Introduction
General speaking, conventional manual or automatic transmission allowed the engine speed within a certain range, and the final drive output speed and torque to meet the driver's needs. The biggest drawback was the need to rely on the transmission to shift gear when the gearbox changes gear, the engine speed will obviously feel increased or decreased, and feeling frustrated by the shift time is generated at this moment. But stepless transmission (CVT) does not produce the shift feeling frustrated during a shift, so that passengers could ride more comfortable vehicles. The advantage for the stepless gearbox allows the engine power was not lost, and always maintained the most efficient in the peak region, but also allowed the engine speed maintained at a certain area, stepless gearbox was easy maintenance due to simple structure. But the disadvantage was the engine torque to the stepless transmission processing, the belt or chain was limited strength, could not able to bear much friction.
However Hydraulic transmission (HST) was widely used in the machine tool industry, construction machinery, construction machinery, vehicles, air transport [1], and its advantages could be listed as following:
1. Drive smoothly: the hydraulic drive unit, since the hydraulic oil shrinkage was very small, under normal pressure could be treated as incompressible, which was relied on a continuous flow of hydraulic oil carried drive, and the tubing hydraulic cushioning device can also be designed and set in so that the transmission buffer was stable.
2. Light, small size: hydraulic transmission compared with the mechanical, electrical and other transmission mode in which the output power at the same conditions, the volume and quality could be reduce, so the inertia was small and the transmission reaction would be quick.
3. Carrying capacity: the hydraulic drive was easy to get a lot of power and torque.
4. Easy to implement variable speed: In hydraulic transmission, regulate the flow of liquid could achieve stepless speed range up to 2000:1, and easily access to a very low speed.
From the transmission of the view, the hydraulic drive system could achieve similar variable speed function. The principle was to use the hydraulic pump to the engine mechanical energy into hydraulic energy, through a change in the hydraulic energy transfer energy through the various control valves, the transmission line, and finally through the hydraulic motors. The high pressure hydraulic energy would transfer to mechanical energy and achieve driving. Wherein to achieve stepless speed change function, the simple way
was changing the hydraulic motor or opening degree of hydraulic pump of this system to provide a continuous and wide variable reduction ratio, but usually a higher or lesser degree of opening of the pressure of the hydraulic motor/ pump would get poor efficiency.
The Origin of the hydraulic hybrid power system could be dating back to 1972, Dunn and Wojciechowski [2] in the energy conversion engineering workshop in the post, the study by the Welfare Adams company VW 311 vehicle engines to run fly wheel, simulated the entire vehicle energy, the device has a 5 gallon pressure accumulator, 4.8 in³/rev variable volume pump and other hydraulic components, hydraulic pump through a simulated vehicle deceleration recovered energy stored in the accumulator and the subsequent release for fly wheel use. From thus research the use of a hydraulic system was beginning at that way, you can recycle most of the original vehicle braking energy. The subsequent scholars continuously explore, 1992 Pourmovahed, Beachley and Fronczak [3] applied the components of hydraulic hybrid power system to conduct simulated match combinations by experiment that flywheel energy recovery model could reach between 61% to 89% recovery energy.
Concerning about the hydraulic power products applied on the vehicle that could be pointed that the 1982 Parker Hannifin Corporation [4] and joint architecture of hybrid systems Cumulo Brake Drive proposed a cascaded architecture hydraulic in 1991 of hybrid systems Cumulo Hydrostatic Drive. In the world the companies promote the hydraulic hybrid power systems and their products are: Bosch Rexroth's Hydrostatic Regenerative Braking System (referred to as HRB), Eaton's Hydraulic Launch Assist (referred to as HLA), Parker Hannifin's RunWise Advanced Series Hybrid Drive (referred RunWise) [5-7] and so on.
2. Modeling
This section applied Mat lab / Simulink software to create feedback-in hybrid vehicles (Hybrid Electric Vehicle, HEV) with a hydraulic hybrid vehicles (Hydraulic Hybrid Vehicle, HHV), and the model was shown in Figure 1 and Figure 2.
2.1. Driving Cycle Model
The study was adopting the new European standard test driving cycle (New European Driving Cycle, NEDC) which was shown in Figure 3, the total driving cycle time was 1180 seconds, from the urban driving cycle (Urban Driving Cycle, UDC) and highway driving cycle (Extra-Urban Driving Cycle, EUDC), which 780 seconds belonged to the urban driving cycle, and the top speed was 50 km/hr, and 400 seconds belonged to highway driving cycle. The maximum speed was 120 km/hr.
2.2. Vehicle Dynamics Model
In order to deal with the dynamics model, the simulation of the resistance comprised a rolling resistance, air resistance, acceleration resistance and the climbing resistance. The speed could be obtained from the NEDC driving cycle, and after proceeding from this cycle the required torque value could be obtained either.
2.2.1. Rolling resistance
As driving a vehicle, the tire was rolling on the wheel. The ground contact area would interact both radial and lateral force of the tire. The ground reaction on tires, which must be accompanied by a deformation energy loss, the cause of energy loss was as the rolling resistance of the wheel is rotated, and the following formula could be expressed as:
\[ R_r = \mu_r \cdot W \] (1)
\( R_r \) Rolling resistance
\( \mu_r \) Rolling resistance coefficient
\( W \) Vehicle Gross Weight.
2.2.2. Air resistance
When the vehicle was traveling, the air pressure acting on the front of the vehicle body was generated, known as air resistance. At low speeds, little effect of air resistance. However, at high speed, because the air resistance was proportional to the square of the speed, so the air resistance was represented as the following formula.
\[ R_a = C_D \cdot \frac{\rho}{2} \cdot A_f \cdot (v - v_w)^2 \] (2)
\( R_a \) Air resistance
\( C_D \) Air resistance coefficient
\( \rho \) Air density
\( A_f \) Orthographic projection area of the vehicle
\( v \) Vehicle velocity
\( v_w \) Air velocity.
2.2.3. Climbing resistance
As the vehicle was traveling uphill, climbing resistance was arising from the opposite direction which would affect the weight of the vehicle itself. When the vehicle was traveling downhill, the vehicle driving force became the anti-resistance, and could be expressed as the following formula:
\[ R_c = W \sin(\theta) \] (3)
- \( R_c \) Climbing resistance
- \( \theta \) Slope angle
2.2.4. Acceleration resistance
In addition to the traveling state of the vehicle on the highway at fixed speeds, most vehicles were at acceleration and deceleration condition. General speaking, the vehicle needed more power than the steady running. The vehicle should entering the acceleration mode to conquer inertial resistance of rotating engine and components, clutch, transmission, drive shafts an, tires and so on, this resistance is called acceleration resistance, the formula could be expressed as following:
\[ R_s = (W + W_f) \cdot \frac{a \cdot G}{g} \] (4)
- \( R_s \) Acceleration resistance
- \( W_f \) The same amount of weight rotating element
- \( \alpha \) Acceleration
- \( G \) Gravity.
2.3. Engine MODEL
In this study the main driving force loaded on the vehicle was 1 liter of 41 kw petrol engine, the engine speed and engine torque could be checked up the table, and therefore the braking ratio of fuel consumption (brake specific fuel consumption, bsfc) could be obtained, and the fuel consumption of the vehicle could be calculated and shown in Figure 4.
2.4. Energy Storage Element Model
For energy storage component parts, comparing hydraulic accumulator power density with the lithium-ion batteries and lead-acid batteries, nickel hydrogen batteries is the highest. But from’’ the energy density’’ point of view, the energy density of the hydraulic accumulator was the lowest, which could be shown in Figure 5.
2.4.1. Battery model
The nickel-metal hydride battery was used in this study, the voltage was 330 V, and power capacity was 4 Ah, and therefore the total electric energy was 1.32 kWh. To create a simple battery model RC circuit diagram which was shown in Figure 6 and the correlation equation could be written as
\[ V_t = V_{oc} - I_{bat} \cdot R_{int} \] (5)
- \( V_{oc} \) Open circuit voltage
- \( R_{int} \) Internal resistance of the battery
- \( V_t \) Battery terminal voltage
- \( I_{bat} \) Output current of the battery
Usually, terminal voltage and current could be measured, and it could be calculated by the following formula:
\[ P_{bat} = I_{bat} \cdot V_{oc} \] (6)
Then put (5) into (6) and the (7) could be obtained
\[ I_{bat} = \frac{V_t - (V_{oc}^2 - 4 \cdot R_{int} \cdot P_{bat})^{0.5}}{2R_{int}} \] (7)
Battery SOC was so called Ampere-Hours, and due to SOC would change with the charge and discharge currents, it
could be obtained from the following formula:
\[ SOC = SOC_{int} - \frac{\int_{0}^{t} \frac{1}{A} \, dt \, dq}{A} \quad (8) \]
2.4.2. Accumulator model
Accumulator specifications were applied balloon-type accumulator with a capacity of 22 L, working pressure was 150 bars to 420 bars. To create a model of the accumulator was shown in Figure 7. And the varied process was according to the laws of thermodynamics, the gas expansion and the actual compression processes, the relationship between pressure and volume could be expressed as the following equations:
\[ PV^n = \text{Constant} \quad (9) \]
\[ P_0 V_0^n = P_1 V_1^n = P_2 V_2^n = \text{Constant} \quad (10) \]
\[ V_1 = \left( \frac{P_2}{P_1} \right)^{\frac{1}{n}} V_2 \quad (11) \]
2.5. Driving Element Model
For parts of the drive elements, the hydraulic motor / pump / generator, a hydraulic motor / pump had a higher power density (kW / kg). The greater power density of the vehicle acceleration and deceleration, the greater ability of the electric motor which was shown in Figure 8.
![Figure 8. Hydraulic motor / pump and electric motor / generator power density [12]](image)
2.5.1. Electric motor model
The 75 kW electric permanent magnet motor was used in this study that was a DC motor with a low-speed torque. According to the reverse-type manner, the torque and speed have been calculated and the motor efficiency curve was shown in Figure 9 through the previously stored.
2.5.2. Generator model
A 32 kW permanent magnet generator was used in this study, and the generator was substantially the same as electric motor model shown in Figure 10.
2.5.3. Hydraulic motor and hydraulic pump models
Hydraulic motor and hydraulic pump models were used oblique axis piston hydraulic motor / pump in this study. And was applied reciprocating plunger in a limited volume movement, so after the inhalation of low pressure hydraulic fluid through the piston, and then compressed volume of high-pressure hydraulic oil would be discharged through the piston. The displacement in this process could be achieved by changing the angle of the swash plate to alter the pressure and flow, and thereby changing the relationship between torque and speed. The hydraulic motor / pump related formula was shown as following:
The fluid flow rate of Hydraulic motor / pump
\[ Q_{P/M} = x_{P/M} \omega_{P/M} D_{P/M} (\eta_{vP/M})^2 \] (15)
The shaft torque Hydraulic motor / pump shaft torque
\[ T_{P/M} = x_{P/M} \Delta P_{P/M} D_{P/M} (\eta_{vp/LP/M})^2 \] (16)
The shaft power of Hydraulic motor / pump shaft power
\[ P_{P/M} = x_{P/M} \Delta P_{P/M} D_{P/M} \omega_{P/M} (\eta_{vp/LP/M})^2 \] (17)
Where \( Q_{P/M} \) was volume flow rate, \( T_{P/M} \) was shaft torque, \( x_{P/M} \) was axis function, \( x_{P/M} \) was the volume ratio which was defined as the percentage displacement of \(-1 \leq x \leq 1\), as \( x \) was positive which was in the pump mode, and as \( x \) was negative which was in the motor mode, \( x \) was not zero for success. \( D_{P/M} \) was the maximum volume displacement, \( \omega_{P/M} \) was axis angular velocity, \( \Delta P_{P/M} \) was the pressure difference between the hydraulic motor / pump inlet and outlet, \( \eta_{vP/M} \) was the was the volume loss efficiency, \( \eta_{vp/LP/M} \) was the mechanical loss efficiency, and \( Z \) was factor of working mode shown as following equation:
\[ Z = \text{sgn}(x) = \begin{cases} +1, & \text{pump mode} \\ -1, & \text{motor mode} \end{cases} \] (18)
The hydraulic motor / pump efficiency was the product of the total volumetric and mechanical efficiency, and usually affecting the operation efficiency was due to a variable (pressure difference and the volume flow rate), the hydraulic motor / pump parameters (volume displacement), and fluid parameters (fluid viscosity, density, volume modulus, etc.).
2.6. HEV and HHV Control Strategies
In order to investigate the HEV and HHV fuel economy, the study set the two control strategies to be the same. And in order to avoid often start engine, it will be set as SOC storage elements was less than 0.3, and then the engine could be started again. Once started engine, SOC must charge storage element back to 0.9 before they can stop the engine. Optimum operating point of the engine speed control torque was set at 55 Nm and 3500 rpm to achieve the best fuel economy.
3. Simulation Results and Discussion
This section will explore a variety of architectures mentioned in Section 2, under the NEDC driving cycle and simulating the depletion of its energy state, the study obtained the performance comparison. And therefore to simulate the differences between HEV and HHV, the basic specifications of the vehicle could be unified as shown in Table 1.
| Parameter | symbol | value | unit |
|--------------------------------|--------|-------|--------|
| Vehicle weight | W | 1500 | kg |
| Rolling resistance coefficient | \( \mu_r \) | 0.008 | - |
| Air resistance coefficient | \( C_d \) | 0.28 | - |
| Vehicle orthographic projection area | \( A_f \) | 2.26 | m² |
| Wheel radius | r | 0.315 | m |
| Maximum vehicle speed | \( v_F \) | 180 | km/hr |
3.1. Hybrid Vehicle Simulation Results
In order to clearly observe and understand the change of battery SOC, so that the NEDC driving patterns could be divided into two sets of simulations. Figure 11 represented the time response of the vehicle speed under the beginning of the first 2500 seconds interval. Figure 12 was shown the electric power level. Fig. 13 was the curve of the battery charge and discharge. Figure 14 was the generator actuated curve. Figure 15 was the battery SOC state. Apparently, the vehicle was started and used the battery as a drive source. As the battery SOC was used up to 0.3, the engine started generating the electricity energy, and could be supplied to the battery while the electric motor was driven, and until the battery SOC reached 0.9, the engine would be shut down. That would meet the original setting control strategies.
3.2. Hydraulic Hybrid Vehicle Simulation Results
In order to compare the simulation results with electric hybrid vehicles, the study also performed two sets of hydraulic hybrid vehicle NEDC driving patterns simulation program. The simulation results was shown in Fig. 16 which was a volume flow rate of the pressure accumulator curve, and the hydraulic pump(actuated pump) curve was shown in figure 17. Figure 18 was the related SOC state. From Figure 16 to 18, which could be found that the number of starts (star-up) of hybrid car would be more frequently than the number of hydraulic hybrid car, and therefore from the study could affirm that the gasoline-electric hybrid-powered life will be shorter than the life of the hydraulic hybrid? From the simulation the actual fuel economy of hydraulic hybrid vehicles was savings 56.7% fuel consumption than Hybrid electric vehicle which was shown in Table 2. The reason was caused by the accumulator, because the braking backfilled
pronounced than the effect of a number of cells, the main difference was the physical change of the charge and discharge of hydraulic was simple, but the accumulator battery charging and discharging process was a chemical change which can vary significantly for greater chemical energy losses.
Figure 16. Accumulator volume flow rate during the first 2500 seconds.
Figure 17. Hydraulic pumps actuation during the first 2500 seconds.
Figure 18. SOC state of the accumulator during the first 2500 seconds.
Table 2. The comparison of fuel economy for HEV and HHV.
| Category | HEV | HHV |
|----------------|------|------|
| Fuel economy\(\text{km/L}\) | 15.82| 24.79|
4. Conclusions
The study used European traffic patterns to simulate vehicle energy changes state, and could be clearly observed in the various components of the actuator status and efficiency in the system, that the hybrid vehicles and hydraulic hybrid fuel economy, energy storage SOC factors such elements could be known.
From simulation results that the pressure accumulator battery has a higher power density compared to the energy density of the hydraulic accumulator. The hydraulic accumulator was short, and should rely on the engine driving or braking kinetic energy stored in a hydraulic accumulator, which was more suitable for the stop-go urban driving patterns, and would actually be used in the vehicles, such as buses, garbage trucks, and so on.
Finally, the simulation results of this study with respect to the hydraulic hybrid vehicle hybrid vehicles could improve fuel economy up to 56.7%. This was the significant contribution on this study.
REFERENCES
[1] GUO Xing home, Lu Huai smoked, Huang Shengming, gas hydraulic science, Gao Books Ltd, 2011.
[2] H. S. Dunn and P. H. Wojciechowski, “High-Pressure Hydraulic Hybrid with Regenerative Braking,” Proceeding of the 7th Intersociety Energy Conversion Engineering Conference, San Diego, CA, pp. 989-995, 1972.
[3] A. Pourmovahed, N. H. Beachley, and F. J. Fronczak, “Modeling of a Hydraulic Energy Regeneration System - Part I: Analytical Treatment,” AEME Journal of Dynamic Systems, Measurement, and Control, pp.155-159, 1992.
[4] Parker’s Hydraulic Hybrid Technologies, R. J. Marotta, 2012, http://www.wwcleancities.org/documents/HydraulicHybrid_Parker_Marotta.pdf
[5] Factsheet HRB, Bosch Rexroth, 2008. http://www.boschrexroth-us.com/country_units/america/united_states/en/Company/Press/trade_show_information/a_downloads/Hydrostatic_Regenerative_Braking_Fact_Sheet.pdf
[6] Hydraulic Launch Assist The Eaton HLA System, Eaton, www.etopiamedia.net/mtw/pdfs/EatonHLA1.ppt
[7] Hydrauliska hybrider - Vad händer, Parker, http://www.ifsfluid.se/Seminarium%20Hybridrifer/Hydrauliska%20hybrider%202011-03-03%20Hybridseminarium%20-%20%20R%20%20Werndin.pdf
[8] E. Tzirakis, et al., Vehicle Emissions and Driving Cycles:
Comparison of The Athens Driving Cycle (ADC) With Ece-15 And European Driving, Cycle (EDC), Global NEST Journal, Vol 8, No 3, 2006 pp 282-290
[9] Baseley, S., et al., Hydraulic Hybrid Systems for Commercial Vehicles, SAE technical paper, 2007.
[10] Cheung Ka Ho, the use of reverse analog composite dynamic energy management motorcycles, Vehicle Engineering, National Taipei University of Technology Master's thesis, Taipei, 2003.
[11] Yunus A. Cengel, Micheal A. Boles, Thermodynamics an Engineering Approach, McGrawHill, 2006.
[12] K. Petter, New system solutions for working hydraulics to achieve energy efficiency improvement, Presentation at IFS 2010 meeting, 27-28 January 2010, Norrköping, Sweden. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4384,
1
],
[
4384,
6467,
2
],
[
6467,
8771,
3
],
[
8771,
11469,
4
],
[
11469,
13161,
5
],
[
13161,
17680,
6
],
[
17680,
18662,
7
],
[
18662,
21529,
8
],
[
21529,
22237,
9
]
]
} |
8f93907c7b7558083ad0fd4f9b63e14abb3776a8 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 39034,
"total-output-tokens": 12342,
"fieldofstudy": [
"Physics"
]
} | The Best Approximation of an Objective State With a Given Set of Quantum States
Li-qiang Zhang, Nan-nan Zhou, and Chang-shui Yu*
Approximating a quantum state by the convex mixing of some given states has strong experimental significance and provides alternative understandings of quantum resource theory. It is essentially a complex optimal problem which, up to now, has only partially solved for qubit states. Here, the most general case is focused on that the approximation of a d-dimensional objective quantum state by the given state set consisting of any number of (mixed-) states. The problem is thoroughly solved with a closed solution of the minimal distance in the sense of $l_2$ norm between the objective state and the set. In particular, the minimal number of states in the given set is presented to achieve the optimal distance. The validity of this closed solution is further verified numerically by several randomly generated quantum states.
1. Introduction
In the past few decades, quantum information technology has been developed rapidly. The essence of quantum information processing is the preparation and the manipulation of quantum states. However, due to inherent limitations, technical, or economic reasons in practical scenario, the required quantum state could not be prepared exactly as we expected. One alternative approach could be the approximate preparation of the state by convex mixing of some disposable quantum states.
In addition, the approximation of a state is also widely implied in the quantum resource theory. As we know, the quantification of quantum features is the core of the resource theory. Many important quantum features such as quantum entanglement,[1–6] quantum coherence,[7–12] quantum discord,[13–18] and so on,[19,20] have been quantitatively studied from the point of resource theory of view. One of the most common methods is to measure the nearest distance between the target state and the free state set.[21–23] For example, the entanglement measure can be quantified by the smallest distance between the target state and the separable state set.[24–27] Quantum discord of a quantum state can be measured by its closest distance from the set of classically correlated quantum states.[13,28–36] Quantum coherence can be described based on the minimal distance between the target quantum state and the convex combinations of the given orthogonal basis.[37–43] Quantum superposition measures the nearest distance between the given state and some linearly independent states.[44–46] Therefore, a most general question extracted is how to optimally approximate an objective quantum state by the convex mixing of some given quantum states.
The optimal approximation of a quantum state with limited states has been addressed in various cases.[47–52] In refs. [47, 48], optimally approximating an unavailable quantum state $\rho$ (quantum channel $\Phi$) by the convex mixing of states (channels) drawn from a set of available states $\{\varphi_i\}$ (channels $\{\Psi\}$) was considered. The choice of available quantum states is a key problem. The approximation of a state by the six eigenstates of three Pauli matrices was studied in ref. [48], which was further revised and supplemented in ref. [49]. Then the approximation by the eigenstates of any two Pauli matrices was investigated in ref. [50] and some interesting trade-off relations were also proposed. Later, the disposable quantum state set was extended from the eigenstates of the Pauli matrix to the eigenstates of any quantum logic gate,[51] and then to arbitrary quantum states without any restriction.[52] Up to now, all the relevant contributions have been only restricted to the qubit states. It remains open whether such an optimal problem could have a closed solution for a general high-dimensional state.
In this paper, we study the optimal approximation of a general d-dimensional quantum state by convex mixing the states in a given state set. We employ the $l_2$ norm to measure the distance between two quantum states. With any given state set, we give the closed solution to the question, that is, we find the minimal distance between the objective state and the optimal state mixed with the states in the set. In particular, we can give the minimal number of the states in the set to achieve the optimal distance. We also prove that the case with the state set including more than $d^2$ states can be transformed into the case with the set including no more than $d^2$ states. In order to validate our closed solution, we investigate several examples with different dimensions in a numerical way. All the examples demonstrate the perfect consistency with our closed solution. The remaining of this paper is organized as follows. In Section 2, we give a brief description of the question of the convex approximation question and the closed solution to the question. In Section 3, we consider several randomly
DOI: 10.1002/andp.202100407
generated examples to test our closed results. The discussion and conclusion are given in Section 4.
2. The Approximation of the Given Objective State
The problem.-To begin with, we would like to first introduce the optimal problem. Let $\rho$ denote an objective state and $S := \{\rho_i, i = 1, 2, \ldots, N\}$ denote a given set of quantum states. Our goal is to prepare a quantum state $\sigma = x_1, x_2, \ldots, x_K = \sum_{i=1}^{K} x_i \rho_i$ with the sub-
scripts of $x$ in increasing order by the convex mixing of $K \leq N$ quantum states in the set $S$ so that the distance between the objective quantum state $\rho$ and prepared quantum state $\sigma$ is the closest, and the vector $\vec{p} = \{p_1, p_2, \ldots, p_K\}$ is the probability vector to be optimized.
For convenience, we consider all the $d$-dimensional states in the representation (labeled by 'X') defined by some Hermitian matrix basis, for example, $\{\chi_i, i = 0, 1, 2, \ldots, d^2 - 1\}$ with $X_i = \frac{1}{\sqrt{d}} \chi_i$. Thus, a $d$-dimensional quantum state $\rho$ in the X representation can be expanded as $\rho = \sum_{i=0}^{d^2-1} r_i X_i$.
The Bloch representation is such a typical example in which case $r_i$ is the element of the Bloch vector. Similarly, we use $r_i$ to represent the vector of $\rho$ in the X representation with its elements $r_{ij} = \text{Tr}(\rho X_{ij})$ and $r_i$ ($r_i$ is its element) to denote the vector of the $i$th state in $S$. In this sense, the distance between our objective state $\rho$ and the state $\sigma$ to be prepared can be given based on the $L_2$ norm as
$$D(\rho, \sigma) = \frac{1}{2} \left\| r_{0} - \sum_{i=1}^{K} p_i r_i \right\|_2^2 \tag{1}$$
with $\|r\|_2 = \sqrt{\sum r_i}$. It is obvious that $D(\rho, \sigma) = 0$ for $\rho = \sigma$ and $D(\rho, \sigma) = 1$ for $\rho \perp \sigma$.
To construct the optimal quantum state, $\sigma$ which is the closest to the state $\rho$ is equivalent to achieve $\min_{\vec{p}} D(\rho, x_1, x_2, \ldots, x_K(\vec{p}))$. Within the linear constraint $\sum_{i=1}^{K} p_i - 1 = 0$, this minimization is a global convex optimization problem on $\vec{p}$, which can be verified by the Hessian matrix of this problem defined by
$$H = \frac{\partial^2 D}{\partial p_i^2} = R_i' R_i \tag{2}$$
with $R_i = \{r_1, r_2, \ldots, r_K\}$ being a $d \times K$ matrix ($K \leq N$), and the inequality convex constraint $-p_i \leq 0$. The global convex optimization provides a good property that the optimal solution can be obtained by the global optimal point if it satisfies the constraints, or at the constraint boundary if the global optimal point is not within the constraint range. A schematic illustration of the convex optimization process is given in Figure 1, where we consider a 2D convex function $D(p_1, p_2)$ as an example. It is shown that the global minimum on the intersection curve is not within the constraint $p_1, p_2 \geq 0$, so the optimal point of the system is just at the lower endpoint of the red curve, that is, $p_1 = 1, p_2 = 0$. In addition, we have to emphasize that $l_1$ norm due to its simple form allows the optimization problem to be analytically solved.
With the above knowledge, we can present our main results about the best approximation of the objective state as follows.
Figure 1. Schematic diagram of the convex optimization process. A convex function $D(p_1, p_2)$ is optimized over $p_1$ and $p_2$ subject to the constraint $p_1 + p_2 - 1 = 0$ shown by the plane C. The inequality constraint $p_1, p_2 \geq 0$ is illustrated by the cuboid. The minimum of $D$ is shown by the lower end-point of the red intersection curve instead of the minimum of the curve.
Theorem 1. Given an objective $d$-dimensional state $\rho$ and a state set $S$ composed of $N$ quantum states $\rho_i$ ($N \leq d^2$), in the X representation, one can define the vector $\vec{B}$ as $\vec{B}(i) = (r_1 - r_i)^2 r_i + \delta_{iK}$ and a matrix $A$ as $A(i, j) = (r_i - r_k)^2 r_j + \delta_{iK}$ with $K \leq N$ and $i, j = 1, 2, \ldots, K$.
The minimal distance between $\rho$ and $\sigma = \sum_{i=1}^{K} p_i \rho_i$ is given by
$$\min_{\vec{p} \in S} D(\rho, x_1, x_2, \ldots, x_K(\vec{p})) \tag{3}$$
where $\vec{p} = A^{-1} \vec{B}$ with rank($A$) = $K$ and $p_i > 0$ required, and $i_0$ denotes the $i$th element in the subset composed of $K$ states from the set $S$.
Proof. For $N \leq d^2$, Equation (1) can be rewritten as
$$D(\rho, \sigma) = \frac{1}{2} \sum_{i=1}^{N} (p_i r_i^T r_j - 2 p_i r_i^T r_j + r_j^T r_j) \tag{4}$$
Consider the Lagrangian function
$$L(p_i, \lambda, \lambda_i) = D(\rho, \sigma) - \sum_{i=1}^{N} \lambda p_i + \lambda \left( \sum_{i=1}^{N} p_i - 1 \right) \tag{5}$$
where $\lambda$ and $\lambda_i$ are the Lagrangian multipliers. The Karush–Kuhn–Tucker conditions are given by
$$\frac{\partial L}{\partial p_i} = \sum_{j} r_j^T r_j - r_j^T r_j - \lambda_i + \lambda = 0$$
\[
\lambda_i p_i = 0, \lambda_i \geq 0, p_i \geq 0, \sum_{j} p_j - 1 = 0, i = 1, 2, 3, \ldots, N
\] (6)
After eliminating \( \lambda \) by \( \frac{\partial}{\partial p_i} - \frac{\partial}{\partial p_j} = 0 \), we have
\[
\sum_{j} (p_j r_j)^T (r_i - r_N) = r_j^T (r_i - r_N) + \lambda_i - \lambda_N, i = 1, 2, 3, \ldots, N - 1
\] (7)
For convenience, we first consider the case all \( p_i \neq 0 \) which mean \( \lambda_i = 0 \) for \( i = 1, 2, 3, \ldots, N \). We rewrite Equation (7) above in matrix form \( A \mathbf{p} = \mathbf{B} \) with \( P(\mathbf{i}) = p_i \) for \( i = 1, 2, 3, \ldots, N \). The determinant of matrix \( A \) is
\[
\det(A) = \det(R_i^T R_i)
\] (8)
with \( R_i = (r_1 - r_N, r_2 - r_N, \ldots, r_{N-1} - r_N) \) being a \( d^2 \times (N - 1) \) matrix.
Case 1: \( \det(A) = 0 \). This means that each column of the matrix \( R_i \) is linearly related. Any quantum state represented by \( \mathbf{r}_i = \sum_{j} p_j \mathbf{r}_j \), with \( p_j \in [0, 1] \) and \( \sum_j p_j = 1 \) must be represented by \( \mathbf{r}_i = \sum_{j} q_j \mathbf{r}_j \) with \( q_j \in [0, 1] \) and \( \sum q_j = 1 \), which is implied by the Caratheodory theorem or explicitly shown in our latter theorem 2. In other words, the optimal solution of \( N \) quantum states is equivalent to that of \( N - 1 \) quantum states. The optimal distance is given by
\[
\min_{i_1 < i_2 < \ldots < i_{N-1}} D(\rho, \chi_{i_1i_2\ldots i_{N-1}}(\tilde{\mathbf{p}}), i_a = 1, 2, 3, \ldots, N - 1
\] (9)
Case 2: \( \det(A) \neq 0 \). One can first calculate
\[
\mathbf{P} = A^{-1} \mathbf{B}
\] (10)
If all \( \tilde{p}_i \in [0, 1] \) in \( \mathbf{P} \), then the optimal weights \( \tilde{p}_i = \tilde{p}_i \). By substituting the optimal weights \( \tilde{p}_i \) into the prepared quantum state \( \chi_{i_1i_2\ldots i_{N-1}}(\tilde{\mathbf{p}}) = \sum_{j} \tilde{p}_j \mathbf{r}_j \), we can obtain the optimal distance \( D(\rho, \chi_{i_1i_2\ldots i_{N-1}}(\tilde{\mathbf{p}})) \). If not all \( \tilde{p}_i \in [0, 1] \), it means that the optimal weights should be at the boundary, that is, at least one of the probabilities \( p_i \) is 0. Thus, one need to consider the mixing of \( N - 1 \) states and the optimization problem is converted to
\[
\min_{i_1 < i_2 < \ldots < i_{N-1}} D(\rho, \chi_{i_1i_2\ldots i_{N-1}}(\tilde{\mathbf{p}})), i_a = 1, 2, 3, \ldots, N - 1
\] (11)
Repeating the process from Equation (7) to Equation (11), until the probabilities \( \tilde{p}_i \in [0, 1] \). Suppose the first valid probability vector \( \mathbf{P} \) is found when considering the mixing of \( M \) states, the optimal distance is taken as the minimal distance over all \( C_M^N \) combinations of the \( M \) states with \( M \leq N \). The proof is completed. \( \square \)
**Theorem 2.** If there are \( N > d^2 \) states in the set \( S \), the optimization approximation is determined by
\[
\min_{i_a < i_b < \ldots < i_{N-1}} D(\rho, \chi_{i_1i_2\ldots i_{N-1}}(\tilde{\mathbf{p}}))
\] (12)
where \( i_a \) denotes the \( i_a \)th state in the set \( S \).
**Proof.** In the \( X \) representation, the prepared states \( \sigma \) can be expressed as \( \mathbf{r}_i = \sum_{j} p_j \mathbf{r}_j \). Caratheodory theorem\(^{18,59}\) shows that \( \mathbf{r}_i \) can be represented by the convex combination of no more than \( d^2 + 1 \) vectors in the set \( \hat{S} := \{ \mathbf{r}_i | i = 1, 2, 3, \ldots, N \} \) such as
\[
\mathbf{r}_i = \sum_{j} q_j \mathbf{r}_j, \text{ with } q_j \geq 0 \text{ and } \sum_{j} q_j = 1
\]
Considering that \( d^2 + 1 \) vectors in \( \hat{S} \) must be linearly independent, there exist \( \ell_i \), \( i = 1, 2, \ldots, d^2 + 1 \) such that \( \sum_{j} \ell_j r_j = 0 \), which implies \( \sum_{i} \ell_i r_i = 0 \) due to \( X_0 = l_i / \sqrt{d} \). Thus one can obtain
\[
\mathbf{r}_i = \sum_{j} q_j \mathbf{r}_j - \alpha \sum_{j} |r_i - r_j| q_j(1 - \alpha \frac{l_i}{q_j}) r_j
\] (13)
Let \( \alpha = \frac{q_i}{\sum_j q_j} = \min_{1 \leq i \leq d^2+1} \left( \frac{q_i}{\sum_j q_j} > 0 \right) \), we will find that
\[
1 - \alpha \frac{l_i}{q_j} = 0, i = \ell' \text{ and } \sum_j q_j(1 - \alpha \frac{l_i}{q_j}) = 1 \text{ which mean that at most } d^2 \text{ vectors in the set } \hat{S} \text{ are enough to convexly construct } \mathbf{r}_i.
\]
It implies that for \( N > d^2 \), the convex mixing of only \( d^2 \) states in \( S \) is enough to achieve the optimal distance. Therefore, we can directly consider all potential combinations of only \( d^2 \) quantum states among the set \( S \). The minimal distance will give our expected optimal result. The proof is finished. \( \square \)
**3. Examples**
To verify the reliability of our theorems, we provide several randomly generated density matrices and compare our closed analytic results with the numerical results. In the following, the objective state \( \mathbf{r}_i \) in the \( X \) representation is given as
\[
\mathbf{r}_i = kr_{i1} + (1 - k) r_{i2}, k \in [0, 1]
\] (14)
where \( r_{i2} \) is given in several special cases and \( r_{i1} \) will be randomly generated by Matlab. The explicit expression of \( N \) quantum states in set \( S = \{ \mathbf{r}_1, \mathbf{r}_2, \ldots, \mathbf{r}_N \} \) in all the below examples are given in Appendix A.
(i) \( d = 2 \) and \( N = 3 \). According to theorem 1, we first consider two states, \( \mathbf{r}_1 \) and \( \mathbf{r}_2 \). The pseudo probability reads
\[
\tilde{p}_1 = \frac{(r_2 - r_1)^T (r_1 - r_3)}{\|r_1 - r_3\|^2_2}, \tilde{p}_2 = 1 - \tilde{p}_1
\] (15)
With all the three states in the set taken into account, the pseudo probability reads
\[
\tilde{p}_1 = \frac{1}{d} (r_1 - r_3)^T \times \left| (r_3 - r_2)(r_2 - r_3)^T - (r_2 - r_3)(r_3 - r_2)^T \right| (r_2 - r_3).
\]
\[
\tilde{p}_2 = \frac{1}{d} (r_2 - r_3)^T \times \left| (r_3 - r_1)(r_3 - r_1)^T - (r_2 - r_3)(r_1 - r_3)^T \right| (r_1 - r_3),
\]
\[
\tilde{p}_3 = 1 - \tilde{p}_1 - \tilde{p}_2.
\] (16)
where
\[ d = \| r_1 - r_2 \|_2^2 - \| r_1 - r_3 \|_2^2 - \| (r_1 - r_2) \|_2^2 \]
Collecting the cases with all \( p_i = \tilde{p}_i \geq 0 \), one can find the minimal distance in terms of
\[ D(\rho, \sigma) = \frac{1}{2} \sum_{i=1}^{n} p_i r_i \]
For example, we can make
\[ r_{01} = (\frac{1}{\sqrt{2}}, 0, 0) \]
which is the maximally mixed state. Then three different kinds of \( r_{01} \) are randomly generated as
\[ r_{01}^1 = (1/\sqrt{2}, -0.0989, 0.1337, -0.1564)^\dagger \]
\[ r_{01}^2 = (1/\sqrt{2}, -0.1810, 0.0522, 0.2173)^\dagger \]
\[ r_{01}^3 = (1/\sqrt{2}, 0.2285, -0.0403, 0.2218)^\dagger \]
The optimal distance denoted by \( D(\rho) \) versus \( k \in [0, 1] \) is plotted in Figure 3a, where the dotted blue, solid red and dashed green lines correspond to \( r_{01}^1, r_{01}^2 \), and \( r_{01}^3 \), respectively. It is shown that our closed analytic solution is completely consistent with the numerical solution. In Figure 3b, we can find that for the optimal approximation of the objective quantum state, the minimal number of quantum states in set \( S \) is up to 4.
(iii) \( d = 3 \) and \( N = 15 \). In this case, \( r_{02} \) is randomly generated as
\[ r_{02} = (1/\sqrt{3}, 0.0568, 0.1463, 0.1405, -0.0456, -0.0531, -0.1342, 0.1669, -0.0918)^\dagger \]
and the three special quantum states are considered for \( r_{01} \) as
\[ r_{01}^1 = (1/\sqrt{3}, 0, 0, 0, 0, 0, 0)^\dagger \],
\[ r_{01}^2 = (1, 1/\sqrt{3}, 1/\sqrt{3}, 1/\sqrt{3}, 1/\sqrt{3}, 1/\sqrt{3}, 1/\sqrt{3})/\sqrt{3} \]
The optimal distance denoted by \( D(\rho) \) versus \( k \in [0, 1] \) is plotted in Figure 4a, which validates our theorem based on the perfect consistency. The Figure 4b shows that the minimal number of quantum states in set \( S \) used to optimally approximate the objective quantum state is no more than 9.
(iv) \( d = 4 \) and \( N = 20 \). Due to the large dimension of the considered states, the concrete expressions of \( r_{01} \) and \( r_{02} \) are given in Appendix A. Similarly, we consider three special quantum states \( \{ r_{01}^1, r_{01}^2, r_{01}^3 \} \), and quantum state \( r_{01}^3 \) is the maximally mixed state. The optimal distance denoted by \( D(\rho) \) versus \( k \in [0, 1] \) is plotted in Figure 5a, which shows the perfect consistency between the numerical and the closed results, and further supports our theorem. As can be seen from
Figure 3. The optimal distance $D(\rho)$ versus various parameters $k$ in (a) for $d = 2$ and $N = 6$. The solid line corresponds to the strictly closed expressions given in our theorems, while the numerical solutions are marked with "+". The minimum number $n$ of quantum states in set $S$ needed for the optimal approximation of each objective state is shown in (b).
Figure 4. The optimal distance $D(\rho)$ versus various parameters $k$ in (a) for $d = 3$ and $N = 15$. The solid line corresponds to the strictly closed expressions, while the numerical solutions are marked with "+". The minimal number $n$ of quantum states needed for the optimal approximation of each objective state is shown in (b).
Figure 5b, the minimal number of quantum states in set $S$ used to approximate the target quantum state is less than or equal to 14. By comparing the figures, we can find that with the increase of the maximally mixed state ratio, the optimal approximate distance tends to 0.
4. Discussion and Conclusion
Before the end, we would like to mention that we have studied the best approximation of an objective state by a limited state set based on $l_2$ norm, which provided an analytically solvable
global convex optimization. In contrast, the Fidelity is only convex for the probability vector $\tilde{p}$ which is not allowable by our method. In addition, both the Fidelity and Trace norm, despite the better properties like contractility, lead to quite complex optimized objective function which is impossible for an analytical solution to a high-dimensional system. However, $l_2$ norm perfectly avoids those shortcomings. Although $l_2$ norm is not contractive, it is undeniably a valid distance of two vectors and there is no problem for the static comparison of two states. In the literature, most of us take it for granted that the distance between two states had better be contractive, just like Fidelity and Trace norm. In fact, in many cases, the contractility is originated from a dynamic process, especially considering the quantum features which cannot be produced by classical operations. For example, in quantum resource theory, there is an explicit requirement akin to/directly related to contractility. Apart from such a dynamic consideration, there is no sufficient reason to require a contractive distance. In other words, contractility is also an additional requirement for the distance. If our approach is used to solve some problem in the resource theory, strictly speaking, our result at most provides the criterion of existence instead of a measure. If one is interested in the optimal distance of two states after some potential operations, one can safely perform the corresponding operations on both the objective state and the set of states, and then employ our approach which is also valid in this case. Even if someone employed our approach in resource theory, a closed expression should be more useful than that without an explicit expression, which is popular in the relevant researches on entanglement such as negativity in high dimensional systems. Here, we only consider the static comparison without any additional constraints such as a dynamic process allowed.
If the given set $S$ is defined by $d$ mutually orthogonal quantum states, the optimal distance provides an alternative measure of quantum coherence of the objective quantum states based on $l_2$ norm, which is equal to the trace norm in the 2D case.\(^7\) If $d$ linearly independent quantum states are given for the set $S$, our results provide a measure of the superposition of the objective states.\(^{44}\) In addition, in the paper, we only consider the approximation of a single-party system, it is worth considering the local or nonlocal approximation of states in a composite system.
In summary, we have given a closed solution to the approximation of a $d$-dimensional objective state by using a given state set. We have not only presented the optimal distance between the objective state and the prepared state, but also given the minimal number of states in the given set $S$ to achieve the best approximation. Numerical tests in several examples validate our closed solutions via perfect consistency. In addition, it is found that for the $d$-dimensional objective quantum state, the optimal distance can be achieved by the convex combination of no more than $d^2$ quantum states. Finally, we emphasize that our closed solution indicates the least number of quantum states to construct the target quantum state approximately, which is beneficial to the practical operation in the experiment.
**Appendix A: The Explicit Forms of the Set $S$ for Examples**
In example (i), the quantum state set $S$ includes 3 quantum states, which can be expressed as
$$r_1 = (1/\sqrt{2}, -0.0453, -0.0429, -0.0774)$$
$$r_2 = (1/\sqrt{2}, -0.3348, -0.2708, -0.2571)$$
$$r_3 = (1/\sqrt{2}, 0.0287, 0.2456, -0.0534)$$
(A1)
In example (ii), the quantum state set $S$ includes six quantum states, which are composed of eigenstates of three Pauli matrix $\{\sigma_x, \sigma_y, \sigma_z\}$, expressed as
$$r_1 = (1, 1, 0, 0)^\top/\sqrt{2}$$
$$r_2 = (1, -1, 0, 0)^\top/\sqrt{2}$$
$$r_3 = (1, 0, 1, 0)^\top/\sqrt{2}$$
$$r_4 = (1, 0, -1, 0)^\top/\sqrt{2}$$
$$r_5 = (1, 0, 0, 1)^\top/\sqrt{2}$$
$$r_6 = (1, 0, 0, -1)^\top/\sqrt{2}$$
(A2)
In example (iii), the quantum state set $S$ is given in operator Hilbert space as
$$r_1 = (0.5774, -0.0089, 0.0192, 0.0446, -0.0585, -0.0403, -0.0061, 0.0094, 0.0210)^\top$$
$$r_2 = (0.5774, -0.0679, -0.0568, 0.0278, -0.0335, 0.0708, -0.1094, 0.1036, -0.1595)^\top$$
$$r_3 = (0.5774, 0.3314, -0.2469, -0.0453, -0.0119, -0.2463, 0.1383, 0.0430, -0.1808)^\top$$
$$r_4 = (0.5774, 0.0138, 0.2443, -0.2903, 0.2369, -0.1108, -0.0694, 0.2347, -0.1709)^\top$$
$$r_5 = (0.5774, -0.1427, -0.0667, -0.4253, -0.3187, -0.1495, -0.3435, 0.3087, 0.2761)^\top$$
(A3)
and the random generated quantum state $r_0$ is
$\text{r}_0 = (0.5000, 0.3480, -0.0903, -0.2264, -0.0123, -0.3373, -0.1569, 0.2523, 0.0478, 0.3409, -0.1137, -0.0728, 0.0766, -0.3191, 0.0155, -0.2063)^T$ \hspace{1cm} (A7)
In addition, the quantum state set $S$ includes 20 randomly generated quantum states which are
$\text{r}_1 = (0.5000, 0.3401, 0.2281, 0.1506, -0.1592, 0.0518, 0.1435, -0.0227, 0.0123, -0.0654, -0.1799, -0.2337, -0.3263, -0.3152, -0.3466, -0.3052)^T$, $\text{r}_2 = (0.5000, 0.2630, 0.2397, -0.0116, 0.3371, -0.0435, -0.2855, 0.2873, 0.3155, 0.0002, -0.0044, 0.1938, -0.3148, 0.2518, -0.0674, -0.1989)^T$, $\text{r}_3 = (0.5000, -0.2184, -0.0078, 0.1946, 0.1876, 0.3716, 0.2003, -0.1040, -0.1933, -0.0483, 0.0962, 0.2114, -0.2066, 0.4027, -0.3182, -0.2010)^T$, $\text{r}_4 = (0.5000, -0.3085, 0.1438, -0.3556, -0.0276, -0.3483, -0.3359, 0.1912, 0.0149, -0.0655, 0.1375, 0.2116, 0.0990, -0.3137, -0.0414, 0.2411)^T$, $\text{r}_5 = (0.5000, -0.2741, -0.1356, 0.0618, 0.2636, -0.1240, -0.2177, 0.1307, 0.0534, 0.3311, 0.3185, 0.3498, 0.3522, 0.1482, -0.0426, -0.1383)^T$ \hspace{1cm} (A8)
\[ r_6 = (0.5000, 0.1112, 0.3263, 0.3190, -0.1469, -0.3317, 0.2964, -0.2435, -0.0953, -0.0306, 0.1241, 0.3175, -0.2460, 0.1503, 0.1725, 0.1075)^T \]
\[ r_7 = (0.5000, -0.3397, 0.1331, -0.3639, -0.0465, -0.3013, -0.0081, -0.1089, 0.0448, 0.2988, 0.2088, 0.1497, 0.3078, 0.3506, 0.0583, 0.0359)^T \]
\[ r_8 = (0.5000, -0.0234, -0.1351, -0.0322, 0.2409, -0.3197, -0.1314, -0.2997, -0.3042, -0.3151, -0.2814, -0.0517, -0.0072, 0.2808, -0.2075, 0.3309)^T \]
\[ r_9 = (0.5000, 0.0011, 0.0720, 0.0828, 0.3043, 0.3365, -0.2482, -0.2899, -0.1409, 0.1969, 0.2455, -0.1839, 0.2696, -0.2972, -0.2457, 0.1112)^T \]
\[ r_{10} = (0.5000, -0.0969, -0.2549, -0.1631, 0.3248, -0.1620, -0.2249, 0.0524, -0.3021, -0.2719, 0.2176, -0.3062, -0.1522, -0.0556, -0.1959, -0.3050)^T \]
(A9)
\[ r_{11} = (0.5000, -0.1085, -0.1859, -0.2159, -0.3368, -0.1676, -0.2280, 0.2087, -0.0767, 0.2550, -0.2157, -0.2451, -0.0837, -0.3492, -0.0487, -0.3334)^T \]
\[ r_{12} = (0.5000, -0.1116, 0.1404, -0.3683, -0.2396, 0.2121, 0.0992, -0.3009, 0.0709, -0.3062, -0.2525, 0.2682, 0.0603, -0.3460, -0.0274, -0.1445)^T \]
\[ r_{13} = (0.5000, 0.2993, -0.2373, -0.1311, -0.0875, -0.1534, 0.1559, 0.1657, -0.2268, 0.3667, -0.1520, 0.0617, -0.1243, 0.3017, -0.2709, -0.3336)^T \]
\[ r_{14} = (0.5000, 0.3539, 0.0031, -0.3141, -0.1757, -0.3098, 0.3047, -0.0659, 0.1496, -0.0462, -0.0051, -0.2103, 0.2230, -0.1621, 0.3111, 0.2460)^T \]
\[ r_{15} = (0.5000, 0.1284, 0.3134, 0.2846, 0.1660, -0.0162, -0.0902, 0.2459, -0.3016, 0.0968, -0.2279, 0.2806, -0.1189, 0.2264, -0.3173, -0.2467)^T \]
(A10)
and
\[ r_{16} = (0.5000, -0.0621, 0.1726, -0.0117, 0.1752, 0.4750, 0.1905, 0.3538, -0.0945, 0.0778, -0.0987, -0.3450, -0.0469, -0.0181, 0.2563, 0.2941)^T \]
\[ r_{17} = (0.5000, -0.3708, -0.1331, -0.2681, 0.2228, -0.0237, 0.0812, -0.3113, -0.2672, -0.2705, 0.1829, 0.0050, -0.1646, -0.1872, 0.3579, 0.0310)^T \]
\[ r_{18} = (0.5000, 0.1800, 0.1847, -0.2499, -0.1384, 0.3771, 0.3414, -0.0918, -0.2475, 0.0291, -0.2798, -0.1287, -0.2310, -0.1423, -0.2583, -0.1931)^T \]
\[ r_{19} = (0.5000, -0.2897, 0.0626, -0.2482, 0.0671, 0.2700, 0.2767, -0.0325, 0.2770, -0.2419, 0.0868, -0.2809, 0.1914, 0.2186, -0.2852, -0.2412)^T \]
\[ r_{20} = (0.5000, 0.2981, -0.3500, 0.0817, -0.1222, -0.4227, -0.1678, 0.1315, 0.3039, 0.0275, 0.2742, -0.0520, 0.1699, 0.2849, 0.0298, 0.1050)^T \]
(A11)
Acknowledgements
This work was supported by the National Natural Science Foundation of China under Grant No. 11775040 and No. 1201130014, the Fundamental Research Fund for the Central Universities under Grant No. DUT20LAB203, and the Key Research and Development Project of Liaoning Province under Grant No. 2020J21000003.
Conflict of Interest
The authors declare no conflict of interest.
Data Availability Statement
Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.
Keywords
best convex approximation, quantum state preparation, quantum coherence
Received: September 1, 2021
Revised: November 5, 2021
Published online: December 30, 2021
[1] C. H. Bennett, H. J. Bernstein, S. Popescu, B. Schumacher, Phys. Rev. A 1996, 53, 2046.
[2] C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, W. K. Wootters, Phys. Rev. A 1996, 54, 3824.
[3] C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, W. K. Wootters, Phys. Rev. Lett. 1996, 76, 722.
[4] P. Horodecki, R. Horodecki, Quantum Info. Comput. 2001, 1, 45.
[5] W. K. Wootters, Quantum Info. Comput. 2001, 1, 27.
[6] R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 2009, 81, 865.
[7] T. Baumgratz, M. Cramer, M. B. Plenio, Phys. Rev. Lett. 2014, 113, 140401.
[8] A. Winter, D. Yang, Phys. Rev. Lett. 2016, 116, 120404.
[9] E. Chitambar, M.-H. Hsieh, Phys. Rev. Lett. 2016, 117, 020402.
[10] A. Streltsov, S. Rana, P. Boes, J. Eisert, Phys. Rev. Lett. 2017, 119, 140402.
[11] K. B. Dana, M. G. Díaz, M. Mejatty, A. Winter, Phys. Rev. A 2017, 95, 062327.
[12] A. Streltsov, S. Rana, M. N. Bera, M. Lewenstein, Phys. Rev. X 2017, 7, 011024.
[13] L. Henderson, V. Vedral, J. Phys. A: Math. General 2001, 34, 356899.
[14] H. Ollivier, W. H. Zurek, Phys. Rev. Lett. 2001, 88, 017901.
[15] A. Datta, A. Shaji, C. M. Caves, Phys. Rev. Lett. 2008, 100, 050502.
[16] T. Tufarelli, D. Girolami, R. Vasile, S. Bose, G. Adesso, Phys. Rev. A 2012, 86, 052326. | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4973,
1
],
[
4973,
9895,
2
],
[
9895,
15880,
3
],
[
15880,
18280,
4
],
[
18280,
19484,
5
],
[
19484,
24169,
6
],
[
24169,
25278,
7
],
[
25278,
27621,
8
],
[
27621,
29620,
9
]
]
} |
74121d5f394f2685a1173c8a187a888aba9903e1 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 22,
"total-fallback-pages": 0,
"total-input-tokens": 50845,
"total-output-tokens": 15317,
"fieldofstudy": [
"Medicine"
]
} | Characterization of Bone Metabolism in Hungarian Psoriatic Arthritis Patients: A Case–Control Study.
Zsofia Petho
University of Debrecen Faculty of Medicine: Debreceni Egyetem Altalanos Orvostudomanyi Kar
Edit Kalina
University of Debrecen Faculty of Medicine: Debreceni Egyetem Altalanos Orvostudomanyi Kar
Zoltan Pap
University of Debrecen Faculty of Medicine: Debreceni Egyetem Altalanos Orvostudomanyi Kar
Katalin Hodosi
University of Debrecen Faculty of Medicine: Debreceni Egyetem Altalanos Orvostudomanyi Kar
Rebeka Falcsik
University of Debrecen Faculty of Medicine: Debreceni Egyetem Altalanos Orvostudomanyi Kar
Adam Balogh
University of Debrecen Faculty of Medicine: Debreceni Egyetem Altalanos Orvostudomanyi Kar
Zoltan Szekanecz
University of Debrecen Faculty of Medicine: Debreceni Egyetem Altalanos Orvostudomanyi Kar
Harjit Pal Bhattoa (✉ [email protected])
University of Debrecen Faculty of Medicine: Debreceni Egyetem Altalanos Orvostudomanyi Kar
https://orcid.org/0000-0002-4909-0065
Research article
Keywords: Psoriatic arthritis, Areal and Volumetric BMD, FRAX, Bone Metabolism, Disease activity
DOI: https://doi.org/10.21203/rs.3.rs-73065/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License.
Read Full License
Abstract
Background: Skeletal manifestations are predominant in psoriatic arthritis (PsA). The aim of this cross-sectional, case-controlled study is the complex assessment of areal and volumetric bone mineral density (BMD), fracture risk, vitamin D status and bone turnover markers, and its association with disease-related variables.
Methods: Lumbar spine (L1-L4) and femur neck (FN) areal, and distal radius (DR) volumetric BMD, 10-year probability of major and hip osteoporotic fracture as assessed by the fracture risk assessment (FRAX) tool, markers of bone metabolism and disease activity were assessed.
Results: Upon comparison of the disease and age- and sex-matched control groups, there was a statistically significant difference in FN areal (0.955±0.145 g/cm$^2$ vs. 1.034±0.148 g/cm$^2$; p=0.001) and DR total volumetric (285.7±61.8 mg/cm$^3$ vs. 369.6±23.6 mg/cm$^3$; p<0.001) BMD, 10 year probability for major osteoporotic (5.0% (0.7%-32%) vs. 3.5% (0%-17.5%); p=0.003) and hip (1.1% (0%-16%) vs. 0.5% (0%-6.1%); p=0.002) fracture and 25-hydroxyvitamin D status (53 (10-120) nmol/L vs. 67 (10-137; p<0.001) nmol/L). As compared to areal assessment, volumetric BMD measurements identified a significantly higher number of patients with low bone mass (T-Score £ -1.00) (34% vs. 88%, p<0.001). Upon multiple linear regression analysis, disease activity score, as determined by DAS28 assessment, was an independent predictor of 10-year probability for major osteoporotic fracture (B (95%CI) = 1.351 (0.379–2.323); p = 0.007).
Conclusion: In the studied PsA cohort, disease activity was an independent predictor of 10-year probability for a major osteoporotic fracture, and complemented assessment of volumetric and areal BMD assured better efficacy at identifying those with low bone mass.
Background
The prevalence of psoriasis is estimated at 1–3% of the world’s population [1]. It is a common skin disease associated with multiple comorbidities and the most prevalent coexisting condition, psoriatic arthritis (PsA) develops in 19.7% of psoriatic patients [2].
In majority of the patients, arthritis is manifested following psoriasis, and in others, it develops simultaneously or before the appearance of skin lesions [3]. Spinal manifestations resemble those in ankylosing spondylitis, and destructive peripheral joint characteristics resemble those of rheumatoid arthritis [4]. Pathologic de novo bone formation, including joint ankylosis, and syndesmophyte formation, characteristically localize to sites of soft-tissue inflammation surrounding the enthesis [5].
Osteoporosis is a systemic skeletal disease characterized by reduced bone mass, microarchitectural damage and increased fragility of bone. Bone loss is a common comorbidity in chronic inflammatory diseases including PsA [6]. A systematic review by Chandran et al, where 21 studies conducted between
2001 and 2014 were included, highlighted the gap in our current knowledge given the non-consensual findings reported on the prevalence of low bone mineral density in PsA [7].
Osteoporosis has been operationally defined on the basis of bone mineral density (BMD) assessment. The most widely validated technique to measure BMD is dual energy X-ray absorptiometry (DEXA), and diagnostic criteria based on the T-score for BMD are a recommended criteria for prescription of pharmaceutical interventions in osteoporosis [8]. According to the WHO criteria, osteoporosis is defined as a BMD that lies ≤ 2.5 standard deviations below the average value for young healthy women (T-score ≤ -2.5 SD) [9, 10]. A major problem with BMD measurement is that these tests alone are not optimal for the detection of individuals at high risk of fracture [11].
On the other hand, peripheral quantitative computed tomography (pQCT) is excellent at three-dimensional quantification of cortical and trabecular bone at various regions of interest, albeit, is not recommended for conventional diagnostic classification [12]. Recent reports have discussed the techniques’ utility in patients suffering from inflammatory rheumatic disease [13, 14].
Fragility fractures are defined as fractures that occur spontaneously or following low-trauma and are potential cause of severe disability along with increased mortality risk [9]. Major advance in fragility fracture risk stratification has been achieved by the development of the fracture risk assessment tool (FRAX). The FRAX tool is based on country specific population-based cohorts that assimilate the risks associated with clinical risk factors (age, sex, body mass index, prior fragility fracture, parental history of hip fracture, steroid use, smoking, alcohol intake, disorders strongly associated with osteoporosis and rheumatoid arthritis) and bone mineral density (BMD) at the femoral neck. The percentage output is a 10-year probability of hip fracture and the 10-year probability of a major osteoporotic fracture (clinical spine, forearm, hip, or shoulder fracture) [15]. Given the clinical, social and economic burden of osteoporotic fractures, the FRAX tool is considered ideal in identifying those at risk and advancing timely preventive or therapeutic interventions.
Presently, studies on complex assessment of areal and volumetric bone mineral density, fracture risk with the FRAX tool, vitamin D and markers of bone turnover in the same cohort of PsA patients are unavailable and the aim of the present cross-sectional, case-controlled study is to examine bone metabolism and evaluate its association with disease variables.
Patients And Methods
Patients and controls:
We enrolled a total of 118 patients presenting for regular scheduled follow-up at the Division of Rheumatology, Faculty of Medicine, University of Debrecen, between September 2017 and June 2018. All were diagnosed with PsA as per the Classification Criteria for Psoriatic Arthritis (CASPAR) [16]. Data from patients with psoriatic arthritis was compared to age- and gender-matched healthy volunteers. The age and sex-matched control group was recruited from staff, and escorts of patients presenting for routine
follow-up. Volunteers with the closest dates of birth and with blood drawn in the same meteorological season were selected for pairing with their PsA counterparts. All study participants gave written informed consent. The study was performed according to the Declaration of Helsinki and approved by the Hungarian Scientific Research Council Ethical Committee (approval No. 14804-2/2011/EKU).
**Disease activity:**
All patients underwent physical examination and disease severity assessment. Disease Activity Score in 28 joints (DAS28), in those with peripheral involvement, Bath Ankylosing Spondylitis Disease Activity Index (BASDAI), in those with spinal involvement, and Psoriasis Area and Severity Index (PASI) were calculated [17–19].
**Laboratory:**
Blood sampling was done after overnight fasting to measure levels of 25-hydroxyvitamin D (25OHD), parathyroid hormone (PTH), osteocalcin (OC), C-terminal telopeptides of type-I collagen (CTx), and procollagen type I amino-terminal propeptide (PINP). Serum 25-OH-D was analyzed using the automated Liaison DiaSorin total 25OHD chemiluminescence immunoassay (CLIA) (DiaSorin Inc., Stillwater, MN, USA). Serum PTH, OC, CTx, and PINP were measured using electrochemiluminescence immunoassay (Roche Diagnostics GmbH, Mannheim, Germany). The inter-assay CV was < 7.8% for 25-OH-D (lower detection limit: 10 nmol/L, upper detection limit: 375 nmol/L), < 7% for PTH (lower detection limit: 0.127 pmol/L, upper detection limit: 530 pmol/L), < 4% for OC (lower detection limit: 0.5 µg/L, upper detection limit: 300 µg/L), < 7% for CTx (lower detection limit: 0.010 µg/L, upper detection limit: 6 µg/L), and < 6% for PINP (lower detection limit: 5 µg/L, upper detection limit: 1200 µg/L). Hypovitaminosis D was defined as 25-OH-D levels < 75 nmol/l as suggested by Dawson-Hughes et al [20] The erythrocyte sedimentation rate (ESR) was assessed with the Westergren method [21] and used in the calculation of the DAS28 score.
**Dual energy X-ray absorptiometry:**
Dual energy X-ray absorptiometry (DEXA) examination was performed using the LUNAR Prodigy (GE-Lunar Corp., Madison, WI, USA) densitometer. Areal BMD was measured at L1–L4 lumbar spine and left femur neck (FN). The coefficient of variation (CV) of the technique at our institute was 0.8% using the anatomical spine phantom measured daily. BMD was expressed as a T score, normalcy, osteopenia and osteoporosis were defined according to the WHO classification [10].
**Peripheral quantitative computer tomography (pQCT):**
Single-slice pQCT assessments of the ultradistal region of the left forearm were performed using a Stratec XCT-2000 instrument (Stratec Medizintechnik GmbH, Pforzheim, Germany) as described by Juhasz et al [13]. In summary, distal sites at 4% of the radius length mainly contain trabecular bone. pQCT can differentiate between cortical and trabecular bone. Total, trabecular, and cortical BMD values are expressed as mg/cm³. The applied setting to acquire the image was 0.59 mm voxel. Analysis was
done with the XCT 6.00 B software (Stratec Medizintechnik GmbH, Pforzheim, Germany) with measuring mask set to radius and threshold density to 269 mg/cm$^3$ to define trabecular bone.
**FRAX:**
A trained study nurse administered a questionnaire to assess the country-specific FRAX index using the tool available online [15]. The data collected was age, sex, weight, height, non-traumatic fracture in the history, parental history of hip fracture, current smoking and alcohol consumption habits, corticosteroid use, diagnosis of rheumatoid arthritis or any condition known to cause low bone mass and femoral BMD.
**Statistical analysis:**
Descriptive statistics are presented, as applicable, as mean, range and standard deviation (SD). The Kolmogorov-Smirnov test was used to check for normality of distribution. The Wilcoxon signed ranks test was used to compare the age- and gender-matched pairs. The Spearman's $\rho$ was calculated for correlation analysis. Univariate and multiple regression analysis using the stepwise method was used to determine correlations and independent associations between parameters. DEXA, pQCT and FRAX parameters were the dependent variables and other parameters were independent variables. The $\beta$ standardized linear coefficients showing linear correlations between two parameters were determined. The B (+ 95% CI) regression coefficient indicated independent association between the dependent and independent variable during changes. $p$ values $< 0.05$ indicated statistical significance. All analyses were performed using the SPSS Statistics software, version 25.0 (IBM Corps., Armonk, NY, USA).
**Results**
Patients (n = 118) presenting with psoriatic arthritis, confirming to the CASPAR diagnostic criteria, were included in this cross-sectional, analyst blinded, age- and sex-matched, case-control study [16]. The mean age (range) of the patients was 53 (25–85) years, with a women:men ratio of 67:51. The mean (range) disease duration for psoriasis and arthritis was 18.4 (1–72) and 11.2 (0–39) years, respectively. In a small percentage of the patients (n = 14, 12%), the diagnosis of psoriasis was confirmed following the diagnosis of arthritis (on an average within 5 years). Compared to the controls, L1-L4 areal BMD (1.281 ± 0.169 gm/cm$^2$ vs. 1.192 ± 0.195 gm/cm$^2$; p < 0.001), FN areal BMD (1.034 ± 0.148 gm/cm$^2$ vs. 0.955 ± 0.145 gm/cm$^2$; p = 0.001), distal radius (DR) total volumetric BMD (369.6 ± 23.6 gm/cm$^3$ vs. 285.7 ± 61.8 gm/cm$^3$; p < 0.001), DR trabecular volumetric BMD (200.6 ± 19.5 gm/cm$^3$ vs. 187.6 ± 47.1 gm/cm$^3$; p = 0.002), DR cortical volumetric BMD (515.9 ± 39.9 gm/cm$^3$ vs. 361.6 ± 92.3 gm/cm$^3$; p < 0.001) and 25OHD (67 (10–137) nmol/L vs. 53 (10–120) nmol/L; p < 0.001) was significantly lower, and the 10 year probability for a major osteoporotic fracture (3.5 (0-17.5) % vs. 5.0 (0.7–35) %; p = 0.003) and hip fracture (0.5 (0-6.1) % vs. 1.1 (0–16) %; p = 0.002), CTx (0.223 (0.100–0.511) µg/L vs. 0.302 (0.040–1.090) µg/L; p < 0.001) and PINP (35.6 (8.2–72.5) µg/L vs. 49.3 (11.0-253.7) µg/L; p < 0.001) were significantly higher in the PsA group (Table 1). The frequency of normal, osteopenia and osteoporotic BMD in PsA patients at
different regions of interest is presented in Table 2. Areal and volumetric BMD showed statistically significant correlation with each other (Table 3).
Table 1
Subject characteristics.
| Parameters | All patients (n = 118) | All controls (n = 118) | p value |
|------------------------------------------------|------------------------|------------------------|---------|
| Age, years (mean, range) | 53 (25–85) | 53 (25–85) | 1.000 |
| Women:Men | 67:51 | 67:51 | 1.000 |
| DAS28, % (mean, range) (n = 110) | 2.60 (0.49–5.85) | - | - |
| BASDAI, % (mean, range) (n = 8) | 1.51 (0.02–3.08) | - | - |
| PASI, % (mean, range) | 3.22 (0-29.40) | - | - |
| Arthritis duration, years (mean, range) | 11.2 (0–39) | - | - |
| Psoriasis duration, years (mean, range) | 18.4 (1–72) | - | - |
| FRAX Major, % (mean, range) (n = 100) | 5.0 (0.7–32) | 3.5 (0-17.5) | 0.003 |
| FRAX Hip, % (mean, range) (n = 100) | 1.1 (0–16) | 0.5 (0-6.1) | 0.002 |
| 10 year probability of major osteoporotic fracture ≥ 20% (n, %) | 1 (1%) | 0 (0%) | - |
| 10 year probability of hip fracture ≥ 3% (n, %) | 8 (8%) | 4 (4%) | - |
| L1-L4 areal BMD, g/cm² (mean ± SD) | 1.192 ± 0.195 | 1.281 ± 0.169 | < 0.001 |
| Femur neck areal BMD, g/cm² (mean ± SD) | 0.955 ± 0.145 (n = 117) | 1.034 ± 0.148 | 0.001 |
| Distal radius total volumetric BMD, mg/cm³ (mean ± SD) | 285.7 ± 61.8 | 369.6 ± 23.6 | < 0.001 |
| Distal radius trabecular volumetric BMD, mg/cm³ (mean ± SD) | 187.6 ± 47.1 | 200.6 ± 19.5 | 0.002 |
| Distal radius cortical volumetric BMD, mg/cm³ (mean ± SD) | 361.6 ± 92.3 | 515.9 ± 39.9 | < 0.001 |
| Calcium, mmol/L (mean, range) | 2.4 (2.2–2.7) | 2.3 (2.1–2.7) | < 0.001 |
| Phosphate, mmol/L (mean, range) | 0.96 (0.6–1.6) | 1.07 (0.6–1.51) | < 0.001 |
DAS28: Disease activity Score in 28 joints; BASDAI: Ankylosing spondylitis disease activity index; PASI: Psoriasis area and severity index; FRAX Major: 10-year probability of a major osteoporotic fracture as assessed by the FRAX tool; FRAX Hip: 10-year probability of a hip osteoporotic fracture as assessed by the FRAX tool; BMD: bone mineral density; CTx: C-terminal telopeptides of type-I collagen; PINP: procollagen type I amino-terminal propeptide; PTH: parathyroid hormone; 25OHD: 25-hydroxyvitamin D. *Femur neck BMD assessment was not performed for one patient as she had bilateral total hip replacement.
### Parameters
| | All patients (n = 118) | All controls (n = 118) | p value |
|-------------------------|------------------------|------------------------|---------|
| Osteocalcin, µg/L (mean, range) | 19.6 (5–77) | 17.9 (8.6–33) | 0.186 |
| CTx, µg/L (mean, range) | 0.302 (0.040–1.090) | 0.223 (0.100–0.510) | < 0.001 |
| PINP, µg/L (mean, range) | 49.3 (11.0-253.7) | 35.6 (8.2–72.5) | < 0.001 |
| PTH, pmol/L (mean, range) | 4.77 (1.43–11.69) | 3.78 (1.6–9.6) | < 0.001 |
| 25OHD, nmol/L (mean, range) | 53 (10–120) | 67 (10–137) | < 0.001 |
| 25OHD < 75 nmol/L | 79% (n = 93) | 58% (n = 68) | - |
| 25OHD < 50 nmol/L | 49% (n = 58) | 28% (n = 33) | - |
DAS28: Disease activity Score in 28 joints; BASDAI: Ankylosing spondylitis disease activity index; PASI: Psoriasis area and severity index; FRAX Major: 10-year probability of a major osteoporotic fracture as assessed by the FRAX tool; FRAX Hip: 10-year probability of a hip osteoporotic fracture as assessed by the FRAX tool; BMD: bone mineral density; CTx: C-terminal telopeptides of type-I collagen; PINP: procollagen type I amino-terminal propeptide; PTH: parathyroid hormone; 25OHD: 25-hydroxyvitamin D. *Femur neck BMD assessment was not performed for one patient as she had bilateral total hip replacement.
### Table 2
| Region of Interest | Normal (n,% ) | Osteopenia (n,% ) | Osteoporosis (n,% ) |
|--------------------------|---------------|-------------------|---------------------|
| Femur neck (n = 117) | 77, 66% | 35, 30% | 5, 4% |
| L1-L4 lumbar spine | 82, 70% | 32, 27% | 4, 3% |
| Distal Radius (total) | 14, 12% | 66, 56% | 38, 32% |
Normal: T Score ≥ -0.99; Osteopenia: T Score between − 1.00 and − 2.49; Osteoporosis: T Score ≤ -2.50.
Table 3
Correlation analysis between areal and volumetric bone mineral density
| Region of Interest | Areal | Volumetric Distal Radius (total) | Distal Radius (total) | Trabecular | Cortical |
|--------------------|------------------------|---------------------------------|-----------------------|------------|----------|
| | Areal | | | | |
| | Volumetric | | | | |
| Areal | Femur neck | Spearman's ρ | 1.000 | 0.526 | 0.496 | 0.374 | 0.422 |
| | | p value | - | < 0.001 | < 0.001 | < 0.001 | < 0.001 |
| L1-L4 | Spearman's ρ | 0.526 | 0.488 | 0.343 | 0.421 |
| | | p value | < 0.001 | < 0.001 | < 0.001 | < 0.001 |
| Volumetric | Distal Radius | Spearman's ρ | 0.496 | 0.488 | 0.601 | 0.842 |
| Distal Radius (total) | | p value | < 0.001 | < 0.001 | < 0.001 | < 0.001 |
| Trabecular | Spearman's ρ | 0.374 | 0.343 | 0.601 | 0.377 |
| | | p value | < 0.001 | < 0.001 | < 0.001 | < 0.001 |
| Cortical | Spearman's ρ | 0.422 | 0.421 | 0.842 | 0.377 |
| | | p value | < 0.001 | < 0.001 | < 0.001 | < 0.001 |
Fracture risk characteristics used in the FRAX tool are presented in Table 4 for PsA patients (n = 100) between 40 and 90 years of age. A 10 year probability of ≥20% for major osteoporotic fracture and 10 year probability of ≥3% for hip fracture was observed in 1 (1%) and 8 (8%) patients, respectively. One patient had probability above treatment threshold for both fracture types.
Table 4
Patients’ fracture risk characteristics used in the FRAX tool.
| Risk Factors | Patients between 40 and 90 years of age (n = 100) |
|--------------------------------------|--------------------------------------------------|
| Age, years (mean, range) | 57 (40–85) |
| Male:Female | 42:58 |
| Weight (kg) (mean, range) | 84 (48–125) |
| Height (cm) (mean, range) | 166 (150–188) |
| Previous Fracture (n, %) | 22 (22%) |
| Parent Fractured Hip (n, %) | 4 (4%) |
| Current Smoking (n, %) | 10 (10%) |
| Glucocorticoids (n, %) | 20 (20%) |
| Rheumatoid Arthritis (n, %) | 0 (0%) |
| Secondary Osteoporosis (n, %) | 16 (16%) |
| Alcohol 3 or more units/day (n, %) | 0 (0%) |
| Femur neck areal BMD, g/cm² (mean ± SD) (n = 99) | 0.941 ± 0.136 |
| FRAX Major, % (mean, range) | 5.0 (0.7–32) |
| FRAX Hip, % (mean, range) | 1.1 (0–16) |
| 10 year probability of major osteoporotic fracture ≥ 20% (n, %) | 1 (1%) |
| 10 year probability of hip fracture ≥ 3% (n, %) | 8 (8%) |
A total of 53 (44.9%) and 62 (52.5%) of the patients were on conventional (Methotrexate, Leflunomide, Hydroxychloroquine or Sulphosalazine) and biologic (Infliximab, Adalimumab, Etanercept, Rituximab, Abatacept, Tocilizumab, Certolizumab, Golimumab or Ustekinumab) disease-modifying anti-rheumatic drugs (DMARD), respectively, either as monotherapy or in a combination. Three (2.5%) PsA patients did not receive therapy as they were suffering from malignant conditions (prostate cancer, breast cancer and malignant melanoma).
Upon univariate analysis of the PsA cohort data, patients with lower FN areal BMD were older, with longer duration of psoriasis and arthritis disease duration, and those with higher FN areal BMD had higher body mass index (BMI) (p<0.05); women had significantly lower L1-L4 areal BMD (p<0.05); those with lower DR total volumetric BMD were older and had longer menopause duration (p<0.05); older patients and women had lower DR trabecular volumetric BMD and those with higher DR trabecular volumetric BMD had longer fertility duration (p<0.05); those with lower DR cortical volumetric BMD were older (p<0.05); the 10 year...
probability of major osteoporosis fracture was higher in patients with more severe disease as evaluated by DAS28, longer psoriasis and arthritis disease duration, and menopause duration (p<0.05); and the 10 year probability of hip fracture was higher in patients with longer psoriasis and arthritis disease, and menopause duration, in those on conventional DMARDs and insufficient vitamin D status with 25OHD levels < 75 nmol/L or < 50 nmol/L (p<0.05) (Table 5).
Table 5
Comparison of PsA patient subsets by univariable analyses
| Dependent variable | Independent variable | Univariate analysis |
|--------------------------------------------------------------|---------------------------|--------------------------------------|
| | | B (95% CI) |
| Femur neck areal BMD | Age | -0.003 (-0.005 - 0.001) |
| | Psoriasis duration | -0.002 (-0.005 - 0.000) |
| | Body Mass Index | 0.004 (0.000 - 0.009) |
| | Arthritis duration | -0.005 (-0.008 - 0.002) |
| L1-L4 areal BMD | Sex (women vs. men) | -0.068 (-0.139 - 0.001) |
| Distal radius total volumetric BMD | Age | -1.563 (-2.397 - 0.729) |
| | Menopause duration | -2.213 (-4.070 - 0.356) |
| Distal radius trabecular volumetric BMD | Age | -0.836 (-1.491 - 0.181) |
| | Sex (women vs. men) | -24.338 (-41.172 - 7.505) |
| | Fertility duration | 2482 (0.124 - 4.480) |
| Distal radius cortical volumetric BMD | Age | -2.116 (-3.376 - 0.857) |
| 10 year probability of major osteoporotic fracture | DAS28 | 1.351 (0.379 - 2.323) |
| | Psoriasis duration | 0.085 (0.001 - 0.170) |
| | Arthritis duration | 0.165 (0.045 - 0.286) |
| | Menopause duration | 0.348 (0.142 - 0.554) |
BMD: Bone mineral density; DAS28: Disease activity Score in 28 joints; cDMARD: Conventional disease-modifying anti-rheumatic drugs; bDMARD: Biologic disease-modifying anti-rheumatic drugs; 25OHD: 25-hydroxyvitamin D.
| Dependent variable | Independent variable | Univariate analysis |
|--------------------|----------------------|---------------------|
| | | B (95% CI) | β | p value |
| cDMARD vs bDMARD | 10 year probability of hip fracture | -2.890 (-5.049 -0.731) | -0.259 | 0.009 |
| Psoriasis duration | 0.054 (0.008–0.100) | 0.230 | 0.021 |
| Arthritis duration | 0.080 (0.013–0.146) | 0.233 | 0.020 |
| Menopause duration | 0.178 (0.051–0.305) | 0.405 | 0.007 |
| cDMARD vs bDMARD | < 75 nmol/L vs ≥75 nmol/L 25OHD | -1.664 (-2.841 -0.487) | -0.273 | 0.006 |
| | < 50 nmol/L vs ≥50 nmol/L 25OHD | -1.800 (-3.317 -0.284) | -0.232 | 0.020 |
BMD: Bone mineral density; DAS28: Disease activity Score in 28 joints; cDMARD: Conventional disease-modifying anti-rheumatic drugs; bDMARD: Biologic disease-modifying anti-rheumatic drugs; 25OHD: 25-hydroxyvitamin D.
Multiple linear regression analyses revealed that age was an independent predictor of both areal and volumetric BMD. Additionally, BMI and arthritis disease duration also predicted FN areal BMD, female sex was an independent predictor of DR trabecular volumetric BMD. DAS28 disease activity score predicted the 10 year probability of major osteoporosis fracture and conventional DMARD predicted the 10 year probability of hip fracture (Table 6).
### Table 6
Multiple regression analysis of bone mineral density and 10-year fracture probability.
| Dependent variable | Independent variable | Multivariable analysis |
|----------------------------------------------------------|----------------------|-----------------------|
| | | B (95% CI) |
| | | β |
| | | p value |
| Femur neck areal BMD | Age | -0.004 (-0.006 -0.002) | -0.334 | <0.001 |
| | Body Mass Index | 0.006 (0.002–0.011) | 0.266 | 0.003 |
| | Arthritis duration | -0.003 (-0.006–0.000) | -0.184 | 0.039 |
| Distal radius total volumetric BMD | Age | -1.563 (-2.397 -0.729) | -0.326 | <0.001 |
| Distal radius trabecular volumetric BMD | Age | -0.905 (-1.538 -0.272) | -0.247 | 0.005 |
| | Sex (women vs. men) | -25.947 (-42.333 -9.560) | -0.274 | 0.002 |
| Distal radius cortical volumetric BMD | Age | -2.116 (-3.376 -0.857) | -0.295 | 0.001 |
| 10 year probability of major osteoporotic fracture | DAS28 | 1.351 (0.379–2.323) | 0.277 | 0.007 |
| 10 year probability of hip fracture | cDMARD vs. bDMARD | -1.139 (-2.270 -0.009) | -0.187 | 0.048 |
BMD: Bone mineral density; DAS28: Disease activity Score in 28 joints; cDMARD: Conventional disease-modifying anti-rheumatic drugs; bDMARD: Biologic disease-modifying anti-rheumatic drugs; 25OHD: 25-hydroxyvitamin D.
The prevalence of hypovitaminosis D (25-OH-D < 75 nmol/L) was 79% and 58% in the PsA and control groups, respectively. A significant association was found between hypovitaminosis D and PsA; the odds for PsA patients to suffer with hypovitaminosis D was 2.74 (95%CI 1.54–4.85, p < 0.001).
**Discussion**
Both areal and volumetric bone mineral density in our patient population was significantly lower than the age and sex-matched controls. This finding is in agreement with a number of studies that have reported PsA patients with an increased risk of low areal bone mineral density [22–27]. But simultaneously is in disagreement with another series of studies that did not report low areal BMD [28–33]. This dichotomy may be due to the non-consistent comparison groups and reported outcomes. Our finding of FN areal BMD significantly correlating with disease duration supports similar previous findings [24, 31, 34].
BMD measured by pQCT have been reported previously by Kocijan et al [35]. Kocijan et al reported that trabecular and not cortical density was significantly lower in the patient population as compared to the controls, this finding is in contrast to our results of decreased trabecular and cortical density in the patient population. A probable explanation for this discrepancy may be due to the fact that our patient cohort is older, with longer psoriasis and arthritis disease duration. The present study is the first where areal BMD has been compared to volumetric BMD in PsA patients, with statistically significant correlation between the two methodologies. This finding is in tally with 2 other studies in patients with inflammatory rheumatic disease [13, 14].
We observed a significantly increased 10-year probability of both major and hip osteoporotic fractures as assessed by the FRAX tool in the studied Hungarian patients with psoriatic arthritis. Probability of fragility fractures has not been reported previously in PsA patients using the FRAX tool. Our probability findings are in concordance with findings where osteoporotic fractures were studied as primary endpoints, reporting higher odds of diagnosis with pathological fractures and elevated risk of all fractures [22, 36, 37]. A cross-sectional study from Spain reported increased prevalence of fragility fractures in postmenopausal PsA patients [28]. A Brazilian study reported longer disease duration as predictor of low-impact fractures [26]. Nonetheless, an Italian study reported no difference in the prevalence of fragility fractures between cases and controls [38].
Beside known predictors of the 10-year probability of fragility fractures, i.e., age and BMD, our findings suggest that in PsA, severe disease activity as assessed by DAS28 is also a noteworthy risk factor.
FRAX assessment and DR volumetric BMD measurement are excellent alternatives when FN BMD cannot be measured, as in our study where one patient had total bilateral hip replacement.
Although patients identified as being osteoporotic with FN areal BMD measurement were also classified as osteoporotic with DR volumetric BMD measurement, volumetric measurements identified a significantly greater number of patients with low bone mass (34% vs. 88%, p<0.001). Although manufacturer provided German reference population is used to derive the T-score with both methodologies, the absence of agreement has also been reported by Marshall et al [39].
Fracture risk assessment using the FRAX tool identified more patients deserving anti-osteoporosis treatment as compared to FN areal BMD assessment (n = 8 vs. n = 6). Patients with major osteoporotic or hip fracture probability in the intervention range, i.e, ≥20% (n = 8) and ≥3% (n = 1), respectively, were also osteoporotic when assessed for DR volumetric BMD, nonetheless, a wide discrepancy was noticed as a significant proportion of the cohort with non-intervention level FRAX probability was identified as osteoporotic (n = 28, 24%). The FRAX tool offers optional inclusion of FN areal BMD and its clinical utility in identification of those at increased risk of fragility fractures may be improved were volumetric BMD values and psoriatic arthritis, as a secondary risk factor, also facilitated in the calculation of fracture probability.
The FRAX tool is designed to assess those between 40 and 90 years of age, given this inherent limitation the fracture probability of the young cannot be assessed. Among those under 40 years of age (n = 18), areal FN BMD assessment identified 3 (17%) and DR volumetric BMD examination identified 16 (89%) psoriatic arthritis patient with low bone density (T Score $\leq$ -1.0). Our observation suggests that volumetric BMD assessment better identifies those at increased fracture probability, and offers opportunity to initiate fracture risk reduction intervention promptly at a younger age. The true burden to osteoporosis may be underestimated with areal BMD measurement alone.
The Hungarian National Healthcare System subsidises antiosteoporotic therapy for those with an osteoporotic T score, based on the WHO classification (T Score $\leq$ -2.5), or with FRAX probability of more than 3% and 20% for hip and major osteoporotic fracture, respectively. Our results suggests that a number of osteoporotic and osteopenic patients deserving fracture risk reducing intervention are missed using areal BMD measurement alone, and as such FRAX assessment.
As compared to the control groups, the studied biochemical markers of bone turnover were significantly elevated suggesting a high bone turnover in the PsA population. This finding is supported by one previous study [40]. Grisar et al reported that CTx levels were significantly higher in the PsA group as compared to the healthy controls [29]. Szentpetery et al reported correlation between the studied bone markers and hand BMD [41]. Borman et al reported correlation between CTx and duration of arthritis and no difference in marker levels comparing patients with and without arthritis [27]. Nonetheless, in our study we found no correlation between the studied parameters and bone markers. The inconsistency in bone marker results in the numerous studies published has been summarized in a review by Jadon et al [42].
Our finding of high hypovitaminosis D prevalence is in concordance with results from quite a few previous studies [40, 43–45]. Although a study has reported that there is no difference in vitamin D levels between patients suffering from psoriasis with and without arthritis, correlation between disease activity and vitamin D levels has also been reported inconsistently [11, 40]. A probable predisposition for hypovitaminosis D in the PsA cohort may be due to the debilitating nature of their condition, and as such, they may not involve in physical activity that may be naturally assumed for a healthy age- and sex-matched counterpart; in addition, patients may shy away from outdoor activity given the psychological burden of their skin condition.
Although not supported by correlation analysis in our study cohort, hypovitaminosis D, high bone turnover and low bone mass may contribute to the increased fragility fracture probability in this population.
There are limitations to our study. Due to difficulties in getting access to the local population register and no commercially available population registers, we employed a method where recruitment of healthy volunteers may have been biased. Validation of our results is deemed mandatory optimally with a substantially larger cohort.
A higher number of study participant could have improved the statistical power of our analyses, nonetheless, we report a high 10-year probability of fragility fractures along with an increased prevalence of hypovitaminosis D in a PsA cohort complemented with low bone mass and high bone turnover; furthermore, the comparison to a systematically selected healthy age- and gender-matched population discards the effect of confounding risk factors.
Although warranting validation, the clinical utility of volumetric BMD examination complemented with traditional DEXA-based areal BMD measurement and FRAX assessment, are readily applicable in the PsA patient population and serve as an inexpensive tool in identifying those at increase fracture risk. Prompt identification, treatment and follow-up of patients at risk would help in reducing the burden of fragility fractures in the PsA patient population.
**Conclusion**
In the studied PsA cohort, disease activity was an independent predictor of 10-year probability for a major osteoporotic fracture, and complemented assessment of volumetric and areal BMD assured better efficacy at identifying those with low bone mass.
**Abbreviations**
25OHD 25-hydroxyvitamin D
BASDAI Bath ankylosing spondylitis disease activity index
bDMARD Biologic disease-modifying anti-rheumatic drugs
BMD Bone mineral density
BMI Body mass index
CASPAR Classification criteria for psoriatic arthritis
cDMARD Conventional disease-modifying anti-rheumatic drugs
CLIA Chemiluminescence immunoassay
CTx C-terminal telopeptides of type-I collagen
CV Coefficient of variation
DAS28 Disease activity score in 28 joints
DEXA Dual energy X-ray absorptiometry
DMARD Disease-modifying anti-rheumatic drugs
Declarations
Ethics approval and consent to participate:
All study participants gave written informed consent. The study was performed according to the Declaration of Helsinki and approved by the Hungarian Scientific Research Council Ethical Committee (approval No. 14804-2/2011/EKU).
Consent for publication:
Not applicable.
Availability of data and materials:
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.
Competing interests:
The authors declare that they have no competing interests.
Funding:
This work is supported by the Hungarian National Scientific Research Fund (OTKA) K105073 research grant (HPB); by the European Union and the State of Hungary and co-financed by the European Social Fund in the framework of TAMOP-4.2.4.A/2-11/1-2012-0001 ‘National Excellence Program ‘(ZS); and by the European Union grants GINOP-2.3.2-15-2016-00015 and GINOP-2.3.2-15-2016-00050 (ZS).
Authors' contributions:
ZP recruited patients, coordinated patient examinations, performed peripheral qCT examinations, administered questionnaires, collected and interpreted data and contributed in writing the manuscript. EK performed the routine laboratory examinations and contributed in writing the manuscript. ZP contributed in data collection and writing the manuscript. KH did the statistical analyses. RF administered questionnaires, contributed in data collection and writing the manuscript, AB conceived the study design and contributed in writing the manuscript. ZS conceived the study design, interpreted data and contributed in writing the manuscript and its critical evaluation. HPB conceived the study design, interpreted data and was a major contributor in writing the manuscript and its critical evaluation.
Acknowledgements:
Not applicable.
References
1. Myers WA, Gottlieb AB, Mease P. Psoriasis and psoriatic arthritis: clinical features and disease mechanisms. Clin Dermatol 2006;24:438–47.
2. Alinaghi F, Calov M, Kristensen LE, Gladman DD, Coates LC, Jullien D et al. Prevalence of psoriatic arthritis in patients with psoriasis: A systematic review and meta-analysis of observational and clinical studies. Am Acad Dermatol 2019;80(1):251-265.e19.
3. Gladman DD, Shuckett R, Russell ML, Thorne JC, Schachter RK. Psoriatic arthritis (PSA)–an analysis of 220 patients. Q J Med 1987;62(238):127-41.
4. Ritchlin CT, Colbert RA, Gladman DD. Psoriatic Arthritis. N Engl J Med 2017;376(10):957-70.
5. Paine A, Ritchlin C. Bone remodeling in psoriasis and psoriatic arthritis: an update. Curr Opin Rheumatol 2016;28: 66-75.
6. Redlich K, Smolen JS. Inflammatory bone loss: pathogenesis and therapeutic intervention. Nat Rev Drug Discov 2012;11:234-50.
7. Chandran S, Aldei A, Johnson SR, Cheung AM, Salonen D, Gladman DD. Prevalence and risk factors of low bone mineral density in psoriatic arthritis: A systematic review. Semin Arthritis Rheum 2016;46:174-82.
8. Colman EG, Food and Drug Administration. The Food and Drug Administration's Osteoporosis Guidance Document: past, present, and future. J Bone Miner Res 2003;18(6):1125-8.
9. Kanis JA. The incidence of hip fracture in Europe. Osteoporos Int 1993;3:10-5.
10. Kanis JA, Melton LJ 3rd, Christiansen C, Johnston CC, Khaltaev N. The diagnosis of osteoporosis. J Bone Miner Res 1994;9:1137–41.
11. Assessment of fracture risk and its application to screening for postmenopausal osteoporosis. Report of a WHO Study Group. Geneva, World Health Organization. WHO Technical Report Series 1994;843.
12. Engelke K, Adams JE, Armbrrecht G, Augat P, Bogado CE, Bouxsein ML et al. Clinical use of quantitative computed tomography and peripheral quantitative computed tomography in the management of osteoporosis in adults: the 2007 ISCD official positions. J Clin Densitom 2008;11:123–62.
13. Juhasz B, Gulyas K, Horvath A, Petho Z, Bhattoa HP, Vancsa A et al. Comparison of peripheral quantitative computed tomography forearm bone density versus DXA in rheumatoid arthritis patients and controls. Osteoporos Int 2017;28:1271–7.
14. Horváth Á, Végh E, Pusztai A, Pethő Z, Hamar A, Czókolyová M et al. Complex assessment of bone mineral density, fracture risk, vitamin D status, and bone metabolism in Hungarian systemic sclerosis patients. Arthritis Res Ther 2019;21:274.
15. https://www.sheffield.ac.uk/FRAX/ assessed 25th of March, 2020.
16. Taylor W, Gladman D, Helliwell P, Marchesoni A, Mease P, Mielants H. Classification criteria for psoriatic arthritis: development of new criteria from a large international study. Arthritis Rheum 2006;54:2665–73.
17. Prevoo ML, Van't Hof MA, Kuper HH, Van Leeuwen MA, Van de Putte LB, Van Riel PL. Modified disease activity scores that include twenty-eight-joint counts: development and validation in a prospective longitudinal study of patients with rheumatoid arthritis. Arthritis Rheum 1995;38:44–8.
18. Garrett S, Jenkinson T, Kennedy LG, Whitelock H, Gaisford P, Calin A. A new approach to defining disease status in ankylosing spondylitis: the bath ankylosing spondylitis disease activity index. J Rheumatol. 1994;21(12):2286–91.
19. Fredriksson T, Pettersson U. Severe psoriasis—oral therapy with a new retinoid. Dermatologica 1978;157:238–44.
20. Dawson-Hughes B, Heaney RP, Holick MF, Lips P, Meunier PJ, Vieth R. Estimates of optimal vitamin D status. Osteoporos Int 2005;16:713–6.
21. Westergren A. Diagnostic tests: the erythrocyte sedimentation rate range and limitations of the technique. Triangle; The Sandoz Journal of Medical Science 1957;3:20–5.
22. Kathuria P, Gordon KB, Silverberg JL. Association of psoriasis and psoriatic arthritis with osteoporosis and pathological fractures. J Am Acad Dermatol 2017;76:1045-1053.e3.
23. Frediani B, Allegrì A, Falsetti P, Storri L, Bisogno S, Baldi F et al. Bone mineral density in patients with psoriatic arthritis. J Rheumatol 2001;28:138-43.
24. Attia EA, Khafagy A, Abdel-Raheem S, Fathi S, Saad AA. Assessment of osteoporosis in psoriasis with and without arthritis: correlation with disease severity. Int J Dermatol 2011;50:30-5.
25. Reddy SM, Anandarajah AP, Fisher MC, Mease PJ, Greenberg JD, Kremer JM et al. Comparative analysis of disease activity measures, use of biologic agents, body mass index, radiographic features, and bone density in psoriatic arthritis and rheumatoid arthritis patients followed in a large U.S. disease registry. J Rheumatol 2010;37:2566-72.
26. Nolla JM, Fiter J, Rozadilla A, Gómez-Vaquero C. Bone involvement in psoriatic arthritis. J Rheumatol 2002;29:1108-9.
27. Borman P, Babaoglu S, Gur G, Bingol S, Bodur H. Bone mineral density and bone turnover in patients with psoriatic arthritis. Clin Rheumatol 2008;27:443-7.
28. Riesco M, Manzano F, Font P, García A, Nolla JM. Osteoporosis in psoriatic arthritis: an assessment of densitometry and fragility fractures. Clin Rheumatol 2013;32:1799-804.
29. Grisar J, Bernecker PM, Aringer M, Redlich K, Sedlak M, Wolozczuk W et al. Ankylosing spondylitis, psoriatic arthritis, and reactive arthritis show increased bone resorption, but differ with regard to bone formation. J Rheumatol 2002;29:1430–6.
30. Harrison BJ, Hutchinson CE, Adams J, Bruce IN, Herrick AL. Assessing periarticular bone mineral density in patients with early psoriatic arthritis or rheumatoid arthritis. Ann Rheum Dis 2002;61:1007–11.
31. D’Epiro S, Marocco C, Salvi M, Mattozzi C, Luci C, Macaluso L et al. Psoriasis and bone mineral density: implications for long-term patients. J Dermatol 2014;41:783–7.
32. Dheda K, Cassim B, Patel N, Mody GM. A comparison of bone mineral density in Indians with psoriatic polyarthritis and healthy Indian volunteers. Clin Rheumatol 2004;23:89.
33. Cortet B, Trouvé MH, Flipo RM. Bone involvement in psoriatic arthritis. J Rheumatol 2002;29:1107–8.
34. Busquets N, Vaquero CG, Moreno JR, Vilaseca DR, Narváez J, Carmona L, Nolla JM. Bone mineral density status and frequency of osteoporosis and clinical fractures in 155 patients with psoriatic arthritis followed in a university hospital. Reumatol Clin 2014;10:89-93.
35. Kocijan R, Finzel S, Englbrecht M, Engelke K, Rech J, Schett G. Differences in bone structure between rheumatoid arthritis and psoriatic arthritis patients relative to autoantibody positivity. Ann Rheum Dis 2014;73:2022–8.
36. Ogdie A, Harter L, Shin D, Baker J, Takeshita J, Choi HK et al. The risk of fracture among patients with psoriatic arthritis and psoriasis: a population-based study. Ann Rheum Dis 2017;76:882-5.
37. Burge R, Dawson-Hughes B, Solomon DH, Wong JB, King A, Tosteson A. Incidence and economic burden of osteoporosis-related fractures in the United States, 2005-2025. J Bone Miner Res 2007;22:465-75.
38. Del Puente A, Esposito A, Costa L, Benigno C, Del Puente A, Foglia F et al. Fragility Fractures in Patients with Psoriatic Arthritis. J Rheumatol 2015;93:36-9.
39. Marshall LM, Lang TF, Lambert LC, Zmuda JM, Ensrud KE, Orwoll ES. Osteoporotic Fractures in Men (MrOS) Research Group. Dimensions and volumetric BMD of the proximal femur and their relation to age among older U.S. men. J Bone Miner Res 2006;21:1197-206.
40. Petho Z, Kulcsar-Jakab E, Kalina E, Balogh A, Pusztai A, Gulyas K et al. Vitamin D status in men with psoriatic arthritis: a case-control study. Osteoporos Int 2015;26:1965-70.
41. Szentpetery A, McKenna MJ, Murray BF, Ng CT, Brady JJ, Morrin M et al. Periarticular bone gain at proximal interphalangeal joints and changes in bone turnover markers in response to tumor necrosis factor inhibitors in rheumatoid and psoriatic arthritis. J Rheumatol 2013;40:653-62.
42. Jadon DR, Nightingale AL, McHugh NJ, Lindsay MA, Korendowych E, Sengupta R. Serum soluble bone turnover biomarkers in psoriatic arthritis and psoriatic spondyloarthropathy. J Rheumatol 2015;42:21-30.
43. Touma Z, Eder L, Zisman D, Feld J, Chandran V, Rosen CF et al. Seasonal variation in vitamin D levels in psoriatic arthritis patients from different latitudes and its association with clinical outcomes. Arthritis Care Res (Hoboken) 2011;63:1440-7.
44. Orgaz-Molina J, Buendía-Eisman CA, Arrabal-Polo MA, Ruiz JC, Arias-Santiago S. Deficiency of serum concentration of 25-hydroxyvitamin D in psoriatic patients: a case-control study. J Am Acad Dermatol 2012;67:931–8.
45. Kincse G, Bhattoa PH, Herédi E, Varga J, Szegedi A, Kéri J, Gaál J. Vitamin D3 levels and bone mineral density in patients with psoriasis and/or psoriatic arthritis. J Dermatol 2015;42:679-84. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
1292,
1
],
[
1292,
4179,
2
],
[
4179,
7406,
3
],
[
7406,
10437,
4
],
[
10437,
13674,
5
],
[
13674,
13826,
6
],
[
13826,
16667,
7
],
[
16667,
18669,
8
],
[
18669,
21068,
9
],
[
21068,
24001,
10
],
[
24001,
24464,
11
],
[
24464,
27127,
12
],
[
27127,
28548,
13
],
[
28548,
31468,
14
],
[
31468,
34809,
15
],
[
34809,
38078,
16
],
[
38078,
39840,
17
],
[
39840,
40334,
18
],
[
40334,
42455,
19
],
[
42455,
45229,
20
],
[
45229,
48353,
21
],
[
48353,
50322,
22
]
]
} |
17e75ffdd5d2cb621c830864f465a5b0078ace31 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 6,
"total-fallback-pages": 0,
"total-input-tokens": 11514,
"total-output-tokens": 3191,
"fieldofstudy": [
"Materials Science"
]
} | Autonomous Positioning and Marking of Flaw Detection Wall-climbing Robot Based on Large Spherical Oil Storage Tanks
Gao-feng SONG¹, Ying WU²*, Yi-bin ZHANG³ and Lu ZHANG⁴
¹Special Equipment Safety Supervision and Inspection Institute of Jiangsu Province
²Southeast University, Automation School
³Nanjing Uni-Specialized Robot Technology Co., Ltd
*Corresponding author
Keywords: Wall-climbing robots, Autonomous positioning, Marking system.
Abstract. The emergence of wall-climbing robots alleviates the limitations of traditional manual flaw detection, and the autonomous positioning and marking system is its core research problem. By installing a three-axis accelerometer and a three-axis gyroscope on the wall-climbing robot, this paper firstly establishes a 3D model of the oil storage tank and stores its data in a database, then realizes the autonomous positioning of the wall-climbing robot on the oil storage tank, and finally marks the unqualified weld seam points.
Introduction
The malfunction of special equipment such as large chemical storage tanks, lifting machinery, and high-pressure vessels may cause catastrophic consequences. To avoid damage to the metal structures of such equipment, extend the service life of the structure and improve the reliability and safety of the structure, the health status of metal structures is determined by appropriate testing methods for early diagnosis, which contributes to the rating of special equipment inspection conclusions and the formulation and implementation of follow-up regulatory measures. It is of great significance for people's life safety assurance and economic benefit protection. Therefore, how to conduct rapid, accurate and reliable comprehensive detection of metal structure damage through certain diagnostic techniques and diagnostic methods is the hot spot of research on special equipment detection technology.
Since the beginning of the 21st century, industrial robots have continuously penetrated from the field of automobile manufacturing to machinery, construction, chemical engineering, aerospace and so on. Intelligent technology is combined with social production and life. For example, the wall-climbing robots studied in this paper are for the detection of special equipment. The application needs to produce an industrial robot that replaces the inspector's work, which can achieve autonomous positioning, weld tracking and marking of unqualified weld seams on large oil storage tanks.
In the research process of the wall-climbing robot, the remote-controlled wall-climbing robot is initially realized, that is, the staff remotely controls the visual operation interface of the console, and the robot goes straight and turns through the keyboard, mouse or handle, as shown in Figure 1.
Therefore, the welding identification technology and the robot autonomous positioning system are added to the remote-controlled wall-climbing robot, which can better realize the intelligence and automation of the robot and save a lot of manpower and material consumption. What is studied in this paper is the robot's autonomous positioning and marking part.
**Establish a 3D Model of the Storage Tank**
To achieve autonomous positioning of the robot, it is first necessary to establish a 3D model of the oil storage tank. The research of 3D spatial modeling method is a hot topic in the field of 3DGIS. Many experts and scholars have made useful explorations in this field. A total of more than 20 spatial modeling methods are proposed, which can be divided into surface-based models and volume-based models. And three models of modeling systems based on hybrid models [1]. Since the oil storage tank is a space entity with regular boundaries and the interior is a hollow entity, the modeling method based on the voxel model is not suitable for constructing a three-dimensional oil storage tank. In this paper, the object-oriented analysis method is used to abstract the basic elements of three-dimensional modeling of oil storage tank into three categories: point, line and surface.
The point class mainly includes the measuring points and characteristic points of the oil storage tank, the line type has characteristic connecting lines, and the surface type mainly includes the basic surface element, the bottom surface of the oil storage tank, the side surface, the top surface, etc. So that the 3D model of the oil storage tank can be constructed by these basic modeling elements through a certain modeling method. Wherein, the feature connecting line is a line segment designated by the user for connecting the feature points. In the 3D modeling process, the generation of the body is mainly composed of the basic surface elements, and the basic surface elements are mainly composed of the characteristic connecting lines. There are usually two types of triangular and quadrilateral elements. In the 3D space surface model expression, the triangular surface element is better than the quadrilateral surface element [2]. The data model that defines the position and shape of an entity by face, line, and point is the boundary representation model, as shown in Figure 2.
The general idea of the 3D model construction of the oil storage tank is to simplify the process, that is, the tank body is first divided, then the parts after the splitting are separately modeled, and finally the models of the splits are integrated. The wall-climbing robot in this paper is mainly applied to the spherical oil storage tank, and its 3D model is shown in Figure 3.
After establishing the 3D model of the tank to be tested, add a unique label to each weld on the tank and set its starting and ending point.
In addition to establishing a 3D model of the oil storage tank, it is necessary to create a database of oil tank wall quality parameters, each of which corresponds to a table in the database including information such as the inspection personnel, the inspection time, the relative position of the inspection points, the quality of the monitoring spot welds, the number of the welds where the monitoring points are located, the inspection pictures, the detection video and the wall thickness.
**Autonomous Positioning of Wall-climbing Robot**
The wall-climbing robot is adsorbed on the surface of the large metal tank by permanent magnet adsorption, and moves on the surface of the tank by wheel movement. It is equipped with high-precision encoders, three-axis accelerometers, three-axis gyroscopes, depth cameras, metal wall flaw detectors, remote communication modules, etc.
The motion module of the wall climbing robot consists of four permanent magnet wheels, two DC motors and two motor drivers. The four permanent magnet wheels are divided into two groups, the left front and rear wheels are a group, and the right front and rear wheels are a group. Each set of magnetic wheels is connected by a transmission mechanism, and each set of transmissions is controlled by a separate set of motor and motor drives. The control module forms a double closed-loop control model. The rotational speed of the magnetic wheels on both sides adopts the
incremental PID control method to precisely control the rotational speed of the magnetic wheels on both sides. The robot realizes free steering by differential mode, as shown in Figure 4.
Figure 4. Double-drive Magnetic Wheel Wall-climbing Robot.
The motion control module of the wall climbing robot also uses a three-axis accelerometer and a three-axis gyroscope sensor. The high-precision encoder can determine whether the robot is slipping by combining the two sensors. When the value of the encoder has been increased and the values of the accelerometer and the gyroscope have not changed greatly, it indicates that the robot is slipping. At this time, the robot will issue a warning and correct the actual movement variable, which makes the speed control more precise [3].
To achieve the autonomous positioning of the wall-climbing robot, that is, to obtain the coordinates of the detection point, it is necessary to use the method of building identification and geometric identification to determine. The first half of the coordinates is determined according to the building identification, that is, the number of welds in the 3D model of the oil storage tank, and the second half of the coordinates is determined according to the geometrical indication, that is, the distance of the detection point from the starting point of the weld. Among them, the distance value is determined by the encoder and the three-axis accelerometer and the three-axis gyroscope. Since the radius of the oil storage tank is large enough, the robot is small enough, so the robot moves almost in the plane as it walks along the weld seam, the direction of the weld is the x-axis, the starting point of the weld is the coordinate origin, and the left hand rule determines y-axis. The movement trajectory of the robot appears as a curve S that fluctuates up and down along x=0 in this coordinate system, and the distance from the point on S on the x-axis to the origin is the distance from the starting point of the solder joint, that is
\[ \text{Distance} = \int f(x, y) \, ds \]
Which \( f(x, y) \) can be obtained by three-axis accelerometer and three-axis gyroscope, \( ds \) can be obtained by encoder.
Unqualified Weld Points Marking
As an important means of fault diagnosis and detection of flaw detection equipment, non-destructive flaw detection technology plays an important role in the aerospace, transportation, energy, electric power, petrochemical, machinery and other industrial sectors. The use of non-destructive testing technology to improve product quality and ensure safe production has achieved significant economic and social benefits. In the petroleum industry, non-destructive testing techniques are increasingly used to ensure the safety and effectiveness of oil production and transportation. Non-destructive testing is a technical means to study the presence or absence of defects in the interior and surface of a product without damage to the material, depending on the internal structure of the product or the presence of defects. At present, flaw detection methods
mainly include: radiographic inspection, ultrasonic flaw detection, eddy current testing and magnetic flux leakage testing.
Compared with other kinds of flaw detection methods, magnetic flux leakage detection has obvious advantages. Magnetic flux leakage detection uses high-sensitivity sensors instead of magnetic powder sprayed on the surface of the workpiece to make the detection more intelligent, to achieve more convenient operation, and the test results are more reliable. The main feature of the magnetic flux leakage testing technology is that the surface of the ferromagnetic material is fast and the detection result is stable and reliable. The probe has the advantages of simple structure, convenient implementation and low cost. Therefore, the method can be applied to the weld inspection of the outer wall of the oil storage tank.
The magnetization curves of different ferromagnetic materials are different. The magnetization curve of common ferromagnetic materials is shown in Figure 5, where point a is the magnetic permeability \( \mu \) maximum point and point b is the magnetic induction intensity \( B \) maximum. As can be seen from the figure, when the magnetic saturation point b is approached, the magnetic field strength increases and the magnetic induction intensity remains substantially unchanged.
When a piece of internally non-defective and crack-free ferromagnetic material is uniformly magnetized, its magnetic path is theoretically composed of magnetic flux passing through the inside of the ferromagnetic material and a very small amount of leakage flux. If there is a defect, the defect area. The thickness is thinner and the magnetic field density is relatively large, so the magnetic reluctance at the defect is too large. At this time, part of the magnetic path is formed by the magnetic flux inside the material and a part of the leakage flux, that is, the magnetic flux will be significantly distorted at the defect [4].
The wall-climbing robot is equipped with a flaw detector. When the robot walks along the weld, the weld quality and wall thickness of the weld are detected. The detection density is no more than 2 mm from the adjacent sampling point, as shown in Figure 6.
After the test is finished, the test data is analyzed. If the weld spot is unqualified, the robot will mark it here with the spot nozzle, and the coordinates of the unqualified weld point are obtained by the robot autonomous positioning. The data is stored in the database of the upper computer, which is convenient for the staff to find and record.
Conclusion
This paper introduces the autonomous positioning and marking of the wall-climbing robot based on large oil storage tanks. Firstly, establish a 3D model of the oil storage tank and mark each weld seam, and create a database to record relevant data. Then realize the autonomous positioning of the wall-climbing robot. Finally, the detected unqualified weld points are marked and stored in the database.
In order to improve the detection efficiency of the actual inspection site, modular non-destructive testing equipment that combines several detection methods is a future development trend. Miniaturization is another development trend. With the in-depth development of the market economy and competitive pressures, companies are paying more and more attention to the cost benefits of production. The technical advantages of automated testing are obvious, such as high efficiency, high security and small disturbances. Combined with artificial intelligence, it is an important goal for the intelligent detection system to achieve the behavior of mobile robots through autonomous decision-making under certain circumstances.
References
[1] Scianna A, Ammosvato A. 3DGIS data model using open source software[A].Core Spatial Databases-Updating, Maintenance and Services-from Theory to Practice[C].ISPRS, 2010, 38" 120-125.
[2] Hou E K, Zhang Z H, Deng N D, et al. Comparison of three roadway 3D modeling methods in OpenGL environment[J]. Mining Research and Development, 2009, 29(5): 59-62.
[3] Liu Z, Song L B, Yu T. An IMU-based human-machine cooperation control algorithm of active dancing robot. Computer Engineering & Science, Vol. 40, No. 1, Jan. 2018.
[4] Yao K, Shen K, Wang Z D, et al. Three-dimensional finite element analysis of residual magnetic field for ferromagnets under early damage[J]. Journal of Magnetism & Magnetic Materials, 2014, 354(3):112-118. | 2025-03-07T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2781,
1
],
[
2781,
5158,
2
],
[
5158,
7130,
3
],
[
7130,
10214,
4
],
[
10214,
12545,
5
],
[
12545,
14774,
6
]
]
} |
908336ffa6f5f43e258e864187dfc4cf167a4d27 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 5,
"total-fallback-pages": 0,
"total-input-tokens": 17415,
"total-output-tokens": 4528,
"fieldofstudy": [
"Medicine"
]
} | Review Article
Short Review/Perspective on Adjacent Segment Disease (ASD) Following Cervical Fusion Versus Arthroplasty
Nancy E. Epstein, M.D., F.A.C.S.1, Marc A. Agulnick, M.D., F.A.A.O.S.2
1Department of Neurosurgery, School of Medicine, State University of New York at Stony Brook, and % Dr. Marc Agulnick 1122 Franklin Avenue Suite 106, Garden City, NY 11530, USA 2Department of Orthopedics, NYU Langone Hospital Long Island and St. Francis Hospital, 1122 Franklin Avenue Suite 106, Garden City, NY 11530, New York, United States.
E-mail: *Nancy E. Epstein - [email protected]; Marc A. Agulnick - [email protected]
ABSTRACT
Background: Although the incidence of radiographic Adjacent Segment Disease (ASD) following anterior cervical diskectomy/fusion (ACDF) or cervical disc arthroplasty (CDA) typically ranges from 2-4%/year, reportedly fewer patients are symptomatic, and even fewer require secondary surgery.
Methods: Multiple studies have documented a 2-4% incidence of radiographic ASD following either ACDF or CDA per year. However, fewer are symptomatic from ASD, and even fewer require additional surgery/reoperations.
Results: In a meta-analysis (2016) involving 83 papers, the incidence of radiographic ASD per year was 2.79%, but symptomatic disease was present in just 1.43% of patients with only 0.24% requiring secondary surgery. In another study (2019) involving 38,149 patients undergoing ACDF, 2.9% (1092 patients; 0.62% per year) had radiographic ASD within an average of 4.66 postoperative years; the younger the patient at the index surgery, the higher the reoperation rate (i.e. < 40 years of age 4.56 X reoperations vs. <70 at 2.1 X reoperations). In a meta-analysis of 32 articles focusing on ASD 12–24 months following CDA, adjacent segment degeneration (ASDeg) occurred in 5.15% of patients, but adjacent segment disease (AS Dis) was noted in just 0.2%/year. Further, AS degeneration occurred in 7.4% of patients after 1-level vs. 15.6% following 2 level fusions, confirming that CDA’s “motion-sparing” design did not produce the “anticipated” beneficial results.
Conclusion: The incidence of radiographic ASD ranges from 2-4% per year for ACDF and CDA. Additionally, both demonstrate lesser frequencies of symptomatic ASD, and the need for secondary surgery. Further, doubling the frequency of ASD following 2 vs. 1-level CDA, should prompt surgeons to limit surgery to only essential levels.
Keywords: Adjacent Segment Disease (ASD); Cervical Spine; Surgery: Cervical Disc Arthroplasty (CDA); Anterior Cervical Diskectomy/Fusion (ACDF); Radiographic ASD; Symptomatic ASD; ASD Requiring Reoperations
INTRODUCTION
The incidence of radiographic Adjacent Segment Disease (ASD) following cervical spine surgery, whether following anterior diskectomy/fusion (ACDF) or cervical disc arthroplasty (CDA), typically ranges from 2-4%/year [Table 1].1-12 However, the frequency of symptomatic ASD and the requirement for secondary surgery in these two populations is less well-defined [Table 1].1-12 In this short review/perspective, studies were carefully selected to include those that focused on the frequencies of ASD...
**Table 1: Summarizing Adjacent Segment Disease following Cervical Spine Surgery.**
| Author [Ref] Year Journal | Study Design | Surgical Data ACFD CDA Other | Data Review | Data Review | Conclusion |
|---------------------------|--------------|------------------------------|-------------|-------------|------------|
| Seo and Choi[7] 2008 Br J Neurosurg | ASD After Fusion Treat RAD Myelopathy | CDA Rationale - Prevent or Limit ASD | Is ASD Part of the Natural History of Degeneration | Short-Term CDA Data for Younger Patients-Aware Not Long-Term Data | Discussion ASD After Fusion vs. CDA |
| Kepler and Hilibrand[4] 2012 Orthop Clin North Am | ASD After Fusion Rad and Myelopathy 2–3%/year | ASD Defined Motion Segment Adjacent to Prior Fusion | ASD May Be Due to Altered BIO after Fusion | ASD Prompted Development of CDA | Literature Shows No Reduced Rate ASD after CDA |
| Cho and Riew[3] 2013 JAAOS | ASD Cervical Fusion ACDF vs. No Fusion AD/FOR | ASD with Fusion: Is 3% per year or 25% at 10 Years | No Fusion Same Rate ASD vs. Fusion | | CDA Similar Incidence ASD |
| Virk et al.[11] 2014 Orthopedics | ASD in Cervical Spine Surgery | ASD Seen on X-ray Due to BIO Risk Factors | Complications of Fusion Listhesis Instability HNP | Complication of Fusion Stenosis | Post Fusion Increased Load Adjacent Level |
| Shriver et al.[9] 2016 Spine J | ASD after CDA MA 32 articles | FO 12–24 Mos CDA | FO-24 Mos CDA | 2 Level Procedures: Higher ASD (15.6%) vs. 1 Level (7.4%) | AS Disease 1 Level CDA 0.8% |
| Shibani et al.[9] 2016 Acta Neurochir (Wein) | ASD/Fusion Rates 1, 2, 3 Level ACDF Using Stand Alone Empty PEEK Cages | FO 12–24 Mos CDA | FO-24 Mos CDA | | |
| Kong et al.[5] 2016 Medicine (Baltimore) | Prevalence ASD PRISMA Rev/MA | XR ASD Symp ASD Reop ASD | 83 Studies | Per Year ASD 2.79% X-ray 1.43% Symptomatic 0.24% Reoperation | Heterogenous Studies |
| Tobert et al.[10] 2017 Clin Spine Surg | ASD Cervical and Lumbar Spine 2–4% Per Year | ASD Leads to Reop Prior Adjacent Level Spondylosis Altered Biomechanics Adjacent to Fusion | Reop for ASD Mean 32 Mos After 1st ACDF | Etiologies ASD Different Approaches |
| Alhashash et al.[1] 2018 Spine | ASD After ACDF 2005–2012 | 70 patients Long-Term Follow-up 3–10 Years After Reop | Reop for ASD Mean 32 Mos-Most at C56 (28%) Next C45 | Risk ASD Deg Changes Preop at 2nd Level or Poor Postop Lordosis Reop Rate Higher with Depression 1.42 X and Psychosis 1.45 X |
| Wu et al.[12] 2019 Int J Surg | Risk Factors Reop for ASD After ACDF | 16-year Cohort Study (Near Perfect Follow-up) | 38,149 Pts 1st ACDF 2.9% (1092) 2nd Surgery Mean 4.66 yrs Later | Risk Reop for ASD Higher Younger Patients<40 4.56 X<50 4.09 X<60 3.09 X<70 2.17 X>70 Higher | |
following predominantly ACDF and CDA, while also looking at different rates of postoperative symptomatic ASD (0.62–1.43%), and the need for reoperations (0.2–0.24%).
**DEFINITION OF ASD**
Virk et al. (2014) defined the various degenerative, radiographic, and/or biomechanical factors predisposing patients to the development of ASD [Table 1]. These factors included: disc disease, stenosis, spondylosis, spondylolisthesis, arthritic changes of facet/uncovertebral joints, or fractures. Although ASD was typically initially described as due to greater stress at adjacent levels following a fusion, subsequent literature showed it also occurs with comparable frequencies following CDA.
**INCIDENCE OF ASD AFTER CERVICAL SURGERY**
Several studies cited 2–4% frequencies of ASD following ACDF, with some also citing comparable rates with non-fusion techniques [Table 1]. Kepler and Hilibrand (2012) observed a 2–3% per year incidence of ASD following cervical fusion [Table 1]. They recommended that ASD frequencies could be mitigated utilizing improved surgical fusion techniques, while also questioning the future potential efficacy of CDA through “motion preserving surgery.” Cho an Riew (2013) found a 3% overall incidence of ASD/year typically following ACDF, noting that this frequency would rise to 25% over a 10 year period. They also showed that the frequency of ASD remained relatively unchanged for non-fusion procedures (anterior diskectomy without fusion or laminoforaminotomy) including CDA. Using the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analysis 2009) guidelines, Kong et al. (2016) evaluated 83 cervical surgical studies utilizing multiple databases, and found that ASD occurred in 2.79% of patients/year; however, only 1.43% were symptomatic/year, while just 0.24% required secondary surgery/year.
**REDUCING THE RISKS AND/OR PREVENTION OF ASD FOLLOWING CERVICAL SURGERY**
Several cervical spine studies, mostly involving ACDF, identified risk factors predisposing patients to developing radiographic ASD, symptomatic ASD, and the need to reoperate on ASD [Table 1]. Tobert et al. (2017) observed a 2–4% frequency of ASD following both cervical and lumbar surgery, largely attributed to; pre-existing spondylotic disease at the adjacent level, degenerative changes at those levels, and/or altered adjacent level “biomechanics” following the index surgical procedures. Looking at the incidence of ASD after 70 ACDF (2005–2012) followed between 3-10 years, Alhashash et al. (2018) showed reoperations for ASD (i.e., based upon X-rays/MR studies) were warranted an average of 32 months after the index ACDF surgery (i.e. 54% single level procedures). Two major factors predisposing to secondary surgery included preoperative “degenerative changes” (74%), or postoperative sagittal malalignment (i.e. lack of adequate lordosis). Butler et al. (2019), similarly noted a 3% incidence of ASD following ACDF per years; ways to avoid ASD included “consider non fusion alternatives,” improve patient selection, pay more attention to preserving lordosis during ACDF (i.e.
sagittal alignment), and considering CDA's for their "motion sparing" design.[2] Most notably, in Wu et al. (2019) series of 38,149 patients undergoing ACDF, 2.9% had radiographic evidence of postoperative ASD observed an average of 4.66 years postoperatively (1092 patients: 0.62%/per year) [Table 1].[11] Of interest, younger patients were more susceptible to ASD and required more frequent reoperations vs. older patients (i.e. < 40 years of age 4.56 fold incidence of reoperations vs. < 70 at 2.17 fold incidence). Further, patients exhibiting depression or psychoses also exhibited higher frequencies (1.42 and 1.45 fold respectively) of warranting additional surgery.
**ACDF Data Largely Excluded ASD Results with Polyetheretherketone (PEEK) Cages**
Notably, we did not specifically focus on the results for ACDF performed with stand-alone polyetheretherketone (PEEK) cages. In Shiban et al. (2016), one year following 265 PEEK cage fusions, 16 (6%) warranted reoperation to address radiographic ASD [Table 1].[8]
**CDA’S “BIOMECHANICAL MOTION SPARING” DESIGN FAILED TO REDUCE ASD**
CDA's, by maintaining "motion" at operated levels, were devised to "theoretically" reduce stress transmitted to adjacent segments [Table 1].[4,6,7] In 2008, Seo and Choi evaluated the frequency of ASD after cervical fusion vs. CDA, focusing on the potential pros and cons of each technique.[7] They questioned whether ASD in part reflected the "natural history" of progressive degeneration rather than simply representing the response to a "fusion." They further emphasized that CDA were recommended for younger patients without significant spondylosis who clearly demonstrated adequately preserved range of motion. Although Kepler and Hilibrand (2012) also emphasized CDA's potential "motion-sparing" capabilities that might limit the risk of ASD, they nevertheless found that so far, the literature did not; "...distinguish a difference in the rate of ASD between fusion and disc replacement." [4]
**CDA'S COMPARABLE ADJACENT SEGMENT DEGENERATION (AS-DEG) VS. ADJACENT SEGMENT DISEASE (AS-DIS) VS. ANTERIOR CERVICAL FUSIONS**
Two studies emphasized that CDA's failed to limit or eliminate ASD when compared with largely anterior cervical fusions [Table 1].[6,9] In their meta-analysis of 32 studies, Shriver et al. (2016) found that at 1-2 postoperative years, there was a 5.1% frequency of AS-Deg, and a 0.2% incidence of AS-DIS.[9] Long-term follow-up data over 24 postoperative months showed that the incidence of both AS-DEG and AS-DIS further increased to 16.6% and 2.6% respectively. Additionally, higher frequencies of ASD occurred after 1-level (7.4%) vs. 2-level CDA procedures (15.6%). Parrish et al. (2021) also noted CDA's comparable 1-2% frequencies of radiographic ASD vs. anterior cervical fusions.[8]
**CONCLUSION**
This short review/perspective of select studies emphasizes how to limit the risk of adjacent segment degeneration (i.e. radiographic, symptomatic, and/or requiring reoperations). This requires; carefully selecting “symptomatic” patients for either ACDF or CDA (i.e., for CDA, younger patients with preserved range of motion without spondylosis), stringently limiting the number of operated levels, and optimizing the surgical "technique" to preserve lordosis.
**Declaration of patient consent**
Patient’s consent not required as there are no patients in this study.
**Financial support and sponsorship**
Nil.
**Conflicts of interest**
There are no conflicts of interest.
**REFERENCES**
1. Alhashash M, Shousha M, Boehm H. Adjacent segment disease after cervical spine fusion: evaluation of a 70 patient long-term follow-up. Spine 2018;43:605-9.
2. Butler JS, Morrissey PB, Wagner SC, Kaye ID, Sebastian AS, Schroeder GD, et al. Surgical strategies to prevent adjacent segment disease in the cervical spine. Clin Spine Surg 2019;32:91-7.
3. Cho SK, Riew DK. Adjacent segment disease following cervical spine surgery. J Am Acad Orthop Surg 2013;21:3-11.
4. Kepler CK, Hilibrand AS. Management of adjacent segment disease after cervical spinal fusion. Orthop Clin North Am 2012;43:53-62.
5. Kong L, Cao J, Wang L, Shen Y. Prevalence of adjacent segment disease following cervical spine surgery: A PRISMA-compliant systematic review and meta-analysis. Medicine (Baltimore) 2016;95:e4171.
6. Parish JM, Asher AM, Coric D. Adjacent-segment disease following spinal arthroplasty. Neurosurg Clin N Am 2021;32:505-10.
7. Seo M, Choi D. Adjacent segment disease after fusion for cervical spondylosis; myth or reality J Neurosurg 2008;22:195-9.
8. Shiban E, Gapon K, Wostrack M, Meyer B, Lehmbarg J. Clinical
and radiological outcome after anterior cervical disectomy and fusion with stand-alone empty polyetheretherketone (PEEK) cages. Acta Neurochir (Wien) 2016;158:349-55.
9. Shriver MF, Lubelski D, Sharma AM, Steinmetz MP, Benzel EC, Mroz TE. Adjacent segment degeneration and disease following cervical arthroplasty: A systematic review and meta-analysis. Spine J 2016;16:168-81.
10. Tobert DG, Antoci V, Patel SP, Saadat E, Bono CM. Adjacent segment disease in the cervical and lumbar spine. Clin Spine Surg 2017;30:94-101.
11. Wu JC, Chang HK, Huang WC, Chen YC. Risk factors of second surgery for adjacent segment disease following anterior cervical disectomy and fusion: A 16-year cohort study. Int J Surg 2019;68:48-55.
12. Virk SS, Niedermeier S, Yu E, Khan SN. Adjacent segment disease. Orthopedics 2014;37:547-55.
Comment: Jamie S. Baisden, M.D.
Professor Department of Neurosurgery, Medical College of Wisconsin, Milwaukee, WI
The FEM stuff we have been doing goes well with this report showing adjacent level stresses throughout the spine with both ACDF and CDA. The Metal on Polymer CDA such as Prestige are stiffer and would be predicted to increase ASD more than a metal on Polymer (Secure-C, Prodisc-C, Mobi-C). These more mobile disc arthroplasties shift the stresses to the index level along the facets. The newer discs like Simplify with different core biomaterials will hopefully “soften” the construct and produce less ASD.
I agree with the “natural history of ASD” and often think of the A as standing for accelerated - both ACDF and CDA - accelerating a natural history. Seems like it boils down to whether you are treating radiculopathy or myelopathy and what is the least procedure a surgeon can do to achieve symptomatic relief without triggering the degenerative cascade. The posterior minimally invasive foraminotomy will be making a comeback in the near future. | 2025-03-06T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3171,
1
],
[
3171,
5892,
2
],
[
5892,
9002,
3
],
[
9002,
13639,
4
],
[
13639,
15532,
5
]
]
} |
515fe6be78ec6ce3f1aa6235e4d384555233ef8b | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 8,
"total-fallback-pages": 0,
"total-input-tokens": 26305,
"total-output-tokens": 9800,
"fieldofstudy": [
"Medicine"
]
} | Epidemiology of neuroendocrine tumors of the appendix in the USA: a population-based national study (2014-2019)
Motasem Alkhayyat\(^a\), Mohannad Abou Saleh\(^b\), Wendy Coronado\(^a\), Mohammad Abureesh\(^c\), Mohammad Zmaili\(^a\), Thabet Qapaja\(^a\), Ashraf Almomani\(^a\), George Khoudari\(^d\), Emad Mansoor\(^e\), Gregory Cooper\(^e\)
Cleveland Clinic Foundation, Ohio; Staten Island University Hospital, NY; University Hospitals Cleveland Medical Center, Ohio, USA
Abstract
**Background** The appendix is the third most common place for neuroendocrine tumors (NETs) along the digestive tract and NETs are the most common neoplasms of the appendix. However, there are limited population-based data on the epidemiology of this disease. Using a large database, we sought to describe the epidemiology and risk association of NETs of the appendix.
**Method** We queried a multi-institutional database (Explorys Inc., Cleveland, OH, USA), comprising 360 hospitals in the United States (US), for patients with a diagnosis of NETs of the appendix from 2014-2019.
**Results** Of the 30,324,050 individuals in the database, 2020 patients had an appendiceal NET diagnosis (0.007%). The most common presenting symptoms included abdominal pain, nausea, vomiting and diarrhea. Patients with appendiceal NETs were more likely to be female (odds ratio [OR] 1.36, 95% confidence interval [CI] 1.24-1.49), Caucasian (OR 2.71, 95%CI 2.40-3.07), with a history of smoking (OR 1.82, 95%CI 1.65-2.01), family history of primary gastrointestinal malignancy (OR 7.26, 95%CI 6.31-8.33), diagnosis of multiple endocrine tumor type 1 (OR 52.31, 95%CI 23.15-118.23), or neurofibromatosis type 1 (OR 16.37, 95%CI 7.24-37.01).
**Conclusions** In a population-based study in the US, using the Explorys database, we found the overall prevalence of NETs of the appendix to be 7 per 100,000 persons. The incidence in the year January 2019-January 2020 was 0.4 per 100,000 individuals. These rates are higher than previously reported and may be more accurate, given the more comprehensive nature of the Explorys database.
**Keywords** Neuroendocrine tumor, appendix, epidemiology, risk factors
Ann Gastroenterol 2021; 34 (5): 713-720
Introduction
Gastroenteropancreatic neuroendocrine tumors (NETs) is an inclusive term referring to NETs of the gastrointestinal (GI) system. Gastroenteropancreatic NETs are commonly divided into pancreatic NETs and luminal carcinoid tumors, also known as luminal NETs [1]. As carcinoid tumors arise from neuroendocrine cells along the GI tract, they can also occur within the appendix [2]. NETs of the appendix have features that differentiate this type from other NETs in the rest of the GI tract. These neoplasms are more frequently benign and usually occur at a younger age. They are also associated with the expression of S-100 [3]. NETs are frequently distributed in the distal third of the appendix and can result in luminal obstruction. Diagnosis is generally made following an appendectomy and histological examination of the appendix [4]. Although most NETs of the appendix (aNETs) are small, asymptomatic and slow-growing, they can be aggressive, invasive, and metastatic [5].
Because appendiceal tumors and NETs are uncommon, research has been limited to single-institution data. The existing body of population studies has largely examined data from the 1980s-2000s [5,6]. A recent population-based study showed a 6.4-fold increase in age-adjusted incidence rates of NETs between 1973 and 2012 [6]. Previous epidemiological data showed that aNETs were the most frequent NETs along the GI tract; however, their relative frequency has decreased as a result of a concomitant overall increase in other types of NETs [7]. Given the inconsistent incidence identified in smaller studies and the rate of change in large population-based studies, an updated investigation to clarify the demographic risk factors and current prevalence is needed. In this study, we also investigated clinically relevant symptoms associated with NETs.
Materials and methods
Database
We performed a retrospective cohort analysis using a multiple health system data analytics and research platform (Explorys Inc., Cleveland, OH, USA), developed and prospectively maintained by IBM Corporation, Watson Health [8]. Explorys captures data from the electronic health records of a total of 360 hospitals from 26 healthcare systems in the United States (US). Data from more than 50 million unique patients, representing approximately 15% of the population across all 50 states, are captured and thus provide a broad regional distribution of population. The “Systematized Nomenclature Of Medicine – Clinical Terms” (SNOMED-CT) hierarchy is used to arrange diagnoses, findings and procedures [9], while SNOMED and RxNorm are used to code for drug prescriptions [10]. Access to Explorys is granted to participating healthcare systems. Informed consent was waived since patient data are de-identified. In order to protect patient confidentiality, the database rounds cell counts to the nearest 10. It is worth highlighting that the Explorys database has been used in multiple medical fields, including gastroenterology [11-15].
Patient selection
Using the Explorys platform, we identified a cohort of patients diagnosed with aNETs during the period of December 2014 and December 2019. We also identified a cohort of patients with a first-ever aNET diagnosis during the year from January 2019 to January 2020.
Risk factors, predisposing medical conditions, and GI signs and symptoms
Using SNOMED-CT codes, we identified possible risk factors, predisposing medical conditions, and associated GI signs and symptoms of aNETs suggested by prior literature. Possible risk factors and predisposing medical conditions included alcohol abuse, smoking, diabetes mellitus, obesity, family history of GI cancer, multiple endocrine neoplasia type 1 syndrome (MEN type 1), neurofibromatosis type 1 (NF type 1), Crohn’s disease (CD), and ulcerative colitis (UC). Signs and symptoms included abdominal pain, diarrhea, nausea, vomiting, flushing, GI bleeding, obstruction, perforation, acute appendicitis, intussusception, and volvulus. Given the cross-sectional nature of the study, a temporal relationship with signs and symptoms was difficult to establish.
Statistical analysis
Demographics and associated diseases of our patient cohort were characterized by descriptive statistics. To calculate the overall period prevalence, we divided the total number of individuals with aNET by the total number of individuals in Explorys (2014-2019). The rate of new cases of aNET in the US in the year 2019-2020 was obtained by dividing the number of individuals with a first-ever aNET diagnosis from January 2019 through January 2020 by the total number of individuals in Explorys in the past year, in an attempt to provide a proxy estimate of annual incidence. The odds ratio (OR) for univariate analysis, its standard error and 95% confidence interval (CI) were calculated using the MedCalc Statistical Software with a case-control design (MedCalc Version 19.1.6). To adjust for confounding factors, we constructed a multivariate regression analysis model using the Statistical Package for Social Sciences (SPSS version 25, IBM Corp.). Variables adjusted for were age, sex, race and multiple comorbidities, including tobacco smoking, alcohol abuse, diabetes mellitus, obesity (body mass index >30), family history of GI malignancy, MEN type 1 syndrome, and NF type 1 syndrome. A P-value < 0.05 was considered statistically significant.
Results
A total of 30,324,050 individuals above 18 years old in the database between 2014 and 2019 composed the source population. Of these, 2020 (0.007%) patients had a SNOMED-CT diagnosis of aNET and represented the study group. The baseline characteristics of the patients and the control group are presented in Table 1. The incidence of new cases of aNET in (2019-2020) was 0.4 per 100,000 individuals.
Interval epidemiology of aNETs
aNETs accounted for 0.2% of all NETs. Of the 2020 patients with aNET, the majority were Caucasian...
Neuroendocrine tumors of the appendix
The overall 5-year prevalence was 7 per 100,000 individuals. The prevalence was highest in age group 75-79 (9.4/100,000) (Fig. 1). Caucasians had the highest prevalence (8.8/100,000) compared to African Americans (4.5/100,000) and Asians (0.1/100,000). The prevalence was higher in females (7.4/100,000) compared to males (5.7/100,000). The prevalence of patients who developed carcinoid syndrome was 8.2%, while 35.3% had appendicitis. Right-sided valve disease was present in 10 of the patients who had carcinoid syndrome. Among 550 patients checked for chromogranin A, 190 (34.5%) had an elevated level, while among 470 checked for 5-hydroxyindoleacetic acid, 110 (23.4%) patients tested positive.
### Table 1 Baseline patient characteristics of aNET and control groups
| Characteristics | aNETs | Non-aNETs |
|----------------------------------|-------|-----------|
| N=2020 | N=30,322,020 |
| Age | (%) | (%) |
| 20-24 | 70 (3.5) | 2,018,690 (6.7) |
| 25-29 | 110 (5.4) | 2,370,450 (7.8) |
| 30-34 | 150 (7.4) | 2,379,730 (7.8) |
| 35-39 | 140 (6.9) | 2,335,990 (7.7) |
| 40-44 | 120 (5.9) | 2,160,570 (7.1) |
| 45-49 | 150 (7.4) | 2,225,140 (7.3) |
| 50-54 | 190 (9.4) | 2,311,150 (7.6) |
| 55-59 | 220 (10.9) | 2,589,580 (8.5) |
| 60-64 | 220 (10.9) | 2,564,930 (8.5) |
| 65-69 | 210 (10.4) | 2,338,080 (7.7) |
| 70-74 | 170 (8.4) | 2,002,480 (6.6) |
| 75-79 | 140 (6.9) | 1,493,860 (4.9) |
| 80-84 | 80 (4.0) | 1,094,580 (3.6) |
| 85-90 | 30 (1.5) | 810,570 (2.7) |
| 90+ | 20 (1.0) | 810,570 (2.7) |
| Sex | | |
| Male | 733 (36) | 12,954,076 (43) |
| Female | 1287 (64) | 17,367,944 (57) |
| Race | | |
| Caucasian | 1705 (84.4) | 19,349,990 (63.8) |
| African American | 153 (7.6) | 3,426,260 (11.3) |
| Asian | 17 (0.8) | 505,494 (1.7) |
| Comorbidities | | |
| Tobacco use | 510 (25.2) | 4,539,110 (15.0) |
| Alcohol abuse | 70 (3.5) | 667,330 (2.2) |
| Hypertension | 860 (42.6) | 8,671,060 (28.6) |
| Diabetes mellitus | 330 (16.3) | 3,673,800 (12.1) |
| Metabolic syndrome x | 30 (1.5) | 164,380 (0.5) |
| Obese | 330 (16.3) | 2,008,960 (6.6) |
| primary GI cancer | 690 (34.2) | 201,130 (0.7) |
| Family history of GI cancer | 110 (5.4) | 426,890 (1.4) |
| MEN 1 | 5 (0.2) | 820 (0.003) |
| NF 1 | 5 (0.2) | 3,710 (0.01) |
| Ulcerative colitis | 34 (1.7) | 139,979 (0.5) |
| Crohn’s disease | 51 (2.5) | 163,212 (0.5) |
### Table 2 Risk factors for neuroendocrine tumors of the appendix using univariate analysis
| Risk factors | OR | 95%CI | P-value |
|-------------------------------------|------|--------|---------|
| Age >65 years old | 1.12 | 1.01-1.23 | 0.0246 |
| Female sex | 1.30 | 1.19-1.42 | <0.001 |
| Caucasian race | 3.35 | 2.95-3.81 | <0.001 |
| Alcohol abuse | 1.58 | 1.25-2.01 | <0.001 |
| Smoking | 1.91 | 1.69-2.15 | <0.001 |
| Obesity | 2.81 | 2.50-3.16 | <0.001 |
| Diabetes mellitus | 1.41 | 1.25-1.59 | <0.001 |
| Family history of primary GI cancer | 3.99 | 3.30-4.84 | <0.001 |
| MEN type 1 | 90.56| 37.55-218.38 | <0.001 |
| NF type 1 | 20.01| 8.32-48.16 | <0.001 |
| Ulcerative colitis | 4.29 | 3.14-5.87 | <0.001 |
| Crohn’s disease | 4.62 | 3.49-6.11 | <0.001 |
OR odds ratio; CI, confidence interval; GI, gastrointestinal; MEN, multiple endocrine neoplasm; NF, neurofibromatosis.
Univariate analysis for risk factors and predisposing medical conditions
Patients with aNET were more likely to be Caucasian and female (Table 2). Patients who developed aNET were more likely to have a history of smoking and alcohol abuse. In terms of predisposing medical conditions, individuals with aNET were more likely to have a diagnosis of obesity, diabetes mellitus, UC, CD, MEN type 1, NF type 1, and family history of GI cancer (Table 2).
Multivariate analysis for risk factors and predisposing medical conditions
In a multivariate regression analysis model to adjust for confounding factors, there was no difference in the risk of aNET between adults (18-65 years) and elderly patients (age >65 years). However, patients who developed aNET were more likely to be female (OR 1.36, 95%CI 1.24-1.49), Caucasian (OR 2.71, 95%CI 2.40-3.07), with a history of smoking (OR 1.82,
95%CI 1.65-2.01), family history of primary GI malignancy (OR 7.26, 95%CI 6.31-8.33), diagnosis of MEN type 1 (OR 52.31, 95%CI 23.15-118.23), or NF type 1 (OR 16.37, 95%CI 7.24-37.01) (Fig. 2).
**Associated GI signs and symptoms**
Patients diagnosed with aNET were more likely to exhibit nausea, vomiting, abdominal pain, diarrhea, and flushing.
They were also more likely to have abdominal obstruction, GI bleeding, acute appendicitis, GI perforation, intussusception, and volvulus (Fig. 3).
**Discussion**
In this study of 2020 patients with aNETs, we found that the greatest distribution of aNET patients occurred in the age range of 50-80 years old. Common symptoms associated with aNET included abdominal pain, acute appendicitis, and nausea. Significant risk factors for aNET were MEN type 1, NF type 1, family history of primary GI cancer, Caucasian race, smoking, and female sex.
The majority of the available reported incidence rates of aNETs are based on the Surveillance, Epidemiology, and End Results (SEER) program. In the analysis of the SEER database between 1973 and 1997, Maggard et al found a relatively stable age-adjusted incidence of aNETs between 1973 (1.2 per million) and 1997 (2.1 per million) compared to other sites [7]. There was a rise in the incidence of rectal, gastric and small bowel carcinoids, with a concomitant decrease in the percentage of appendiceal carcinoid tumors. More specifically, 31.8% of all carcinoids were located in the appendix between the period 1973 to 1979, compared with 12.0% in the period of 1990-1997 [7]. Subsequent analysis of the same database between 1973 and 2003 showed an age-adjusted incidence of 0.58 per 1,000,000 people per year [5].
In the most recent analysis from the SEER database, for the period between 2000 and 2009, Marmor et al reported annual incidences of aNETs of 0.17 and 0.27 per 100,000 individuals in 2000 and 2009, respectively [16]. The decrease in age-adjusted incidence is perhaps attributable to the fact that incidental appendectomies were more commonly done in the past. In our study, we found that the overall incidence between January 2019 and January 2020 was 0.4 per 100,000, higher than previously reported. While this might be attributed to the differences in databases, as the SEER program includes only malignant forms of carcinoid tumors, it may also reflect a rise in the incidence of aNETs [5,6].
Large population studies evaluating trends in the incidence of aNETs during the period 1983-1998 identified a higher incidence in younger individuals: 15-19 years of age in women and 20-29 years of age in men [17]. In a review by Goede et al the average age for aNET diagnosis was in the fourth decade of life [4], and in another large study with 11,427 carcinoid tumors the average age of patients with aNETs was 54.4 years [7]. Our data revealed a greater prevalence in the 50-80 age range. These differences could be a result of shifting incidence rates across decades, as the current population studies concerning carcinoid tumors have largely been based on data from the 1980s-2000s. Given the evidence of incidence changes reported in the 2000s, there may have been changes in the prevalence across the past 2 decades. The prevalence of aNETs in review articles is reported to be 0.2-0.9% in patients undergoing appendectomy [3,4]. The 20-year prevalence of aNETs between 1993-2012, based on the SEER database, was 2 per 100,000 persons [6]. In our study, we found a higher period prevalence of 7 per 100,000 individuals. As
mentioned previously, this may reflect a rising prevalence, but the difference might also be related to the inclusion of only malignant forms of carcinoid tumors in the SEER program.
Comparing the prevalence of aNETs in other countries, a prospective study in Austria over a one-year period, performed by Niederle et al reported a rate of 0.08 per 100,000 malignant aNETs in 2004 [18]. Taal et al reported the age-standardized incidence of NETs to be 1.8 and 1.9 per 100,000 for Dutch males and females, respectively, among which aNETs accounted for 27% of total cases [19]. Comparable incidences were reported in a study conducted in Sweden, with 0.4 and 0.8 per 100,000 for males and females, respectively [17]. In comparison, Ploeckinger et al demonstrated that aNETs accounted for 3.2% in a cohort of 1236 patients in Germany [20], similar to a Taiwanese study that reported a prevalence of 3.6% of aNETs among a cohort of 2187 NETs [21]. A slightly higher prevalence was reported in Argentina in a study conducted by O'Connor et al who reported a prevalence of 7.6% of aNETs among a cohort of 461 patients with gastroenteropancreatic NET [22]. A recent Turkish study showed that aNETs account for 0.39% of total appendectomies, consistent with the prior literature (0.2-0.7%) and comparable to the prevalence in our study (0.2% of total NETs) [23].
Several articles have noted that the incidence of aNETs is higher in the female population, which may be an effect of higher appendectomy rates in younger women [4,5,7]. Analysis of racial distribution showed that Caucasian patients account for the majority of cases of aNETs: 87% of the cases in SEER analysis between 1988 and 2003. In our study, we found a higher rate of developing aNETs among females compared to males (7.4 vs. 5.7/100,000) and a higher rate in Caucasian (8.8/100,000) compared to other races. Based on the multivariate analysis model, we found female sex and Caucasian race are more likely to be associated with aNETs.
Risk factors and associated medical comorbidities are not commonly discussed in the literature, probably because NETs are incidental findings. There are few studies that have explored the association between hypertension, smoking and developing aNETs. The primary discussion in the literature lies with carcinoid syndrome and its effect on the heart due to the secretion of serotonin when tumors have invaded the liver. In these cases, blood pressure can be labile, with hypertension or hypotension. The rate of hypertension in cancer patients is similar to that in the general population (29%); however, the prevalence is higher in patients who have undergone chemotherapy (37%) [24]. Given that the prevalence of hypertension is elevated compared to the general population, further research is needed to understand its significance in patients with NETs. Tobacco smoking is a well-known risk factor for multiple neoplasms; however, little is known about its effect on the development of NETs. A few small studies showed an approximately twofold greater risk of developing GI NETs [25,26]. In a larger case-control study, Rinzivillio et al demonstrated a proportional positive association between the amount of smoking and the risk of small bowel NETs [27]; however, other studies did not reach the same conclusion [28].
In our study, smoking was more strongly associated with aNETs, even after adjusting for genetic syndromes and family history of primary GI malignancy. Obesity and diabetes are established risk factors for the development of NETs, and this is consistent with our findings [29]. Furthermore, we found that patients with aNETs are more likely to have other GI malignant tumors. The literature is limited in regard to the association of aNET with extra-appendiceal GI cancers.
A previous study of risk factors associated with NETs identified a family history of neoplasm [28]. In this study, we also found significantly greater odds of aNET associated with a family history of GI cancer, after adjusting for multiple confounders. Furthermore, a family history of carcinoid tumors was found to be associated with a greater risk of developing NETs, as well as other cancers [30]. It is known that NETs have some association with MEN type 1 syndrome, and this was demonstrated in the current study [17]. NF type I is linked to a higher risk of pancreatic and luminal NETs, more prominently reported in the ampulla of Vater as well as the appendix [31], consistent with our findings.
Inflammatory bowel disease (IBD), including UC and CD, is well-known to predispose to the development of adenocarcinoma of the colon [32]. Several reports linked IBD to a greater risk of NETs, based on the finding of elevated numbers of neuroendocrine cells in inflamed mucosa. It has been suggested that long-standing inflammation is directly responsible for the development of NETs, in a similar fashion to the underlying pathophysiology of colorectal neoplasm [33-35]. In a prospective study conducted in Spain, which included 590 patients with IBD followed for 7 years, 80 patients developed different cancers. The relative risk for developing NETs in patients with IBD was 13.1 (95% CI 1.82-29.7) [36]. Using a univariate analysis model, we found that patients with IBD are at higher risk of developing aNETs. The risk was comparable between CD and UC patients.
There are a few limitations to this study that largely stem from the nature of the database. Data entry and classification can be a source of potential bias and may influence the true estimates of diseases. Unfortunately, patients’ information in the database is de-identified and pathology results cannot be verified for each corresponding patient, while survival data are also not available in Explorys. However, it is important to note that, compared to ICD coding, SNOMED-CT allows for more concepts to be coded per clinical document, making it more accurate in terms of documenting diagnoses and pertinent patient information. Moreover, Explorys has been validated and used in multiple specialties, including gastroenterology [37-39]. Despite the aforementioned limitations, it is worth highlighting that this is the largest and one of the few studies to date to evaluate the epidemiology, and risk factors of patients with aNETs in the US population. In comparison to the SEER database, which includes only malignant pathologies, Explorys captures both benign and malignant pathologies. The data also provide a much-needed update to the existing body of population studies, which has largely focused on data from the 1980s-2000s. We also report symptoms associated with the aNET population, not commonly identified in the literature. Using multivariate analysis, several steps were implemented to avoid confounding bias.
In conclusion, this is the largest study to date utilizing a non-SEER database to evaluate the epidemiology, risk factors,
Summary Box
**What is already known:**
- Gastroenteropancreatic neuroendocrine tumors (NETs) are divided into pancreatic NETs and luminal carcinoid tumors
- The majority of epidemiological studies are based on the Surveillance, Epidemiology, and End Results database
**What the new findings are:**
- The overall prevalence of NET of the appendix (aNET) was 7 per 100,000 persons, while the incidence during a single year (January 2019 to January 2020) was 0.4 per 100,000 individuals
- Common symptoms associated with aNET included abdominal pain, acute appendicitis and nausea
- Significant risk factors for aNET were multiple endocrine neoplasia type 1, neurofibromatosis type 1, family history of gastrointestinal cancer, Caucasian race, smoking, and female sex
References
1. Gluckman CR, Metz DC. Gastric neuroendocrine tumors (carcinoids). *Curr Gastroenterol Rep* 2019;21:13.
2. Tchana-Sato V, Detry O, Polus M, et al. Carcinoid tumor of the appendix: a consecutive series from 1237 appendectomies. *World J Gastroenterol* 2006;12:6699-6701.
3. Carr NJ, Sobin LH. Neuroendocrine tumors of the appendix. *Semin Diagn Pathol* 2004;21:108-119.
4. Goede AC, Caplin ME, Winslet MC. Carcinoid tumour of the appendix. *Br J Surg* 2003;90:1317-1322.
5. Mullen JT, Savarese DM. Carcinoid tumors of the appendix: a population-based study. *J Surg Oncol* 2011;104:41-44.
6. Dasari A, Shen C, Halperin D, et al. Trends in the incidence, prevalence, and survival outcomes in patients with neuroendocrine tumors in the United States. *JAMA Oncol* 2017;3:1355-1342.
7. Mazzardi MA, O’Connell JB, Ko CY. Updated population-based review of carcinoid tumors. *Ann Surg* 2004;240:117-122.
8. IBM Corporation. The IBM Explorers Platform: liberate your healthcare data. Available from: https://www.ibm.com/downloads/cas/4P0QB9JN [Accessed 13 May 2021].
9. US National Library of Medicine Unified Medical Language System (UMLS). Systematized Nomenclature of Medicine–Clinical Terms (SNOMED CT). Available from: https://www.nlm.nih.gov/research/umls/Snomed/snomed_main.html [Accessed 13 May 2021].
10. Nelson SJ, Zeng K, Kilbourne J, Powell T, Moore R. Normalized names for clinical drugs: RxNorm at 6 years. *J Am Med Inform Assoc* 2011;18:441-448.
11. Al-Kindi SG, Oliveira GH. Prevalence of preexisting cardiovascular disease in patients with different types of cancer: the unmet need for onco-cardiology. *Mayo Clin Proc* 2016;91:81-83.
12. Mahadevan U, Martin CF, Dubinsky M, Kane SV, Sands BE, Sandborn W. 960 Exposure to anti-TNF therapy in the third trimester of pregnancy is not associated with increased adverse outcomes: results from the PIANO registry. *Gastroenterology* 2014;146:S5-170.
13. Al-taii H, Al-Kindi SG, Oliveira GH, et al. Aspirin use and risk of cholangiocarcinoma: External validation with big data. *Hepatology* 2017;65:1241-1242.
14. Alkhayyat M, Abu Saleh M, Aggarwal M, et al. Pancreatic manifestations in rheumatoid arthritis: a national population-based study. *Rheumatology (Oxford)* 2021;60:2366-2374.
15. Alkhayyat M, Aburessh M, Gill A, et al. Lower rates of colorectal cancer in patients with inflammatory bowel disease using Anti-TNF therapy. *Inflamm Bowel Dis* 2021;27:1052-1060.
16. Marmor S, Portschy PR, Tuttle TM, Vignir BA. The rise in appendiceal cancer incidence: 2000-2009. *J Gastrointest Surg* 2015;19:743-750.
17. Hemminki K, Li X. Incidence trends and risk factors of carcinoid tumors: a nationwide epidemiologic study from Sweden. *Cancer* 2001;92:2204-2210.
18. Niederle MB, Hackl M, Kasner K, Niederle B. Gastroenteropancreatic neuroendocrine tumours: the current incidence and staging based on the WHO and European Neuroendocrine Tumour Society classification: an analysis based on prospectively collected parameters. *Endocr Relat Cancer* 2010;17:909-918.
19. Taal BG, Visser O. Epidemiology of neuroendocrine tumours. *Neuroendocrinology* 2004;80 (Suppl 1):3-7.
20. Ploeckinger U, Kloeppel G, Wiedenmann B, Lohmann R; representatives of 21 German NET Centers. The German NET-registry: an audit on the diagnosis and therapy of neuroendocrine tumours. *Neuroendocrinology* 2009;90:349-363.
21. Tsal HJ, Wu CC, Tsai CR, Lin SF, Chen LT, Chang JS. The epidemiology of neuroendocrine tumours in Taiwan: a nation-wide cancer registry-based study. *PLoS One* 2013;8:e62487.
22. O’Connor JM, Marmissolle F, Bestani C, et al. Observational study of patients with gastroenteropancreatic and bronchial neuroendocrine tumours: a nationwide epidemiologic study from Sweden. *Cancer* 2001;92:2204-2210.
23. Bayhan Z, Yildiz YA, Akdeniz Y, et al. Appendix neuroendocrine tumor: retrospective analysis of 4026 appendectomy patients in a single center. *Emerg Med Int* 2020;2020:4030527.
24. Mouhayer E, Saharaeddin A. Hypertension in cancer patients. *Tex Heart Inst J* 2011;38:263-265.
25. Faggiano A, Ferolla P, Grimaldi F, et al. Natural history of gastroentero-pancreatic and thoracic neuroendocrine tumors. Data from a large prospective and retrospective Italian epidemiological study: the NET management study. *J Endocrinol Invest* 2012;35:817-823.
26. Kaerlev L, Teglbjaerg PS, Sabroe S, et al. The importance of smoking and medical history for development of small bowel carcinoid tumor: a European population-based case-control study. *Cancer Causes Control* 2002;13:27-34.
27. Rinzivillo M, Capuro G, Campana D, et al. Risk and protective
factors for small intestine neuroendocrine tumors: a prospective case-control study. *Neuroendocrinology* 2016;103:531-537.
28. Hassan MM, Phan A, Li D, Dagohoy CG, Leary C, Yao JC. Risk factors associated with neuroendocrine tumors: A U.S.-based case-control study. *Int J Cancer* 2008;123:867-873.
29. Leoncini E, Carioli G, La Vecchia C, Boccia S, Rindi G. Risk factors for neuroendocrine neoplasms: a systematic review and meta-analysis. *Ann Oncol* 2016;27:68-81.
30. Hiripi E, Bermejo JL, Sundquist J, Hemminki K. Familial gastrointestinal carcinoid tumours and associated cancers. *Ann Oncol* 2009;20:950-954.
31. Basile U, Cavallaro G, Polistena A, et al. Gastrointestinal and retroperitoneal manifestations of type 1 neurofibromatosis. *J Gastrointest Surg* 2010;14:186-194.
32. Nadeem MS, Kumar V, Al-Abbasi FA, Kamal MA, Anwar F. Risk of colorectal cancer in inflammatory bowel diseases. *Semin Cancer Biol* 2020;64:51-60.
33. Grassia R, Bodini P, Dizioli P, et al. Neuroendocrine carcinomas arising in ulcerative colitis: coincidences or possible correlations? *World J Gastroenterol* 2009;15:4193-4195.
34. West NE, Wise PE, Herline AJ, Muldoon RL, Chopp WV, Schwartz DA. Carcinoid tumors are 15 times more common in patients with Crohn's disease. *Inflamm Bowel Dis* 2007;13:1129-1134.
35. Freeman HJ. Appendiceal carcinoids in Crohn's disease. *Can J Gastroenterol* 2003;17:43-46.
36. Algaba A, Guerra I, Castaño A, et al. Risk of cancer, with special reference to extra-intestinal malignancies, in patients with inflammatory bowel disease. *World J Gastroenterol* 2013;19:9359-9365.
37. Khoudari G, Alkhayyat M, Abou Saleh M, et al. The epidemiology of pancreatic cancer and the association with acetylsalicylic acid in the United States: a population-based study. *Pancreas* 2020;49:1207-1212.
38. Khoudari G, Mansoor E, Click B, et al. Rates of intestinal resection and colectomy in inflammatory bowel disease patients after initiation of biologics: a cohort study. *Clin Gastroenterol Hepatol* 2020 Oct 14 [Online ahead of print], doi: 10.1016/j.cgh.2020.10.008.
39. Khan D, Abureesh M, Alkhayyat M, et al. Prevalence of myocardial infarction in patients with chronic pancreatitis. *Pancreas* 2021;50:99-103. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3205,
1
],
[
3205,
8157,
2
],
[
8157,
13553,
3
],
[
13553,
13901,
4
],
[
13901,
17092,
5
],
[
17092,
24010,
6
],
[
24010,
29393,
7
],
[
29393,
31620,
8
]
]
} |
697ca4a49035273381eaaab2a0579746e68e3ca7 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 6,
"total-fallback-pages": 0,
"total-input-tokens": 20202,
"total-output-tokens": 7725,
"fieldofstudy": [
"Medicine",
"Biology"
]
} | Protein Expression of DNA Damage Signaling Molecules in Patients with Oral Squamous Cell Carcinoma
Jigna S Joshi1, Hemangini H Vora2, Nandita R Ghosh3, Jignesh V Goswami4 and Trupti Trivedi*1
1Clinical Carcinogenesis Lab, Gujarat Cancer and Research Institute, Asarwa, Ahmedabad, India
2Immunohematology Lab, Gujarat Cancer and Research Institute, Asarwa, Ahmedabad, India
3Tumor biology Lab, Gujarat Cancer and Research Institute, Asarwa, Ahmedabad, India
4Department of Surgical Oncology, Gujarat Cancer and Research Institute, Asarwa, Ahmedabad, India
Abstract
Purpose: Oral squamous cell carcinoma (OSCC) is mainly attributable to tobacco use which may cause errors in DNA synthesis leading to mutation. Eukaryotic cells have evolved the pathways to detect such damages. Disturbance in DNA damage signaling molecules might play a fundamental role in the pathogenesis of OSCC. Therefore, our aim of this study is to evaluate the protein expression of Mre11, Rad50, H2AX, 53BP1 and BRCA1 in patients with OSCC.
Materials and Method: Protein expression of Mre11, Rad50, H2AX, 53BP1 and BRCA1 were studied immunohistochemically from paraffin embedded tumor tissues of 100 patients with OSCC. Expression was scored by modified histo-score (H-score). Data were evaluated statistically using SPSS software.
Results: Nuclear protein expression was observed for the Mre11, Rad50, H2AX and 53BP1 while cytoplasmic expression was observed for BRCA1 protein. Significant association was observed between Mre11 protein expression and nodal extension (p=0.019), Rad50 protein expression and advance disease stage (stage I/II; p=0.015), 53BP1 protein expression and buccal mucosa cancer (p=0.045). Further, amongst all the studied biomarkers, Mre11 was significantly associated with reduced relapse free survival (RFS) in both univariate (p=0.045) and multivariate survival (p=0.040) analysis. None of the other studied DNA damage signaling molecules were associated with reduced relapse or death rate after the adjuvant therapies.
Conclusion: Our results suggests that amongst all studied signaling molecules strong expression of Mre11 protein is associated with increased recurrence rate suggesting it might be used as prognostic tool in the analysis of tumor specimen of OSCC.
Keywords: Oral squamous cell carcinoma; Mre11; Rad50; H2AX; BRCA1; 53BP1.
Introduction
High incidence of oral squamous cell carcinoma (OSCC) is attributable to high prevalence of life style habits such as smoking, chewing tobacco and high alcohol consumption which functions as a cofactor. As a result of that every cell in the body experiences DNA damages such as single stranded breaks (SSBs) and double-strand breaks (DSBs). Such damages are particularly harmful to the cell as they causes base pair mismatch which is strongly associated with cancer susceptibility [1]. DNA damage can
have deleterious effects, as it interferes with DNA replication and transcription and ultimately results in mutations and chromosomal aberrations. In dividing cells, if DNA damages are not repaired, causes errors during DNA synthesis leading to mutations that can give rise to cancer. Thus, individuals with an inherited impairment in DNA repair capability are often at increased risk of cancer [2].
Previously, we have identified a mediator of DNA damage check point protein (MDC1) as a significant predictor of OSCC [3]. Therefore, we hypothesized that deficiencies in DNA damage signalling molecules might play fundamental roles in the pathogenesis of OSCC. These include several sensor proteins like Mre11, Rad50, H2AX, 53BP1 and BRCA1. Mre11 is a core protein of the MRN complex, co-localize at the site of DNA DSBs along with Nibrin and Rad50 and forms distinctive foci upon ionizing radiation [4-6]. Rad50 acts as a bridge at the junction of DNA DSBs and facilitates the recognition and processing of broken DNA ends by Mre11 exonuclease activity and holds the broken strand of DNA together during the repairing process [4]. Earlier, in head & neck cancers, Rad50 has been explored as a potential therapeutic target [7]. When mutation occurs in Rad50 gene it leads to the formation of an abnormally small, non-functional version of Rad50 protein. Further, one of the earliest steps in the cellular response to DSBs is the phosphorylation of histone H2AX at serine 139, resulting in γH2AX [8]. During 30 minutes after DSB formation, large numbers of γ-H2AX molecules form in the chromatin around the break site, creating a focus where proteins involved in DNA repair accumulate [9]. 53BP1 is known to be an activator of p53 [10]. However, 53BP1 also has p53 independent functions, and deletion of both 53BP1 and p53 has a synergistic effect on tumor development and was considered to induce apoptosis by activating tumor-suppressor gene p53 [11] but recently, it has been found that 53BP1 plays a critical role in the DNA damage repair to maintain cell genomic stability and in prevention of tumor development [12,13]. BRCA1 is tumor suppressor and genome guardian protein [14]. It participates in processes such as cell cycle checkpoint; activation; transcription regulation and DNA repair [15]. Nuclear BRCA1 functions in transcriptional regulation, DNA damage response, repair and cell proliferation [16]. When localized in the cell cytoplasm triggers apoptosis via a p53-independent mechanism in human breast cancer cells [17,18], BRCA1 gets fused to RAD51 and gets phosphorylated. This interaction between BRCA1 and RAD51 suggests a possible participation in the detection and recombination of DSBs.
On the basis of this information the aim of the present study was to investigate the association between the expression of Mre11, Rad50, H2AX, 53BP1 and BRCA1 status and various clinicopathological parameters in cohort of patients with OSCC and to evaluate the prognostic relevance of all variables in terms of survival.
**Material and Methods**
**Patients**
A total of 100 previously untreated patients with histopathologically confirmed OSCC of tongue and buccal mucosa enrolled at The Gujarat Cancer & Research Institute (GCRI) between year 2011 and 2014 were included in the study. Written consent of the patients prior to surgery was obtained. Clinical and pathological details were documented in a predesigned performa; which included age, gender and anatomic site, clinical TNM staging (tumor, node, and metastasis classification of malignant tumors according to American Joint Committee on Cancer), nodal status and histopathological differentiation. Out of 100 OSCC patients, 20% (20/100) patients had stage I, 22% (22/100) of patients had stage II, 18% (18/100) patients had stage III and 40% (40/100) patients had stage IV disease in current study. Postoperative treatment included radiotherapy and chemotherapy, instituted by the radiotherapy and medical oncology units of the GCRI, respectively (Table 1).
**Follow-up study**
Follow-up status of the patients was verified and regularly updated from the patients’ case files maintained at the GCRI. Patients were monitored for a minimum period of 24 months from the date of diagnosis for survival analysis. Out of 100, only 90 patients could be followed for a minimum period of 24 months or died within that period were included for overall survival (OS) analysis out of which 43% (39/90) patients died within that period. While, out of them 12 patients who died because of the persistent disease within 24 months were omitted for relapse free survival (RFS) analysis. Thus, RFS was carried out in total 78 patients. Out of them 41% (32/78) patients developed recurrence within that period. RFS was expressed as the number of months from the date of surgery to the loco-regional relapse (Table 1).
| Parameters | Total patients N (%) |
|------------|----------------------|
| Age (Range: 21-81 years) | 100 (100) |
| Median : 45 Years | 47 (47) |
| ≤45 | 53 (53) |
| Gender | 75 (75) |
| Male | 25 (25) |
| Female | 61 (61) |
| Anatomic site | 39 (39) |
| Tongue | 14 (14) |
| Buccal mucosa | 86 (86) |
| Tobacco habit | 71 (71) |
| Absent | 29 (29) |
| Present | 20 (20) |
| Tumor stage | 22 (22) |
| T1/T2 | 18 (18) |
| T3/T4 | 40 (40) |
| Nodal status | 59 (59) |
| Negative | 41 (41) |
| Histologic grade | 50 (50) |
| Well differentiated | 50 (50) |
| Moderate/Poorly differentiated | 100 (100) |
| Treatment | 54 (54) |
| Surgery (s) followed by | 30 (30) |
| RT | 54 (54) |
| RT+CT | 30 (30) |
Interpretation of IHC
Paraffin embedded section of OSCC tumor tissues (N=100) with 4-μm thickness were collected on 3-aminopropyltriethoxysilane-coated glass slides. Immunostaining was performed on sections as described previously [19]. Briefly, sections were deparaffinized in xylene and rehydrated in graded alcohol. The sections were incubated with hydrogen peroxide solution prepared in methanol for 15 minutes to quench the endogenous peroxidase activity and then cooked for 10 minutes with 10mM tri-sodium citrate buffer (pH-6.0) in boiling water bath for antigen retrieval. Thereafter, slides were incubated with primary antibodies at 4°C overnight in a moist chamber. Before applying primary antibody, non specific conjugations were blocked using rabbit specific HRP/DAB (ABC) detection IHC kit (Abcam, Cambridge, UK). Primary antibodies with the appropriate dilution used in the study are depicted in Table 2. Antibody detection was achieved using 3, 3’-diaminobenzidin (DAB) as chromogen, counter stained with Mayer’s haematoxylin, dehydrated in ethanol, mounted in dibutyl phthalate xylene (DPX), cover slipped and then observed under light microscope. As a positive control tissue section with intense staining for the given marker was included with each staining procedure while, for negative control, the primary antibody was replaced with tris-buffered saline.
Table 2. Primary antibodies used for expression of DNA damage signaling molecule
| Antigen | Primary antibody | Dilution | Staining pattern |
|---------|-----------------|----------|-----------------|
| Mre11 | Rabbit monoclonal, clone:31H4 (Cell signaling technology, 4847) | 1:50 | Nuclear |
| Rad50 | Mouse monoclonal, clone:1383 (Genetex, GTX70228) | 1:50 | Nuclear |
| H2AX | Rabbit monoclonal, clone: EPR89S (Genetex, GTX62983) | 1:1000 | Nuclear |
| BRCA1 | Mouse monoclonal, clone:GLK-2 (Santa cruz biotechnology, sc-56030) | 1:10 | Cytoplasmic |
| 53BP1 | Rabbit polyclonal (Invitrogen, A14034) | 1:200 | Nuclear |
Results
Incidence of protein expression and correlation with clinicopathological parameters
In the set of 100 OSCC patients of the current study, the incidence of protein expression of DNA damage signaling molecules was at following rates; Mre11 68% (68/100), Rad50 87% (87/100), BRCA1 82% (86/100) while for H2AX and 53BP1 it was 100% (100/100). Amongst studied molecules, nuclear protein expression was observed for Mre11, Rad50, H2AX and 53BP1 while cytoplasmic protein expression was observed for BRCA1 in patients with OSCC (Figure 1).
Correlation between biomarker expression and clinicopathological parameters
Clinicopathological characteristics of the OSCC patients included in the present study was age, gender, site of tumor, habit, tumor size, clinical stage, nodal status and tumor differentiation. Strong expression of Mre11 protein was significantly higher in patients with nodal extension (p=0.019; Figure 2A) whereas protein expression of Rad50 was significantly higher in patients with advanced stage disease (p=0.015; Figure 2B). Strong expression of 53BP1 protein was significantly higher in patients with buccal mucosa cancer as compared to patients with tongue carcinoma (p=0.045; Figure 2C). However, neither strong nor weak expression of H2AX, BRCA1 was associated with any of the clinicopathological parameters mentioned above. Protein expression of combined DNA damage signaling molecule analysis results are depicted in Table 3, which indicated that Rad50 was significantly positively correlated with H2AX (p=0.008) and 53BP1 (p=0.024). While, H2AX was...
significantly positively correlated with 53BP1 (p=0.001). However, expression of Mre11 protein expression did not show any significant correlation with protein expression of other studied DNA damage signaling molecules.
Table 3. Intercorrelation of DNA damage signaling molecules in patients with OSCC
| | Mre11 | Rad50 | H2AX | BRCA1 |
|--------|---------|---------|---------|---------|
| Rad50 | r +0.060| | | |
| p | 0.552 | | | |
| H2AX | r +0.113| +0.263 | | |
| p | 0.263 | 0.008* | | |
| BRCA1 | r -0.105| +0.161 | +0.049 | |
| p | 0.297 | 0.111 | 0.625 | |
| 53BP1 | r +0.110| +0.226 | +0.341 | +0.085 |
| p | 0.277 | 0.024* | 0.001* | 0.402 |
*statistically significant
Survival analysis
Univariate Kaplan-Meier survival analysis revealed that patients with strong expression of Mre11 protein had a significant reduced RFS (p=0.045; Table 4; Figure 3) whereas none of the other studied DNA damage signaling molecules were associated with reduced relapse. However, Mre11 failed to show any significant association with overall survival (Figure 4). At the same time all of the studied biomarker Mre11, Rad50, BRCA1, H2AX and 53BP1 failed to show any significant association with shorter OS in patients with OSCC. However, multivariate survival analysis by Cox regression forward step wise model showed Mre11 as a significant independent prognosticator in predicting reduced relapse rate in patients with OSCC (B= 0.764, HR=2.147, p=0.040).
Table 4. Univariate relapse free survival analysis of DNA damage signaling molecules using Kaplan-Meier survival function in patients with OSCC
| Variables | N=78 | Patients Relapsed N (%) | Log-rank | df | p |
|-----------|------|-------------------------|----------|----|-------|
| Mre-T1 | | | | | |
| Weak | 37 | 11 (30) | 4.006 | 1 | 0.045 |
| Strong | 41 | 21 (51) | | | |
| Rad-50 | | | | | |
| Weak | 38 | 15 (39) | 0.091 | 1 | 0.763 |
| Strong | 40 | 17 (42) | | | |
| H2AX | | | | | |
| Weak | 44 | 17 (39) | 0.298 | 1 | 0.585 |
| Strong | 34 | 15 (44) | | | |
| BRCA1 | | | | | |
| Weak | 44 | 19 (43) | 0.183 | 1 | 0.669 |
| Strong | 34 | 13 (38) | | | |
| 53BP1 | | | | | |
| Weak | 50 | 21 (42) | 0.076 | 1 | 0.783 |
| Strong | 28 | 11 (35) | | | |
Survival analysis in relation to treatment offered
Kaplan-Meier univariate survival analysis did not show any significant correlation of protein expression of studied DNA damage signaling molecules with RFS or OS when treated with surgery followed by either radiotherapy or chemo-radiotherapy in patients with OSCC (data not shown).
Discussion
Numerous factors are thought to be involved in DNA damage signalling, processing and repair. However, present study evaluated clinical significance of DNA damage sensor molecules such as Mre11, Rad50, H2AX, BRCA1 and 53BP1 and correlated with various clinicopathological parameters and analyzed its role in the disease outcome. In the present study, a significant high incidence of strong Mre11 protein expression
was found in patients with lymphnode positivity than patients with lymphnode negativity indicating its association with aggressive tumor behavior. Additionally, in patients with serous ovarian cancer also, a significant high expression of Mre11 was noted in moderately differentiated tumors [20]. In current study, a significant high incidence of strong Rad50 protein expression was found in patients with advanced stage (stage III/IV) disease indicating its expression increases with disease advancement. In accordance, Ali-Fehmi et al observed an association of Rad50 protein expression with advanced disease stage in patients with ovarian cancer [21]. However, BRCA1 protein expression was not significantly correlated with any of the clinicopathological parameters in current study. In serous ovarian cancer, strong BRCA1 protein expression was significantly correlated with advanced stage disease and suggested its utility as prognostic factor in analysis of tumor biopsies and in determination of circulating tumor cells [21]. Further, a significant high incidence of strong 53BP1 protein expression was observed in patients with buccal mucosa cancer suggested an association of 53BP1 expression with excessive DNA damage to buccal mucosa due to longer exposure of tobacco to the buccal mucosa as compared to tongue. In lung adenocarcinoma, 53BP1 was correlated with advanced tumor stage, habit of cigarette smoking and lymphovascular invasion reflecting its association with increased tumor cell growth, metastasis and poor prognosis [22].
Univariate survival analysis by Kaplan-Meier revealed that strong Mre11 protein expression was significantly associated with high incidence of disease relapse in patients with OSCC. On the other hand, few studies on Mre11 expression have suggested an association of high Mre11 expression with improved survival rate in patients with colorectal cancer, breast cancer and bladder cancer [23,24]. Such discrepancy in the results might be because of difference in cell morphology, scoring method, patient inclusion criteria and treatment and geographical difference of conducted study. It has been also observed that germ line mutations in Mre11 complex genes lead to hereditary susceptibility to breast and/or ovarian cancer development which may play a role in other cancers too [25]. While, univariate survival analysis failed to show significant difference in incidence of disease relapse and death with Rad50, BRCA1 protein expression in OSCC patients which might be because of the either mutation in Rad50 gene or the activation of apoptotic pathway in which DSb repair pathways are blocked. Additionally, Rad50 is associated with several proteins such as BRCA1, ATM and CHK2 responsible for the hereditary susceptibility to ovarian and breast cancer development [25]. The present study did not show prognostic significance of the H2AX on disease relapse and death in OSCC patients. Further, a contradictory study showed that a significant reduced OS was observed in OSCC patients with positive expression of γH2AX protein [26]. The γH2AX also did not show significant association with disease outcome in patients with colorectal cancer, however, a tendency of worse survival was observed in those patients who had loss of γH2AX and underwent the pre-operative radiotherapy suggesting that DSb repair deficient tumors were radioresistant [27]. Further, higher levels of γH2AX proved as a significant predictor for reduced OS in patients with non-small cell lung cancer, triple negative breast cancer and in endometrial cancer [28]. The possible reason of such difference in finding could be due to the phosphorylation of H2AX which occurs only after the development of DNA DSBs [26]. Further, Chen et al reported BRCA1 in 17 breast tumors and these tumors exhibited cytoplasmic expression of BRCA1 suggested such aberrant staining pattern could be due to the intragenic mutation which ultimately leads to the loss of function of BRCA1 protein in patients with breast cancer [29]. In current study, 53BP1 protein expression did not show any significant correlation with RFS and OS in patients with OSCC. In pancreatic cancer, 53BP1 expression was not found to be correlated with various clinicopathological parameters and patients’ survival. However, low expression of 53BP1 protein expression was found to modify the prognostic value of other predictive factors of pancreatic cancer such as level of CA 19-9 and lymphnode ratio (LNR) in such a way that high CA 19-9 and high LNR were associated with worse OS in pancreatic cancer while, with high 53BP1, LNR and CA19-9 were no longer associated with OS [30].
In relation to treatment, Mre11, Rad50, H2AX, BRCA1 and 53BP1 protein expression failed to demonstrate reduced relapse or death rate in subgroup of patients treated with surgery alone, surgery followed by radiotherapy and surgery followed by chemo-radio therapy (data not shown). Further, when these sensor molecules were correlated with each other, it was observed that, Mre11 did not show any significant correlation with any of the sensor molecule of the DDR pathway. A significant positive correlation was noted of Rad50 with H2AX and 53BP1 while, H2AX was significantly positively correlated with 53BP1, indicating that activation of any of the MRN complex molecule (Mre11/Rad50/Nibrin) may lead to initiation of further repair cascade.
To conclude, by profiling key signaling molecules of DNA damage repair (DDR) pathway in OSCC patients we have demonstrated that protein expression of Mre11 and Rad50 are strongly associated with disease advancement in OSCC. Further, strong expression of Mre11 protein is associated with increased recurrence rate suggesting their potential utility as prognostic tool in the analysis of tumor specimen. Moreover, as OSCC represents an especially lethal cancer with higher recurrence rate and limited therapeutic options, we believe that these association studies further underpin the DDR pathway as a novel area of potential therapeutic intervention for OSCC.
Acknowledgement
Authors are thankful to the Gujarat Cancer Society & The Gujarat Cancer Research Institute for providing financial support for the fulfillment of this study.
References
1. Van Gent DC, Hoeijmakers JH, Kanaar R. Chromosomal stability and the DNA double-stranded break connection. Nat Rev Genet. 2001; 2(3): 196–206. doi:10.1038/35056049
2. Bernstein C, Bernstein H, Payne CM, Garewal H. DNA repair/pro-apoptotic dual role proteins in five major DNA repair pathways: fail-safe protection against carcinogenesis. *Mutat Res.* 2002; 511(2): 145-178. doi: 10.1016/S1383-5742(02)00009-1
3. Dave JH, Vora HH, Ghosh NR, Trivedi TI. Mediator of DNA damage checkpoint protein 1 (MDC1) as a prognostic marker for patients with oral squamous cell carcinoma. *J Oral Pathol Med.* 2017; 46(4): 253-258. doi: 10.1111/jop.12558
4. Assenmacher N, Hopfner KP. MRE11/RAD50/NBS1: complex activities. *Chromosoma.* 2004; 113(4): 157-166. doi: 10.1007/s00412-004-0306-4
5. Shrivastav M, De Haro LP, Nickoloff JA. Regulation of DNA double-strand break repair pathway choice. *Cell Res.* 2008; 18(1): 134-147. doi: 10.1038/cr.2007.111
6. Flores-Pérez A, Rafaelli LE, Ramírez-Torres N, Aréchaga-Ocampo E, Frías S, Sánchez S, et al. RAD50 targeting impairs DNA damage response and sensitizes human breast cancer cells to cisplatin therapy. *Cancer Biol Ther.* 2014; 15(6): 777-788. doi: 10.1089/cbt.2014.0024
7. Figures MR, Wobb J, Araki K, Liu T, Zhu H, et al. Head and neck squamous cell carcinoma targeted chemosensitization. *Otolaryngol Head Neck Surg.* 2009; 141(2): 177-183. doi: 10.1016/j.otohns.2009.04.22
8. Rogakou EP, Nieves-Neira W, Boon C, Pommier Y, Bonner WM. Initiation of DNA fragmentation during apoptosis induces phosphorylation of γH2AX histone at serine 139. *J Biol Chem.* 2000; 275(13): 9390-9395.
9. Gorgoulis VG, Vassiliou LV, Karakaidos P, Zacharatos P, Kotsinas A, Lilioglou T, et al. Activation of the DNA damage checkpoint and genomic instability in human precancerous lesions. *Nature.* 2003; 424(6950): 907-913. doi: 10.1038/nature01485
10. Wang B, Matsuoka S, Carpenter PB, Eldjegi SJ. 53BP1, a mediator of the DNA damage checkpoint. *Science.* 2002; 298(5597): 1435-1438. doi: 10.1126/science.1076182
11. Morales JC, Franco S, Murphy MM, Bassing CH, Mills KD, Adams MM, et al. 53BP1 and p53 synergize to suppress genomic instability and lymphomagenesis. *Proc Natl Acad Sci USA.* 2006; 103(9): 3310-3315. doi: 10.1073/pnas.0512519103
12. Cao L, Xu X, Bunting SF, Liu J, Wang RH, Cao LL, et al. Development of Serous Ovarian Cancer is Associated with the Expression of Homologous recombination Pathway Proteins. *Pathol Oncol Res.* 2014; 20(4): 931-938. doi: 10.1007/s12253-014-9776-8
13. Rybanska-Spaeder I, Reynolds TL, Chou J, et al. 53BP1 is limiting for NHEJ repair. *J Cell Biochem.* 2010; 111(12): 3762-3770. doi: 10.1002/jcb.22517
14. Santivasi WL, Wang H, Wang T, Yang Q, Mo X, Brogi E, et al. MRE11 expression is predictive of cause-specific survival following radical radiotherapy for muscle-invasive bladder cancer. *Cancer Res.* 2010; 70(18): 7017-7026. doi: 10.1158/0008-5472.CAN-10-1202
15. Heikkinen K, Karpinnen S, Soini Y, Mäkinen M, Winquist R. Mutation screening of Mre11 complex genes: indication of RAD50 involvement in breast and ovarian cancer susceptibility. *J Med Genet.* 2003; 40(12): e131. doi: 10.1136/jmg.40.12.e131
16. Oliveira-Costa JP, Oliveira LR, Zanetti R, Chavichiolli Buim ME, et al. BRCA1 and γH2AX as independent prognostic markers in oral squamous cell carcinoma. *Oncoscience.* 2014; 1(5): 383-391. doi: 10.18632/oncoscience.47
17. Beggs AD, Domingo E, McGregor M, Presz M, Johnstone E, Midgley R, et al. Loss of expression of the double strand break repair protein ATM is associated with worse prognosis in colorectal cancer and loss of Ku70 expression is associated with CIN. *Oncotarget.* 2012; 3(11): 1348-1355. doi: 10.18632/oncotarget.694
18. Matthaios D, Foukas PG, Kefala M, Hounits P, Trypaniades IG, et al. γ-H2AX expression detected by immunohistochemistry correlates with prognosis in early operable non-small cell lung cancer. *Onco Targets Ther.* 2012; 5: 309-314. doi: 10.2147/OTT.S36995
19. Chen Y, Chen CF, Riley DJ, Alred DC, Chen PL, Von Hoff D, et al. BRCA1 expression is a modifier of the prognostic value of lymph node ratio and CA 19-9 in pancreatic adenocarcinoma. *BMC Cancer.* 2013; 13: 155. doi: 10.1186/1471-2407-13-155 | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2867,
1
],
[
2867,
8449,
2
],
[
8449,
12050,
3
],
[
12050,
15777,
4
],
[
15777,
22195,
5
],
[
22195,
26273,
6
]
]
} |
3db979f509c760f5a71540d5a7335094abfe3bc6 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 12,
"total-fallback-pages": 0,
"total-input-tokens": 45104,
"total-output-tokens": 14178,
"fieldofstudy": [
"Environmental Science"
]
} | A review of malaria transmission dynamics in forest ecosystems
Narayani Prasad Kar, Ashwani Kumar, Om P Singh, Jane M Carlton and Nutan Nanda
Abstract
Malaria continues to be a major health problem in more than 100 endemic countries located primarily in tropical and sub-tropical regions around the world. Malaria transmission is a dynamic process and involves many interlinked factors, from uncontrollable natural environmental conditions to man-made disturbances to nature. Almost half of the population at risk of malaria lives in forest areas. Forests are hotbeds of malaria transmission as they provide conditions such as vegetation cover, temperature, rainfall and humidity conditions that are conducive to distribution and survival of malaria vectors. Forests often lack infrastructure and harbor tribes with distinct genetic traits, socio-cultural beliefs and practices that greatly influence malaria transmission dynamics. Here we summarize the various topographical, entomological, parasitological, human ecological and socio-economic factors, which are crucial and shape malaria transmission in forested areas. An in-depth understanding and synthesis of the intricate relationship of these parameters in achieving better malaria control in various types of forest ecosystems is emphasized.
Keywords: Forest malaria, Transmission dynamics, Deforestation, Vector behavior, Socio-economic factors, Tribal communities
Background
Stratification of global malaria
Malaria is an infectious disease caused by parasites belonging to the genus Plasmodium. It is endemic in 104 tropical and subtropical countries, comprising half of the world’s population (3.4 billion people) [1], of which 2.57 billion are at risk for *P. falciparum* [2], and 2.5 billion for *P. vivax* [3]. *P. malariae* and *P. ovale* contribute a very small proportion of malaria infections but the population at risk of *P. malariae* is distributed all over sub-Saharan Africa, most parts of Southeast Asia, western Pacific islands, and Amazonian Basin [4,5]. *P. ovale* is prevalent in Africa [5], and it is also reported from Asia-Pacific regions [6]. *P. knowlesi*, the fifth human parasite [7] is essentially a primate malaria species that is being reported from remote forested areas of Southeast Asian countries [8-11].
Forest malaria
Definition of “forest” The ‘forest ecotype’ is defined by UNESCO as terrain with a tree canopy cover of more than 10% and an area of more than 0.5 hectares, including natural forests and plantations [12] with a minimum tree height of 5 m, including coffee, rubber, cork oak, and fruit tree plantations, wind break and shelter belts more than 20 m width [13]. Forest vegetation is categorized as rain forest, deciduous forest, scrub forest, highland rain forest, and highland alpine forest [14]. The former three are usually distributed in low to mid latitude and the last two are part of the high altitude biome.
Impact of forest malaria Forest ecosystems are well known to support transmission of malaria, significantly contributing to the global disease burden. A global assessment reports that “closed forests within areas of malaria risk cover approximately 4.8 million km²” [12]. Almost half the malaria risk is estimated to occur among people living in forested areas (1.4 billion) accounting for 11.7, 18.7, 35.1 and 70.1 million population respectively from 1.5 million km² in the Amazon region, 1.4 million km² in Central Africa, 1.2 million km² in the...
Western Pacific, and 0.7 million km$^2$ in South–East Asia [15, 16]. Corresponding forest areas containing these malaria risk zones are 11.16 million to 15.71 million km$^2$, 6.53 million–7.80 million km$^2$, 1.93 million–5.19 million km$^2$, 2.70 million–2.72 million km$^2$ [12, 15, 16]. Controlling malaria in these forested regions of the world has been a major challenge [17].
**Summarizing hidden risks of malaria in forests**
Most studies of forest malaria are focused on local factors associated with malaria transmission. These include distance from forest, impact of deforestation and reforestation, effect of forest on microclimate, vector bionomics, *Plasmodium* species survival, and human activities in forests. In this review we analyze the underlying factors influencing transmission of malaria in forests worldwide. Mosquito vectors vary according to forest locality and their behavior changes with the forest micro-climate [18], human population, and their social behaviors [19, 20]. Forest communities are generally tribal and cope with poor infrastructure. Certain practices like slash and burn cultivation, overnight stays within forests in order to collect forest produce, hunting, wide open household construction, and cattle ranching, increase vulnerability to malaria. It can be challenging to educate forest communities about malaria control, and without their cooperation it is difficult to control malaria [21]. Now, worldwide malaria communities are aiming at malaria eradication/elimination [22, 23], a proposition, which is impractical without prevention of re-introduction/re-emergence from hidden foci/un-controlled forest malaria [22, 24]. Malaria had declined during the previous eradication era in many regions of the world, some of which subsequently experienced resurgence and suffered from its consequences [23, 25–27]. The problem of malaria in forests is compounded by hidden reservoirs of malaria infections that are not fully addressed [28, 29]. The origin and evolution of drug and insecticide resistance are often found associated with the forest and near forest areas [24, 30–32]. In addition to existing asymptomatic infections, the presence of primate malaria parasites and their zoonotic vectors might pose additional challenges to human health in the forest and forest fringe areas [33–35], where malaria surveillance is generally poor [33, 36]. Occasional focal outbreaks (unstable transmission) might occur when malaria transmission extends from the forest shade (nidus) to peri-urban and urban areas [37], where much higher density of human population and presence of vectors could fuel large epidemics.
**Key factors which make forest different from other ecosystems**
The major factors, that differentiate forest from other ecosystems in relation to malaria transmission dynamics, are the influence of forest on temperature buffering, rainfall [38], humidity [39–41], tree canopy [42], flora, fauna [43], high organic content in breeding pools [44], and lack of infrastructure [45]. It is difficult to develop infrastructure in forests due to their uneven land forms, presence of streams, and dense vegetation. Additionally, poor communication hinders malaria control activities particularly during the rainy season [21, 45]. Furthermore, forests with hilly land forms are more malarigenic, as their slopes form small rapid streams that facilitate breeding of efficient malaria vectors [46]. Forest influences vector distribution and bionomics, and also the distribution of the malaria parasites. Forested areas are primarily inhabited by tribes [47, 48], whose illiteracy and strong beliefs in age old traditions and practices and a fear of outside world leads to reliance on indigenous treatment for malaria [49]. These factors are discussed in detail in the following sections.
**Review**
**Influence of topographic parameters in forested regions**
Topographic factors influence malaria transmission dynamics in forests differently compared to other regions [38, 40, 50–52] as forests harbor forest adapted malaria vectors [53, 54] which respond differentially to these parameters due to their genetic makeup and presence of forest influences their ecology to a great extent in comparison to less or no forest areas [18, 28, 52, 55].
**Temperature, rainfall, and humidity**
In forested highlands of East Africa, average temperature in the previous month and rainfall in the previous two months have shown a linear-quadratic relationship with *Anopheles gambiae* density [51]. Another study in the same region showed that the ratio of rainfall over precipitation/potential evapo-transpiration was the driving force for *An. gambiae* and *An. arabiensis* population increase [40]. The same vector studied in The Gambia showed rapid population increase towards the end of the dry season, and maximally after onset of rains when humidity increases [56]. Generally trees in the forests add moisture in the air by transpiration and help in lowering temperature, thus increasing precipitation. The moist environment and breeding sites created by rainfall increase vector population, their longevity and hence increase malaria transmission [19].
**Vegetation**
Vegetation near human habitation increases the population of forest malaria vectors and thus increases malaria transmission [57–59]. Villages with more broadleaf forests, and wetland vegetation in Belize and in forested villages of Bangladesh have higher malaria rates [60, 61] due to effective density of forest vectors [61]. Forest
Vectors usually prefer tree canopy coverage [42,62] and are known to take shelter in tree holes [63,64]. Forest flora and sugar availability have also been shown to be crucial determinants of vectorial capacity. The availability of plant sugar increased egg numbers [43,65] and survival potential of An. gambiae beyond ages at which they are old enough to transmit malaria [66]. In addition, leaves falling into larval habitats assure sustainable micro-climatic conditions and food for larvae, which favor vectors like An. dirus in South-East Asia [52].
**Bodies of water**
Mosquitoes mature in bodies of water (their larval habitat) and disperse according to their flight range. For example An. gambiae and An. funestus populations were observed decreasing with increasing distance from the Yala river in Kenya [42]. Even a small change in the distance from bodies of water can influence malaria transmission [19,67], Anopheles fluviatilis [68], Anopheles maculatus [68,69] and An. minimus [52,68,69] are prevalent near streams of water in forested areas having cooler climate and tree canopy [70], but An. dirus larvae grow well in small, clear and stagnant bodies of water in forested areas of Asia [52,68]. In Africa, An. gambiae s.s larvae grow better in bodies of water under dense forest canopy rather than sparse forest coverage [71]. Generally, larvae of forest vectors develop better in bodies of water under tree canopy where the water temperature is buffered and usually 3–3.5 degrees Celsius lower than that of sun-exposed bodies of water [71].
**Deforestation**
Reduction of dense tree shade increases exposure of vector breeding sites and resting places to sunlight, hence altering vector habitats. Studies have shown preference for forest shade by, An. dirus [52,72], An. fluviatilis [72,73], An. minimus [72,74], and An. funestus [74,75], An. darlingi [72] and contrastingly, preference for sunlight is shown by some of the species of An. gambiae [72,75], and An. maculatus [68,69,76]. Changing density of anophelines due to deforestation has been reported worldwide, and its relation to niche width and sunlight preference were reviewed in meta-analysis/tabulation [72], and it was found that changes in anophelines density and malaria incidence varied by type of development, agriculture, and locality [72]. It was predicted that deforestation in central Africa and tropical America might increase malaria [12,77], whereas in Asia deforestation would result in reduction in malaria [78]. As predicted in the Sahara region, malaria incidence increased due to deforestation as a consequence of increased vector density of An. gambiae and An. arabiensis [72], and increase in An. funestus and An. gambiae population in Sub-Saharan Africa [72]. Similarly deforestation increased the population of the South American vectors An. darlingi and An. aquasalis [72], accompanied by increased malaria in Guyana and Amazonia [72]. The predicted reduction in malaria in deforested regions of Asia may be due to a decrease in forest-loving (halophbic) vectors like An. dirus in Thailand and An. fluviatilis in India [73,79]. However, malaria transmission was accelerated by An. minimus due to deforestation in Thailand and India [80], as well as An. culicifacies in Nepal and Sri Lanka [72], and An. philippinensis, An. annularis, and An. varuna in India [80]. A risk of increased malaria in response to deforestation exists if vectors like An. darlingi are present in a deforested habitat [81], as the biting rate of An. darlingi has been estimated to increase 278 times in the deforested regions [82]. Thus deforestation affects malaria transmission depending upon the vector diversity of a particular region.
**Entomological parameters of forested regions**
**Impact of forest and forestation on vector abundance**
The vector species in forest ecoregions reflect their preference or adaptability to the forest ecotype. Malaria transmission dynamics in forests may be the output of more than one vector [83]. Different vector species or sympatric sibling species may be present in a particular region whose populations fluctuate according to seasons [52,84]. In the dense, hilly forested Thai-Myanmar border region, more An. dirus were found at the start while more An. baimaii were found towards the middle of the wet season [52]. In the less forested southern part of Thailand, however, An. cracens dominated over An. baimaii at the beginning of the wet season though by the end of the wet season An. scanloni dominated An. cracens [52,84]. In the subtropical mountainous forest of northwestern Argentina, An. argyritarsis was more abundant than An. pseudopunctipennis and both the vectors attained their peaks during spring [85]. Among the species of the Gambiae Complex, An. gambiae s.s. is less adapted to hotter conditions than An. arabiensis [86,87], hence the former is more abundant in forest than desert in comparison with the latter species, as reflected by their spatial and temporal distribution in Africa [29,54,88-90]. During dry periods when the primary forest vector (e.g., An. gambiae s.s.) population decreases, the secondary vector (e.g., An. arabiensis) takes over the transmission of malaria.
Mannmade forests including significantly large plantation areas or reforestation also cause habitat change and influence malaria vector abundance leading to changes in malaria transmission scenarios. For example malaria increased due to a coffee plantation in Thailand [91], palm plantations in Cameroon [92], Papua New Guinea [93] and Malaysia [94]; rubber plantation in Cameroon [95], Thailand [91] and orchard plantations in Thai-Myanmar and other South-East Asia regions [91,96,97].
Commercial plantations and reforestation, which increase human insurmount, increases man-vector encounter and malaria transmission in those areas [78,91,96,97].
Behavior of forest-adapted vector forms
Some non-forest vectors have distinct forest forms that exhibit alteration in chromosomal banding pattern and show altered bionomics compared to their non-forest forms [53,54,98]. The variation in vector forms is accompanied by differences in vectorial capacity, biting habits and differential resistance to insecticides, thus influencing vector control strategies [99,100] in response to malaria transmission [98,101]. Obsomer et al., 2007 in their review on An. dirus in Asian forested zones, emphasized forest environment, human behavior, and insecticide usage over vector genetics to account for the vector's behavioral heterogeneity [52], which also supports the earlier views of Trung and co-workers [18,28]. They reviewed behavioral heterogeneity of anophelines in South-East Asia with reference to forest, hill, and other factors and found that early evening shift in the human biting rhythm of An. dirus A (An. dirus) and An. minimus A (An. minimus Theobald), and higher degree of exophagy are inversely related to distance from forests and hills [52]. The forest form of An. gambiae has shown stronger exophilic in southern Sierra Leone whereas the Savannah form was mostly endophilic [98]. Daytime biting by An. dirus was also observed in the forest, where very little sunlight penetrates through the tree canopy [52,102].
Non-forest vectors showed altered bionomics in the forest. For example An. culicifacies which is mainly endophilic [103] but in dense forests of central India, it is reported mainly exophilic in nature [104]. Similarly An. gambiae was observed to be highly exophilic and anthropophagic in a forested region compared to a non-forested region of southern Sierra [55]. The highest anthropophagic index and sporozoite positivity was observed in the savanna forest region for all four major malaria vectors An. gambiae, An. funestus, An. arabiensis, and An. moucheti in Nigeria [105], and for An. gambiae in Southern Ethiopia [106] and Madagascar [107] in comparison with the less forested rainforest region of south-western Nigeria, where An. arabiensis was largely zoophilic, whereas An. gambiae, An. melas and An. moucheti remained predominantly anthropophagic [108]. The impact of forest/deforestation on vector populations, their bionomics and malaria incidence is summarized in Table 1.
Parasitological factors in relation to vector and host
Plasmodium species distribution in forested regions
Plasmodium in humans is little influenced by forest factors, as its secondary lifecycle is completed in a homeotherm. However, the primary life cycle occurs in an ectothermic vector, which is very much influenced by environment. Intrinsic incubation period is triggered by unknown phenomena [115] but extrinsic incubation period is inversely related to temperature and also depends upon Plasmodium species and the vector [116]. P. vivax and P. falciparum have shorter extrinsic incubation periods and are also the most common human malaria parasites [117]. P. vivax can survive in places like the Central Andes where the weak vector An. pseudopunctipennis and fluctuating environmental conditions prevail and are compensated by the short extrinsic incubation period of P. vivax, long intrinsic incubation periods in the human liver [118], and by forest cover that increases the life expectancy of the vector [109]. Plasmodium species have evolved to fit local vectors, as observed in P. falciparum in rural Cameroon by shortening sporogony [119] as survival of the vector influences Plasmodium distribution [120]. An increase in vectorial capacity of An. gambiae was reported in deforested areas of Kenya as deforestation led to a decrease in duration of sporogony of P. falciparum [109]. Plasmodium malariae, P. knowlesi and P. ovale cases are rare and mainly confined to remote forested areas and are usually underreported as these are often mis-identified [121-123].
Risk of primate malaria to humans in forest regions
The presence of a non-human primate Plasmodium species in forest foci poses a constant risk of host switching to nearby human populations due to deforestation, with its associated insurgence of the human population [124]. Anopheles in subgenus Kerteszia (An. Kerteszia cruzii, An. Kerteszia bellator), are vectors of human and simian plasmodia in areas like Atlantic forest in South America [33,34]. It is possible that zoonosis may be present in such areas, as the parasites found in monkeys (P. simium and P. brasilianum) are genetically similar/related to human plasmodia (P. vivax and P. malariae) [35]. Such cases occur, albeit infrequently, inside the forest or on its edges whose identity may be confused with human Plasmodia being morphologically similar [33]. The simian Plasmodium could switch over to humans as appears to have occurred in the case of P. cynomolgi in India [125], P. simium in Brazil [126,127], P. knowlesi in Malaysia [20,124]. The presence of asymptomatic human reservoirs together with infected monkeys could maintain malaria transmission in a situation where routine malaria surveillance and control are difficult [33,36].
Parasite reservoir and drug resistance
Stability of malaria transmission in endemic areas is also reported to be associated with asymptomatic P. falciparum and P. vivax reservoirs and hypnozoite reservoirs of P. vivax [128,129]. Asymptomatic malaria is often
associated with forested regions of the world [130-133]. Due to the asymptomatic reservoir [131], ‘stable endemic malaria’ is maintained continuously in forested areas [134], and in non-forested areas with unstable environments the reservoir plays a very important role in bridging transmission seasons, as human reservoirs help the parasite in escaping from a harsh environment during which the vector population also decline below the critical transmissible level [134]. For example, intense perennial transmission through an asymptomatic malaria reservoir was reported in the forested riverine areas of Tanzania [131] and Gabon [130]. Asymptomatic patients having sub microscopic presence of parasites [129,135] act as a reservoir [132,136,137] and ready source of infection in vectors [136] and are one of the hidden obstacles in malaria control in forests.
Patients infected with drug-resistant Plasmodium carry transmissible gametocytes for a very long time, and act as reservoirs. Plasmodium falciparum and P. vivax are reported to be more often associated with drug resistance in forested areas where intensity of malaria transmission is higher and malaria control often neglected. For these reasons the forested Thai-Cambodia border is believed to be the “epicenter” for the origin of chloroquine resistance and evolution of multidrug resistance [24,30,31]. Recently, partial artemisinin-resistance in P. falciparum has emerged from the same area [24,32]. The faster dissemination of drug resistant strain is likely due to the presence of some of the very efficient forest vectors in South-East Asia such as An. dirus and An. minimus; these vectors showed 66% and 44% susceptibility to a drug-resistant strain of P. falciparum infected patient blood respectively [28,52], and the number of oocysts of the drug-resistant type was reportedly higher in An. dirus [52]. Chloroquine-resistant foci have also been found associated with An. dirus in South Asia [52,138].
### Human ecological and socioeconomic factors
**Known malarigenic practices of forest natives**
Deep forest areas are primarily inhabited by indigenous populations of ethnic minorities and tribals [47,48] that are in little touch with outer world and mostly dependent on the forest for sustenance [139]. Such communities are mostly illiterate, prone to superstition beliefs, and poor at communicating with malaria control workers. Tribes inhabiting forests have conserved traditions and practices that have remarkable impacts on malaria transmission [17] thus these forest dwelling people are vulnerable to malaria [21]. Slash and burn is a functional element of forest area farming practices in many parts of the world [17,140] leading to deforestation and succession of halophilic vectors, hence changes in the malaria transmission pattern [17]. In this type of cultivation, 1–2 members of the family stay in a hut near the farm overnight, which in turn exposes them to malaria vectors [17,140]. For example, malarigenic conditions are created in the central mountainous and forested part of Vietnam where the Rag Lays tribes practice slash and burn [17,140], and also by commercial logging, and cattle ranching [141]. Certain ethnic groups in India ritually plaster their houses with fresh cow dung and mud that masks the insecticide on treated walls and render it
### Table 1 Impact of forest/deforestation on vector populations, their bionomics and malaria incidence
| Malaria vectors | Increase in anthropophagy | Increase in exophily/exophagy | Increase in vector population/malaria |
|-----------------|----------------------------|-------------------------------|--------------------------------------|
| An. gambiae | Forested region of Southern Sierra [55] | Forested region of Southern Sierra [55] | Deforested region of Africa [72,109] |
| An. arabiensis | Savannah-forest region of Nigeria [105] | Forested region of Nigeria [110] | Deforested region of Africa [72] |
| An. funestus | Savannah-forest region of Nigeria [105] | No increase in exophagy reported from rain forest zone of Nigeria [110] | Deforested region of Africa [72] |
| An. dirus | Forested region of Thailand [52], & Vietnam [17] | Forested region of Vietnam [17,28] | Forested regions of Asia [72] |
| An. fluviatilis | Forested region of Orissa, India [111] | Forested region of Central India [104] | Forested region of Orissa, India [111] |
| An. minimus | Forested region of Orissa, Cambodia [112] | Forested region of Central Cambodia [112] | Deforested region of Central Vietnam [18] |
| An. culicifacies | Forested region of Orissa, India [111] | Forested region of Central India [104] | Deforested region of Asia [72] |
| An. maculatus | Forested region of Orissa, Cambodia [112] | Forested region of Kratie province, Cambodia [112] | Forested region of Central Vietnam [18] |
| An. darlingi | Deforested region of Peruvian Amazon [82] | Forested region of Brazil [113] | Deforested region of South America [72,82] and near forest area of South America [114] |
| An. aquasalis | Forested region of Guayana, Venezuela [67] | Deciduous dry forested region of Venezuela [67] | Deforested region of South America [72] |
ineffective for vector control [142]. Traditionally women cover more of their bodies and perhaps for this reason were found to be at lower malaria risk than men [17,61,143]. In many tribal cultures both men and women consume alcoholic beverages on a regular basis and this practice results in reduced self-protection against mosquito bites. Interestingly, it has been found that beer consumption increases human attractiveness to An. gambiae in experiments conducted in Burkina Faso [144].
Population migration in forest areas Populations move within and out of the forest for a variety of reasons and this helps in malaria dissemination [145,146]. Daily short-distance movement is done for cattle grazing, hunting, fishing, farming, collecting forest products like leaf, wood, fruit, flower and honey, etc. [147]. Such movements increase the contact with efficient malaria vectors when night halt is done in the forest [145,148,149] and even in the daylight where vectors like An. dirus prevails [52,140]. Short-term movement of forest inhabitants to medium distances is observed during sowing and harvesting seasons [38]. Generally this type of movement draws malaria from forested areas to plain field areas [145]. For example, increase in movement of people both within the highlands of New Guinea and also between holo and hyper-endemic lowland areas and the highlands increased malaria spread [150]. Non-forest populations also visit forest areas for animal grazing and wood collection [151]. Refugees have been settled and many resettlement programs have been launched in forest areas, for example, in India, Bangladeshi refugees were shifted to the forested Chittagong hill district and the forested area of the Orissa—Chhattisgarh border near Bastar under ‘Dandakaranya’ project. The refugees contracted malaria from native tribes, which led to epidemics in Bastar [152,153]. According to Lindsay et al., “Many of the first European settlers in Africa who sought refuge from the heat and diseases of the plains by moving to the cool and salubrious highlands also carried malaria with them” [154].
Poor infrastructure and communication Forest inhabitants usually construct houses with mud, and infection increased among those living in muddy or poorly constructed houses near vector breeding places in Egypt [155], Ethiopia [156] and Kenya [42]. An. minimus A in central Vietnam exhibits a high anthropophilic and endophagic ratio, most likely influenced by the largely open houses with incomplete walls that allow it to easily detect human stimuli and enter into houses [157].
Health infrastructure and surveillance are neglected in remote forest areas [158] and it becomes impractical in the rainy season where road infrastructure is poor or absent [159]. Unfortunately, the rainy season is also the peak transmission period in most malarious areas [160] when adequate surveillance is required as patients find it difficult to access health facilities due to climatic and communication problems [21,45]. Thus the indigenous population generally relies on the health practices of local faith healers and/or quacks [161-163]. Modern health infrastructure among sparsely distributed forest settlements is far from adequate [139,164]. It is reported that treatment seeking behavior is inversely related to the distance from a health facility and communication problems [21,165,166].
People’s conceptions and cooperation Different perceptions about malaria have been reported among tribal groups in different parts of the world. Certain tribes believe that malaria is caused by spirits, angry deities, black magic, or consider it a self-limiting fever in countries like India [167] and southwest Ethiopia [165]. Low cost treatment with traditional medicines, good accessibility and good communication with quacks are preferred most in remote forest areas far from government health centers as reported in rural Ethiopia [168]. In the forest areas health seeking is directly related to culture, faith and affordability of the health care [21,165]. It is observed that “health services may be underutilized and several health care instructions may be ineffective or ignored in traditional and transitional societies where people’s ideas and behavioral patterns conflict with the knowledge being passed to them” [161]. Generally poverty is the next most important factor in accessing a distant healthcare facility besides illiteracy, superstition, and cultural faith among the indigenous populations of most forest regions in Bangladesh [143]. Poor forest inhabitants do not own a bed net primarily due to a lack of availability of affordable nets in spite of the fact that they know the benefits of nets and would want to use them [169,170]. Hence not having bed nets, poor people cover their body and face with blankets, burn wood and shrubs to ward off mosquitoes, and due to lack of affordable modern medical facility they practice traditional remedies [171]. Surveillance is poor in remote forested areas [172] and presumptive treatment using antimalarials in low doses is taken for all sorts of fever [173], accelerating the development of drug resistance [174,175]. Thus the origin and evolution of drug resistance was reported first in forested remote areas like Cambodia and the Thai-Myanmar border areas [176].
Suggestions for overcoming major challenges to curbing malaria transmission in forest ecosystems Forests escape malaria control efforts mainly due to inadequate roads and poor communication [21]. Communication infrastructure development should be the first priority as this will open new ways and opportunity to the inhabitants and boost their socio-economic status. Establishing
and development of accessible health facilities and making them available to inhabitants by reducing gaps between locals and health providers can improve the situation. Social awareness for malaria control and involvement of traditional health providers and NGOs may help in filling the gaps in backward forested areas [21,162].
Malaria transmission respects no political boundaries and in forested borders people often migrate across the borders and carry malaria as seen in Thai-Myanmar border. The population migrations in forested regions are due to various reasons but mainly due to availability of work [49,97]. Military camps, radar stations, police, and other armed forces camps and big development projects like road and other infrastructure development, mining, agricultural activities like tea, rubber, coffee plantation and construction of dams employ large numbers of migrant workers. These people acquire malaria easily from natives [152]. The vulnerable migrants and refugees need to be screened and treated for malaria promptly. The military and other camps in forested region are required to put large efforts to fight against malaria together with the local people.
Tribals in forest areas, often hidden from outer world, are generally conservative and reluctant in treatment seeking. Social inhibitions, ignorance, superstitions, and negligence promote tolerance in symptomatic or asymptomatic malaria carriers, who do not seek treatment themselves and act as reservoirs of malaria parasites [21,143]. Mass screening may be useful in order to assess malaria sero-positivity among communities where asymptomatic malaria prevails and people are less prompt in seeking treatment [23]. Antigen based species specific rapid diagnostic test kits should be used in forested areas for instant on-site detection and treatment. Primitive nomadic tribes need to be accessed by the healthcare providers and should be given place in social structure and are required to be encouraged to use healthcare and other facilities.
Forests are reported to be the epicenter of drug resistance spread and low attainment rates in malaria control. Therefore, strictly controlled administration of antimalarials with periodic assessment of drug resistance status is suggested in forested areas. Molecular markers associated with antimalarial resistance need to be evaluated in the high transmission forested areas and can help in saving the valuable antimalarials for posterity [176].
Deforestation and climate change can conspire with other factors of forest-malaria to cause a boom in vector species and increases in their vectorial dimensions [20,82]. Ecological succession of malaria vectors attributable to climate and ecological changes needs to be explored and frequent inspection of abundance of vector species and an update on their distribution pattern, bionomics and behavioral changes in forested areas are justified for effective vector control measures.
Conclusion
Strong links exist between various factors influencing malaria transmission dynamics in forest ecosystems. Slight change in any of the factors affects the others, culminating in a different transmission pattern. Change in the vegetation cover and deforestation alters the distribution and behavior of malaria vectors. Human ecological and socioeconomic traits also affect exophagy, anthropophagy, biting rhythm, and resting behavior of vectors. The genetic traits of communities residing in forest areas and their health-seeking behaviors are crucial for parasite prevalence and precipitation of drug resistance. Moreover, insurgence of human populations and developmental activities in forests are important in altering the transmission pattern. Thus malaria transmission in forest areas is a complex process involving interplay between topographical, entomological, parasitological and human factors (Figure 1). Studies carried out in forested areas in different parts of the world generally focus on one or a few of the many factors which may not be adequate in understanding complexities of the malaria situation arising out of interaction of several factors. This review can help understand the complex interlinks between different factors acting simultaneously to influence malaria transmission. Predictive models of malaria transmission can be worked out for forest areas of different ecoregions by taking into account all relevant weighted factors. Based on in-depth understanding of the intricate relationship of various parameters,
situation specific vector/malaria control strategies can be developed and implemented to address malaria problem in the forests. Although implementation of such strategies is primarily a responsibility of the government and local health authorities, NGO workers, local medicine practitioners and traditional faith healers would be important as these are acceptable to the communities residing in remote forested areas. At the same time establishing a good rapport through interaction between implementers and the communities is essential for the success and sustenance of malaria control programs in forest ecosystems.
Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
NPK mined the literature as a part of his PhD thesis work. NPK and NN wrote the manuscript. AK, OP, and JMC added and improved overall manuscript structure and contents. All authors read and approved the final manuscript.
Acknowledgements
The authors are thankful to the Director, National Institute of Malaria Research, New Delhi for providing necessary facilities to undertake this review. We thank Dr. Lalitha Ramanathapuram for making available full text articles referred in this review and Dr. Steven Sullivan for editing and proof reading. This study was supported by NIH/National Institute of Allergy and Infectious Diseases award U19AI086765, and by an NIH/Fogarty International Center Global Infectious Disease research training grant D43TW007884. The content of this manuscript is solely the responsibility of the authors and does not necessarily represent the official views of the Fogarty International Center or the National Institutes of Health. This manuscript bears the NIMR publication screening committee approval no. 001/2013.
Author details
1Indian Council of Medical Research, National Institute of Malaria Research, Sector-D, Dwarka, New Delhi 110077, India. National Institute of Malaria Research, DHS Building, Campal, Panjai, Field Unit Goa-403001, India.
2Department of Biology, New York University, 12 Waverly Place, New York, NY 10009, U.S.A.
Received: 30 September 2013 Accepted: 23 May 2014 Published: 9 June 2014
References
1. WHO: World Malaria Report. 2013. Switzerland: World Health Organization; 2013:1–199.
2. Gething PW, Patil AP, Smith DL, Guerra CA, Johnston GL, Tatem AJ, Hay SI. A new world malaria map. Plasmodium falciparum endemicity in 2010. Malar J 2011, 10:578.
3. Gething PW, Elyazar IR, Moyes CL, Smith DL, Battle KE, Guerra CA, Patil AP, Tatem AJ, Howes RE, Myers MF, George DB, Horby P, Wertheim HF, Price RN, Mueller I, Laird JD, Hay SI. A long neglected world malaria map: Plasmodium vivax endemicity in 2010. PLoS Negl Trop Dis 2012, 6:e1814.
4. Collins WE, Jeffery GM. Plasmodium malariae: parasite and disease. Clin Microbiol Rev 2007, 20:579–592.
5. Obare P, Ogutu B, Adams M, Odera JS, Lilley K, Dosso D, Adhiambo C, Ovwusu-Agyei S, Binika F, Wanjia E, Johnson J. Misclassification of Plasmodium infections by conventional microscopy and the impact of remedial training on the proficiency of laboratory technicians in species identification. Malar J 2013, 12:113.
6. Sutherland CJ, Tamirzian N, Nolder D, Oguke M, Jennison C, Pukrittayakamee S, Dolecek C, Hien TT, Do Rosario VE, Arez AP, Pinto J, Michon P, Escalante AA, Forster F, Burke M, Lee R, Blase M, Otto TD, Barnwell JW, Pain A, Williams J, White NJ, Day NP, Snounou G, Lockhart PJ, Chiodini PL, Imwong M, Ploidy SD. Two nonrecombining syntenic forms of the human malaria parasite Plasmodium ovale occur globally. J Infect Dis 2010, 201:1544–1550.
7. White NJ. Plasmodium knowlesi: the fifth human malaria parasite. Clin Dis 2008, 46:172–173.
8. Putaporntip C, Honrirampong T, Seethamchais S, Kobasa T, Limkittrkrit K, Cui L, Jongsuttiwes S. Differential prevalence of Plasmodium infections and cryptic Plasmodium knowlesi malaria in humans in Thailand. J Infect Dis 2009, 199:1143–1150.
9. Singh B, Kim Sung J, Matusop A, Radhakrishnan A, Shamal SS, Cox-Singh J, Thomas A, Conway DJ. A large focus of naturally acquired Plasmodium knowlesi infections in human beings. Lancet 2004, 363:1017–1024.
10. Van den Eede P, Van HN, Van Overmeir C, Nyhlingh T, Hung Le X, Manh HH, Anne J, D’Alessandro U, Erhart A: Human Plasmodium knowlesi infections in young children in central Vietnam. Malar J 2009, 8:249.
11. Nyhlingh I, Noorazian YM, Huat TC, Jiram AI, Yusri YM, Azahari AH, Norparina I, Norrnan I, Lokmamnakham S: Plasmodium knowlesi in humans, macaques and mosquitoes in peninsular Malaysia. Parasit Vectors 2008, 1:26.
12. Guerra CA, Snow RW, Hay SI: A global assessment of closed forests, deforestation and malaria risk. Ann Trop Med Parasitol 2006, 100:189–204.
13. Snelder DJ, Lasco RD, NlRlibrary I, Smallholder Tree Growing for Rural Development and Environmental Services Lessons from Asia. Dordrecht: Springer; 2008:1–493.
14. Breckle S-W, Walter H: Walter’s Vegetation of the Earth: The Ecological Systems of the Geo Biopshere. Berlin [u.a.]: Springer; 2002:1–236.
15. Achard F, Eva HD, Sibig HJ, Mayaux P, Gallego J, Richards T, Malingreau JP: Determination of deforestation rates of the world’s humid tropical forests. Science 2002, 297:999–1002.
16. Mayaux P, Holmgren P, Achard F, Eva H, Sibig HJ, Branthomme A: Tropical forest cover change in the 1990s and options for future monitoring. Philos Trans R Soc Lond B Biol Sci 2005, 360:373–384.
17. Erhart A, Ngo DT, Phan VK, Ta TT, Van Overmeir C, Speybroeck N, Olsomer V, Le NT, Le KT, Coosemans M, D’Alessandro U: Epidemiology of forest malaria in central Vietnam: a large scale cross-sectional survey. Malar J 2005, 4:58.
18. Trung HD, Bortel WV, Sochantha T, Keokchatchain K, Bieri OJ, Coosemans M: Behavioural heterogeneity of Anopheles species in ecologically different localities in Southeast Asia: a challenge for vector control. Trans Med Int Health 2005, 10:251–262.
19. Walker M, Winskill P, Basanez MG, Mwanga MM, Mbogo C, Beier JC, Midega JT: Temporal and micro-spatial heterogeneity in the distribution of Anopheles vectors of malaria along the Kenyan coast. Parasit Vectors 2013, 6:311.
20. Alia H, Surin J, Mahmoud R, Shafie A, Mohd Zin J, Mohammad N M, Ibrahim AS, Rundi C: Spatial distribution of malaria in Peninsular Malaysia from 2000 to 2009. Parasit Vectors 2014, 7:186.
21. Ribera JM, Hausmann-Muela S: The straw that breaks the camel’s back. Redirecting health-seeking behavior studies on malaria and vulnerability. Med Anthropol Q 2011, 25:103–121.
22. Tatem AJ, Smith DL, Gething PW, Kabaria CW, Snow RW, Hay SI: Ranking of elimination feasibility between malaria-endemic countries. Lancet 2010, 376:1579–1591.
23. Hamaizna B, Moonga RA, Sikaala CH, Kamulivo M, Bennett A, Eisele TP, Miller J, Seyoum A, Kilian GN: Monitoring, characterization and control of chronic, symptomatic malaria infections in rural Zambia through monthly household visits by paid community health workers. Malar J 2014, 13:128.
24. Salud OM: Global Malaria Control and Elimination: Report of a Meeting on Containment of Artisanal Malaria. 19 January 2008, Geneva, Switzerland. Geneva: WHO; 2008:1–29.
25. Hui SI, Guerra CA, Tatem AJ, Noor AM, Snow RW: The global distribution and population at risk of malaria: past, present, and future. Lancet Infect Dis 2004, 4:327–336.
26. Carter R, Mendis KN: Evolutionary and historical aspects of the burden of malaria. Clin Microbiol Rev 2002, 15:364–394.
27. Fuller DO, Parentis MS, Hassan AN, Beier JC: Linking land cover and species distribution models to project potential ranges of malaria vectors: an example using Anopheles arabiensis in Sudan and Upper Egypt. Malar J 2012, 11:264.
28. Trung HD, Van Bortel W, Sochantha T, Keokchatchain K, Quang NT, Cong LD, Coosemans M: Malaria transmission and major malaria vectors in different geographical areas of Southeast Asia. Trop Med Int Health 2004, 9:230–237.
29. Charlwood JD, Viljoen A, Billinghury PF: Dry season refugia of malaria-transmitting mosquitoes in a dry savannah zone of east Africa.
Am J Trop Med Hyg 2000, 62(2A–4):732–737.
30. Gathmann I, Pittet A, Lesage A, Iwamorung Nor, Lindegarde N, Min Lwin M, Zav T, Arnerberg A, De Radigues X, Nosten P: Plasmodium vivax resistance to chloroquine in Daiwei, southern Myanmar.
Trop Med Int Health 2008, 13(10):837–842.
31. Nosten F, ter Kuile F, Chongsuephaisiddhi T, Luxemburger C, Webster HK, Edstein M, Phiaupun L, Thew KL, White NJ: Mefloquine-resistant falciparum malaria on the Thai-Burmese border.
Lancet 1991, 337:1140–1143.
32. Dondorp AM, Yeung S, White L, Nguon C, Day NP, Socheat D, von Seidlein L: Artemisinin resistance: current status and scenarios for containment.
Nat Rev Microbiol 2010, 8:272–280.
33. Duarte AM, Pereira DM, de Paula MB, Fernandes AR, Urbinatti PR, Ribeiro AF, Mello MH, Matos MO Jr, Macchi LF, Fernandes LN, Natal D, Malafonte RS: Natural infection in anopheles species and its implications for autochthonous malaria in the Atlantic Forest in Brazil.
Parasit Vectors 2013, 6:58.
34. Deane LM, Ferreira Neto JA, Lima MM: The vertical dispersion of Anopheles (Kerteszi) cruzi in a forest in southern Brazil suggests that human cases of malaria of simian origin might be expected.
Mem Inst Oswaldo Cruz 1984, 79:461–463.
35. Waters AP, Higgins DG, McCutchan T: Evolutionary relatedness of some primate models of Plasmodium.
Mol Biol Evol 1993, 10:914–923.
36. De Castro Duarte AV, Malafonte RS, Cerutti C Jr, Curado I, De Paiva BR, Maeda AV, Yamasaki T, Summa MEL, Neves DDOA, De Oliveira SG: Plasmodium infections in Brazilian wild monkeys: reservoirs for human infections?
Acta Trop 2008, 107:179–185.
37. Rosenberg R: Current status of malaria in Malaysia.
III. Breeding habits of Anopheles dirus.
Am J Trop Med Hyg 1982, 31:192–201.
38. Rubio-Pays Y, Zimmerman RH: Ecoregional classification of malaria vectors in the neotropics.
J Med Entomol 1997, 34:499–510.
39. Minakawa N, Sanyo G, Mogi M, Githae A, Yan G: The effects of climatic factors on the distribution and abundance of malaria vectors in Kenya.
J Med Entomol 2002, 39:833–841.
40. Koenraadt CJ, Githae AK, Tallokin W: The effects of rainfall and evapotranspiration on the temporal dynamics of Anopheles gambiae s.s. and Anopheles arabiensis in a Kenyan village.
Acta Trop 2004, 90:141–153.
41. Aragão MB: Some microclimatic measurements, in a forest of the “bromeliad-malaria” region, in Santa Catarina, Brazil. III. Conditions of humidity measured with hygrometers.
Rev Bras Med 1960, 12:395–414.
42. Zhou G, Munga S, Minakawa N, Githae AK, Yan G: Spatial relationship between adult malaria vector abundance and environmental factors in western Kenya highlands.
Am J Trop Med Hyg 2007, 77:29–35.
43. Manda H, Gounga LC, Foster WA, Beier JC, Githure JI, Hassanali A: Effect of discriminative plant-sugar feeding on the survival and fecundity of Anopheles gambiae.
J Med Entomol 2007, 44:116–121.
44. Oketch BA, Gounga LC, Yan G, Githure JI, Beier JC: Larval habitats of Anopheles gambiae s.s. (Diptera: Culicidae) influence vectors evolution to Plasmodium falciparum parasites.
Malar J 2007, 6:50.
45. Lim ES: Current status of malaria in Malaysia.
Southeast Asian J Trop Public Health 1992, 23(Suppl 4):43–49.
46. Rattananithkul R, Green CA, Panyim S, Noigamol C, Chanaimongkol S, Vannakana DC, Jallow E, Beig B, Lindsay SW, Conway DJ: Dry season ecology of Anopheles gambiae complex mosquitoes in The Gambia.
Malar J 2008, 7:156.
47. Mouchet J, Carnevale P: Impact of changes in the environment on vector-transmitted diseases.
Sante 1997, 2:263–269.
48. Pavlovska EN: Natural NMR: The implications of human-mosquito interactions.
In: Special Reference to the Landscape Ecology of Zoanthropozoans. Urbana: University of Illinois Press; 1966:1–261.
49. O’Loughlin SM, Okbayashi T, Honda M, Kitaoka Y, Kishino H, Somborn P, Sochantta T, Nambaya S, Saikia PK, Dev V, Walton C: Complex population history of two Anopheles dirus mosquito species in Southeast Asia suggests the influence of Pleistocene climate change rather than human-mediated effects.
J Evol Biol 2008, 21:1553–1569.
50. Hake S, Masuoka P, Varois E, Roberts DR: Spatial correlations of mapped malaria rates with environmental factors in Belize.
Central America Int J Health Geogr 2004, 3:9.
51. Haque U, Sunahara T, Hashizume M, Shields T, Yamamoto T, Haque R, Glass GE: Malaria prevalence, risk factors and spatial distribution in a hilly forest area of Bangladesh.
Plos One 2011, 6:e18008.
52. Mfane YA, Zhou G, Lawson BW, Githae AK, Yan G: Effects of microclimatic changes caused by deforestation on the survivorship and reproductive fitness of Anopheles gambiae in western Kenya highlands.
Am J Trop Med Hyg 2006, 74:772–778.
53. Yadav RS, Sharma VP, Chand SK: Mosquito breeding and resting in treeholes in a forest ecosystem in Orissa.
Indian J Malar 1997, 348:16–18.
54. Gunasekaran K, Sahu SS, Parida SK, Sadanandane C, Jambulingam P, Das PK: Anopheles funeana of Korupat district, Orissa state, with particular reference to transmission of malaria.
Indian J Med Res 1989, 89:340–343.
55. Gary RE Jr, Foster WA: Anopheles gambiae feeding and survival on honeydew and extra-floral nectar of peridomestic plants.
Malar J 2004, 1:102–107.
56. Okech BA, Gounga LC, Killeen GF, Knols BG, Kabiru EW, Beier JC, Yan G, Githure JI: Inference of sugar availability and indoor microclimate on survival of Anopheles gambiae mosquitoes.
African J Ecol 2007, 45:111–114.
57. Bockarie MJ, Service MW, Toure YT, Traore S, Barnish G, Greenwood BM: The ecology and behaviour of the forest form of Anopheles gambiae s.s. Parasitology 1993, 35(Suppl):3–8.
58. Javara M, Pinder M, Drakeley CJ, Iwakonnka DC, Jallow E, Boegh C, Lindsay SW: Current status of malaria in Myanmar border region: biting habits, feeding behaviour and entomological inoculation rates.
Malar J 2003, 2:843–849.
59. Bockarie MJ, Service MW, Toure YT, Traore S, Barnish G, Greenwood BM: The ecology and behaviour of the forest form of Anopheles gambiae s.s. Parasitology 1993, 35(Suppl):3–8.
60. Muthukumar M, Prasittisuk C, Kondrashin AV: Agricultural development and arthropod-borne diseases: a review.
Rev Saude Publica 1991, 25:165–178.
164. Manguin S: Biodiversity of Malaria in the World. Montrouge: John Libbey Eurotext; 2008.
165. Adera TD: Beliefs and traditional treatment of malaria in Kishe settlement area, southwest Ethiopia. Ethnopharmacol Med J 2003, 41:25–34.
166. Alves MJ, Barata LC, Barata Rde C, de Almeida Mdo C, Gutierrez EB, Wanderley DA, de Andrade JC: Socioeconomic aspects of subjects with imported malaria in the metropolitan area of Sao Paulo, Brazil. I. Characterization of the population and knowledge about the disease. Rev Saude Publica 1990, 24:253–258.
167. Dhillon HS, Kar SB: Malaria eradication and investigation of cultural patterns and beliefs among tribal population in India. Int J Health Educ 1965, III:31–40.
168. Deressa W, Ali A, Hallemarian D: Malaria-related health-seeking behaviour and challenges for care providers in rural Ethiopia: implications for control. J Biosoc Sci 2008, 40:115–135.
169. Elphick H, Elphick D: Factors that contribute to the low use of bed nets in a malaria endemic zone of sub-Saharan Africa: a questionnaire survey in a rural population in Zambia. Cent Afr J Med 2003, 49:87–89.
170. Pulford J, Hetzel MW, Bryant M, Siba PM, Mueller I: Reported reasons for not using a mosquito net when one is available: a review of the published literature. Malar J 2011, 10:83.
171. Esse C, Utzinger J, Tschannen AB, Raso G, Pfeiffer C, Granado S, Koudou BG, NGoran EK, Cisse G, Girardin O, Tanner M, Obriot B: Social and cultural aspects of 'malaria' and its control in central Cote d’Ivoire. Malar J 2008, 7:224.
172. Moore SJ, Min X, Hill N, Jones C, Zaiwing Z, Cameron MW: Border malaria in China: knowledge and use of personal protection by minority populations and implications for malaria control: a questionnaire-based survey. BMC Public Health 2008, 8:344.
173. Gosling R, Drakeley C, Mwita A, Chandramohan D: Presumptive treatment of fever cases as malaria: help or hindrance for malaria control? Malar J 2008, 7:132.
174. Talisuna AO, Langi P, Bakyaita N, Egwang T, Mutabingwa TK, Watkins W, Van Mark E, D’Alessandro U: Intensity of malaria transmission, antimalarial-drug use and resistance in Uganda: what is the relationship between these three factors? Trans R Soc Trop Med Hyg 2002, 96:310–317.
175. Hastings IM, Watkins WM: Intensity of malaria transmission and the evolution of drug resistance. Acta Trop 2005, 94:218–229.
176. Alam MT, Vinayak S, Congpuong K, Wongsrichanalai C, Satimai W, Slutsker L, Escalante AA, Barnwell JW, Udhayakumar V: Tracking origins and spread of sulfadoxine-resistant Plasmodium falciparum dhps alleles in Thailand. Antimicrob Agents Chemother 2011, 55:155–164. | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3485,
1
],
[
3485,
9036,
2
],
[
9036,
14753,
3
],
[
14753,
20323,
4
],
[
20323,
25535,
5
],
[
25535,
31243,
6
],
[
31243,
35763,
7
],
[
35763,
43630,
8
],
[
43630,
49952,
9
],
[
49952,
49952,
10
],
[
49952,
49952,
11
],
[
49952,
52595,
12
]
]
} |
803e6e3c644f7a3e5622efdffc188c7550ebd3b3 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 28004,
"total-output-tokens": 8359,
"fieldofstudy": [
"Biology"
]
} | Ethnomedicinal uses of plants by Santal tribe of Alipurduar district, West Bengal, India
Aninda Mandal¹*, Tamalika Adhikary¹, Debarun Chakraborty², Priti Roy¹, Joy Saha², Anushree Barman¹, Poulami Saha¹
¹ Department of Botany, A. B. N. Seal College, Cooch Behar, West Bengal, India. Tel.: +91 9434602182
² Department of Botany, Cooch Behar Panchanan Barma University, Cooch Behar, West Bengal, India
Abstract
Objectives: To document the traditional knowledge on medicinal plants used by the Santal tribe residing at seven different villages in Alipurduar district of West Bengal, India to treat common human ailments. Methods: The field survey was conducted during July 2018 to January 2020 using guided field-walk method. Santal traditional medicinal practitioners (locally called Kabiraj) and local knowledgeable Santal men and women were interviewed with the help of pretested semi-structured questionnaires to record their knowledge on ethnomedicinal uses of local vegetation in their surroundings. The questionnaire covered aspects like local name, scientific name, family, used parts, ethnomedicinal uses, among others. Plants were collected mostly during the flowering stage and routine method of herbarium techniques was followed and the collected plants were identified using relevant sources. Findings: Altogether 73 medicinal plants of 45 families were recorded to be used to treat 38 types of diseases ranging from very common physical problems to complex diseases. Fabaceae represents the highest number (5 species) of medicinal plants. Herbs (39.73%) and trees (38.36%) represent the dominant life-forms and mostly the plants were collected from the natural habitat (56.16%). For the preparation of medicine, leaves were found to be most frequently used (47.50%) plant part than the others. In general, ethnomedicines were prepared from the fresh plant materials and were administered orally (66.25%) or topically (33.75%). Applications: Documentation of medicinal plants used by the Santals in the treatment of various diseases could further be utilised to develop new drugs and pharmaceutical products. However, to achieve sustainable development, conservation, cultivation and proper utilisation of medicinal plants should be monitored scientifically. Novelty: Utilization of medicinal plants by the Santal tribe has been documented for the first time from Alipurduar district and has enriched the existing database of medicinal plants.
Keywords: Ethnomedicine; medicinal plants; Santal; traditional knowledge; Alipurduar; West Bengal
https://www.indjst.org/
1 Introduction
India, the home of the World’s largest number of indigenous people (8.6% of the total population of India) (1) has a rich herbal heritage. It is well known that the tribal people are mostly dependent on plants than the other communities for their daily livelihood, especially for herbal medicine. Even today, in developing countries, more than 80% population is directly dependent on herbal medicine for healthcare (2,3). In India, the use of medicinal plants for the treatment of diverse variety of ailments has been recorded from ancient times (4,5) and the documentation of such traditional knowledge on ethnomedicine has developed many modern medicines (6,7).
Santals, one of the Adivasis, the third-largest tribes in India after Bhil and Gond, mainly found in the states like Jharkhand, West Bengal, Assam, Tripura, Bihar and Odisha. In West Bengal, they constitute 47.43% of the total tribal population, of which 94.02% lives in rural areas (Census India 2011; http://censusindia.gov.in/). The people from rural areas mostly depend on the herbal or traditional medicine in spite of the development of modern medicine due to low cost of herbal medicine, unavailability of primary healthcare services and the side effect of the synthetic drugs (8). Santals are the descendants of the Austroic-speaking Proto-Australoid race (9). As they have lived on this land probably for thousands of years, they are a rich depository and guardians of indigenous traditional knowledge on medicinal plants (10) and most of the knowledge passed on by verbal means from one generation to another and very rarely documented (11). So, documentation of the medicinal plants used by them can play an important role in the conservation of indigenous knowledge as well as such documentation may be a potential source of discovery of newer and effective drugs. However, day-by-day the population to carry on traditional knowledge is reducing due to the impact of Western lifestyle (12) and less interest on the usefulness of medicinal plants are available in their surroundings (13).
Several ethnobotanical studies on medicinal plants have been conducted in different districts of West Bengal over the past six decades (14–36), focusing primarily on various ethnic groups, but documentation of the ethnobotanical knowledge of Santal tribe is very scanty (37–39).
Scientific documentation of the traditional knowledge of Santal tribe in Alipurduar district of West Bengal is not made so far as per literature surveyed. Sukla and Chakravarty (40) and Raj et al. (41) have reported 18 and 140 medicinal plant species respectively, from the adjoining villages of Chilapatta Reserve Forest of Alipurduar district, West Bengal utilised by several communities like Rava, Ekka, Oraon, Mech, Nepali, Cherwa, etc. other than the Santal tribe. Chaudhury et al. (42) have documented 215 ethnomedicinal plant species used by the Lodha tribe from six different districts of West Bengal including the district Alipurduar.
Keeping this in view, the present study is designed to explore the traditional knowledge on medicinal plants used by Santal tribe residing at seven different villages in Alipurduar district of West Bengal, India.
2 Methodology
2.1 Study area
Alipurduar district is situated on the East bank of Kaljani River on the foothills of the Himalayas (26.489°N 89.527°E), it is known for its rich floristic composition. The district is in under developing status and mostly the rural people depend on the forest plants to treat common physical problems. The present field survey was carried out at seven different villages. The villages namely, Paschim Jitpur (26°32'48.89"N 89°31'14.31"E), Dakshin Majherdabri (26°31'9.12"N 89°33'47.93"E), Jasodanga (26°31'30.45"N 89°37'34.26"E), Salsalabari (26°30'2.64"N 89°36'16.96"E) and Bheukdabri (26°29'20.69"N 89°34'33.10"E) - located at the south side of Buxa Wildlife Sanctuary; Kunjanagar (26°33'26.80"N 89°14'41.02"E) – adjoining village of Torsa Forest; and the village Kadambini Tea Garden (26°31'15.49"N 89°14'5.93"E) are mostly inhabited by Santals (Figure 1).
2.2 Data collection
A total of four field trips were completed for the documentation of traditional knowledge on medicinal plants during July 2018 to January 2020. The data were collected with the help of pretested semi-structured questionnaires (43). Two Santal traditional healers and other knowledgeable persons were interviewed. Prior Informed Consent (PIC) was taken from each informant before interview. Information about the plants were recorded with regards to their vernacular/ Santal name(s), plant parts used, uses, process of preparation of medicine either individually or in combination with other plant parts, and mode of application and dosages for the treatment of a particular disease(s). Plant specimens were collected in their flowering condition as far as possible with guided-walk. Routine methods of plant collection and herbarium techniques (44) have been followed during the study. Digital photographs of the plants were also taken wherever possible. Plant specimens were identified with the help of relevant floras and standard literatures (45–47) and the voucher specimens were kept at the Department of Botany, A. B. N. Seal College, Cooch Behar.
3 Results and Discussion
The results of the field survey have been presented in Table 1. The collected medicinal plants are arranged in alphabetical order according to families and then according to genus and species within - each family. Information regarding Santal name(s) (as recorded during the field work), scientific name, family, habit, parts used and ethnomedicinal uses for each species have also been provided. In most cases, however, the precise method of the preparation of medicine and dosage of administration were not disclosed. As the tribal healers were afraid that on disclosure of such knowledge to the outsiders, their value as a medicine man gets affected.
https://www.indjst.org/
3.1 Medicinal plants recorded and their distribution into families
The present field survey has recorded a total of 73 ethnomedicinal plants belonging to 69 genera and 45 families (Table 1; Figure 2) used by the Santal tribal healers and other Santal men and women. Distribution of plants within families shows variation. The family Fabaceae is represented by the highest number of species (5 species, 6.85%) followed by Apocynaceae (4 species, 5.48%), Acanthaceae, Amaranthaceae, Arecaceae, Cucurbitaceae, Moraceae, Piperaceae and Solanaceae (3 species each, 4.11%), Amaryllidaceae, Asteraceae, Combretaceae, Lamiaceae, Poaceae, Rutaceae and Zingiberalesae (2 species each, 2.74%) and the rest 29 families represented by single species (1.37%). The members of the family Fabaceae contain active chemical constituents like flavonoids, alkaloids, coumarins, tannins, etc., which are used extensively in the treatment of wide variety of human diseases.
Result on the growth habit of the plants shows that herb (29 species, 39.73%) and tree (28 species, 38.36%) dominates among the plant type followed by climber (9 species, 12.33%) and shrub (7 species, 9.59%). Mostly the plants were collected from natural habitat (56.16%) and the rest from the home gardens (43.84%). Besides, collection from natural vegetation, cultivation of medicinal plants in their home garden probably indicated their dependency on ethnomedicine to get relief from common physical problems.
3.2 Plant parts used, mode of preparation and routes of administration
For the preparation of medicine, various plant parts (Table 1; Figure 3) are found to be used by the Santals. Leaves (47.50%) are found to be the dominant plant parts used followed by fruits (11.25%), bark (10.0%), roots and seeds (6.25% each), latex (5.0%), bulb, stem, tuber
and rhizome (2.50% each) and flower, whole plant and branch (1.25% each). Most of the ethnobotanical reports confirmed that leaves are the dominant plant parts used in the preparation of medicine\(^{30,36,37,41,42,50-54}\). Use of plant parts other than leaves may harm the mother plant\(^{37,55}\) and in the present study maximum utilization of leaves indicates sustainable use of the biological resources by the Santals.
Mode of preparation of the medicine encompasses extract (32.5%), paste (21.25%), decoction (20.0%), juice (15.0%), latex (5.0%), ointment (3.75%) and cooked (2.5%), and all the time fresh plant parts were used for medicine preparation. They believe that the fresh plant materials are more effective than the dry ones as - reported earlier by Habibur Rahaman and Karmakar\(^{37}\). Majority of remedies are taken orally (66.25%) followed by topical (33.75%) administration.
| SN | Vernacular Name(s) | Scientific Name | Family | Habit | Parts used | Ethnomedicinal uses |
|----|--------------------------------|---------------------------|------------------|-------------|--------------|-------------------------------------------------------------------------------------|
| 1 | Kalmegh | *Andrographis paniculata* (Brum. f.) Nees | Acanthaceae | Herb | Leaf | Leaf extract is taken orally for 3 days in stomach problems. |
| 2 | Kulekhara | *Hygrophila auriculata* Schumach. | Acanthaceae | Herb | Leaf | Freshly prepared leaf extract is used to treat anemia. |
| 3 | Harbakama | *Justicia adhatoda* L. | Acanthaceae | Shrub | Leaf | Leaf extract is given in an iron pot for purification and then taken orally to treat cough. |
| 4 | Cipcirap | *Achyranthes aspera* L. | Amaranthaceae | Herb | Leaf, root | i) Leaf paste is used to treat skin disease. ii) Fresh root decoction is used for abortion. Crushed whole plant is applied to snake bite. |
| 5 | Gai gandhaori | *Amaranthus viridis* L. | Amaranthaceae | Herb | Whole plant | The flower extract is used in dysentery. |
| 6 | Kukruchubaha | *Celosia cristata* (L.) Kuntze | Acanthaceae | Herb | Flower | The flower extract is used in dysentery. |
| 7 | Peaj | *Allium cepa* L. | Amaryllidaceae | Herb | Bulb | The paste of the bulb is used in the treatment of joint pain. |
| 8 | Rasun | *A. sativum* L. | Amaryllidaceae | Herb | Bulb | The juice made from the bulb is used in the treatment of ear problems. |
| 9 | Aam | *Mangifera indica* L. | Anacardiaceae | Tree | Bark | Juice obtained from crushed bark is orally administered for diarrhoea. |
| 10 | Mandargom | *Annona squamosa* L. | Annonaceae | Tree | Fruit | Fruit is given for digestion. |
| 11 | Rote ara, Dholamanamoni | *Centella asiatica* (L.) Urban | Apiaceae | Herb | Leaf | Leaf extract is mixed with a pinch of salt and taken orally in dysentery. |
| 12 | Chatni | *Alstonia scholaris* (L.) R.Br. | Apocynaceae | Tree | Latex | The Latex is massaged on the fractured bone. |
| 13 | Akana | *Colatropis gigantea* (L.) Dryand. | Apocynaceae | Shrub | Leaf | Heated leaves with a layer of oil are used as heat treatment in fractured bone. |
| 14 | Baromasia | *Catharanthus roseus* (L.) G.Don | Apocynaceae | Herb | Leaf | Leaf decoction is used in the treatment of diabetes. |
| 15 | Sarpagandha | *Rauvolfia serpentina* (L.) Benth. ex Kurz | Apocynaceae | Herb | Root | Root paste is used to treat cuts and wounds and applied on snake bite. Decoction of the root is also used to treat fever and hypertension. |
| 16 | Kachu | *Colocasia esculenta* (L.) Schott | Araceae | Herb | Leaf, tuber | Leaf and tuber curry is taken with food to treat constipation. |
| 17 | Berel gua | *Areca catechu* L. | Arecaceae | Tree | Seed | Nuts are chewed to treat dysentery. |
| 18 | Taal | *Borassus flabellifer* L. | Arecaceae | Tree | Young leaf | The juice of young leaves mixed with water is given in cases of dysentery. |
| 19 | Narkol | *Cocos nucifera* L. | Arecaceae | Tree | Dry fruit | Copra of the dry fruit is crushed to extract oil which is used for ear pain. |
| 20 | Shatamul | *Asparagus racemosus* Willd. | Asparagaceae | Climber | Root | Dried root extract is used to treat dysentery and urine disorder. |
| 21 | Ghritakumari | *Aloe vera* (L.) Burm.f. | Asphodelaceae | Herb | Leaf | Paste prepared from leaf used for skincare. |
| 22 | Tite pati | *Artemisia vulgaris* L. | Asteraceae | Herb | Leaf | It is used to treat nose bleeding, asthma, nervous affections. |
| 23 | Kusumbibaha | *Ta getes erecta* L. | Asteraceae | Herb | Leaf | Leaves extract is used to stop bleeding. |
| 24 | Purai nari | *Basella alba* L. | Basellaceae | Climber | Leaf | Leaf decoction is used in the treatment of diarrhoea. |
| 25 | Banahata, Suri mala | *Oroxylum indicum* (L.) Benth. ex Kurz | Bignoniaceae | Tree | Bark | Stem bark paste is taken orally in the morning in an empty stomach to treat jaundice. |
| 26 | Shimul | *Bombax ceiba* L. | Bombacaceae | Tree | Bark | Juice made from the bark is used in excessive menstrual discharge. |
Continued on next page
| SN | Vernacular Name(s) | Scientific Name | Family | Habit | Parts used | Ethnomedicinal uses |
|----|--------------------|-----------------|--------|-------|------------|--------------------|
| 27 | Anaros | Ananas comosus | Bromeliaceae | Herb | Leaf | The whitish thick basal portion of the leaf is made into a paste and consumed in the treatment of fever. |
| 28 | Ganja | Cannabis sativa | Cannabaceae | Herb | Leaf | Leaf paste is used in bowel complaints |
| 29 | Papaya | Carica papaya | Caricaceae | Tree | Latex, leaf | i) Latex is used as a cleansing agent during menstruation and abortion. ii) Leaf paste is used in bone fracture. |
| 30 | Kouha | Terminalia arjuna (Roxb.) | Combretaceae | Tree | Bark | Bathing with bark decoction reduces body pain. |
| 31 | Boyra | T. bellirica (Gaertn.) | Combretaceae | Tree | Seed | Seeds are used to treat dysentery. |
| 32 | Sornolota | Cuscuta reflexa | Convolvulaceae | Climber | Stem | Juice prepared from the stem is used in stomach problem. |
| 33 | Pathorkuchi | Bryophyllum pinnatum (Lam.) Oken | Crassulaceae | Herb | Leaf | A red hot iron rod is dipped into leaf juice and two teaspoon juice is taken orally thrice daily for a week in diuretic, muscle relaxant, tumor, abdominal pain, etc. |
| 34 | Kenduri | Coccinia grandis (L.) Voigt | Cucurbitaceae | Climber | Leaf | Leaves extract is used to treat hypertension, diabetes. |
| 35 | Kahu botke | Diplocyclos palma tus (L.) C. Jeffrey | Cucurbitaceae | Climber | Leaf | Leaf decoction is used in the treatment of stomach pain. |
| 36 | Karla | Momordica charantia L. | Cucurbitaceae | Climber | Leaf, fruit | Five teaspoon of leaf or fruit extract is taken orally once daily to prevent diabetes, stomach disorder, asthma, anemia. |
| 37 | Sarjam | Shorea robusta | Dipterocarpaceae | Tree | Young leaf | Young leaf paste is used to treat wounds. |
| 38 | Eradom | Ricinus communis L. | Euphorbiaceae | Shrub | Seed | Seed oil applied on belly in stomach ache. |
| 39 | Babla | Vachellia nilotica (L.) P.J.H.Hurter & Mabb. | Fabaceae | Tree | Pods | Pods are prescribed in dysentery. |
| 40 | Murut | Butea monosperma (Lam.) Taub. | Fabaceae | Tree | Seed | Seed are ground into powder and one teaspoon full of powder is mixed with half cup full of water and taken orally once a day in an empty stomach in the treatment of intestinal worm. |
| 41 | Raher | Cajanus cajan (L.) Millsp. | Fabaceae | Shrub | Leaf | Leaves extract is used in jaundice. |
| 42 | Chakoda, Chakaoda | Senna sophera (L.) Roxb. | Fabaceae | Shrub | Leaf | Leaves decoction is used as laxative. |
| 43 | Jojo dare | Tamarindus indica L. | Fabaceae | Tree | Fruit | Fruit is used as laxative. |
| 44 | Durfa | Leucas aspera (Willd.) Link | Lamiaceae | Herb | Leaf | Leaves are crushed and mixed with a little salt and two drops of the juice applied to the nose in headache problem. |
| 45 | Tulsi | Ocimum tenuiflorum L. | Lamiaceae | Herb | Leaf | Leaves extract is mixed with ginger paste and honey is used to treat cough. |
| 46 | Jarul | Lagerstroemia speciosa (L.) Pers. | Lythraceae | Tree | Bark | Bark extract is used as astringent. |
| 47 | Ulatkambal | Abroma augustum (L.) L.f. | Malvaceae | Shrub | Root | Root extract is used to treat the menstrual disorder. |
| 48 | Neem | Azadirachta indica A.Juss. | Meliaceae | Tree | Leaf | Take a regular bath in warm Neem water in the itching problem. |
| 49 | Kanthal | Artocarpus heterophyllus Lam. | Moraceae | Tree | Latex | Latex is used to treat skin problem. |
| 50 | Loa | Ficus racemosa L. | Moraceae | Tree | Latex | Latex mixed with water taken orally to treat diarrhoea. |
Table 1 continued
| SN | Vernacular Name(s) | Scientific Name | Family | Habit | Parts used | Ethnomedicinal uses |
|----|--------------------|-----------------|--------|-------|------------|---------------------|
| 51 | Sahora | *Streblus asper* | Moraceae | Tree | Twig/branch | Used in toothache, also used as tooth brush. i) Mature leaves are boiled and taken orally to treat high blood pressure. ii) Bark extract is used to treat epilepsy. |
| 52 | Chainna | *Moringa oleifera* | Moringaceae | Tree | Leaf, bark | The sap obtained by injuring the lower side of the stock is used in liver problem. Juice is made from bark and taken orally in stomach ache and gastric problem. |
| 53 | Kayra | *Musa paradisiaca* | Musaceae | Herb | Stem | Leaves are made into a paste and taken two teaspoons for 2-3 days for stomach ache or 10-12 days for gastric problems. |
| 54 | Kodedare | *Syzygium cumuni* | Myrtaceae | Tree | Bark | i) Decoction of dried fruit juice is used in the treatment of diarrhoea, dysentery and anemia. ii) Leaf decoction is used to treat fever. |
| 55 | Tandi chatam ara | *Oxalis corniculata* | Oxalidaceae | Herb | Leaf | Dried fruit decoction is used to treat cough, dysentery. |
| 56 | Amla, merel | *Phyllanthus emblica* | Phyllanthaceae | Tree | Fruit, leaf | Leaf juice is used externally for head-ache. Also used for easy delivery. |
| 57 | Pan | *Piper betle* | Piperaceae | Climber | Leaf | i) Fruit decoction is used to treat dysentery. ii) Bark extract is used to reduce lethargy. |
| 58 | Ralee | *P. longum* | Piperaceae | Climber | Fruit, bark | Dried fruit decoction is used to treat cough, dysentery. |
| 59 | Golmirac | *P. nigrum* | Piperaceae | Climber | Fruit | The leaves of the plant are crushed and taken orally to treat blood dysentery. |
| 60 | Chini daare | *Scoparia dulcis* | Plantaginaceae | Herb | Leaf | Leaves are made into a paste (by teeth) and used to stop bleeding. |
| 61 | Dhubi ghas | *Cynodon dactylon* | Poaceae | Herb | Leaf | The root paste is used to treat vaginal disease. |
| 62 | Kharkosa, Patoaghas | *Eleusine indica* | Poaceae | Herb | Root | The leaf extract is taken orally to prevent pregnancy. |
| 63 | Jiyeti | *Persicaria barbata* | Polygonaceae | Herb | Leaf | Paste of seeds is good for leucorrhoea. |
| 64 | Kul | *Ziziphus mauritiana* | Rhamnaceae | Tree | Seed | Leaf decoction is used to treat aphthae. |
| 65 | Kodom | *Neolamarckia cadamba* | Rubiaceae | Tree | Leaf | i) Fruit juice is taken orally in stomach problem. ii) Leaf paste used to treat fever. |
| 66 | Singedaro | *Aegle marmelos* | Rutaceae | Tree | Ripe fruit, leaf | Fruit juice is used to treat intestinal worm. Leaves are made into a paste, warmed and applied on the abscess. |
| 67 | Jambir | *Citrus medica* | Rutaceae | Tree | Fruit | Leaf decoction is given orally to the snake-bite patient. |
| 68 | Dhutra | *Datura metel* | Solanaceae | Tree | Shrub | Boiled tubers are taken with a little salt in stomach pain. |
| 69 | Tamakur | *Nicotiana tabacum* | Solanaceae | Herb | Leaf | Leaf decoction is taken orally with sugar for nerve stimulant. |
| 70 | Alu | *Solanum tuberosum* | Solanaceae | Herb | Tuber | Rhizome paste is used to treat cuts and wounds. |
| 71 | Cha | *Camellia sinensis* | Theaceae | Tree | Leaf | The rhizome paste is used to treat cough. |
| 72 | Shasang | *Carcuma longa* | Zingiberaceae | Herb | Rhizome | |
| 73 | Ada | *Zingiber officinale* | Zingiberaceae | Herb | Rhizome | |
3.3 Diseases treated
Altogether 38 types of physical problems (Figure 4) were found to be treated by the use of the documented medicinal plants. Most of the herbal preparations are found to be used by the Santals to treat dysentery (11 species, 15.07%), followed by abdominal pain and skin diseases (6 species, 8.22% each), stomach problems and female disorders (5 species, 6.85% each), cough and cold, diarrhoea and fever (4 species, 5.48% each).
each), anemia, bone fracture, cuts and wounds, diabetes, hypertension, snake bite (3 species, 4.11% each), among others. This clearly suggests the great extent of traditional knowledge possessed by the healers and the other tribal people to treat several diseases. This knowledge is passed down by verbal means from one generation to another. In the study area, the traditional knowledge is also taught to the interested younger ones (only Santals) by the elders in a 5-days custom (starts on Maha Panchami of Durga puja festival) called Dasabionga. However, recent generations are less aware regarding the importance of the rich traditional knowledge on medicinal plants in their elders. This observation is corroborated with the previous studies as reported by Khatun and Rahman\(^{12}\) and Uniyal et al.\(^{13}\).
### 4 Conclusion
Scientific documentation of traditional knowledge of Santal tribe from the district Alipurduar is done for the first time which will definitely enrich the database. Their knowledge on ethnomedicinal plants is no doubt very rich in the treatment of very common physical problems to complex diseases. This knowledge may be helpful for the development of modern drugs. Day-by-day due to various reasons the natural vegetation degradation is rampant, it will be helpful for further research. Cultivation and sustainable utilization of the threatened taxa is utmost necessity in order to maintain their population in nature.
### Acknowledgement
Authors are thankful to the Santal traditional healers and other knowledgeable persons of the studied area who have participated in the field survey and provided valuable information of ethnomedicinal plants. Grateful regards to the Officer-in-Charge, A. B. N. Seal College and Head, Department of Botany, A. B. N. Seal College for necessary laboratory facilities. Finally, the authors acknowledge the other faculty members of Botany Department, A. B. N. Seal College for their kind guidance and encouragement during the study. The authors are sincerely indebted to the anonymous reviewers for providing valuable suggestions.
### References
1. Faizi S, Nair PK. Adivasis: The World's Largest Population of Indigenous People. Development. 2016;59(3-4):350–353. Available from: https://dx.doi.org/10.1057/s41301-017-0115-8.
2. Farnsworth NR, Akerele O, Bingel AS, Soejarto DD, Guo Z. Medicinal plants in therapy. *Bulletin of the World Health Organization*. 1985;63(6):965–981.
3. WHO. Diet, nutrition and prevention of chronic diseases. 2003. Report of the Joint WHO/FAO Expert Consultation. Geneva, World Health Organisation (WHO).
4. Tulsidas. 1631 Samvat. In: and others, editor. *Ramcharitmanas*.
5. Charak. Charak. Drdbhala. In: and others, editor. The Charak Samhita explained by K. Sastri and G.N. Chaturvedi. Varanasi. Chaukhamba Bharti Academy. 1996.
6. Cox PA, Ballick MJ. The ethnobotanical approach to drug discovery. *Scientific American*. 1994;270(6):82–87.
7. Fabricant DS, Farnsworth NR. The value of plants used in traditional medicine for drug discovery. *Environmental Health Perspective*. 2001;109(suppl 1). doi:10.1289/ehp.011094169.
8. Tiwari DN. Medicinal plants for health care. *Yojana*. 1999;44(6):8–17. Date accessed: 01/04/2020. Available from: http://yojana.gov.in/cms/(S(uawpx4eotnju5xnxtxhpg455))/pdf/Yojana/English/1999/2008-02-11%20(6).pdf.
9. Guha BS. Racial Elements in the Population. Bombay. Oxford University Press. 1944.
10. Moniruzzaman, Bairagee JJ, Kamal Z, Shoma JE, Ton moy AJ, Islam MT, et al. Ethnomedicinal practices among the Hembrom clan of the Santal tribe in Setabganj of Dinaapur District, Bangladesh. *Journal of Chemical and Pharmaceutical Research*. 2015;7(6):76–79.
11. Arzu Y, Thagajaran T. Medicinal Plants used by the Rastafarian Community in Belize. *International Journal of Herbal Medicine*. 2016;4(3):15–20.
12. Khatun MR, Rahman AHMM. Ethnomedicinal uses of plants by Santal Tribal peoples at Nawabganj upazila of Dinaapur district, Bangladesh. *Bangladesh Journal of Plant Taxonomy*. 2019;26(1):117–126. Available from: https://dx.doi.org/10.3329/bjpt.v26i1.41926. doi:10.3329/bjpt.v26i1.41926.
[https://www.indjst.org/](https://www.indjst.org/)
| 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2582,
1
],
[
2582,
8577,
2
],
[
8577,
10393,
3
],
[
10393,
11462,
4
],
[
11462,
17286,
5
],
[
17286,
21194,
6
],
[
21194,
25477,
7
],
[
25477,
29765,
8
],
[
29765,
29765,
9
]
]
} |
9006bcab302456d23bab30ce29a043c9f2b4b9d8 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 3,
"total-fallback-pages": 0,
"total-input-tokens": 8418,
"total-output-tokens": 2680,
"fieldofstudy": [
"Medicine"
]
} | THE ECTOPIC SPLEEN-INCIDENTAL FINDING ON PELVIC MAGNETIC RESONANCE IMAGING
SUMMARY
The ectopic spleen (ES) is a rare variation occurred depend on the absence or laxity of the suspensory ligaments. The ES is a rarely diagnosed clinical condition. Less than 500 symptomatic patients have been reported. Less than 0.25% of splenectomies are performed on the ES. Patients are usually asymptomatic. It’s diagnosed incidentally in general. The incidence is not clear. ES incidence is reported less than 0.5%. However, this rate covers all of the relocations (1). The pelvic ES is a rarely encountered condition. Since the spleen is a reticuloendothelial system organ, the variations like accessory spleen can be misdiagnosed as lymph nodes because of similarity with sonographic echogenicity and computed tomography density. The ectopic spleen may be confused with mass and may be damaged during procedures such as blind paracentesis. Advanced imaging techniques such as magnetic resonance imaging (MRI) are not routinely diagnosis of the ectopic spleen because these lesions are usually asymptomatic. For this reason, clinical physicians and radiologists rarely encounter with MRI appearance of the ectopic spleen. The incidence of trauma, torsion, and infarction increase in the presence of ES. Knowing the presence of ES increases the accuracy of diagnosis in patients with trauma (1,2). A 21 years old female patient with incidentally detected pelvic ES was presented accompanying by MRI findings.
CASE REPORT
A 21-year-old female patient was admitted to the dermatology clinic for erythematous skin rashes. In radiological assessment, hepatobiliary ultrasonography was showed fatty liver and parenchymal nonspecific hypoechoic areas near the portal hilum. The gallbladder and bile ducts were normal.
In the laboratory, liver function tests and blood haemogram values were normal. Upper abdominal MRI was requested because of detected hypoechoic liver areas on ultrasound. On MRI, there was diffuse hepatic steatosis except for the parenchyma around the portal vein. The hypoechoic sonographic focuses in the liver were evaluated to be focal fatty sparing of the liver. However, the spleen was not observed in normal localization in the left upper quadrant. An appearance similar to a mass was detected in the left lower quadrant of the abdomen in the lower sections of MRI imaging, so the radiological examination was shifted to the pelvic region. Pelvic MRI showed an ES located in the left iliac fossa. Hilum was in 180 degrees rotation according to normal. Thereby, rotation anomaly was present (Figure 1A and 1B).
Figure 1A and 1B. Axial (1A) and coronal (1B) T2-weighted images; localized in the left iliac fossa, the hilum was 180 degrees opposite to normal (posterolateral ectopic spleen)
INTRODUCTION
Spleen variations are common encountered in daily routine. Variations include common ones such as the accessory spleen but also rare types such as the ectopic spleen (ES). Less than 500 symptomatic cases of ES have been reported, and less than 0.25% of splenectomies are performed caused by ES. Patients are usually asymptomatic. ES incidence is less than 0.5%. However, this rate covers all of the relocations (1). The pelvic ES is a rarely encountered condition since the spleen is a reticuloendothelial system organ, the variations like accessory spleen can be misdiagnosed as lymph nodes because of similarity with sonographic echogenicity and computed tomography density. The ectopic spleen may be confused with mass and may be damaged during procedures such as blind paracentesis. Advanced imaging techniques such as magnetic resonance imaging (MRI) are not routinely diagnosis of the ectopic spleen because these lesions are usually asymptomatic. For this reason, clinical physicians and radiologists rarely encounter with MRI appearance of the ectopic spleen. The incidence of trauma, torsion, and infarction increase in the presence of ES. Knowing the presence of ES increases the accuracy of diagnosis in patients with trauma (1,2). A 21 years old female patient with incidentally detected pelvic ES was presented accompanying by MRI findings.
Spleen size was in the upper limit of normal (125x42 mm). On T1 and T2 weighted images, parenchymal signals were similar to normal spleen signal. On contrast-enhanced images, the parenchyma homogeneously enhanced. There were no contrast defects typical of infarction (Figures 2A and 2B) or an accessory spleen.
Even if ES cases are mostly asymptomatic, they can cause non-specific complaints such as abdominal pain, nausea, and vomiting due to the compression effect on abdominal organs. The most serious and feared complication is torsion. Patients with torsion develop severe abdominal pain, fever, nausea, and vomiting. Physical examination shows a palpable mass in the abdomen (7). Laboratory tests are generally non-specific, but signs of increased inflammatory parameters, hypersplenism, and functional asplenia may occur. Our case had no active complaint.
The diagnosis of ES is usually made incidentally by imaging methods taken for a different reason. Spleen shadow is not observed in normal localization on abdominal X-ray. The localization, size and blood supply of the spleen can be evaluated by ultrasonography. If torsion has developed, there is no blood supply in the splenic hilum and parenchyma, increased arterial resistance, and decreased venous flow (8). The spleen is not in normal localization on computed tomography. A similar density with the spleen, the existence of the hilum and morphologic appearance are diagnostic. The spiral appearance of splenic vessels and significant decrease in spleen density compared to the liver are evidence of torsion.
The contrast-enhanced computed tomography also provides information about the blood supply of the spleen. The absence of parenchymal contrast enhancement is auxiliary to the diagnosis of torsion (9). In our case, parenchymal enhancement was homogeneous. There was no contrast defect in favor of infarct. Also, accessory spleen tissue was not observed in another localization on abdominal MR images.
The treatment of asymptomatic patients is conservative. Splenopexy operations have become prominent in cases without signs of infarct, torsion and hypersplenism because of the importance of the spleen in the immune system and the increase in fatal infections after splenectomy. In the case of torsion, detorsion is tried and the viability of the spleen is evaluated. Despite detorsion, if the viability of the spleen does not return, splenectomy is inevitable, and infarction occurs (8). In recent years, laparoscopic splenectomy is the most preferred surgical method because of the short hospitalization time and faster recovery period.
**REFERENCES**
1. Qazi SA, Mirza SM, Muhammad AM, Al Arrawi MH, Al-Suhailani YA. Wandering spleen. Saudi J Gastroenterol. 2004 Jan;10(1):1-7. PMID: 19861821. URL: https://pubmed.ncbi.nlm.nih.gov/19861821/
2. Blouhos K, Boulas KA, Salpigktidis I, Baretta N, Hatzigeorgiadis A. Ectopic spleen: An easily identifiable but commonly undiagnosed entity until manifestation of complications. Int J Surg Case Rep. 2014;5(8):451-4. doi: 10.1016/j.ijscr.2014.05.010. Epub 2014 May 28. PMID: 24973525; PMCID: PMC4147574. URL: https://pubmed.ncbi.nlm.nih.gov/24973525/
3. Gayer G, Zissin R, Apter S, Atar E, Portnoy O, Itzchak Y. CT Findings in congenital anomalies of the spleen. Br J Radiol. 2001 Aug;74(884):767-72. doi: 10.1259/bjr.74.884.740767. PMID: 11511506. URL: https://pubmed.ncbi.nlm.nih.gov/11511506/
4. Feroci F, Miranda E, Moraldi L, Moretti R. The torsion of a wandering pelvic spleen: A case report. Cases J. 2008;1(1):149. Published 2008 Sep 10. doi:10.1186/1757-1626-1-149 URL: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2553057/
5. Varga I, Galfiova P, Adamkov M, Danisovic L, Polak S, Kubikova E, Galbavy S. Congenital anomalies of the spleen from an embryological point of view. Med Sci Monit. 2009 Dec;15(12):RA269-76. PMID: 19946246. URL: https://pubmed.ncbi.nlm.nih.gov/19946246/
6. Lebron R, Self M, Mangram A, Dunn E. Wandering spleen presenting as recurrent pancreatitis. JSLS. 2008;12(3):310-313. URL: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3015861/
7. Danaci M, Belet U, Yalin T, Polat V, Nurol S, Selçuk MB. Power Doppler sonographic diagnosis of torsion in a wandering spleen. J Clin Ultrasound. 2000 Jun;28(5):246-8. doi: 10.1002/(sici)1097-0096(200006)28:5<246::aid-jcu6-3.0.co;2-#. PMID: 10800003. URL: https://pubmed.ncbi.nlm.nih.gov/10800003/
8. Soleimani M, Mehrabi A, Kashfi A, Fonouni H, Büchler MW, Kraus TW. Surgical treatment of patients with wandering spleen: report of six cases with a review of the literature. Surg Today. 2007;37(3):261-9. doi: 10.1007/s00595-006-3389-0. Epub 2007 Mar 9. PMID: 17342372. URL: https://pubmed.ncbi.nlm.nih.gov/17342372/
9. Ben Ely A, Zissin R, Copel L, Vasserman M, Hertz M, Gottlieb P, Gayer G. The wandering spleen: CT findings and possible pitfalls in diagnosis. Clin Radiol. 2006 Nov;61(11):954-8. doi: 10.1016/j.crad.2006.06.007. PMID: 17018308. https://pubmed.ncbi.nlm.nih.gov/17018308/ | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4170,
1
],
[
4170,
7591,
2
],
[
7591,
9161,
3
]
]
} |
105571d8da6280f0b5356876725d5b44e8f2467f | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 23276,
"total-output-tokens": 5348,
"fieldofstudy": [
"Physics",
"Mathematics"
]
} | On the Irreps of the $N$-Extended Supersymmetric Quantum Mechanics and Their Fusion Graphs.
Francesco Toppan$^a$
$^a$CBPF, Rua Dr. Xavier Sigaud 150, cep 22290-180, Rio de Janeiro (RJ), Brazil
E-mail: [email protected]
March 27, 2022
Abstract
In this talk we review the classification of the irreducible representations of the algebra of the $N$-extended one-dimensional supersymmetric quantum mechanics presented in hep-th/0511274. We answer some issues raised in hep-th/0611060, proving the agreement of the results here contained with those in hep-th/0511274. We further show that the fusion algebra of the 1D $N$-extended supersymmetric vacua introduced in hep-th/0511274 admits a graphical presentation. The $N = 2$ graphs are here explicitly presented for the first time.
1 Introduction
The one-dimensional $N$-extended supersymmetric quantum mechanics is an important and active research subject in many areas of both mathematics and physics. We refer to [1] and [2] for more comprehensive recent reviews of some of its aspects which, due to space-time limitations, cannot be covered in the present talk. Here we will focus on two main topics. At first, we make a review of the current status of the classification of the irreducible linear representations of the algebra associated with the one-dimensional supersymmetric quantum mechanics. In the following it will be presented a graphical interpretation of the 1D fusion algebra introduced in [3].
Concerning the classification of the irreps, the basic references are [4] and [3]. In [4] it was proven, essentially, that the irreps fall into classes of equivalence characterized by an associated Clifford algebra irrep (the connection between Clifford algebras and extended supersymmetries of 1D quantum mechanics was previously shown in [5, 6, 7]). In [3] this result was used as the starting point to produce a classification of the irreps. In this work a presentation of the results of [3] will be made. Some issues raised in [8] (see also [9]) will be answered, proving the compatibility of their results with the [3] classification.
It seems appropriate to present this seminar in a Symposium in honour of Jerzy Lukierski. Even if our collaboration did not involve the topics here discussed, the results here presented, however, were made possible by applying a formalism first elaborated in our common works (especially [10]).
2 The classification of the irreps
The finite linear irreps of the $D = 1$ $N$-extended supersymmetry algebra
$$\{Q_i, Q_j\} = \delta_{ij}H$$
(where the $Q_i$'s, $i, j = 1, \ldots, N$, are the supersymmetry generators and $H$ is the hamiltonian) are expressed by the set of $(n_1, n_2, \ldots, n_l)$ symbols representing the field-contents of the irreps. The non-negative integers $n_i$'s specify the number of fields of dimension $d_i = d_1 + \frac{i-1}{2}$ entering an irrep (the constant $d_1$ can be arbitrarily chosen). The fields whose dimension differs by $\frac{1}{2}$ have opposite statistics (bosonic/fermionic). The number $l$ specifies the number of different dimensions of the fields entering an irrep and is referred to as the “length” of the irrep; $l$ must satisfy the condition $l \geq 2$, with the $l = 2$ irreps being known in the literature as the “minimal-length” or “root” multiplets. In [3] it was explicitly presented the complete list of the allowed $(n_1, n_2, \ldots, n_l)$ field contents for $N \leq 10$. An algorithmic construction for computing the field contents for arbitrarily large values of $N$ was produced and selected $N > 10$ examples were given. The list in [3] is understood as follows: for any $N$, $(n_1, n_2, \ldots, n_l)$ is present if and only if there exists at least one $N$-irrep with the given field content. As an example, the length-4 $(1, 7, 7, 1)$ field content is present for $N = 5, 6, 7$, but not for $N = 8$, meaning that there are no irrep with the given field content for $N = 8$, but there is (at least one) such irrep for $N = 5, 6, 7$.
The construction of [3] heavily relied on the [4] results which we briefly summarize here. All $N$-irreps of length $l \geq 3$ are obtained from the set of $\overline{Q}_j$ operators acting on root
multiplets after applying an acceptable dressing transformation $\overline{Q}_i \rightarrow D\overline{Q}_i D^{-1} = Q'_i$.
The dressing operator $D$ is a diagonal operator whose entries are either 1 or positive powers of $H$. “Acceptable” refers to the fact that the whole set of $Q'_i$ transformed operators must be regular (that is, as matrix operators, they must not contain any entry with $\frac{1}{H}$ or higher poles). Two distinct acceptable operators $D_1$, $D_2$ leading to the same field content applied on the same set of $\overline{Q}_i$ root multiplets operators are given by a permutation of their diagonal entries. $D_1$, $D_2$ are obviously related by a similarity transformation, $D_2 = SD_1S^{-1}$ (it is worth recalling that the exchange of the diagonal elements in, e.g., a $2 \times 2$ diagonal matrix $D$ is recovered in terms of the $2 \times 2$ similarity matrix $S = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$). Similarity transformations between two acceptable dressings of given field-content and for a fixed set of $\overline{Q}_i$ operators acting on root multiplets form a group of transformations which corresponds to a subgroup $\tilde{G}$ of the permutation group of the diagonal elements of the dressing transformations.
Concerning the length-2 root multiplets the situation is the following. They are recovered by an associated Clifford irrep of Weyl type (i.e., whose generators are in block antidiagonal form) through the following position
$$\overline{Q}_i = \frac{1}{\sqrt{2}} \begin{pmatrix} 0 & \sigma_i \\ \tilde{\sigma}_i \cdot H & 0 \end{pmatrix},$$
(2)
where $\sigma_i$ and $\tilde{\sigma}_i$ are matrices entering the associated Clifford generators
$$\Gamma_i = \begin{pmatrix} 0 & \sigma_i \\ \tilde{\sigma}_i & 0 \end{pmatrix}, \quad \{\Gamma_i, \Gamma_j\} = 2\delta_{ij}.$$
(3)
The $N$ Clifford generators entering (3) are recovered from the block-antidiagonal space-like generators of the $Cl(p,q)$ Clifford algebras (with $(p,q)$ signature) according to the following scheme:
$$\begin{array}{ccc}
Cl(2+8m,1) & \rightarrow & N = 1 \mod 8 \\
Cl(3+8m,2) & \rightarrow & N = 2 \mod 8 \\
Cl(4+8m,3) & \rightarrow & N = 3 \mod 8 \\
Cl(5+8m,0) & \rightarrow & N = 3, 4 \mod 8 \\
Cl(6+8m,1) & \rightarrow & N = 5 \mod 8 \\
Cl(9+8m,0) & \rightarrow & N = 5, 6, 7, 8 \mod 8
\end{array}$$
(4)
The maximal value for $N$ corresponds to $N = p - 1$ (the “oxidized” cases [3]). The reduced supersymmetries (for $N < p - 1$) are obtained by selecting a proper subset of the block antidiagonal $Cl(p,q)$ space-like generators. Notice that, unlike the other values of $N$, the $N = 3, 5 \mod 8$ cases can be recovered in two different ways.
For a fixed value of $N$, the $N$ Clifford generators entering (3) can be uniquely chosen up to similarity transformations (this result is in consequence of the unicity of the real irreducible Clifford algebra representations for $p - q \neq 1, 5 \mod 8$).* This important property applies in particular to the reduced values of $N$, implying that two different choices
*Please notice that this new set of similarity transformations acts on supersymmetry operators for root multiplets; it should not be confused with the set of similarity transformations acting on dressing operators.
of the $N < p - 1$ proper subset of block antidiagonal space-like generators are equivalent. It also implies that the two ways in (4) of recovering the $N = 3, 5 \mod 8$ supersymmetries are equivalent, producing root multiplets which are related by similarity transformations. For any given $N$ the (3) Clifford generators associated to supersymmetric root multiplets can be canonically chosen. They can be presented as matrices whose non-vanishing entries are $\pm 1$. A group $G$ of similarity transformations relates all choices of Clifford generators whose non-vanishing entries are $\pm 1$. The dressing transformations, applied to each set of Clifford generators of this type, produce irreps with the same field-contents. Taking into account these properties, the [3] classification of the field-contents produces a classification of the linear finite irreps of the $D = 1 \ N$-extended supersymmetry. The $(n_1, \ldots, n_l)$ symbol uniquely characterizes the irreps upon which the $D \overline{Q}_i D^{-1}$ supersymmetry operators act. The $\overline{Q}_i$ operators acting on root multiplets are related by the group $G$ of similarity transformations, while the acceptable dressing operators $D$ are related by the group $\tilde{G}$ of similarity transformations. Under this equivalence class of transformations, $(n_1, \ldots, n_l)$ uniquely specifies an irrep.
The complete list of $(n_1, \ldots, n_l)$ irreps for $N \leq 10$ is furnished in [3] and will not be reproduced here.
3 Irreps fusion algebras and the associated graphs
The notion of fusion algebra of the supersymmetric vacua of the $N$-extended one dimensional supersymmetry was introduced in [3]. The tensoring of two zero-energy vacuum-state irreps (irreps associated with the zero energy eigenvalue of the hamiltonian operator $H$) can be symbolically written as
$$[i] \times [j] = N_{ij}^k [k]$$ \hspace{1cm} (5)
where $N_{ij}^k$ are non-negative integers specifying the decomposition of the tensored-products irreps into its irreducible constituents. The $N_{ij}^k$ integers satisfy a fusion algebra with the following properties
1) Constraint on the total number of component fields,
$$\forall \ i, j \ \sum_k N_{ij}^k = 2d$$ \hspace{1cm} (6)
where $d$ is the number of bosonic (fermionic) fields in the given irreps.
2) The symmetry property
$$N_{ij}^k = N_{ji}^k$$ \hspace{1cm} (7)
3) The associativity condition,
$$[i] \times ([j] \times [k]) = ([i] \times [j]) \times [k]$$ \hspace{1cm} (8)
which implies the commutativity of the $(N_{ij}^k)^T = N_{ji}^k$ fusion matrices.
Fusion algebras can also be nicely presented in terms of their associated graphs. The $N = 1$ and $N = 2$ fusion graphs are produced in the Appendix (with two subcases for each
$N$, according to whether or not the irreps are distinguished w.r.t. their bosonic/fermionic statistics). Let us discuss here how to present the [3] results in graphical form. The irreps correspond to points. $N_{ij}^k$ oriented lines (with arrows) connect the $[j]$ and the $[k]$ irrep if the decomposition (5) holds. The arrows are dropped from the lines if the $[j]$ and $[k]$ irreps can be interchanged. The $[i]$ irrep should correspond to a generator of the fusion algebra. This means that the whole set of $N_i = N_{ij}^k$ fusion matrices is produced as sum of powers of the $N_i = N_{ij}^k$ fusion matrix.
Let us discuss explicitly the $N = 2$ case. We obtain the following list of four irreps (if we discriminate their statistics):
\[ [1] \equiv (2, 2)_{Bos}; [2] \equiv (1, 2, 1)_{Bos}; [3] \equiv (2, 2)_{Fer}; [4] \equiv (1, 2, 1)_{Fer} \tag{9} \]
The corresponding $N = 2$ fusion algebra is realized in terms of four $4 \times 4$, mutually commuting, matrices given by
\[
N_1 = \begin{pmatrix}
1 & 2 & 1 & 0 \\
0 & 2 & 0 & 2 \\
1 & 0 & 1 & 2 \\
0 & 2 & 0 & 2
\end{pmatrix} \equiv X; N_2 = N_4 = \begin{pmatrix}
0 & 2 & 0 & 2 \\
0 & 2 & 0 & 2 \\
2 & 0 & 2 \\
0 & 2 & 0 & 2
\end{pmatrix} \equiv Y; N_3 = \begin{pmatrix}
1 & 0 & 1 & 2 \\
0 & 2 & 0 & 2 \\
1 & 2 & 1 & 0 \\
0 & 2 & 0 & 2
\end{pmatrix} \equiv Z. \tag{10}
\]
The fusion algebra admits three distinct elements, $X, Y, Z$ and one generator (we can choose either $X$ or $Z$), due to the relations
\[
Y = \frac{1}{8}(X^3 - 2X), \quad Z = -\frac{1}{4}(X^3 - 6X^2 + 4X). \tag{11}
\]
The vector space spanned by $X, Y, Z$ is closed under multiplication
\[
X^2 = Z^2 = ZX = X + 2Y + Z, \\
XY = Y^2 = YZ = 4Y. \tag{12}
\]
This fusion algebra corresponds to the “smiling face” graph (Figure 4 in the Appendix).
## 4 Conclusions
The supersymmetric quantum mechanism is a fascinating subject with several open problems. The potentially most interesting one concerns perhaps the construction of off-shell invariant actions with the dimension of a kinetic term for large values of $N$ (let’s say $N > 8$). They could provide some hints towards an off-shell formulation of higher-dimensional supergravity and $M$-theory. The fusion algebras, which encode the information of the decomposition of tensor representations, could provide useful in attacking this problem.
Concerning the representation theory itself, some questions are still opened. The authors of [8] pointed out the existence of inequivalent (starting from $N \geq 5$) supersymmetry irreps with the same field content. They explicitly discussed the $N = 5$ $(6, 8, 2)$ and the $N = 6$ $(6, 8, 2)$ irreps, producing in both cases two inequivalent irreps. These results are in agreement with those in [3]. At first it must be noticed that $(6, 8, 2)$ is an admissible field content for both $N = 5$ and $N = 6$ irreps, see [4]. The inequivalences obtained in [8] correspond to a different notion of the equivalence relation than the one here discussed (their equivalence class is w.r.t.
the general linear transformations of the supersymmetry generators and/or fields). It produces a refinement of the equivalence relation here employed. To spot the differences, one can use the valid analogy of the classification of simple Lie algebras. Simple Lie algebras over the complex numbers are classified by the Dynkin’s diagrams, while simple Lie algebras over the reals are obtained by the real forms. The \((n_1, \ldots, n_l)\) field contents work as Dynkin’s diagrams, uniquely specifying the irreps under the class of equivalence here discussed.
Concerning the classification of irreps, the present status is the following. The complete classification of the irreps under the equivalence relation here discussed was produced in [3] (explicit results were furnished for \(N \leq 10\)). At present, no classification of irreps is yet available under the [8] notion of the equivalence relation.
Appendix: the \(N = 1, 2\) fusion graphs.
We present here four fusion graphs of the \(N = 1\) and \(N = 2\) supersymmetric quantum mechanics irreps. The “A” cases below correspond to ignore the statistics (bosonic/fermionic) of the given irreps. In the “B” cases, the number of fundamental irreps is doubled w.r.t. the previous ones, in order to take the statistics of the irreps into account. The construction of the graphs is discussed in the main text.
Figure 1: Fusion graph of the \(N=1\) superalgebra, \(A\) case, 1 irrep \(((1,1))\), no bosons/fermions distinction.
Figure 2: Fusion graph of the N=1 superalgebra, B case, 2 irreps \(((1, 1)_{Bos} \text{ and } (1, 1)_{Fer})\) with bosons/fermions distinction.
Figure 3: Fusion graph of the N=2 superalgebra, A case, 2 irreps \(((2, 2) \text{ and } (1, 2, 1))\), no bosons/fermions distinction.
Figure 4: Fusion graph of the N=2 superalgebra, B case, 4 irreps, bosons/fermions distinction, “the smiling face”. From left to right the four points correspond to the [2] – [1] – [3] – [4] irreps, respectively. The lines are generated by the $N_1 \equiv X$ fusion matrix, see (10).
Acknowledgments
I am grateful to the organizers of the Max Born Symposium for the kind invitation. I am pleased to thank my collaborators Z. Kuznetsova and M. Rojas for the main results here presented. Concerning fusion graphs, I have profited of helpful discussions with R. Coquereaux, while F.V. Fortaleza de Vasconcelos is credited for the drawings. This work received financial support from CNPq and FAPERJ.
References
[1] S. Bellucci and S Krivonos, hep-th/0602199.
[2] F. Toppan, POS (IC2006) 033 (also hep-th/0610180).
[3] Z. Kuznetsova, M. Rojas and F. Toppan, JHEP 0603 (2006) 098 (also hep-th/0511274).
[4] A. Pashnev and F. Toppan, J. Math. Phys. 42 (2001) 5257 (also hep-th/0010135).
[5] M. de Crombrugghe and V. Rittenberg, Ann. Phys. 151 (1983) 99.
[6] M. Baake, M. Reinicke and V. Rittenberg, J. Math. Phys. 26 (1985) 1070.
[7] S.J. Gates Jr. and L. Rana, Phys. Lett. B 352 (1995) 50 (also hep-th/9504025); Phys. Lett. B 369 (1996) 262 (also hep-th/9510151).
[8] C.F. Doran, M.G. Faux, S.J. Gates Jr., T. Hubsch, K.M. Iga and G.D. Landweber, hep-th/0611060.
[9] C.F. Doran, M.G. Faux, S.J. Gates Jr., T. Hubsch, K.M. Iga and G.D. Landweber, math-ph/0603012.
[10] J. Lukierski and F. Toppan, Phys. Lett. B 539 (2002) 266 (also hep-th/0203149). | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
780,
1
],
[
780,
4200,
2
],
[
4200,
7478,
3
],
[
7478,
10229,
4
],
[
10229,
13248,
5
],
[
13248,
14729,
6
],
[
14729,
15008,
7
],
[
15008,
16468,
8
],
[
16468,
16552,
9
]
]
} |
3913f3faa6c39cc7f621580eda7385d182b2f133 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 12,
"total-fallback-pages": 0,
"total-input-tokens": 45201,
"total-output-tokens": 16532,
"fieldofstudy": [
"Medicine"
]
} | Dietetic intervention in psoriatic arthritis: the DIETA trial
Beatriz F. Leite1*, Melissa A. Morimoto1, Carina M. F. Gomes1, Barbara N. C. Klemz1, Patrícia S. Genaro2, Nittin Shivappa3, James R. Hébert3, Nágila R. T. Damasceno4 and Marcelo M. Pinheiro1
Abstract
Aim: To evaluate whether dietary pattern changes, antioxidant supplementation or 5–10% weight loss could improve disease activity (skin and joint) in patients with psoriatic arthritis (PsA).
Methods: A total of 97 PsA patients were enrolled in this 12-week randomized, double-blinded, placebo-controlled trial. Patients were randomized into three groups: Diet-placebo (hypocaloric diet + placebo supplementation); Diet-fish (hypocaloric diet + 3 g/day of omega-3 supplementation; and Placebo. Food intake (3-day registry, Healthy Eating Index (HEI), and the Dietary Inflammatory Index (DII)), body composition (whole-body dual-energy X-ray absorptiometry (DXA), weight and waist circumference) and disease activity (PASI, BSA, BASDAI, DAS28-ESR, DAS28-CRP and MDA) were evaluated at baseline and after the 12-week intervention. Statistical analysis used the intention-to-treat approach. The P value was considered to indicate significance when below 0.05.
Results: After 12 weeks, DAS28-CRP and BASDAI scores improved, especially in the Diet-placebo group (−0.6 ± 0.9; p = 0.004 and −1.39 ± 1.97; p = 0.001, respectively). In addition, a higher proportion of patients achieved minimal disease activity (MDA) in all groups. The Diet-fish group showed significant weight loss (−1.79 ± 2.4; p = 0.004), as well as waist circumference (−3.28 ± 3.5, p < 0.001) and body fat (−1.2 ± 2.2, p = 0.006) reductions. There was no significant correlation between weight loss and disease activity improvement. Each 1-unit increase in the HEI value reduced the likelihood of achieving remission by 4%. Additionally, each 100-cal daily intake increase caused a 3.4-fold DAS28-ESR impairment.
Conclusion: A 12-week hypocaloric intervention provided suitable control of joint disease activity in patients with PsA, regardless of weight loss. Adding omega-3 supplementation caused relevant body composition changes but not disease activity improvement.
Trial Registration: The study was recorded on Clinicaltrials.gov (NCT03142503).
Keywords: Psoriatic arthritis, Antioxidant, Diet, Randomized clinical trial, Food intake, Body composition measurements
Introduction
Psoriatic arthritis (PsA) is a chronic inflammatory disease that affects 20–33% of patients with psoriasis (Ps) [1]. The joint and skin outcomes are associated with multiple comorbidities, particularly metabolic syndrome (MetS), obesity, hypertension and diabetes [2]. These findings suggest a potential link between adiposity and Ps/PsA, highlighting a possible fat-joint-skin axis mediated by...
cells and proinflammatory cytokines, oxidative stress, dysbiosis and nutritional inadequacy [3].
More recently, it was demonstrated that an increased body mass index (BMI) caused a 50-fold greater likelihood of having PsA [4], as well as a lower chance of achieving disease remission [2] and worse response to pharmacological treatment, including a higher switching rate [2]. In addition, a significant association between disease activity and body composition measurements, such as a positive correlation with fat mass and a negative correlation with lean mass, has been reported [5]. Some studies have also shown weight gain after using tumor necrosis factor (TNF-α) blockers [6], suggesting that adjustments of these agents based on body weight are necessary to achieve a better drug response and lower toxicity [7].
Several nonpharmacological strategies, including weight loss and antioxidant supplementation, have had beneficial effects on obesity [8, 9], dyslipidemia [10, 11], nonalcoholic fatty liver disease [10] and diabetes [11]. However, only two controlled clinical trials evaluated the impact of weight loss on the disease activity of patients with PsA [7, 12]. Di Mino et al. [7] demonstrated that a 5 to 10% reduction in body weight increased the chance of disease remission, and Abou-Raya et al. [12] reported that the combination of a hypocaloric diet and exercise was a suitable intervention to improve PsA disease activity, depression and fatigue.
Based on the potential adjuvant effect of weight loss on the improvement of the clinical response of PsA patients, the aim of this study was to evaluate whether a dietary pattern change added to antioxidant supplementation or a 5–10% weight loss could improve the disease activity in patients with PsA, including skin and joint outcomes and inflammatory markers.
**Methods**
**Study design and sampling**
A sample of 85 patients was calculated based on an α error of 5% and β of 20% and was increased by 15% to minimize potential losses during follow-up. Thus, 97 patients aged 18 years or older with PsA, according to the Classification Criteria of Psoriatic Arthritis (CASPAR) [13], were enrolled in this 12-week randomized, double-blinded, placebo-controlled clinical trial (Fig. 1).
Patients with PsA were recruited from Sao Paulo’s Hospital (Sao Paulo, Brazil) and other rheumatology facilities.
(Heliopolis Hospital and Public State Hospital, Sao Paulo, Brazil) from September 2012 to May 2014. Patients with gastrointestinal, endocrine, pulmonary, kidney, hepatic, and neuromuscular diseases; with an HIV-positive diagnosis; who were pregnant or breastfeeding, or who had a history of cancer were excluded. Patients taking anabolic steroids, protein supplements, vitamins, multivitamins, or antioxidants or who were allergic to fish and shellfish products were also excluded. Specific medications for PsA and physical activity were required to be stable for the 3 months prior to enrollment.
The study was approved by the Ethics Committee of Research at the Federal University of Sao Paulo (CAAE: 00591412.5.0000.5505) and was recorded on Clinicaltrials.gov (NCT03142503). Subjects were included in the study after signing an informed consent form, in accordance with the Declaration of Helsinki.
Randomization
Patients were equally randomized using randomizer.org into three different groups: Diet-Placebo—a hypocaloric diet plus placebo supplementation (1 g of soybean oil, 3 times a day); Diet-Fish—a hypocaloric diet plus omega 3 supplementation (362 mg of EPA and 242 mg of DHA, 3 times a day); and Placebo: 1 g of soybean oil 3 times a day and no dietary intervention. After 12 weeks, 91 patients completed the study, corresponding to 93.8% of the original sample (dropout rate = 6.2%) (Fig. 1). All tools and measurements, including food intake records, physical activity, disease activity, body composition, and lab tests, were analyzed before and after the 12-week intervention.
Dietary intervention
The patient diet was tailored, supervised and calculated by a well-trained nutritionist according to the nutritional needs, dietary habits, culture, socioeconomic level and routine of each individual patient. The diet for overweight and obese patients considered their basal metabolic rate [14] and included a 500-kcal restriction, as proposed by the Institute of Medicine [15, 16]. For eutrophic patients, the diet was calculated without a caloric restriction, aiming at maintaining their weight [15]. In both cases, macronutrients were divided into 45–65% carbohydrates, 10–35% proteins and 20–35% lipids [16], with reduced saturated fat (<7% of daily caloric intake—DCI) and increased monounsaturated (20% of DCI) and polyunsaturated (6–10% of DCI) fats [17]. The omega-6:omega-3 ratio was 5:1, and cholesterol intake was lower than 300 mg a day [17]. Daily fiber consumption was 20–30 g [18].
All patients were instructed to make 3 main meals (breakfast, lunch and dinner), have 2 or 3 snacks between meals, and increase their intake of water, fruits and vegetables, avoiding processed foods.
In monthly meetings, the dietitian checked the patient’s diet adherence with a 24-h diet record and performed weight and waist circumference measurements. A brief anamnesis concerning concomitant drug use, current physical activity, sleep pattern, gut changes and side effects during the intervention was performed. Supplement exchange and pill count were also evaluated.
To ensure compliance with the nutritional intervention, patients were contacted monthly by e-mail or telephone. In addition, the nutritionist was available online throughout the intervention to clarify any doubts or complaints.
Patients who were not allocated to a diet group (Diet-Placebo or Diet-Fish) were counseled to maintain their habitual diet. After the 12-week intervention, a healthy diet was prescribed to these patients (placebo group).
Outcome measurements
To evaluate the activity and severity of PsA skin involvement, the psoriasis area severity index (PASI) [19] and body surface area (BSA) [20] were used. Joint assessment was performed using tools such as the disease activity score (DAS28-ESR and DAS28-CRP) [21]. Axial complaints were evaluated using the Bath Ankylosing Spondylitis Disease Activity Index (BASDAI) [22]. Functional capacity was evaluated using the health assessment questionnaire (HAQ) [23]. Minimal disease activity (MDA) was also used to identify patients in remission and assess the response to this particular intervention [24].
Three-day food records (3-DFR) were used to evaluate food intake. All subjects were asked to record their food and beverage intake for 3 days: 2 weekdays (alternate days) and one weekend day (Saturday or Sunday). Nutrient data were calculated using The Food Processor SQL – Professional Nutrition. Energy was adjusted using the residual method described by Willett and Stamper [25] in Analysis Software and Databases – ESHA Research, USA, 2010. To enhance the accuracy of nutritional data, the Diet Quality Index (DQI) [26] and Dietary Inflammatory Index (DII) [27] were also calculated.
Metabolic syndrome (MetS) was defined according to the Harmonization criteria [28], which assess the presence of dyslipidemia, hypertension, insulin resistance and central obesity as risk factors.
To analyze physical activity status, the International Physical Activity Questionnaire (IPAQ-short form) [29] and metabolic equivalents (METS) [29] were used. Patients were placed into the following categories: inactivity, minimal activity or health-enhancing physical activity, a high activity category.
Body composition measurements were assessed using dual-energy X-ray absorptiometry (DXA, GE-Lunar...
Radiation Corporation, DPX MD+, Madison, WI, USA) according to the standard protocol for acquisition and analysis suggested by the International Society Clinical Densitometry (ISCD). Measurements included total lean mass (kg), skeletal lean mass (kg), total and regional adipose tissue (kg e %), total bone mineral density (g/cm²), and bone mineral content (g). The coefficients of variation were 1.14%, 1.64%, 1.53%, 1.62%, 0.67%, and 1.72%, respectively [30]. To identify low appendicular lean mass (ALM), Baumgartner’s method was used for patients older than 50 years, and Rosetta’s method was used for those under 50 years old, according to sex [31]. The fat mass index (FMI) was calculated using the equation proposed by NHANES III, with reference values of 5–9 kg/m² for females and 3–6 kg/m² for males [32].
Statistical analysis
Descriptive statistics are expressed as the mean, standard deviation, and frequency (%).
The association between two categorical variables was verified using the chi-square test or, in cases of small samples, Fisher’s exact test. The linear associations between two variables of numerical nature were evaluated by Pearson’s correlation.
For the evaluation of the behavior of the means of the clinical variables at two time points per treatment group, analysis of variance (ANOVA) with repeated measures was used, with group as a fixed factor. ANOVA was used to analyze data with a normal distribution, which was verified using the Kolmogorov–Smirnov test. For nonnormally distributed data, the means of the groups at each time point were compared using the Kruskal–Wallis nonparametric test. The means of each group between time points were compared using the nonparametric Wilcoxon test.
The McNemar test was used to determine whether there were differences in a dichotomous dependent variable between two related groups with a continuous dependent variable.
The comparison of two means was performed using Student’s t test. For nonnormally distributed data, the nonparametric Mann–Whitney test was used.
An intention-to-treat analysis was performed for all outcomes. To evaluate the simultaneous effects of sex, age, joint and cutaneous disease time, group (nutritional intervention) and capsule count, multiple linear regression was used. Logistic regression was used for dependent variables of a dichotomous nature (DAS28-VHS, DAS28-PCR and MDA classes). Linear regression presents normality as one of the assumptions. In all regression models, due to the large number of explanatory variables versus sample size, the variables whose associations with the dependent variable were significant at 10% in the univariate analysis were selected for the model. Initially, all the selected explanatory variables were included in the model, and then the variables that were nonsignificant at 5% were excluded one by one in order of significance (backward method). P values below 5% were considered indicative of significance. All data were analyzed using SPSS version 20.0.
Results
Age, sex, disease duration, body composition measurements, comorbidities, disease activity (joint and skin) and concomitant medications were similar between the groups at baseline (Table 1). There was a high prevalence of hypertension, diabetes, and overweight/obesity among the patients, regardless of intervention group. Normal BMI was observed in 12.1% of the placebo group, 19.4% of the diet-fish group and 15.6% of the diet-placebo group.
Most patients were physically inactive or minimally active, according to the IPAQ. Approximately 60% were postmenopausal women, and nearly 20% were taking hormone replacement therapy (data not shown).
After the 12-week nutrition intervention, all groups had a reduction in DAS28-CRP values (p = 0.004), although the Diet-placebo group showed a disease activity improvement nearly three times higher than that of the Placebo group. Considering only the skin outcome, there was no significant change. An MDA outcome was achieved for all groups (p = 0.006) (Table 2). Although not significant, the Diet-placebo group had a fourfold greater likelihood of improving the DAS28-ESR value than the Placebo group (exp B = 4.049).
There was no significant change regarding physical activity or therapy with disease-modifying antirheumatic drugs (DMARDs), including conventional synthetic and biologic agents, and medications related to metabolism, such as insulin, statins, and other antidiabetic drugs, after the 12-week intervention (Table 1). Although all groups had significant weight loss, only the Diet-fish group had body composition changes, including body fat, fat mass index and waist circumference reduction during the follow-up time. However, no relevant lean mass changes were observed. Surprisingly, only the Diet-placebo group showed a significant food intake improvement, as shown by a reduced DII value and decreased calorie (kcal/kg) and fat consumption (Table 3). In addition, there was no difference between the prescribed (1687.7 ± 339.6 kcal) and consumed (1737.8 ± 840.2 kcal) diets (p = 0.63) of patients in the diet intervention groups.
Interestingly, a dietary inflammatory pattern improvement was associated with higher micronutrient intake but not macronutrient consumption, except in the Diet-placebo group, which had a significant fat intake...
Table 1 Baseline clinical data of the PsA patients, according to intervention group
| | Placebo (n = 33) | Diet-fish (n = 32) | Diet-placebo (n = 32) | P |
|--------------------------------------|------------------|--------------------|-----------------------|----------|
| Age (years) | 53.6 (10.2) | 54.6 (13.7) | 51.2 (15.1) | 0.59 |
| Women, n (%) | 18 (54.5) | 17 (54.8) | 18 (54.5) | 1.00 |
| Length joint disease (months) | 157.1 (133.9) | 162.8 (140.1) | 147.8 (231.4) | 0.18 |
| Length skin disease (months) | 238.9 (162.8) | 216.8 (153.9) | 237.4 (227.1) | 0.87 |
| Weight (kg) | 76.2 ± 16.2 | 76.5 ± 14.2 | 80.2 ± 16.1 | 0.57 |
| Height (m) | 1.62 ± 0.09 | 1.60 ± 0.08 | 1.62 ± 0.01 | 0.76 |
| Body Mass Index (kg/m²) | 28.9 ± 4.9 | 29.9 ± 5.3 | 30.5 ± 6.2 | 0.47 |
| Waist Circumference (cm) | 101.8 ± 12.7 | 103.6 ± 12.8 | 104.1 ± 14.3 | 0.77 |
Comorbidities
| | | | | |
|--------------------------------------|------------------|--------------------|----------------------|----------|
| Diabetes, n (%) | 8 (24.2) | 9 (28.1) | 3 (9.4) | 0.14 |
| Hypertension, n (%) | 15 (45.5) | 15 (46.9) | 15 (46.9) | 1.00 |
| Dyslipidemia, n (%) | 18 (54.5) | 12 (37.5) | 13 (39.4) | 0.27 |
Skin disease activity
| | | | | |
|--------------------------------------|------------------|--------------------|----------------------|----------|
| PASI | 2.51 ± 3.79 | 3.41 ± 6.10 | 3.49 ± 6.31 | 0.92 |
| BSA | 3.59 ± 7.04 | 3.74 ± 5.83 | 5.07 ± 12.6 | 0.80 |
Joint disease activity
| | | | | |
|--------------------------------------|------------------|--------------------|----------------------|----------|
| DAS28-CRP | 2.93 ± 1.19 | 2.83 ± 1.55 | 2.98 ± 1.35 | 0.75 |
| DAS28-ESR | 3.56 ± 1.32 | 3.31 ± 1.21 | 3.39 ± 1.60 | 0.61 |
| Number of tender joints | 5.16 ± 6.95 | 2.53 ± 3.44 | 3.58 ± 4.32 | 0.12 |
| Number of swollen joints | 2.91 ± 3.67 | 2.23 ± 2.60 | 2.30 ± 3.41 | 0.66 |
| HAQ | 1.02 ± 0.73 | 0.84 ± 0.62 | 0.90 ± 0.71 | 0.52 |
PsA concomitant medications
| | | | | |
|--------------------------------------|------------------|--------------------|----------------------|----------|
| GC, n (%) | 5 (15.2) | 3 (9.4) | 3 (9.4) | 0.66 |
| NSAIDs, n (%) | 5 (15.2) | 5 (15.6) | 2 (6.3) | 0.42 |
| Monotherapy (MTX, LEF or CsA), n (%) | 18 (54.5) | 23 (71.8) | 23 (71.8) | 0.23 |
| TNF blockers, n (%) | 15 (45.4) | 12 (37.5) | 9 (28.1) | 0.80 |
| TNF blockers plus MTX or LEF, n (%) | 7 (21.2) | 8 (25.0) | 6 (18.7) | 0.83 |
Physical activity (IPAQ)
| | | | | |
|--------------------------------------|------------------|--------------------|----------------------|----------|
| Inactive | 21 (72.4) | 21 (72.4) | 18 (60.0) | 0.43 |
| Minimally active | 7 (24.1) | 8 (27.6) | 12 (40.0) | 0.43 |
| Sufficiently active | 1 (3.4) | 0 | 0 | 0.43 |
| Active | 0 | 0 | 0 | 0.43 |
| Very active | 0 | 0 | 0 | 0.43 |
| MET-minutes/week | 945.1 ± 2544.7 | 781.3 ± 1366.9 | 817.9 ± 2167.3 | 0.95 |
Concomitant medications
| | | | | |
|--------------------------------------|------------------|--------------------|----------------------|----------|
| Insulin, n (%) | 2 (6.1) | 4 (12.5) | 1 (3.1) | 0.33 |
| Statins, n (%) | 10 (30.3) | 17 (53.1) | 6 (18.7) | 0.01 |
| Antidiabetic, n (%) | 7 (21.2) | 10 (31.2) | 3 (9.4) | 0.09 |
| Antihypertensive, n (%) | 14 (42.4) | 16 (50.0) | 16 (50.0) | 0.84 |
Biomarkers (12 h-fasting)
| | | | | |
|--------------------------------------|------------------|--------------------|----------------------|----------|
| Triglycerides | 168.2 ± 105.8 | 112.1 ± 40.7 | 137.7 ± 91.1 | 0.03 |
| Total Cholesterol | 196.6 ± 37.2 | 184.9 ± 44.5 | 205.9 ± 44.2 | 0.05 |
| LDL-cholesterol | 115.5 ± 27.2 | 115.3 ± 41.4 | 130.6 ± 38.5 | 0.08 |
| HDL-cholesterol | 45.1 ± 12 | 48.7 ± 11.1 | 49.5 ± 10.8 | 0.75 |
| Glyceremia | 102.8 ± 29.1 | 103.6 ± 31.0 | 102.3 ± 43.7 | 0.98 |
| Insulin | 20.2 ± 17.1 | 17.1 ± 13.3 | 13.0 ± 10.2 | 0.13 |
Bold indicates \( p \) statistically significant (\( \leq 0.05 \))
BSA: Body Surface Activity, CsA: Cyclosporine, D: diet plus placebo, D+S: diet plus supplementation, DAS: Disease Activity Score, HAQ: Healthy Activity Questionnaire, GC: Glucocorticoid, HDL: High Density Lipoprotein, Kcal: Kilocalories, METS: Metabolic Equivalent, MTX: Methotrexate, LEF: Leflunomide, LDL: Low Density Lipoprotein, NSAIDs: Non-steroidal anti-inflammatory drugs, PASI: Psoriasis Activity Severity Index, PsA: Psoriatic Arthritis, TNF: Tumor Necrosis Factor, IPAQ: International Physical Activity Questionnaire.
Table 1 (continued)
Activity Questionnaire: METs: Metabolic Equivalents
| | Placebo | Diet-Fish | Placebo | Diet-Fish | Placebo | Diet-Fish |
|--------------------------|-----------|-----------|-----------|-----------|-----------|-----------|
| MDA, n (%) | (60–100%) | 69.7% | (60–100%) | 71.00% | (60–100%) | 69.7% |
| HAQ | 0.96 ± 0.3 | 0.96 ± 0.3 | 0.96 ± 0.3 | 0.96 ± 0.3 | 0.96 ± 0.3 | 0.96 ± 0.3 |
| PASI | 1.96 ± 0.3 | 1.96 ± 0.3 | 1.96 ± 0.3 | 1.96 ± 0.3 | 1.96 ± 0.3 | 1.96 ± 0.3 |
| BASDAI | 1.5 ± 0.3 | 1.5 ± 0.3 | 1.5 ± 0.3 | 1.5 ± 0.3 | 1.5 ± 0.3 | 1.5 ± 0.3 |
| DAS28-CRP | 2.93 ± 1.19| 2.93 ± 1.19| 2.93 ± 1.19| 2.93 ± 1.19| 2.93 ± 1.19| 2.93 ± 1.19|
| DAS28-ESR | 2.98 ± 1.35| 2.98 ± 1.35| 2.98 ± 1.35| 2.98 ± 1.35| 2.98 ± 1.35| 2.98 ± 1.35|
| BSA | 3.59 ± 7.04| 3.59 ± 7.04| 3.59 ± 7.04| 3.59 ± 7.04| 3.59 ± 7.04| 3.59 ± 7.04|
Table 2 Skin and joint disease activity outcomes before and after a 12-week dietetic intervention
| | Baseline | 12-week | Difference | p intra group | p between groups |
|--------------------------|----------|---------|------------|---------------|------------------|
| DAS28-ESR | Placebo | 3.56 ± 1.3 | 3.46 ± 1.2 | -0.10 ± 1.4 | 0.3 |
| | Diet-Fish| 3.31 ± 1.2 | 3.50 ± 1.4 | 0.19 ± 1.6 | 0.3 |
| | Placebo | 3.40 ± 1.6 | 2.90 ± 1.44| -0.49 ± 0.89| 0.3 |
| DAS28-CRP | Placebo | 2.93 ± 1.19| 2.72 ± 1.0 | -0.21 ± 1.15| 0.004 |
| | Diet-Fish| 2.83 ± 1.55| 2.43 ± 1.0 | -0.40 ± 1.11| 0.004 |
| | Placebo | 2.98 ± 1.35| 2.33 ± 1.1 | -0.66 ± 0.90| 0.004 |
| BSA | Placebo | 3.59 ± 7.04| 2.48 ± 3.0 | -0.89 ± 4.7 | 0.1 |
| | Diet-Fish| 3.71 ± 6.1 | 5.04 ± 15.0| 0.95 ± 2.4 | 0.1 |
| | Placebo | 5.14 ± 12.9| 4.29 ± 9.4 | -0.53 ± 4.4 | 0.1 |
| BASDAI | Placebo | 2.94 ± 1.96| 2.31 ± 1.84| -0.63 ± 1.5 | 0.04 |
| | Diet-Fish| 2.51 ± 1.83| 2.70 ± 2.40| 0.19 ± 1.67| 0.56 |
| MDA, n (%) | Placebo | 6 (18.2%) | 9 (27.3%) | +9.1% | 0.006 |
| | Diet-Fish| 9 (28.1%) | 11 (34.4%) | +6.3% | 0.006 |
| | Placebo | 7 (21.9%) | 11 (34.3%) | +12.4% | 0.006 |
Discussion
The DIETA trial showed that a 12-week supervised nutritional intervention, including a 500-cal restriction, dietetic counseling and omega-3 supplementation, was...
Table 3 Body composition measurements, food intake and physical activity before and after the 12-week nutrition intervention
| | Baseline | 12-week | Difference | p intra group¹ |
|--------------------------|------------|------------|------------|----------------|
| **Weight (kg)** | | | | |
| Placebo | 76.2±15.8 | 75.8±15.4 | -0.4±1.9 | 0.004 |
| Diet-Fish | 76.7±14.4 | 74.9±14.4 | -1.79±2.4 | 0.004 |
| Diet-Placebo | 78.3±17.3 | 78.1±16.8 | -0.28±3.2 | 0.004 |
| p between groups² | 0.82 | 0.82 | | |
| **Body Mass Index (kg/m²)** | | | | |
| Placebo | 28.9±4.9 | 28.8±4.8 | -0.15±0.7 | 0.01 |
| Diet-Fish | 29.8±5.4 | 29.1±5.4 | -0.69±0.9 | 0.01 |
| Diet-Placebo | 30.0±6.58 | 29.9±6.5 | -0.07±1.4 | 0.01 |
| p between groups² | 0.76 | 0.76 | | |
| **Waist circumference (cm)** | | | | |
| Placebo | 101.0±13.2 | 100.7±13.1 | -0.29±1.8 | < 0.001 |
| Diet-Fish | 104.0±13.3 | 100.8±12.8 | -3.28±3.5 | < 0.001 |
| Diet-Placebo | 104.1±14.3 | 102.3±13.4 | -1.81±4.2 | 0.027¹ |
| p between groups² | 0.82 | 0.82 | | |
| **Total body fat mass (kg)** | | | | |
| Placebo | 35.0±11.8 | 35.0±11.4 | -0.01±2.2 | 0.99¹ |
| Diet-Fish | 40.1±8.3 | 38.8±8.7 | -1.2±2.2 | 0.006¹ |
| Diet-Placebo | 39.5±13.7 | 40.6±11.8 | 1.1±5.2 | 0.82¹ |
| p between groups² | 0.25ᵇ | 0.15ᵇ | | |
| **Appendicular lean mass (kg)** | | | | |
| Placebo | 21.0±5.7 | 21.0±5.6 | +0.01±0.6 | 0.18 |
| Diet-Fish | 19.6±4.8 | 19.5±4.6 | -0.2±0.8 | 0.18 |
| Diet-Placebo | 20.4±5.0 | 20.2±5.1 | -0.2±1.0 | 0.18 |
| p between groups² | 0.54 | 0.54 | | |
| **Fat mass index (kg/m²)** | | | | |
| Placebo | 13.0±5.2 | 13.4±5.2 | 0.3±1.7² | 0.52ᵃ |
| Diet-Fish | 15.9±4.3 | 15.2±4.3 | -0.6±1.0⁶ | 0.002ᵃ |
| Diet-Placebo | 14.8±6.6 | 15.5±6.2 | 0.7±3.4 | 0.95ᵃ |
| p between groups² | 0.14ᵇ | 0.35ᵇ | | |
| **Appendicular lean mass/IMC² * ** | | | | |
| Placebo | 0.73±0.20 | 0.75±0.19 | +0.002±0.02| 0.59 |
| Diet-Fish | 0.67±0.19 | 0.68±0.18 | +0.01±0.02 | 0.59 |
| Diet-Placebo | 0.69±0.20 | 0.70±0.20 | +0.006±0.04| 0.59 |
| p between groups² | 0.38 | 0.38 | | |
| **Diet** | | | | |
| **Energy intake (kcal/ kg)** | | | | |
| Placebo | 26±12.7 | 25.9±8.9 | -0.9±13.5 | 0.73 |
| Diet-Fish | 26.3±10 | 25.1±14.1 | -0.96±11.1 | 0.64 |
| Diet-Placebo | 26.1±12.9 | 23.6±12 | -4.58±10.8 | 0.04 |
| p between groups² | 0.43 | 0.43 | | |
| **Carbohydrate intake (g)** | | | | |
| Placebo | 265.5±49.0 | 236.9±32.3 | -28.6±38.3 | 0.59 |
| Diet-Fish | 260.7±54.3 | 226.1±50.0 | -34.6±38.4 | 0.59 |
| Diet-Placebo | 248.3±45.1 | 230.7±36.5 | -17.6±51.0 | 0.59 |
| p between groups² | 0.38 | 0.38 | | |
| **Fat intake (g)** | | | | |
| Placebo | 60.1±17.3 | 55.5±10.2 | -4.6±13.4 | 0.07 |
| Diet-Fish | 61.2±15.1 | 59.8±14.0 | -1.4±11.8 | 0.52 |
Table 3 (continued)
| | Baseline | 12-week | Difference | p intra group\(^1\) |
|--------------------------|------------|-----------|------------|---------------------|
| Diet-Placebo | 68.1 ± 18.6| 56.8 ± 9.5| -11.4 ± 15.2| < 0.001 |
| p between groups\(^2\) | 0.12 | 0.25 | | |
| **Protein intake (g)** | | | | |
| Placebo | 85.9 ± 17.8| 92.2 ± 25.7| +6.3 ± 28.1| 0.24 |
| Diet-Fish | 86.8 ± 16.7| 86.2 ± 23.5| +0.6 ± 22.4| 0.24 |
| Diet-Placebo | 84.5 ± 18.7| 88.4 ± 18.1| +3.9 ± 25.6| 0.24 |
| p between groups\(^2\) | 0.77 | 0.77 | | |
| **Omega 3 intake (g)** | | | | |
| Placebo | 0.4 ± 0.1 | 0.4 ± 0.7 | +0.08 ± 0.6| 0.47 |
| Diet-Fish | 0.4 ± 0.1 | 0.5 ± 0.7 | +0.15 ± 0.7| 0.47 |
| Diet-Placebo | 0.4 ± 0.1 | 0.7 ± 1.1 | +0.36 ± 1.1| 0.47 |
| p between groups\(^2\) | 0.96 | 0.03 | | |
| **Omega 3 intake + supplement (g)** | | | | |
| Placebo | 0.4 ± 0.1 | 0.4 ± 0.7 | +0.08 ± 0.6| 0.47 |
| Diet-Fish | 0.4 ± 0.1 | 3.5 ± 0.73| +3.17 ± 0.7| < 0.001 |
| Diet-Placebo | 0.4 ± 0.1 | 0.7 ± 1.1 | +0.36 ± 1.1| 0.47 |
| p between groups\(^2\) | 0.96 | < 0.001 | | |
| **Ratio omega 6: omega 3 intake** | | | | |
| Placebo | 8.11 ± 4.25| 6.45 ± 4.96| -1.65 ± 4.90| 0.003 |
| Diet-Fish | 8.52 ± 5.00| 6.08 ± 5.96| -2.43 ± 7.68| 0.003 |
| Diet-Placebo | 8.36 ± 5.67| 5.95 ± 4.77| -2.40 ± 6.89| 0.003 |
| p between groups\(^2\) | 0.98 | 0.98 | | |
| **Healthy eating index**| | | | |
| Placebo | 63.0 ± 13.3| 64.6 ± 14.8| 1.6 ± 13.3 | 0.22 |
| Diet-Fish | 66.4 ± 10.4| 64.2 ± 11.7| -2.2 ± 11.2| 0.22 |
| Diet-Placebo | 63.6 ± 12.1| 69.1 ± 11.3| 5.6 ± 13.3 | 0.22 |
| p between groups\(^2\) | 0.64 | 0.64 | | |
| **Dietary inflammatory index** | | | | |
| Placebo | 2.4 ± 0.9 | 0.9 ± 1.1 | -1.4 ± 1.1 | < 0.001 |
| Diet-Fish | 2.2 ± 1.0 | 1.1 ± 1.2 | -1.1 ± 1.0 | < 0.001 |
| Diet-Placebo | 2.8 ± 0.8 | 1.0 ± 1.2 | -1.8 ± 1.3 | < 0.001 |
| p between groups\(^2\) | 0.50 | 0.50 | | |
| **Physical exercise** | | | | |
| METs (minutes/week) | | | | |
| Placebo | 945.1 ± 2544.6| 379.5 ± 409.4| -670.82 ± 2704.55| 0.067 |
| Diet-Fish | 781.3 ± 1366.9| 440.5 ± 532.6| -340.8 ± 1120.15| 0.067 |
| Diet-Placebo | 817.91 ± 2167.3| 660.11 ± 1786.8| -157.80 ± 821.22| 0.067 |
| p between groups\(^2\) | 0.882 | 0.882 | | |
| METs(calories/day) | | | | |
| Placebo | 166.33 ± 469.06| 70.53 ± 82.38| -95.80 ± 508.69| 0.084 |
| Diet-Fish | 140.56 ± 236.28| 75.59 ± 94.88| -64.97 ± 199.57| 0.084 |
| Diet-Placebo | 156.60 ± 394.02| 140.71 ± 365.58| -16.6 ± 201.50| 0.084 |
| p between groups\(^2\) | 0.756 | 0.756 | | |
Bold indicates p statistically significant (< 0.05)
Kcal: Kilocalories, P: Placebo, IPAQ: International Physical Activity Questionnaire; METs: Metabolic Equivalents
\(^1\) ANOVA with repeated measures or Wilcoxon test (*)
\(^2\) ANOVA with repeated measures or Kruskal–Wallis test (\(*\))
The cutoff points for low appendicular lean mass that identifies sarcopenia was a grip strength less than 26 kg for men and less than 16 kg for women, according to the FNIH[34]
effective in improving the disease activity and modifying the body composition measurements of patients with PsA. It is worth emphasizing that a hypocaloric diet plus omega-3 supplementation was more effective than a hypocaloric diet alone in promoting weight loss and fat mass and waist circumference reduction but had no extra beneficial effects on disease activity. In addition, our data suggested that increased energy intake and worse diet quality may negatively affect joint activity and reduce the likelihood of achieving disease remission, regardless of weight loss or body composition changes.
Our group previously reported a close relationship between body composition and disease activity in PsA patients. While fat mass was positively correlated with joint disease activity, lean mass was negatively associated with it, suggesting a possible harmful link between fat and joint disease activity. It was also observed that patients with severe joint disease activity had more bodily fat than patients in remission or with low disease activity [5].
Interestingly, all three groups had some clinical joint improvement, particularly the Diet-placebo group, with a 0.66 reduction in their DAS28-CRP scores, highlighting an early (12 weeks) moderate EULAR response [33], instead of the 24 weeks that would be expected in pharmacologic clinical trials [34]. Nonetheless, no significant skin changes were observed after three months of follow-up. The lack of a cutaneous response could be explained by low PASI and BSA values at baseline or chronicity of disease. Although we did have sufficient data regarding 68/66 joint counts to perform the DAPSA (Disease Activity in Psoriatic Arthritis), we obtained significant results using other instruments, including a nonspecific (DAS28-CRP) assessment and another more specific and more complete assessment of skin and articular outcomes (MDA) for PsA.
A recent meta-analysis demonstrated that obesity or overweight may decrease the chance of achieving
Table 4 Disease activity outcomes according to diet intervention after 12 weeks
| | Placebo | Diet-fish | Diet-placebo |
|-------------------|---------|-----------|--------------|
| | Baseline| 12 weeks | Baseline | 12 weeks | Baseline | 12 weeks |
| | N | % | N | % | N | % |
| MDA | 27 | 100 | 28 | 100 | 31 | 100 |
| Activity | 21 | 77.8 | 19 | 67.9 | 24 | 77.4 |
| Remission | 6 | 22.2 | 9 | 33.3 | 7 | 22.6 |
| DAS28-ESR | 28 | 100 | 26 | 100 | 27 | 100 |
| Moderate/severe activity | 16 | 57.1 | 16 | 61.5 | 14 | 51.9 |
| Remission/low activity | 12 | 42.9 | 10 | 38.5 | 13 | 48.1 |
| DAS28-CRP | 19 | 100 | 19 | 100 | 20 | 100 |
| Moderate/severe activity | 8 | 42.1 | 4 | 21.1 | 10 | 50 |
| Remission/low activity | 11 | 57.9 | 15 | 78.9 | 10 | 50 |
Bold indicates \( p \) statistically significant (\( \leq 0.05 \))
MDA: Minimal Disease Activity; DAS28: Disease Activity Score; ESR: Erythrocyte Sedimentation Rate; CRP: C Reactive Protein
\( p – \) McNemar test, (–) It was not possible to perform McNemar test—not all levels of the variable were present in both moments of evaluation,
Table 5 Skin and joint outcomes based on weight changes, BMI and waist circumference category
| | Diet-fish | Diet-placebo |
|-------------------|-----------|--------------|
| | Baseline | 12 weeks | Baseline | 12 weeks |
| | N | % | N | % |
| MDA | 49 (62.8%)| 29 (37.2%) | 40 (53.3%)| 35 (46.7%)|
| Activity or Activity or Remission/Remission or Activity | 0.81a | 0.73a |
| Weight change (%) | Maintenance | 4 (80%) | 1 (20%) | 2 (40%) | 5 (60%) |
| | < 5% loss | 22 (57.9%) | 16 (42.1%)| 20 (55.6%)| 36 (44.4%)|
| | 5–10% loss| 6 (66.7%) | 3 (33.3%) | 3 (37.5%) | 5 (62.5%) |
| | Weight gain | 17 (65.4%) | 9 (34.6%) | 15 (57.7%) | 11 (42.3%) |
Bold indicates \( p \) statistically significant (\( \leq 0.05 \))
\( p – \) Nível descritivo do teste de Qui-Quadrado ou exato de Fisher(*)
remission or a low level of disease activity [35] in patients with rheumatic diseases, such as rheumatoid arthritis or PsA. According to Mok et al. [36], inflammation and oxidative stress can be a possible link between obesity and rheumatic diseases. This possibility has been previously described by the presence of multiple biomarkers of inflammation (C-reactive protein, sulphhydryl and hydroperoxide), such as those observed in obese individuals [37, 38] and PsA patients [39]. Thus, weight loss should be considered an important approach for managing patients with PsA, although we did not observe a relationship between weight loss and disease activity, as previously reported [2, 7]. According to Di Minno et al. [7], a weight loss of more than 5 or 10% would be sufficient to increase the probability of achieving MDA. In our study, we observed that few patients (10%) met this target, and improvements were more closely related to quality of diet than weight loss itself.
A recent study regarding bariatric surgery and other procedures to lose weight showed a significant incidence of PsA reduction after bypass, but not after the gastric band, regardless of weight loss level [40]. The authors proposed that these findings may be related to changes in insulinotropic hormones, including glucagon-like peptide-1 (GLP-1). GLP-1 contributes to weight loss and inflammatory marker reduction, such as tumor necrosis factor, which is essential for minimizing systemic inflammation and controlling PsA disease activity [40]. In addition, some studies have demonstrated that GLP-1 release and the regulation of energy homeostasis may be enhanced by nutrient intake (protein [41], omega-3 [42], monounsaturated fatty acid [42] and fiber [42]) and reduced by higher carbohydrate consumption [43]. Although we did not observe any protein or carbohydrate intake changes, we hypothesized that the improved disease activity observed in the present study could have been influenced by GLP-1 release after DII reduction and increased fiber and omega-3 consumption, regardless of weight loss.
In addition to the reduced DII score, we showed that restricting energy consumption contributed to changes in relevant targets for decreasing one of the major triggers of MetS [44], which is closely related to PsA [45]. Recently, Leite et al. [5] reported that inadequate food consumption, including high total calorie intake, low antioxidant vitamin intake, a poor quality diet and a proinflammatory pattern, was common among patients with PsA and that there were associations between joint disease activity and fat intake and between skin activity and higher intake of trans fat and sodium. Our results confirm the ability of a hypocaloric diet to significantly improve the quality of nutrients and modulate articular activity, as demonstrated for each 1-unit increase in HEI values, which was related to a reduced likelihood of achieving remission in 4% of patients. Additionally, each 100-cal daily intake increase caused a 3.4-fold DAS28-ESR score impairment. Interestingly, the benefits observed in the Diet-placebo group were not improved by the addition of omega-3 present in fish oil.
Although omega-3 supplementation has not been shown to provide any extra benefits to disease activity, this fatty acid combined with hypocaloric diet counseling improved the adiposity of patients with excess visceral fat. Considering our best knowledge and a lack of information about omega-3 supplementation in PsA, our study was the first to evaluate the role of a dietetic approach, including this fatty acid, on disease activity in patients with PsA. Furthermore, omega-3 supplementation was associated with improved MetS parameters, such as dyslipidemia, hypertension and insulin resistance, as well as reduced waist circumference, body weight, obesity, pain and rates of nonalcoholic fatty liver disease [46]. We believe that these findings could be more relevant in longer clinical trials, as reported by Flachs et al., who noted some improvement in mitochondrial oxidation capacity, lipid metabolism and inflammation [47].
Importantly, it is already well established that nonpharmacologic interventions have a low rate of adherence. Therefore, a limitation of our results is not evaluating levels of omega-3 and its metabolites in plasma or cell membranes to avoid the information bias that has been amply described in food records [48], as well as a lack of information regarding DAPSA (Disease Activity in Psoriatic Arthritis). It is also very difficult to measure real food behavior and dietary changes because the provided information is subjective. Moreover, dietary patterns are closely linked to culture, habits, emotions and economic status, which makes it difficult to promote relevant and longer modifications [49]. Nevertheless, the adherence level was monitored at the dietitian’s monthly appointments, aiming to identify low adherence, complaints, and doubts about supplementation (adverse effects). Another limitation in the relatively short follow-up period for a chronic disease and reduced long-term compliance with the diet and supplements. Regardless of these points, this randomized clinical trial (RCT) has important relevance because it is the first RCT designed to assess the effectiveness of a supervised dietary intervention plus omega-3 fatty acid supplementation on disease activity in patients with PsA. In addition, no change in PsA, concomitant medications or physical activity was made during the 12-week intervention, reinforcing the role of diet in the context of immunometabolism.
Therefore, dietary counseling aimed at losing or controlling weight could be part of the global protocol for
PsA patients. In addition, supervised exercises could contribute to weight loss, lean mass gain and better disease activity control.
Conclusion
A 12-week supervised nutritional intervention, including a 500-cal restriction, dietetic counseling, and omega-3 supplementation, was effective in improving the disease activity and body composition of patients with PsA, regardless of weight loss, but was related to food pattern and diet quality improvement. The DIETA trial, a nonpharmacologic approach, is an inexpensive, suitable, and efficient approach that could be combined with standardized drug therapy. The addition of omega-3 supplementation did not improve disease activity or inflammatory parameters but promoted relevant body composition changes that can be modulated by indirect pathways of disease activity.
Acknowledgements
Not applicable.
Author contributions
All authors equally contributed to this study. All authors read and approved the final manuscript.
Funding
This study was supported by FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) (Grants 2012/18701-2 and 2012/18789-7) and by CAPES.
Availability of data and materials
The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials.
Declarations
Ethics approval and consent to participate
The study was approved by the Ethics Committee of Research at the Federal University of São Paulo (CAAE: 00591412.5.0000.5502) and was recorded on Clinicaltrials.gov (NCT0314266). Subjects were included in the study after signing an informed consent form, in accordance with resolution 466 from CONEP (Comissão Nacional de Ética em Pesquisa/National Committee of Ethics in Research; CNS/466) in 2012.
Consent for publication
We confirm that the data presented here have not been published elsewhere and that the article has not been submitted to any other journal. We give our consent for the publication of the article Dietary IntervEntion in psoriatic Arthritis: The DIETA trial.
Competing interests
The authors declare no competing interests.
Author details
1Rheumatology Division, Universidade Federal de São Paulo, Escola Paulista de Medicina (UNIFESP/EPM), 204 Leandro Dupré St., Room 74, Villa Clementino, São Paulo, SP 04025-010, Brazil. 2Department of Nutrition, Vale Do Paraíba University, 2911 Shishima Hitfumi Av, Urbanova, Sao Jose dos Campos, Sao Paulo 12244-000, Brazil. 3Cancer Prevention and Control Program and Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, SC, USA. 4Nutrition Department, Public Health School, Sao Paulo University, 715 Dr Arnaldo Av, Pacaembu, São Paulo, SP 01246-904, Brazil.
Received: 12 November 2021 Accepted: 23 March 2022 Published online: 06 April 2022
References
1. Ranza R, Carneiro S, Qureshi AA, Martins G, Rodrigues JJ, Romiti R, Barros TB, Carneiro J, Sampiao AL, Gryczszan R, et al. Prevalence of psoriatic arthritis in a large cohort of Brazilian patients with psoriasis. J Rheumatol. 2015;42:829–34.
2. Gisondi P, Del Giglio M, Di Francesco V, Zamboni M, Girolomoni G. Weight loss improves the response of obese patients with moderate-to-severe chronic plaque psoriasis to low-dose cyclosporine therapy: a randomized, controlled, investigator-blinded clinical trial. Am J Clin Nutr. 2008;88:1242–7.
3. Davídovics BB, Sattar N, Prinz J, Puig L, Emery P, Barker JN, van de Kerkhof P, Stahlé M, Nestle FO, Girolomoni G, Krueger JG. Psoriasis and systemic inflammatory diseases: potential mechanistic links between skin disease and co-morbid conditions. J Invest Dermatol. 2010;130:1785–96.
4. Love TJ, Zhu Y, Zhang Y, Wall-Burns L, Ogdie A, Getfand JM, Choi HK. Obesity and the risk of psoriatic arthritis: a population-based study. Ann Rheum Dis. 2012;71:1273–7.
5. Leite BF, Morimoto M, Pinheiro MM, Genaro PS, Damasceno NRT. Food intake, metabolic profile and oxidative stress in patients with Psoriatic Arthritis. Ann Nutr Metab. 2015;67(suppl 1):1–601.
6. Renzo LD, Saraceno R, Schipani C, Rizzo M, Bianchi A, Noce A, Esposito M, Tiberti S, Chimenti S. A DEL: Prospective assessment of body weight and body composition changes in patients with psoriasis receiving anti-TNF-alpha treatment. Dermatol Ther. 2011;24:446–51.
7. Di Minno MN, Peluso R, Iervolino S, Russolillo A, Lupoli R, Scarpa R, CarRDS Study Group. Weight loss and achievement of minimal disease activity in patients with psoriatic arthritis starting treatment with tumour necrosis factor α blockers. Ann Rheum Dis. 2014;73(6):1157–62. https://doi.org/10.1136/annrheumdis-2012-202812.
8. Van Gemert WA, May AM, Schuit AJ, Oosterhof BY, Peeters PH, Monnickhof EM. Effect of weight loss with or without exercise on inflammatory markers and adipokines in postmenopausal women: the SHAPE-2 trial, a randomized controlled trial. Cancer Epidemiol Biomarkers Prev. 2016;25:799–806.
9. Polus A, Zapala B, Razny U, Gielicz A, Kiec-Wilk B, Malczewska-Malec M, Sarnak M, Childs CE, Calder PC, Dembinska-Kiec A. Omega-3 fatty acid supplementation influences the whole blood transcriptome in women with obesity, associated with pro-resolving lipid mediator production. Biochim Biophys Acta. 2016;1861:1746–55.
10. He XX, Wu XL, Chen RP, Li X, Luan Z, Cheng XM, Wang ZM. Effectiveness of omega-3 polyunsaturated fatty acids in non-alcoholic fatty liver disease: a meta-analysis of randomized controlled trials. PLoS ONE. 2016;11:e0162368.
11. Chen C, Yu X, Shao S. Effects of omega-3 fatty acid supplementation on glucose control and lipid levels in type 2 diabetes: a meta-analysis. PLoS ONE. 2015;10:e0139565.
12. Abu-Raya A, Abu-Raya S, Helmii M. P00076 effect of exercise and dietary weight loss on symptoms and systemic inflammation in obese adults with psoriatic arthritis: randomized controlled trial. Ann Rheum Dis. 2014;73:89–90.
13. Taylor W, Gladman D, Helmwell P, Marchesoni A, Mease P, Melants H. Classification criteria for psoriatic arthritis: development of new criteria from a large international study. Arthritis Rheum. 2006;54:2665–73.
14. World Health Organization. Human energy requirements. Rome: Food and Agriculture Organization, 2004.
15. Institute of Medicine. Dietary reference intakes: applications in dietary planning. Washington: National Academies Press, 2002.
16. Padovani RM, Amaya-Farfán J, Colugnati FAB, Domene SMÁ. Dietary reference intakes: aplicabilidade das tabelas em estudos nutricionais. Rev Nutr. 2006;19:741–60.
17. Santos RD, Gagliardi ACM, Xavier HT, Magno CD, Cassani R, Lottenberg AMP, Casella Filho A, Araújo DB, Cesena FY, Alves RJ, et al. Diretriz sobre o consumo de gorduras e saúde cardiovascular. Arq Bras Cardiol. 2013;100:1–40.
18. Sposito AC, Caramelli B, Fonseca FAH, Bertolami MC, Afune Neto A, Souza AD, Lottenberg AMP, Chacra AP, Faldui AA, Laires-Vale AA, et al. IV Diretriz Brasileira sobre Dislipidemias e Prevenção da Aterosclerose: Departamento de Aterosclerose da Sociedade Brasileira de Cardiologia. Arq Bras Cardiol. 2007;88:2–19.
19. Fredriksson T, Pettersson U. Severe psoriasis–oral therapy with a new retinoid. Dermatologica. 1978;157:238–44.
| 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2817,
1
],
[
2817,
5193,
2
],
[
5193,
10550,
3
],
[
10550,
15886,
4
],
[
15886,
23081,
5
],
[
23081,
25944,
6
],
[
25944,
30409,
7
],
[
30409,
34805,
8
],
[
34805,
39402,
9
],
[
39402,
45119,
10
],
[
45119,
52244,
11
],
[
52244,
52244,
12
]
]
} |
d05fc4263ce838d9da9095feb5a47635314d7858 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 8,
"total-fallback-pages": 0,
"total-input-tokens": 18424,
"total-output-tokens": 5864,
"fieldofstudy": [
"Computer Science",
"Business"
]
} | E-Commerce Consumer Privacy Protection Based on Differential Privacy
Guorong Zhong
1International School, Beijing University of Posts and Telecommunications, Beijing 100876, China
Abstract: With the advent of the era of big data, human society is facing unprecedented opportunities and challenges. In many fields where big data is widely used, e-commerce is undoubtedly a crucial one. While the advanced data analysis technology penetrates into every link of e-commerce transaction, it not only brings about convenience, but also causes many adverse effects. On the one hand, this paper analyzed both the current situation of consumer privacy security on e-commerce platform and the increasingly mature application of differential privacy in various IT fields. It is found to be promising that with its good feature of privacy ambiguity, consumer privacy protection in differential privacy mechanism can meet the requirements of a more robust development of e-commerce in big data era. On the other hand, this paper briefly discussed about consumer protection in legal level, inspired by relevant researches done on GDPR.
1. Introduction
With profound development of network communication technology, mobile devices and intelligent terminals, the type and scale of data owned by society is experiencing explosive growth. According to the 2015 IDC monitoring report, the world has officially entered the ZB era in 2010, and the global data volume will roughly be doubled every two years, which means that the amount of data generated by human in the last two years is equal to the total amount of data generated before.
The broad development prospect of big data has attracted the attention of all sectors of society. Researchers in various fields are trying to understand people's needs from the perspective of data, develop new platforms and explore new opportunities, so as to improve social and economic benefits. Big data has penetrated into every corner of people's life, and optimized people's lifestyle in areas such as medical treatment and transportation. Big data plays an important role as a core driving force, especially in e-commerce. Nevertheless, e-commerce platform has an unshirkable responsibility for the leakage of personal privacy in the process of online shopping. In an integrated online shopping process, traces of consumers will be left on the network in various ways. Online merchants collect these great amount of user information, analyze user characteristics, adjust product release patterns, and eventually enhance the individuality of retrieval results imperceptibly, all in the purpose of obtaining greater economic benefits. According to CNNIC's 2013 research report on the information security situation of Chinese netizens, the proportion of personal information leakage in network shopping has reached 42.9%, which was second only to cases of fraudulent information and fraudulent websites.
This paper attempts to discuss the privacy concerns of online consumers' personal information under the e-commerce platform, and discuss how to strengthen the privacy protection of online
consumers based on differential privacy technology. In addition, by analyzing the situation, causes and effects of the problem, and combining with the legal level, this paper will propose feasible suggestions and assessment countermeasures for personal privacy protection.
2. Background
2.1. The trend of big data in e-commerce
The advent of the era of big data poses the human society unprecedented opportunities as well as challenges. Among the multiple fields that big data has already taken extensive applications, e-commerce would with no doubt be a vital one. On the one hand, penetration of data analyzing technology into every single link of e-commerce transactions brings us about much convenience. On the other hand, however, it triggers a few adverse effects.
2.1.1. Benefits
In 2016, Ning Jiajun pointed out that with nowadays rapid development of e-commerce, data has unconsciously become a flood in the tide of world economy and an important part of the field’s composition. Compared with traditional offline sales, e-commerce possesses a greater capability in producing large amount of data. Mountains of brand, commodity and customer information can form a highly connected aggregation through the internet. Furthermore, the collection, integration and analysis of these information enable online merchants, more quickly and accurately, to locate users’ requirements, figure out new business opportunities, and thereby affect the process of decision-making and improve the efficiency of operations. In 2006, the MIT Technology Review stated that Alibaba Group has completed a transition from the early electric business enterprise to a world technology pioneer, when the double eleven global shopping carnival of 2016 had just ended and created a series of new miracles in the world history of retails. On that single day, turnover reached 120.7 billion yuan, and wireless accounted for 82%. In addition, the carnival peaked 175000 transactions and 120000 payment per second, covering 235 countries and regions[1]. From the Alibaba’s advanced technology innovation, it can be seen that big data’s advantages on high dimensional data quantity and strong data processing ability are perfectly displayed on the e-commerce platform.
2.1.2. Drawbacks
As is mentioned before, big data has provided huge amount of users’ behavior data on the one hand, making it an indispensable impetus for the development of e-commerce. On the other hand, its limitations and drawbacks are hindering the steady progress of e-commerce as well. It includes difficulties in information filtering process due to low data density, and privacy issues in which information is abused or stolen. Among them, the information privacy has no doubt to be the biggest barrier for e-commerce platform to gain further development in the era of big data. When the profound development of internet technology is taking place, the openness of data on e-commerce platform and the frequency of data interaction, together with the risk in privacy leakage are on the increase. Nowadays threats to users’ private information on e-commerce platform come from mainly two aspects. One is private browsing habits exposed through traces on web page, the other is key information such as online payment password being stolen. First, as we can see from a complete process of online shopping, a series of steps from user registration, web browsing, order formation, online payment to the final logistic transportation will be taken. What canny e-merchants can do is far more than accessing these seemingly indistinctive cumbersome of a single user, they will also try putting fragment information together and obtain a user image as perfect as possible, and if this happens, users’ privacy is in great danger. Second, electronic finance has won favor of the public due to its convenience and efficiency, but in the meantime, security flaws still exist in even advanced preventive measures like face recognition and fingerprint payment. Thus, how to improve the poor security situation and perfect the e-commerce consumer privacy protection mechanism is a thorny problem to the long-term development of e-commerce.
2.2. Definition of consumer privacy and reasons for consumer privacy leakage
The concept of privacy is pretty extensive since it is involved in numerous fields of social science. Nevertheless, scholars from all walks of life have not agreed on a precise and unified concept of privacy so far. In a manner, privacy is described as a multidimensional, flexible and dynamic concept, and it changes with the experience of life. It is an overlap concept which is both secret, confidential and anonymous, safe and ethical, meanwhile depending on special situations (such as time, location, occupation, culture and reasons), therefore it being extremely hard to be defined in general[2]. From the perspective of e-commerce consumers in the era of big data, the traditional privacy definition is changing from information regarded too sensitive for a person or a group to let others know (such as diseases and bank deposits) to information that is able to identify personal characteristics (such as id number and daily life tracks).
Correspond to the definition of consumer privacy above, this paper’s point of view on consumer privacy leakage is incidents that any information concerning consumers’ identity and therefore has any economic value was inadvertently abused, maliciously stolen or illegally traded. The cause of consumer privacy leakage is complex and extensive, which can be roughly classified into lack of personal information protection consciousness, economic value of privacy information being impressive and imperfection of relevant legal system. Driven by factors given above, online merchants will make use of bias privacy policy to maximum interests of their own, which results in consumer privacy leakage.
3. Current situation of privacy protection in e-commerce
E-commerce is a booming field in the past resent few years as public dependence towards the internet is gradually enhanced. Online consumer privacy protection has also become one of the hottest topics at present. The lack of privacy protection technology and relevant legislation on e-commerce platforms undoubtedly brings huge resistance to online consumer privacy protection.
3.1. Observation of e-commerce consumer behavior
Specific online consumer behavior is sure to be closely related to any privacy leakage that may be caused by a series of links of shopping on the Internet. In the process of online shopping, there are two kinds of consumer behavior that lead to the disclosure of consumers' privacy. Firstly, entering sensitive information (such as website or bank account password) in network environment is the main cause of direct consumer privacy leakage. Many consumers are accustomed to relying on the password memorizing function provided by the website, but are often lack of clear concept and high alert to the detailed record principles that cookies on the devices will follow behind screen. Secondly, binding registration regulations and sharing behavior in online shopping also have a high risk of indirectly revealing consumers' privacy. When making online purchase, it is inevitable for consumers to register on the online platform provided by merchants and fill in relevant personal information (name, id number, etc.). In this way, our personal information is tied together indiscriminately. Rapid development of internet technology also makes increasingly keen on sharing shopping information. However, what they do not know is that such sharing behavior will virtually strengthen the association between two accounts and further expose the common consumption habits of both parties.
3.2. Recent trend of privacy protection
The high degree of freedom and interactivity of big data result in great changes in the traditional way people make purchase. Nevertheless, information processing technology is also improving in the mean time, leaving many privacy vulnerabilities for criminals. Information leakage in online shopping is not individual case any longer, but a focus issue affecting the development of the entire e-commerce industry. For example, e-commerce merchants can reorganize the original data set according to data relevance by multi-directional processing seemingly useless information, so as to obtain the consumer privacy that ought to be hidden in the first place. It is quite obvious that traditional privacy protection technologies are not enough to withstand the further developed internet mechanism, and are unable to
cut off the way consumer privacy leakage takes place on e-commerce platform. A brand new theoretical mechanism of privacy protection, which is more suitable for the development demands of the era of big data and of better quality, needs to be developed and applied urgently.
4. The Analysis of Privacy Protection in E-commerce
4.1. Privacy protection in Differential privacy
Differential privacy is a new definition of privacy mechanism, proposed by Dwork in 2006, which is different from traditional privacy ones[3]. Under the definition of differential privacy, the result of the data set computation is insensitive to the change of a specific record. Therefore, the risk of privacy disclosure of a record due to its addition to the data set is controlled in a very small and acceptable range. Attackers cannot obtain accurate individual information by observing the calculation results[4]. In recent years, a great many achievements have been made in the research of differential privacy in numerous fields. Based on existing researches, this paper summarizes and assumes the theoretical development of differential privacy and its application in the field of consumer information protection in e-commerce.
4.1.1. Definition
Differential privacy is a vital law on defining personal privacy, with extremely rigorous mathematical definition while the common output is usually the result of some kind of data mining, whose content is determined by the type of query. On the e-commerce platform, the common output can be expressed as the identity query result in the form of "whether a customer buys a certain item", the count query result in the form of "how many customers buy a certain item in total", or the histogram query result in the form of "how many customers buy a certain item every four hours".
The definition of differential privacy and its applicability to consumer privacy protection on e-commerce platforms cannot be understood without considering the situation that the common output will face in reality. When the consumer data set D is collected by the e-commerce platform, traditional privacy information processing method can theoretically protect personal privacy to a certain extent by deleting identifier attributes (such as name, ID card and ID number). However, this is far from enough in practice. Other attributes without identifiabilities themselves also exist in the dataset collected, such as birthday, gender, place of residence, browsing and purchase record. It is of great chance that an attacker combines the information with identifier attributes obtained from elsewhere with information that has no identity symbols in D to obtain the intersected data set T, which represents the victim set of privacy leakage.
In view of the above situation, the new privacy mechanism, differential privacy, proposed in 2006 will solve the real problem that traditional privacy cannot satisfy. Differential privacy describes the contribution of individual privacy to the common output. By adding noise to the original data, privacy attackers cannot infer the data content other than query results based on background knowledge.
The theoretical definition of differential privacy is given below, with reference[5].
**Definition 2.1 (ε-Differential Privacy)** An algorithm A satisfies ε-differential privacy (ε-DP) if and only if for any datasets D and D' that differ on one element, we have
\[
\forall t \in \text{Range}(A) : \Pr[A(D) = t] \leq e^\epsilon \Pr[A(D') = t]
\]
(2.1)
The condition (2.1) is equivalent to
\[
\forall t \in \text{Range}(A) : \Pr[A(D) = t] \leq e^\epsilon \Pr[A(D') = t]
\]
(2.2)
Where D and D ' are adjacent data sets with only one set of data difference; A(D) and A(D ') are output results based on K. \Pr[A(D)] belongs to Sj is the risk of privacy leakage. The privacy parameter \epsilon is the privacy budget. The smaller the value of \epsilon, the higher the privacy protection
In short, differential privacy ensures that individual data has no impact on the common output of the data set, making it impossible for attackers to obtain individual privacy through public output and background knowledge, thus achieving the purpose of privacy protection.
4.1.2. Technology
A mechanism that satisfies the differential privacy definition can be seen as an interface between the private data set and the common output, ensuring that all common output about a particular query is similar. In other words, the common output is almost independent of any individual, and the degree of dependence is controlled by the privacy budget set by the data owner. That is to say, the existence or absence of an individual cannot significantly change the public output in this mechanism. The main method to implement the differential privacy mechanism is to add noise, and the two commonly used noise mechanisms are Laplace mechanism and exponential mechanism respectively, and Laplace mechanism satisfies differential privacy protection by applying appropriate noise to the data of numerical query results, which we will make further discussion.
Suppose function $f$ is a query function providing $\epsilon$-DP, $f(n) = \text{count}(I) + \text{noise}$, where noise is a noise subject to some random distribution. Let's say $X$ is equal to noise, then we have
$$\forall t, \frac{\Pr[f(D) = t]}{\Pr[f(D') = t]} = \frac{\Pr[\text{count}(D) + X = t]}{\Pr[\text{count}(D') + X' = t]} \leq e^\epsilon$$
Take $d = \text{count}(D) - \text{count}(D')$, then we can obtain
$$\forall x, \frac{\Pr[X = x]}{\Pr[X' = x + d]} \leq e^\epsilon$$
In order to ensure that the above formula is constant, we need to ensure that $d$ is less than or equal to delta $f(\Delta f)$, delta $f$ (sensitivity) is defined as follows
$$\Delta f = \max_{D \neq D'} |\text{count}(D) - \text{count}(D')|$$
And from here we can see that the distribution of the noise is actually the Laplace distribution
$$\text{Lap}\left(\frac{\Delta f}{\epsilon}\right)$$
we take it as $\beta = \frac{\Delta f}{\epsilon}$, then we have
$$\Pr[\text{Lap}(\beta) = x] = \frac{1}{2\beta} e^{-|x|/\beta}$$
$$\frac{\Pr[\text{Lap}(\beta) = x]}{\Pr[\text{Lap}(\beta) = x + d]} \leq e^\beta \leq e^\beta = e^\epsilon$$
Then can be obtained, which satisfies the mathematical definition of differential privacy.
In short, Laplace mechanism is to add noise to the output of the original function. When noise of $f$ is 0, that is, when count value is the output, $Pr$ probability is at the highest level. When $f(D)$ create noise with the probability of $Pr$, $f(D')$ create noise in the probability of $Pr'$, they output the same value equals the value of count’, and the $Pr$ and $Pr'$ probability ratio are controlled within the $\exp(\epsilon)$[6].
4.1.3. Application
Due to good characteristics, differential privacy has developed into a recognized privacy standards, and is applied in gradually from academia to industry. Google[7] took the lead in deploying differential privacy mechanism in Chrome browser in 2014, so as to discover the phenomenon of webpage hijacking without knowing the settings of users’ home pages. Apple[8] announced on WWDC in 2016 that the differential privacy mechanism was deployed in iOS10 to count the frequency of emoji used and update the dictionary without knowing users’ keyboard input. Microsoft[9] also began to collect application usage data by using differential privacy mechanism in the creator update of Windows in the autumn of 2017.
In conclusion, if the thriving e-commerce platform wants to achieve steady and long-term development, it must possess professional knowledge of privacy protection to make necessary modifications to the traditional data mining mechanism, so that the new mechanism can meet the requirements of differential privacy protection. In this way, the security of user data sets which maintain the operation of e-commerce platforms will be ensured, and the privacy information of consumers will be protected. This complies with the basic literacy requirements of data owners in the era of big data.
4.2. Privacy protection in legal level
The progress of computing ability, storage capacity and advanced network technology enables companies a wider range of collection, processing and connection of data. What’s more, companies now tend to put data into various use, such as personalized service and marketing, which on the legal level, leaves even bigger obstacles in personal information protection. Although the personal information protection act has long been included in the legislative agenda of our China, due to its complexity, however, the process has been very slow. By far, no specialized laws concerning personal information protection or privacy rights have been issued, some of the relevant regulations are only involved in other laws in haste. Because the concepts of these laws and regulations are too general and not systematic, along with the ambiguity in the definition of personal information and privacy in China, victims of privacy leakage incidents on e-commerce platforms in the country often suffer losses when they resort to law, while the illegal merchants enjoy profits as owners of vast amount of information.
On the contrary, as early in the 1960s, data privacy laws have first appeared in European and American countries. In May 2016, the European parliament voted to pass the new General Data Protection Regulation (GDPR), which aims to more vigorously curb the abuse of personal information, strengthen the protection of personal privacy, and then force to replace the original data protection directive in May 2018[10]. After the implementation of GDPR, more than 500 million people in 28 member states of the European Union can be directly protected by it. It is worth mentioning that although the UK has started the process of leaving the European Union, GDPR has also been approved and officially launched since May 25 in the country. It is without doubt that GDPR will be another historic shift in the process of personal privacy protection in Europe.
According to the provisions of GDPR, enterprises should obtain the consent of users in the collection, storage and use of personal information, and users should have absolute control over their personal data. Among the 12 updated user rights in GDPR, the right to be forgotten, the right to restrict processing and the right to transfer data are most impressive, and the implementation of the former two is of great practical significance to the protection of consumer privacy on e-commerce platforms. At the policy level of China, we should strengthen the reflection of normative mechanisms in these aspects, carry out severe penalty towards illegal acts and cases that seriously infringe upon personal privacy, and effectively establish the protection system of personal privacy security.
4.3. The Optimization of Privacy Protection in E-commerce
China is a country with a large population base. According to statistics, the number of internet users in China accounts for one-fifth of the total number of internet users in the world. With the development of internet technology and electronic data processing technology, the huge amount of personal
information brought by numerous users under several major e-commerce platforms in China is facing great challenges.
The organic combination of multiple effective approaches is urgently needed to solve this problem. Firstly, individual awareness of privacy protection should not be underestimated. Consumers who participate in e-commerce activities should be more sensitive to protect personal information and keep a vigilant eye on potential privacy leakage flaws in any process involving registration and payment. Secondly, laws and regulations concerning network privacy security also need to be further concerned by the public. It is necessary for Chinese government to be deeply aware of the seriousness of the problem and strengthen its determination to introduce laws and regulations into solving it. The last and most important measure is to introduce the differential privacy protection mechanism, which is more perfect than the traditional privacy protection technology, into the actual operation process of information processing on e-commerce platforms, so as to fundamentally reduce or even eliminate the occurrence of online consumer privacy leakage.
5. Conclusion
The rapid development big data has brought huge opportunities as well as challenges to the field of e-commerce. Nowadays, with the development of mobile internet technology, information carried by the internet is more and more easy to be obtained, and the consequent personal information leakage brings about increasingly acute contradictions. Privacy leakage has gradually become one of the hottest topics in today’s society. From the perspective of the current situation of consumer privacy security on e-commerce platform, this paper has done the following work to improve the consumer privacy security of this platform based on differential privacy technology.
(1) On the basis of reading and studying relevant literature at home and abroad, the concepts of online consumer information privacy and online consumer privacy leakage are sorted out and summarized. Meanwhile, combined with the information interactivity of online shopping behavior on e-commerce platform in comparison with traditional off-line shopping behavior, this paper proposes a new understanding and definition of online consumer privacy leakage.
(2) In the research on the theory of differential privacy technology and its existing industrial applications, this paper proposes a new idea of introducing this privacy protection technology into the field of consumer privacy protection on e-commerce platforms. Differential privacy technology has a good feature of privacy ambiguity, while e-commerce is one of the most focal platforms in data mining and processing nowadays. The combination of these two will certainly be a key step and an inevitable trend of the development of the era of big data.
Reference:
[1] Sohu News. http://www.sohu.com/a/119101428_197955.
[2] Liu Yahui, Zhang Tieying, Jin xiaolong, Cheng Xueqi. Personal privacy protection in the era of big data. Computer research and development. 2015, 52 (1): 229-247.
[3] C. Dwork, F. Mcsherry, K. Nissim, A. Smith. Calibrating noise to sensitivity in private data analysis, in Proceedings of Theory of Cryptography, Springer, 2006: 265-284.
[4] Xiong Ping, Zhu Tianqing, Wang Xiaofeng. Differential privacy protection and its application. Journal of computer science, January 2014, volume 37, issue 1.
[5] Ninghui Li, Min Lyu, Dong Su, Weining Yang. Differential Privacy: From Theory To Practice. 2016.
[6] Open Source in China. https://my.oschina.net/keyven/blog/730740.
[7] U. Erlingsson, V. Pihur, and A. Korolova, “Rappor: Randomized aggregatable privacy preserving ordinal response,” in Proceedings of the 2014 ACM SIGSAC conference on computer and communications security, ACM, 2014, pp. 1054–1067.
[8] Apple Differential Privacy Team, “Learning with privacy at scale,” Apple Machine Learning Journal, vol. 1, 8 Dec. 2017.
[9] B. Ding, J. Kulkarni, and S. Yekhanin, “Collecting telemetry data privately,” in Advances in Neural
Information Processing Systems, 2017, pp. 3574–3583.
[10] Christina Tikkinen-Piri, Anna Rohunen, Jouni Markkula. EU General Data Protection Regulation Changes and implications for personal data collecting companies. computer law & security review 34 (2018) 134–153. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3123,
1
],
[
3123,
7303,
2
],
[
7303,
11751,
3
],
[
11751,
15697,
4
],
[
15697,
18505,
5
],
[
18505,
22969,
6
],
[
22969,
27025,
7
],
[
27025,
27291,
8
]
]
} |
506a007034647ba5d9727281a7445f8c7445b10c | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 32911,
"total-output-tokens": 13965,
"fieldofstudy": [
"Medicine",
"Biology"
]
} | Retrospective Cohort Study
High tacrolimus intra-patient variability is associated with graft rejection, and *de novo* donor-specific antibodies occurrence after liver transplantation
Arnaud Del Bello, Nicolas Congy-Jolivet, Marie Danjoux, Fabrice Muscari, Laurence Lavayssière, Laure Esposito, Anne-Laure Hebral, Julie Bellière, Nassim Kamar
Data sharing statement: No additional data are available.
Open-Access: This article is an open-access article which was selected by an in-house editor and fully peer-reviewed by external reviewers. It is distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc/4.0/
Manuscript source: Unsolicited manuscript
Correspondence to: Arnaud Del Bello, MD, Doctor, Department of Nephrology and Organ Transplantation, CHU Rangueil, TSA 50032, Cedex 9, Toulouse 31059, France. [email protected]
Telephone: +33-5-61323923
Fax: +33-5-61323989
Received: December 5, 2017
Peer-review started: December 5, 2017
First decision: January 18, 2018
Revised: March 6, 2018
Accepted: March 31, 2018
Published online: March 28, 2018
Abstract
**AIM**
To investigate the role of tacrolimus intra-patient variability (IPV) in adult liver-transplant recipients.
**METHODS**
We retrospectively assessed tacrolimus variability in a cohort of liver-transplant recipients and analyzed its effect on the occurrence of graft rejection and *de novo* donor-specific antibodies (dnDSAs), as well as graft...
survival during the first 2 years posttransplantation. Between 02/08 and 06/2015, 116 patients that received tacrolimus plus mycophenolate mofetil (with or without steroids) were included.
RESULTS
Twenty-two patients (18.5%) experienced at least one acute-rejection episode (BPAR). Predictive factors for a BPAR were a tacrolimus IPV of > 35% [OR = 3.07 (1.4-8.24), P = 0.03] or > 40% [OR = 4.16 (1.38-12.50), P = 0.01], and a tacrolimus trough level of < 5 ng/mL [OR=3.68 (1.3-10.4), P =0.014]. Thirteen patients (11.2%) developed at least one dnDSA during the follow-up. Tacrolimus IPV [coded as a continuous variable: OR = 1.1, 95%CI (1.0-1.12), P = 0.006] of > 35% [OR = 4.83, 95%CI (1.39-16.72), P = 0.01] and > 40% [OR = 9.73, 95%CI (2.65-35.76), P = 0.001] were identified as predictors to detect dnDSAs. IPV did not impact on patient- or graft-survival rates during the follow-up.
CONCLUSION
Tacrolimus-IPV could be a useful tool to identify patients with a greater risk of graft rejection and of developing a de novo DSA after liver transplantation
Key words: Variability; Liver transplantation; Donor-specific antibodies; Immunosuppression
© The Author(s) 2018. Published by Baishideng Publishing Group Inc. All rights reserved.
Core tip: Tacrolimus intra-patient variability (Tac IPV) was associated with kidney-graft rejection and worse long-term outcomes, but until now, was not well studied after liver transplantation in adult recipients. We found that the coefficient of variability-IPV of tacrolimus was a predictive factor for acute rejection and the occurrence of de novo donor-specific antibodies (DSA) after liver transplantation in a retrospective cohort of 116 recipients treated with tacrolimus and mycophenolate mofetil. This could be a useful tool to identify patients with a greater risk of graft rejection and of developing a de novo DSA after liver transplantation.
Del Bello A, Congy-Jolivet N, Danjoux M, Muscari F, Lavayssière L, Esposito L, Hebral AL, Bellière J, Kamar N. High tacrolimus intra-patient variability is associated with graft rejection, and de novo donor-specific antibodies occurrence after liver transplantation. World J Gastroenterol 2018; 24(16): 1795-1802
Available from: URL: http://www.wjgnet.com/1007-9327/full/v24/i16/1795.htm DOI: http://dx.doi.org/10.3748/wjg.v24.i16.1795
INTRODUCTION
Tacrolimus (Tac) is considered a cornerstone within immunosuppression protocols to prevent T-cell and antibody-mediated rejection after liver transplantation[1-3]. However, this treatment presents a narrow therapeutic index: overexposure can lead to clinically serious events[4] thus necessitating regular therapeutic drug monitoring, whereas underexposure can lead to acute or chronic graft rejection[4-6]. Inter-individual variability from Tac therapy may be explained by the polymorphism of cytochromes P450 3A4 and 5 (responsible for biotransformation of Tac)[7] and the drug transporter ABCB1[8], circadian rhythms[9] and also drug-drug interactions[10]. In addition to inter-individual variability, the pharmacokinetics of Tac can vary within individual patients. The concept of intra-patient variability (IPV) refers to the fluctuations in Tac blood concentrations (and consequently episodes of over- and under-immunosuppression) that some patients experience over time[11]. Several non-modifiable and modifiable factors contribute to Tac IPV (e.g., polymorphism in CYP3A genes, the circadian rhythm of Tac exposure, gastrointestinal events such as diarrhea, cholestasis, changes in protein levels, anemia, but also drug-drug interactions with macrolides orazole anti-fungal treatments, foods, or changes in formulation or generic substitution)[11], but non-adherence to Tac seems to be the main cause of IPV[12,13]. It was previously suggested that higher degree of Tac IPV was associated with kidney-graft rejection and worse long-term outcomes after kidney transplantation[14,15]. Similar limited data have been reported after liver transplantation[16,17], mainly in pediatric cohorts. Moreover, little is known concerning the relationship between Tac variability and the occurrence of donor-specific antibodies (DSAs). Herein, we retrospectively assessed the variability of Tac in a cohort of liver-transplant recipients and analyzed its impact on the number of acute rejections, the occurrence of de novo DSAs, and patient- and graft-survival rates.
MATERIALS AND METHODS
Patients
Between February 2008 (i.e., the date when the solid-phase Luminex assay was set up in our institution) and June 2015, a total of 298 adult patients received a liver transplant from deceased donors (DDLT) in our center. Patients excluded from the study were those that died within the first month posttransplantation (n = 34), those that needed a re-transplant during the first month (n = 2), and those that received a transplant with a preformed DSA (mean fluorescence intensity cut-off > 1000) directed against human leukocyte antigen (HLA) A, B, Cw, DR, DQ, or DP (n = 37). In order to avoid confounding factors associated with others immunosuppressive treatments, only patients that received and were maintained under Tac and mycophenolate mofetil (MMF) (with or without steroids) were included in this study (Figure 1). All patients but five received Tac given twice daily (Prograf®). The other five received Tac once daily (Advagraf®). We excluded patients that had Tac or MMF withdrawn.
The target concentration of Tac trough level was 7-10 ng/mL during the first 3 mo, and 5-10 ng/mL thereafter during the follow-up. Each participant was followed for 2 years or until re-transplantation (n = 3) or death (n = 6). The median follow-up was 24 mo (range: 6-24). All rejection episodes were biopsy proven. Biopsies were only performed for cause during the study period and were analyzed according to the Banff criteria\textsuperscript{18-20}. Graft failure was defined as the need for re-transplantation or as death from liver failure.
Detection of cytomegalovirus was performed using real-time PCR, as previously described\textsuperscript{21}, at month 3, 6, 12, and 24, and at any other time if clinically indicated.
**Intra-patient variability**
Tac trough levels were routinely assessed using high-performance liquid chromatography-linked tandem mass spectrometry (HPLC-MS) at discharge, then monthly between months 1-6, and thereafter at months 9, 12, 15, 18, and 24. To calculate the IPV of Tac, at least three Tac trough levels from each patient had to be available. The median number of available Tac measurements was 10 (range: 4-12).
Tac IPV was estimated using the coefficient of variability (CV). The CV-IPV was calculated as follows: CV-IPV (%) = [(standard deviation/mean Tac trough-level concentration) × 100. Because all patients received the same drug dose between discharge and M24, the obtained levels were corrected for the corresponding daily dose of tacrolimus (CV C\textsubscript{0}/D-IPV). In addition, because some patients were converted from one formulation to another during the follow-up, we calculated CV and CV C\textsubscript{0}/D-IPV after excluding the Tac trough levels obtained during the adjustment dose period, i.e., the month following a switch.
To compare IPV with the two formulations of Tac, the Tac twice-daily CV-IPV was calculated using Tac trough levels obtained from patients that received Tac twice daily since transplantation until last follow-up and those obtained in patients switched for Tac once daily before the switch. The Tac once-daily CV-IPV was calculated using Tac trough levels from patients that received Tac once daily since transplantation until the last follow-up, and those obtained from patients that were later switched from twice- to a once-daily formulation after the switch (this excluded Tac trough levels obtained in the month following the switch).
**Immunological analyses**
All patients were screened for anti-HLA DSAs at transplantation, and at month 3 and 12, and annually thereafter. Additional screening was performed in case of graft dysfunction. LumineX\textsuperscript{a} assays were used to determine the specificity of class I HLA in A/B/Cw and class II in DR/DQ/DP IgG antibodies in the recipients’ sera (centrifuged at 10000 g for 10 min) using Labscreen single Ag HLA class-\textsuperscript{I} and class-\textsuperscript{II} detection tests (One Lambda, Canoga Park, CA, United States), according to the manufacturer’s instructions. The presence and specificity of antibodies were then detected using a Labscreen 100\textsuperscript{®}, and the mean fluorescence (baseline) value for each sample in each bead was evaluated. The baseline value was calculated as follows: [raw sample mean fluorescence intensity (MFI)-raw negative serum control MFI-negative-bead raw MFI sample-negative-bead raw MFI negative serum control]. A baseline value of > 1000 was considered positive.
**Statistical analyses**
Categorical variables are expressed as percentages and comparisons between groups were made using the chi-squared test or, if appropriate, Fisher’s exact test. Continuous variables were expressed as medians and ranges, and compared using the Mann-Whitney test. Logistic regression analysis was used to determine the predictors for acute-rejection episodes and the occurrence of de novo anti-HLA DSAs. Variables with a P < 0.1 in the univariate analyses were included in the stepwise multivariable analyses. P < 0.05 was considered statistically significant.
**RESULTS**
The patients’ characteristics at transplantation are presented in Table 1. All liver transplantations performed in this study were performed from DDLT. The mean DDLT age was 51 ± 17 years. To note, one DDLT was < 18 years, and 4 DDLT were > 80 years.
**Tacrolimus levels and variability**
During the follow-up, 44 (38%) patients were switched from Tac immediate-release given twice a day (Prograf\textsuperscript{®}), to Tac once a day to improve quality of life. The switch was performed at a mean of 15 (range: 1-18) mo post-
transplantation.
Mean tacrolimus trough level was 8 ± 3 ng/mL during the follow-up (Table 1). The mean dose of Tac was 6.8, 6.7, 6.4, 5.9, 5.4, 5.1, 4.8, and 4.6 mg/d, respectively, at discharge and at months 1, 3, 6, 9, 12, 18, and 24. Forty-five (38.8%) patients presented with a Tac trough level of < 5 ng/mL at least once during the follow-up. The overall mean Tac CV-IPV was 32 ± 12% [median CV-IPV 30.5% (7.6-80.6)]. Tac CV-IPV distribution is presented in Figure 2. The 1st, 2nd, 3rd, and 4th quartiles were, respectively, 25%, 30.5%, 36.5%, and 80.6%. The mean Tac CV-IPV was 30% ± 11% in patients given Tac once daily and was 32% ± 12% in patients that received Tac twice daily (\( P = 0.10 \)). The mean Tac CV-IPV in the five patients that had received Tac once-daily since transplantation was 30% ± 7%.
In the 44 patients that were converted from Tac twice-daily to once daily, the mean values of Tac CV-IPV were 32.3% ± 12% and 30% ± 12% before and after the switch, respectively (\( P = 0.21 \)).
Table 1 Characteristics of the liver-transplant recipients
| Variable | \( n = 116 \) |
|-------------------------------------------------------------------------|---------------------|
| Donors’ age at transplantation, yr (range) | 53 (9-85) |
| Recipients’ age at transplantation, yr (range) | 57 (18-72) |
| Recipients’ gender: male, \( n \) (%) | 96 (83) |
| Initial liver disease, \( n \) (%) | |
| Alcohol | 49 (43) |
| Viral (HCV, HBV) | 36 (31) |
| Autoimmune disease (AIH, PSC, PBC) | 13 (11) |
| Other \(^1\) | 18 (17) |
| Median MELD score at transplantation (range) (%) | 22 (6-40) |
| Positive HCV RNA at transplantation, \( n \) (%) | 21 (18) |
| Re-transplantation, yes \( n \) (%) | 3 (3) |
| Induction therapy, yes \( n \) (%) | 87 (75) |
| Polyclonal antibodies, \( n \) (%) | 9 (8) |
| Interleukin-2 receptor blocker, \( n \) (%) | 78 (67) |
| Conversion during the follow-up from twice-daily to once daily tacrolimus, \( n \) (%) | 42 (36) |
| Number of patients receiving tacrolimus once daily, \( n \) (%) | 5 (4) |
| At discharge | |
| Month 1 | 8 (7) |
| Month 3 | 9 (8) |
| Month 6 | 12 (10) |
| Month 9 | 18 (16) |
| Month 12 | 26 (31) |
| Month 18 | 39 (34) |
| Month 24 | 47 (41) |
| Tacrolimus trough level (ng/mL) | 7.6 ± 3 |
| At discharge | |
| Month 1 | 8 ± 3 |
| Month 3 | 8.4 ± 3 |
| Month 6 | 8.4 ± 3 |
| Month 9 | 7.4 ± 3 |
| Month 12 | 7.8 ± 3 |
| Month 18 | 7.5 ± 2 |
| Month 24 | 6.9 ± 3 |
| Mycophenolate mofetil dose (mg/d) | 1700 ± 600 |
| At discharge | |
| Month 3 | 1250 ± 550 |
| Month 6 | 1100 ± 450 |
| Month 12 | 1000 ± 300 |
| Month 24 | 1000 ± 300 |
| Steroids (mg/d) | |
| At discharge: Yes \( n \) (%) | 116 (100) |
| Dose (mg/d) | 20 ± 12 |
| Month 3: Yes \( n \) (%) | 114 (98) |
| Dose (mg/d) | 8 ± 4 |
| Month 6: Yes \( n \) (%) | 110 (95) |
| Dose (mg/d) | 7 ± 5 |
| Month 12: Yes \( n \) (%) | 104 (90) |
| Dose (mg/d) | 6 ± 6 |
| Month 24: Yes \( n \) (%) | 97 (84) |
| Dose (mg/d) | 5 ± 2 |
\(^1\)Polycystic disease \( n = 7 \), NASH syndrome \( n = 4 \), Wilson disease \( n = 2 \), bile duct atrophy \( n = 1 \), drug intoxication \( n = 2 \), and cryptogenic cirrhosis \( n = 1 \). HBV: Hepatitis B virus; HCV: Hepatitis C virus; AIH: Auto-immune hepatitis; PSC: Primary sclerosing cholangitis; PBC: Primary biliary cirrhosis.
Overall mean CV C₀/d- IPV was 73% ± 43%. It was 69% ± 29% with Tac twice-daily compared to 79% ± 50% for Tac given once daily (P = 0.9).
**Incidence of acute rejection and de novo donor-specific antibodies**
During the follow-up, 22 patients (19%) presented with at least one episode of acute rejection. The time between transplantation and a diagnosis of acute rejection (i.e., the date of the biopsy) was 3.5 mo (range: 0.5-12). Fourteen patients (12%) experienced a T-cell steroid-sensitive acute rejection, and six patients (5%) presented with a T-cell steroid-resistant acute rejection, which was treated with polyclonal antibodies. One patient presented with an acute antibody-mediated rejection at 4 mo posttransplantation. The Tac CV-IPV in this patient was high: CV-IPV of 63.2% and CV C₀/d- IPV = 68.2%. The risk factors for acute rejection after liver transplantation are presented in Table 2. The predictive factors for a biopsy-proven acute rejection were a Tac trough level of < 5 ng/mL [OR = 3.68; 95%CI (1.30-10.41), P = 0.014], the Tac CV-IPV (coded as a continuous variable) [OR = 1.1; 95%CI (1.01-1.11), P = 0.008], a CV-IPV of > 35% [OR = 3.07; 95%CI (1.14-8.24), P = 0.03], and a CV-IPV of > 40% [OR = 4.16; 95%CI (1.38-12.50), P = 0.01]. Twenty-one of the 22 patients that presented with an acute-rejection episode were receiving Tac twice daily when the rejection was diagnosed.
Thirteen patients (11.2%) presented with at least one de novo DSA during the posttransplantation follow-up (nine anti-HLA class II, three anti-HLA class I, one anti-HLA class I and II). Only one of these patients developed an antibody-mediated rejection. The median time between transplantation and detection of a de novo DSA was 3.5 mo (range: 1-12). The risk factors for acute rejection and de novo donor-specific antibodies during the follow-up are presented in Table 2. The predictive factors for a biopsy-proven acute rejection were a Tac trough level of < 5 ng/mL [OR = 3.68; 95%CI (1.30-10.41), P = 0.014], the Tac CV-IPV (coded as a continuous variable) [OR = 1.1; 95%CI (1.01-1.11), P = 0.008], a CV-IPV of > 35% [OR = 3.07; 95%CI (1.14-8.24), P = 0.03], and a CV-IPV of > 40% [OR = 4.16; 95%CI (1.38-12.50), P = 0.01]. Twenty-one of the 22 patients that presented with an acute-rejection episode were receiving Tac twice daily when the rejection was diagnosed.
**Table 2 Risk factors for a graft-rejection episode**
| Variable | Univariate analyses | Multivariate analyses |
|----------|---------------------|----------------------|
| | OR | 95%CI | P value | OR | 95%CI | P value |
| MELD score > 30 (n = 31) | 0.55 | 0.12-1.90 | 0.42 | - | - | - |
| Initial liver disease | 1.34 | 0.44-3.90 | 0.61 | - | - | - |
| (1) Alcohol cirrhosis (n = 49) vs (2, 3, 4) | 0.38 | 0.18-1.68 | 0.34 | - | - | - |
| (2) Viral disease (n = 36) vs (1, 3, 4) | 0.71 | 0.12-4.47 | 0.07 | 1.00 | 0.51-1.15 | 0.210 |
| (3) Auto-immune ILD (n = 13) vs (1, 2, 4) | 0.49 | 0.05-2.37 | 0.52 | - | - | - |
| (4) Other (n = 18) vs (1, 2, 3) | 0.22 | 0.22-1.55 | 0.42 | - | - | - |
| Induction therapy, yes (n = 87) vs no | 3.89 | 0.70-20.13 | 0.06 | 2.87 | 0.61-13.47 | 0.180 |
| Polyclonal antibodies (vs other) | 0.40 | 0.14-1.70 | 0.08 | 0.52 | 0.185-1.50 | 0.230 |
| IL2R blockers (vs other) | 0.98 | 0.35-2.88 | 1.00 | - | - | - |
| Donors’ age > 50 yr (n = 69) | 0.61 | 0.20-2.01 | 0.41 | - | - | - |
| Recipients’ age > 50 yr (n = 92) vs (1, 2, 3) | 1.96 | 0.54-6.45 | 0.22 | - | - | - |
| HCV-RNA + At transplantation (n = 21) vs (1, 3, 4) | 2.30 | 0.63-7.82 | 0.20 | - | - | - |
| De novo DSAs during the FU (n = 13) vs no | 2.80 | 0.64-11.19 | 0.13 | - | - | - |
| Tacrolimus trough level < 5 ng/mL (n = 34) vs (1, 2, 3) | 3.00 | 1.05-8.96 | 0.02 | 3.68 | 1.30-10.41 | 0.014 |
| CV-IPV tacrolimus (continuous variable) vs other | 2.70 | 1.88-13.45 | 0.01 | 1.10 | 1.01-1.11 | 0.008 |
| CV-IPV > 35% vs <35% | 3.05 | 1.05-8.96 | 0.03 | 3.07 | 1.14-8.24 | 0.030 |
| CV-IPV > 0% | 2.97 | 0.91-9.30 | 0.04 | 4.16 | 1.38-12.50 | 0.010 |
| CV-C₀/d-IPV | 1.89 | 0.67-5.74 | 0.24 | - | - | - |
FU: Follow-up; ILD: Initial liver disease; HCV: Hepatitis C virus; CV-IPV: Coefficient of variability-intra-patient variability; CV-C₀/d-IPV: Coefficient of variability corrected for the corresponding daily dose-intra-patient variability.
**Figure 2 Distribution of tacrolimus according to intra-patient variability.**
Overall mean CV C₀/d- IPV was 73% ± 43%. It was 69% ± 29% with Tac twice-daily compared to 79% ± 50% for Tac given once daily (P = 0.9).
Table 3 Risk factors for developing de novo donor-specific antibodies after liver transplantation.
| Variable | Univariate analyses | Multivariate analyses |
|---------------------------------|---------------------|-----------------------|
| | OR | 95%CI | P value | OR | 95%CI | P value |
| MELD score > 30 (n = 31) | 1.84 | 0.43-7.10 | 0.33 | - | - | - |
| Initial liver disease | - | - | - | - | - | - |
| (1) Alcohol cirrhosis (n = 49) vs (2, 3, 4) | 0.58 | 0.12-2.22 | 0.53 | - | - | - |
| (2) Viral disease (n = 36) vs (1, 3, 4) | 0.98 | 0.21-3.86 | 1.0 | - | - | - |
| (3) Autoimmune ILD (n = 13) vs (1, 2, 4) | 1.51 | 0.14-8.46 | 0.64 | - | - | - |
| (4) Other (n = 18) vs (1, 2, 3) | 2.79 | 0.55-11.83 | 0.64 | - | - | - |
| Induction therapy, yes (n = 87) | 1.61 | 0.41-7.61 | 0.55 | - | - | - |
| Polyclonal antibodies (vs other) | 0.59 | 0.70-18.00 | 0.60 | - | - | - |
| IL2R blockers (vs other) | 1.1 | 0.28-5.28 | 1.0 | - | - | - |
| Donors’ age > 50 yr (n = 69) | 0.78 | 0.20-3.00 | 0.77 | - | - | - |
| Recipients’ age > 50 yr (n = 92) | 0.36 | 0.09-1.58 | 0.10 | 0.2 | 0.07-0.85 | 0.3 |
| HCV RNA+ at transplantation (n = 21) | 1.41 | 0.23-6.23 | 0.70 | - | - | - |
| Steroid withdrawal during the FU (n = 19) | 0.39 | 0.01-3.01 | 0.69 | - | - | - |
| Tacrolimus trough level ≤ 5 ng/mL (n = 34) | 1.59 | 0.38-6.05 | 0.52 | - | - | - |
| CV-IPV tacrolimus (continuous variable) | 1.92 | 1.28-21.39 | 0.08 | 1.1 | 1.0-11.2 | 0.006 |
| CV-IPV > 35% | 4.66 | 1.22-19.82 | 0.02 | 4.83 | 1.39-16.72 | 0.01 |
| CV-IPV > 40% | 9.10 | 2.28-40.63 | < 0.001 | 9.73 | 2.65-35.76 | 0.001 |
| CV-C/d-IPV | 3.15 | 5.47-27.31 | 0.005 | 1.0 | 0.97-1.02 | 0.09 |
FU: Follow-up; ILD: Initial liver disease; HCV: Hepatitis C virus; CV-IPV: Coefficient of variability-intra-patient variability; CV-C/d-IPV: Coefficient of variability corrected for the corresponding daily dose-intra-patient variability.
Factors for a de novo DSA are presented in Table 3. The Tac CV-IPV [coded as a continuous variable: OR = 1.1, 95%CI (1.0-1.12), P = 0.006], and a CV-IPV of > 35% [OR = 4.83, 95%CI (1.39-16.72), P = 0.01] or of > 40% [OR = 9.73, 95%CI (2.65-35.76), P = 0.001] were identified as predictors for the occurrence of de novo DSAs detection.
Survival of patients
During the follow-up, six patients died [at a mean of 13 mo (range: 6-23) posttransplantation]. The causes of death were infections (n = 3), cardiovascular (n = 2), and neoplastic (n = 1) complications. No difference in Tac CV-IPV was observed between patients that died during the follow-up (CV-IPV 33% ± 6%) and those that did not (CV-IPV 32% ± 12%; P = 0.70). Three patients required re-transplantation at month 5, 10, and 14, respectively, for ischemic cholangitis that occurred posttransplantation. During the follow-up, 24 patients presented with posttransplant replication of cytomegalovirus. No difference in Tac CV-IPV was observed between patients with replication of cytomegalovirus (CV-IPV 32% ± 9%) and those without replication (32% ± 12%, P = 0.90).
DISCUSSION
High IPV has been previously associated with a greater risk of graft rejection, an accelerated progression of chronic histological lesions, and worse long-term survival after kidney transplantation[11,14,22,23]. In pediatric liver-transplants, Tac variability was associated with late acute rejection[16]. In the present study, we investigated the impact of Tac variability in 116 adult liver-transplant recipients. In order to avoid confounding factors, we focused on patients that received a graft without preformed DSAs and that had received Tac associated with MMF. Although the mean Tac trough level was 8 ± 3 ng/mL during the study period, nearly 40% of patients had a Tac trough level of < 5 ng/mL at least once during the follow-up. Tac CV-IPV varied from 7.6%-80.6% (median 30.5%), and median Tac CV C/d-IPV was 62% (18-147). Almost one-third of patients presented with a Tac CV-IPV of > 35%. This high value is similar to those reported in previous studies, mainly after kidney transplantation[24,25]. In kidney-transplant[13,25] and pediatric liver-transplant patients[16], high CV-IPV was associated with an increased risk of acute rejection. In the present study, we found that a Tac trough level of < 5 ng/mL, the Tac CV-IPV (coded as a continuous variable), a CV-IPV of > 35%, and a CV-IPV > 40% were independent predictive factors for a biopsy-proven graft rejection.
Posttransplant positive DSAs were associated with decreased graft survival and increased acute or chronic graft rejections[2,3,26]. It has been previously suggested that iterative transplantation, low levels of calcineurin inhibitors, the use of cyclosporine (compared to Tac), and non-adherence can promote the development of a de novo DSA after liver transplantation[21]. Herein, we found that the Tac CV-IPV (coded as a continuous variable), a CV-IPV of > 35%, and CV-IPV > 40% were independent predictive factors for the occurrence of a de novo DSA. Similar data, reported after kidney transplantation[24], from a cohort of 310 adult kidney-transplant patients given Tac twice-daily during the first year posttransplant, showed that a history of acute rejection, re-transplantation and a Tac CV greater than 30% were associated with the occurrence of a de novo DSA. In our study, one patient presented with an acute antibody-mediated rejection associated with an anticlass Il de novo DSA at 3 mo after liver transplantation.
Interestingly, this patient had high tacrolimus variability (CV-IPV 63.2%, CV C0/d-IPV 68.2%). None of the other 12 patients that developed a DSA experienced an acute antibody-mediated rejection. However, it was suggested that patients with positive DSAs would present lower graft survival, consecutive to chronic antibody mediated rejection rather than to acute antibody-mediated rejection episodes.
In several studies, but not all, the use of once-daily tacrolimus compared to a twice daily formulation has been found to improve adherence and to reduce IPV. In the present study, no difference between Tac formulations was observed.
This study has several limitations. Because of its retrospective design, we could not evaluate the cause of Tac variability. It has been suggested previously that non-adherence is the main cause of Tac variability. However, in our study, adherence was not evaluated using objective methods, such as those previously reported using electronic devices. Moreover, we did not evaluate MMF variability in our study because we do not perform this analysis routinely in our center. Of note, conflicting results have been reported concerning the use of MMF variability after solid-organ transplantation. It was also previously suggested that pre-transplant determination of CYP3A5 and MDR1 polymorphisms allows more rapid achievement of therapeutic Tac trough level. However, no association between the pharmacogenomics parameters and Tac intra-patient variability is expected and was reported.
In conclusion, we found that the CV-IPV of Tac was a predictive factor for acute rejection and the occurrence of a de novo DSA after liver transplantation. This could be a useful tool to identify patients with a greater risk of graft rejection and of developing a de novo DSA after liver transplantation. Future studies should investigate the role of Tac IPV on long-term outcomes, on chronic graft rejection, and over-immunosuppression-related diseases (cancer, and related immunocompromised infections).
ARTICLE HIGHLIGHTS
Research background
Tacrolimus (Tac) is considered a cornerstone within immunosuppression protocols to prevent T-cell and antibody-mediated rejection after liver transplantation. However, this treatment presents a narrow therapeutic index: overexposure can lead to clinically serious events, thus necessitating regular therapeutic drug monitoring, whereas underexposure can lead to acute or chronic graft rejection. The concept of intra-patient variability (IPV) refers to the fluctuations in Tac blood concentrations (and consequently episodes of over- and under-immunosuppression) that some patients experience over time.
Research motivation
Tac-IPV is an inexpensive assay to explore fluctuations in Tac blood concentrations. We investigated the potential usefulness of Tac-IPV to predict the incidence of donor specific antibodies and graft rejection episodes.
Research objectives
Our aim was to investigate the role of tacrolimus IPV in adult liver-transplant recipients.
Research methods
We retrospectively assessed tacrolimus variability and analyzed its effect on the occurrence of graft rejection and de novo donor-specific antibodies.
Research results
Twenty-two patients experienced at least one acute-rejection episode (BPAR). Predictive factors for a BPAR were a tacrolimus IPV of > 35% or > 40%, and a tacrolimus trough level of < 5 ng/ml. Thirteen patients developed at least one dnDSA during the follow-up. Tacrolimus IPV and tacrolimus IPV of > 35%, and > 40% were identified as predictors to detect dSDAs. IPV did not impact on patient- or graft-survival rates during the follow-up.
Research conclusions
In our study higher Tac-IPV was associated with graft rejection and occurrence of DSAs.
Research perspective
Tacrolimus-IPV could be a useful tool to identify patients with a greater risk of graft rejection and of developing a de novo DSA after liver transplantation.
REFERENCES
1. Price DC. Radioisotopic evaluation of the thyroid and the parathyroids. Radiol Clin North Am 1993; 31: 991-1015 [PMID: 8362060 DOI: 10.1016/14651858.CD011639.pub2]
2. Kaneko H, O’Leary JG, Banuelos N, Jennings LW, Susskind BM, Klintmalm GB, Terasaki PI. De novo donor-specific HLA antibodies decrease patient and graft survival in liver transplant recipients. Am J Transplant 2013; 13: 1541-1548 [PMID: 23721554 DOI: 10.1111/ajt.12212]
3. European Association for the Study of the Liver. EASL Clinical Practice Guidelines: Liver transplantation. J Hepatol 2016; 64: 433-485 [PMID: 26597456 DOI: 10.1016/j.jhep.2015.10.006]
4. de Mare-Bredemeijer EL, Metselaar HJ. Optimization of the use of Calcineurin inhibitors in liver transplantation. Best Pract Res Clin Gastroenterol 2012; 26: 85-95 [PMID: 22482528 DOI: 10.1016/j.bpg.2012.01.017]
5. Rodriguez-Perálvarez M, Germani G, Papastergiou V, Tsochatzis E, Thalassinos E, Luong TV, Rolando N, Dhillon AP, Patch D, O’Beirne J, Thorburn D, Burroughs AK. Early tacrolimus exposure after liver transplantation: relationship with moderate/severe acute rejection and long-term outcome. J Hepatol 2013; 58: 262-270 [PMID: 23023010 DOI: 10.1016/j.jhep.2012.09.019]
6. Del Bello A, Congy-Jolivet N, Muscari F, Lavaysière L, Esposito L, Cardeau-Desangles I, Guitard J, Dörö G, Suc B, Duffas JP, Alric L, Bureau C, Danjoux M, Guilleau-Frugier C, Blancher A, Rostaing L, Kamar N. Prevalence, incidence and risk factors for donor-specific anti-HLA antibodies in maintenance liver transplant patients. Am J Transplant 2014; 14: 867-875 [PMID: 24580771 DOI: 10.1111/ajt.12651]
7. Staatz CE, Tett SE. Clinical pharmacokinetics and pharmacodynamics of tacrolimus in solid organ transplantation. Clin Pharmacokinet 2004; 43: 623-653 [PMID: 15244495 DOI: 10.1007/s40262-015-0282-2]
8. Hesselink DA, Bouamar R, Elens L, van Schaik RR, van Gelder T. The role of pharmacogenetics in the disposition of and response to tacrolimus in solid organ transplantation. Clin Pharmacokinet 2014; 53: 123-139 [PMID: 24249597 DOI: 10.1007/s40262-013-0203-3]
9. Tada H, Satoh S, Inuma M, Shimoda N, Murakami M, Hayase Y, Kato T, Suzuki T. Chronopharmacokinetics of tacrolimus in kidney transplant recipients: occurrence of acute rejection. J Clin Pharmacol 2003; 43: 859-865 [PMID: 12953343 DOI: 10.1177/001218650304300603]
10. van Gelder T. Drug interactions with tacrolimus. Drug Saf 2002; 25: 707-712 [PMID: 12167066 DOI: 10.2165/00002018-20022510-0-00003]
11. Shuker N, van Gelder T, Hesselink DA. Intra-patient variability
in tacrolimus exposure: causes, consequences for clinical management. *Transplant Rev* (Orlando) 2015; **29**: 78-84 [PMID: 25687818 DOI: 10.1016/j.trre.2015.01.002]
12 Shemes E, Shneider BL, Savitzky JK, Arnott L, Gondolesi GE, Krieger NR, Kerkar N, Magid MS, Stubler ML, Schneider J, Yehuda R, Emre S. Medication adherence in pediatric and adolescent liver transplant recipients. *Pediatrics* 2004; **113**: 825-832 [PMID: 15060234 DOI: 10.1542/peds.113.4.825]
13 Pollock-Barzux SM, Finkelstein Y, Manlhiot C, Dipchand AI, Hebert D, Ng VL, Solomon M, McCrindle BW, Grant D. Variability in tacrolimus blood levels increases the risk of late rejection and graft loss after solid organ transplantation in older children. *Pediatr Transplant* 2010; **14**: 968-975 [PMID: 21040278 DOI: 10.1111/j.1399-0621.2010.01409.x]
14 Borra LC, Roodnat JI, Kal JA, Mathot RA, Weimar W, van Gelder T. High within-patient variability in the clearance of tacrolimus is a risk factor for poor long-term outcome after kidney transplantation. *Nephrol Dial Transplant* 2010; **25**: 2757-2763 [PMID: 20190242 DOI: 10.1093/ndt/gfq098]
15 Ro BI, Sin SI, Yang J, Moon KC, Kim YS, Kim SI, Ahn C, Ha J. Impact of tacrolimus intraintestinal variability and CYP3A5 genotypic polymorphism on acute rejection in kidney transplantation. *Ther Drug Monit* 2012; **34**: 680-685 [PMID: 23149441 DOI: 10.1097/FTD.0b013e3182731809]
16 Shemes E, Bucuvalas JC, Anand R, Mazariagos GV, Alonso EM, Venick RS, Reyes-Mugica M, Annunziato RA, Shneider BL. The Medication Level Variability Index (MLVI) Predicts Poor Liver Transplant Outcomes: A Prospective Multi-Site Study. *Am J Transplant* 2017; **17**: 2668-2678 [PMID: 28321975 DOI: 10.1111/ajt.14276]
17 Christina S, Annunziato RA, Schiano TD, Anand R, Vaidya S, Chuang K, Zack Y, Florman S, Shneider BL, Shemes E. Medication level variability index predicts rejection, possibly due to nonadherence, in adult liver transplant recipients. *Liver Transplant* 2014; **20**: 1168-1177 [PMID: 24931127 DOI: 10.1002/lt.23930]
18 Banff schema for grading liver allograft rejection: an international consensus document. *Hepatology* 1997; **25**: 658-663 [PMID: 9049215 DOI: 10.1002/hep.1840250508]
19 Demetris AJ, Adams D, Bellamy C, Blakolmer K, Clouston A, Dhillon AP, Fung J, Gouw A, Gustafsson B, Haga H, Harrison D, Hart J, Hubscher S, Jaffe R, Khettry U, Lassman C, Lewin K, Martinez O, Nakazawa Y, Neil D, Pappo O, Parikh M, Randhawa P, RasoulRockenschaub S, Reinholt F, Reynolds M, Robert M, Tamasandas B, Wara W, Wiesner R, Wernerson A, Wrba F, Wyatt J, Yamabe H. Update of the International Banff Consensus Document. *Am J Transplant* 2016; **16**: 603-614 [PMID: 26469278 DOI: 10.1111/ajt.13476]
20 Kypers DR, Peeters PC, Senesseal JJ, Kianna MN, Vrijens B, Kristanto P, Dobbels F, Vanrenterghem Y, Kanaan N; ADMIRAD Study Team. Improved adherence to tacrolimus once-daily formulation in renal recipients: a randomized controlled trial using electronic monitoring. *Transplantation* 2013; **95**: 333-340 [PMID: 23263559 DOI: 10.1097/TP.0b013e3182725532]
21 Mengelle C, Sandres-Sauné K, Pasquier C, Rostaing L, Mansuy JM, Marty M, Da Silva I, Attal M, Massip P, Izopet J. Automated extraction and quantification of human cytomegalovirus DNA in whole blood by real-time PCR assay. *J Clin Microbiol* 2003; **41**: 3840-3845 [PMID: 12904398 DOI: 10.1128/JCM.41.8.3840-3845.2003]
22 Taber DJ, So Z, Fleming JN, McGillicy JY, Posadas-Salas MA, Treiber FA, Dubay D, Sinivas TR, Mauldin PD, Moran WP, Baliga PK. Tacrolimus Trough Concentration Variability and Disparities in African American Kidney Transplantation. *Transplantation* 2017; **101**: 2931-2938 [PMID: 28658199 DOI: 10.1097/TP.0000000000001840]
23 Vanhove T, Vermeulen T, Annaert P, Lerut E, Kypurs DRJ. High Intrapatient Variability of Tacrolimus Concentrations Predicts Accelerated Progression of Chronic Histologic Lesions in Renal Recipients. *Am J Transplant* 2016; **16**: 2954-2963 [PMID: 27013142 DOI: 10.1111/ajt.13803]
24 Rodrigo E, Segundo DS, Fernández-Fresnedo G, López-Hoyos M, Benito A, Ruiz JC, de Cos MA, Arias M. Within-Patient Variability in Tacrolimus Blood Levels Predicts Kidney Graft Loss and Donor-Specific Antibody Development. *Transplantation* 2016; **100**: 2479-2485 [PMID: 26703349 DOI: 10.1097/TP.0000000000001640]
25 Hsiao M, Fernández HE, Gjertson D, Ettenger RB, Tsai EW. Monitoring nonadherence and acute rejection with variation in blood immunosuppressant levels in pediatric renal transplantation. *Transplantation* 2015; **99**: 918-922 [PMID: 21857278 DOI: 10.1097/TP.0000000000001040]
26 O’Leary JG, Kaneko H, Jennings LW, Bañuelos N, Susskind BM, Terasaki PI, Klintmalm GB. Preformed class II donor-specific antibodies are associated with an increased risk of early rejection after liver transplantation. *Liver Transplant* 2013; **19**: 973-980 [PMID: 23780820 DOI: 10.1002/lt.23687]
27 O’Leary JG, Cai J, Freeman R, Banuelos N, Hart B, Johnson M, Jennings LW, Kaneku H, Terasaki PI, Klintmalm GB, Demetris AJ. Proposed Diagnostic Criteria for Chronic Antibody-Mediated Rejection in Liver Allografts. *Am J Transplant* 2016; **16**: 603-614 [PMID: 26469278 DOI: 10.1111/ajt.13476]
28 Kypers DR, Peeters PC, Senesseal JJ, Kianna MN, Vrijens B, Kristanto P, Dobbels F, Vanrenterghem Y, Kanaan N; ADMIRAD Study Team. Improved adherence to tacrolimus once-daily formulation in renal recipients: a randomized controlled trial using electronic monitoring. *Transplantation* 2013; **95**: 333-340 [PMID: 23263559 DOI: 10.1097/TP.0b013e3182725532]
29 van Hooff J, Van der Walt I, Callmeyer J, Miller D, Dawood S, Moosa MR, Christiaans M, Karpf C, Undre N. Pharmacokinetics of Tacrolimus in stable kidney transplant recipients after conversion from twice-daily to once-daily tacrolimus formulations. *Ther Drug Monit* 2012; **34**: 46-52 [PMID: 22249344 DOI: 10.1097/FDM.0b013e318244a47d]
30 Weiland M, Bauer S, Brekenmeier S, Burgwinkel P, Glander P, Kreutz R, Lorkowski C, Slowinski T, Neumayer HH, Budde K. Differential impact of the CYP3A5*1 and CYP3A5*3 alleles on pre-dose concentrations of two tacrolimus formulations. *Pharmacogenet Genomics* 2011; **21**: 179-184 [PMID: 20818295 DOI: 10.1097/FPC.0b013e32832a0f85]
31 Shaker N, Cadogan M, van Gelder T, Roodnat JI, Kho MM, Weinmar W, Hesselin DA. Conversion from twice-daily to once-daily tacrolimus does not reduce intrapatient variability in tacrolimus exposure. *Ther Drug Monit* 2015; **37**: 262-269 [PMID: 25262525 DOI: 10.1097/TP.0000000000000136]
32 Tang JT, Andrews LM, van Gelder T, Shi YY, van Schaik RH, Wang LL, Hesselin DA. Pharmacogenetic aspects of the use of tacrolimus in renal transplantation: recent developments and ethnic considerations. *Expert Opin Drug Metab Toxicol* 2016; **12**: 555-565 [PMID: 27010623 DOI: 10.1576/17425255.2016.1170808]
P-Reviewer: Chiu KW, Sergi CM, Sugawara Y S-Editor: Wang XJ L-Editor: A E-Editor: Huang Y
| 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
1748,
1
],
[
1748,
7193,
2
],
[
7193,
11802,
3
],
[
11802,
18315,
4
],
[
18315,
23454,
5
],
[
23454,
29305,
6
],
[
29305,
35810,
7
],
[
35810,
42759,
8
],
[
42759,
42759,
9
]
]
} |
bb36d7557b821131bc11940d15d1e096ed2e0f25 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 44,
"total-fallback-pages": 0,
"total-input-tokens": 253102,
"total-output-tokens": 54485,
"fieldofstudy": [
"Mathematics"
]
} | ISOMORPHISM TYPES OF HOPF ALGEBRAS IN A CLASS OF ABELIAN EXTENSIONS. I.
LEONID KROP
Abstract. There is no systematic general procedure by which isomorphism classes of Hopf algebras that are extensions of \( kF \) by \( kG \) can be found. We develop the general procedure for classification of isomorphism classes of Hopf algebras which are extensions of the group algebra \( kC_p \) by \( kG \) where \( C_p \) is a cyclic group of prime order \( p \) and \( kG \) is the Hopf algebra dual of \( kG \), \( G \) a finite abelian \( p \)-group and \( k \) is an algebraically closed field of characteristic 0. We apply the method to calculate the number of isoclasses of commutative extensions and certain extensions of this kind of dimension \( \leq p^4 \).
Keywords Hopf algebras, Abelian extensions, Crossed products, Cohomology Groups
Mathematics Subject Classification (2000) 16W30 - 16G99
0. Introduction
There is no systematic general procedure by which isomorphism classes of Hopf algebras that are extensions of \( kH \) by \( kG \) can be found. The purpose of this article is to fill this gap in case \( H = C_p \) and \( G \) is a finite abelian \( p \)-group for a prime \( p \), and \( k \) is an algebraically closed field of characteristic zero.
Let us agree to write \( \text{Ext}(kC_p, kG) \) for the set of all equivalence classes of extensions of \( kC_p \) by \( kG \). Elements of \( \text{Ext}(kC_p, kG) \) possess two special features. Every algebra \( H \) there is equivalent as extension to smash product \( kG \# kC_p \) with respect to a certain action of \( C_p \) on \( kG \), and \( kC_p \) is central in the dual Hopf algebra \( H^* \). The action of \( C_p \) on \( kG \) induces an action \( \prec \) of \( C_p \) on \( G \), the corresponding \( ZC_p \)-module is denoted by \( (G, \prec) \). In consequence, \( H \) is determined up to equivalence by a pair \((\tau, \prec)\) where \( \tau : kC_p \to kG \otimes kG \) is a 2-cococycle deforming the tensor product coalgebra structure of \( kG \otimes kF \). Abelian extensions with undeformed multiplication were studied by M.Mastnak [11]. We
Date: 4/14/14.
Research partially supported by a grant from the College of Liberal Arts and Sciences at DePaul University.
adopt a version of his notation $H^2_c(\mathbb{k}C_p, \mathbb{k}G, \cdot)$ for the group of Hopf 2-cocycles.
The first major result is a structure theorem for the group $H^2_c(\mathbb{k}C_p, \mathbb{k}G, \cdot)$. It states that if $G$ is any finite abelian $p$-group with $p > 2$, or a finite elementary 2-group then there is a $C_p$-isomorphism
$$H^2_c(\mathbb{k}C_p, \mathbb{k}G, \cdot) \simeq H^2(C_p, \widehat{G}, \cdot) \times H^2_N(G, \mathbb{k}^*)$$
where $\widehat{G}$ is the dual group of $G$, $H^2(C_p, \widehat{G}, \cdot)$ is the second cohomology group of $C_p$ over $\widehat{G}$ with respect to the action $\cdot$, and $H^2_N(G, \mathbb{k}^*)$ is the kernel in the Schur multiplier of $G$ of the norm mapping. We point out that formula (0.1) can be seen as a generalization of the Baer’s exact sequence for the cohomology group $H^2(G, C_p)$ of central extensions of $G$ by $C_p$ [2, p.34]. For, setting $\cdot = \text{triv}$, the trivial action, we show (Section 4) that $H^2_c(\mathbb{k}C_p, \mathbb{k}G, \text{triv})$ coincides with $H^2(G, C_p)$ while $H^2(C_p, \widehat{G}, \text{triv})$ and $H^2_N(G, \mathbb{k}^*)$ can be identified with $\text{Ext}^1_{\mathbb{k}}(G, C_p)$ and $\text{Hom}(\wedge^2G, C_p)$, respectively. Hence (0.1) turns into the splitting of the norm mapping. We recall that by a fundamental result of D. Stefan [21] the number of isomorphism types in any of our classes is finite. In the case at hand, we show that there is a bijection between isotypes of noncocommutative Hopf algebras in $\text{Ext}^1_{\mathbb{k}}(\mathbb{k}C_p, \mathbb{k}G)$ and the orbits of $\mathcal{G}(\cdot)$ in $H^2_c(\mathbb{k}C_p, \mathbb{k}G, \cdot)$ not contained in the subgroup $H^2_{cc}(\mathbb{k}C_p, \mathbb{k}G, \cdot)$ parametrizing cocommutative extensions.
Let $I(\cdot, \cdot)$ be the set of automorphisms of $G$ intertwining actions $\cdot$ and $\cdot'$. $I(\cdot, \cdot')$ is an $A(\cdot)$-set, in fact a single orbit of $A(\cdot)$ in $\text{Aut}(G)$. For every $\alpha \in A_p$ fix some $\lambda_\alpha$ in $I(\cdot, \cdot')$. The group $\mathcal{G}(\cdot)$ is the subgroup of $\text{Aut}(G)$ generated by $A(\cdot)$ and all $\lambda_\alpha$. In fact, $\mathcal{G}(\cdot)$ is a crossed product of $A(\cdot)$ with a subgroup of $A_p$. It transpires that $H^2_c(\mathbb{k}C_p, \mathbb{k}G, \cdot)$ is a $\mathcal{G}(\cdot)$-module. The orbits of $\mathcal{G}(\cdot)$ in $H^2_c(\mathbb{k}C_p, \mathbb{k}G, \cdot)$ determine isotypes of extension in the following way. Let us denote by $[\cdot]$ the set of all actions $\cdot'$ isomorphic to $\cdot$ for some $\alpha$. We designate $\text{Ext}^1_{\mathbb{k}}(\mathbb{k}C_p, \mathbb{k}G)$ to the set of all equivalence classes of extensions whose $C_p$-action belongs to $[\cdot]$. We recall that by a fundamental result of D. Stefan [21] the number of isomorphism types in any of our classes is finite. In the case at hand, we show that there is a bijection between isotypes of noncocommutative Hopf algebras in $\text{Ext}^1_{\mathbb{k}}(\mathbb{k}C_p, \mathbb{k}G)$ and the orbits of $\mathcal{G}(\cdot)$ in $H^2_c(\mathbb{k}C_p, \mathbb{k}G, \cdot)$ not contained in the subgroup $H^2_{cc}(\mathbb{k}C_p, \mathbb{k}G, \cdot)$ parametrizing cocommutative extensions.
Assuming $G$ elementary abelian and $p$ odd we extend the bijection to all isoclasses in $\text{Ext}_{G}^{1}(kC_{p}, kG)$. This is done by showing that for cocommutative extensions $G$-orbits in $H_{cc}^{2}(kC_{p}, kG, \triangleright)$ coincide with $A(\triangleright)$-orbits there, and furthermore their isoclasses in are in 1 − 1 correspondence with the orbits of $A(\triangleright)$ in $H_{cc}^{2}(kC_{p}, kG, \triangleright)$.
The last part of the paper is devoted to explicit calculations of the orbit set in several cases. For concrete calculations the smaller space $X(\triangleright) := H^{2}(C_{p}, G, \triangleright) \times H^{2}_{N}(G, k^{*})$ is most convenient. $X(\triangleright)$ gets its $G(\triangleright)$ action by transport of action via isomorphism (0.1). The action is component-wise for every odd $p$. Assuming $G$ an elementary $p$-group and $p$ odd we show that there are $\lfloor \frac{3n+2}{2} \rfloor$ orbits for $\triangleright = \text{triv}$. We also describe orbit sets for all actions on elementary $p$-group $G$ of order $p^{3}$. Lower order cases, viz. $|G| = p, p^{2}$ are known with $|G| = p$ and $|G| = p^{2}$ due to [15] and [14], respectively.
The paper is organized in six sections. In Section 1 we review the necessary facts of the theory of abelian extension. In section 2 we prove formula (0.1) for the groups $H_{cc}^{2}(kC_{p}, kG, \triangleright)$. Section 3 contains the isomorphism and bijection theorems. In Sections 4 and 5 we determine the orbit sets for commutative extensions with $G$ elementary $p$-group, and all extensions with $G$ elementary $p$-group of order $\leq p^{3}$, respectively, and compute the number of isoclasses.
0.1. Notation and Convention. In addition to notation introduced in the Introduction we will use the following.
- $A^{*}$ the group of units of a commutative ring $A$.
- $\Gamma^{n}$ direct product of $n$ copies of group $\Gamma$.
- $\text{Fun}(\Gamma, A^{*})$ the group of all functions from $\Gamma$ to $A^{*}$ with pointwise multiplication. We will identify groups $\text{Fun}(G^{n}, (kF^{m})^{*})$, $\text{Fun}(F^{m}, (k^{G^{m}})^{*})$ and $\text{Fun}(G^{n} \times F^{m}, \mathbb{k})$ via $f(a)(x) = f(x)(a) = f(a, x)$ where $a \in G^{n}, x \in F^{m}$.
- $Z^{2}(\Gamma, A^{*}, \bullet), B^{2}(\Gamma, A^{*}, \bullet)$ and $H^{2}(\Gamma, A^{*}, \bullet)$ are the group of 2-cocycles, 2-coboundaries, and the second degree cohomology group of $\Gamma$ over $A^{*}$ with respect to an action $\bullet$ of $\Gamma$ on $A$ by ring automorphisms.
- $\delta_{\Gamma}$ the differential of the standard cochain complex for cohomology of the triple $(\Gamma, A^{*}, \bullet)$ [12, IV.5].
- $Z_{p^{n}}$ cyclic group of order $p^{n}$ additively written.
- By abuse of notation we will often use the same symbol for an element of $Z^{2}(\Gamma, A^{*}, \triangleright)$ and its image in $H^{2}(\Gamma, A^{*}, \triangleright)$.
Throughout the paper we treat the terms $\Gamma$-module, $\Gamma$-linear, etc as synonymous to $\mathbb{Z}\Gamma$-module, $\mathbb{Z}\Gamma$-linear, etc.
1. Background Review
1.1. Extensions of Hopf Algebras. Let $k$ be a ground field. In this paper we are concerned with finite-dimensional Hopf algebras over $k$. For a Hopf algebra $H$ we use the standard notation $H^+ = \text{Ker} \varepsilon$. Let $\pi : H \to K$ be a morphism of Hopf algebras. We let $H^{\text{cor}}$ and $^{\text{cor}}H$ denote subalgebras of right/left coinvariants [17, 3.4]. We adopt H.-J. Schneider’s definition of a Hopf algebra extension [19]. In our context it is stated as follows.
**Definition 1.1.** A Hopf algebra $C$ is an extension of a Hopf algebra $B$ by a Hopf algebra $A$ if there is a sequence of Hopf mappings
\[ A \xrightarrow{\iota} C \xrightarrow{\pi} B. \]
with $\iota$ monomorphism, $\pi$ epimorphism, $\iota(A)$ normal in $C$ and $\text{Ker} \pi = \iota(A)^+C$.
We add some comments to the definition. By [20, Remark 1.2] or [17, 3.4.3] we have the fundamental fact that $\iota(A) = C^{\text{cor}}$. It follows that our definition coincides with the definition of extension in [1]. Conversely, the equality $\iota(A) = C^{\text{cor}}$ is equivalent to the equality $\iota(A) = ^{\text{cor}}C$ [3, 4.19], and both of them imply $\iota(A)$ is normal [3, 4.13]. Even more is true. Either condition $\iota(A) = C^{\text{cor}}$ or $\text{Ker} \pi = \iota(A)^+C$ renders the sequence (E) an extension. For details see [1, 3.3.1].
1.2. Abelian Extensions. We assume in what follows the ground field $k$ to be an algebraically closed field of characteristic 0 and $C$ to be a finite-dimensional Hopf algebra. An extension (E) is called abelian if $A$ is commutative and $B$ is cocommutative. It is well-known [10, Theorem 1] and [17, 2.3.1] that in this case $A = k^G$ and $B = kF$ for some finite groups $G$ and $F$. Below we consider only extensions of this kind and we use the notation
\[ (A) \quad k^G \xrightarrow{\iota} H \xrightarrow{\pi} kF. \]
To simplify notation we will refer to the Hopf algebra $H$ in a sequence (A) as an extension of $kF$ by $k^G$. Essential to the theory of abelian extensions is a result in [18], or general theorems [20, 2.4], [13, 3.5], asserting $H$ is a crossed product of $kF$ over $k^G$. The theorem entails existence of a mapping called section (see, e.g. [1, 3.1.13])
\[ (1.1) \quad \chi : kF \to H \]
\[ \text{A short independent proof for abelian extension is given in the Appendix} \]
giving rise to the crossed product structure on $H$. This means $H = \mathbb{k}^G\chi(F)$ with the multiplication
$$
(1.2) \quad (f\chi(x))(f'\chi(y)) = f(\chi(x)f'\chi^{-1}(x))\chi(x)\chi(y) = f(\chi(x)f'\chi^{-1}(x))[\chi(x)\chi(y)\chi^{-1}(xy)]\chi(xy)
$$
for $f, f' \in \mathbb{k}^G, x, y \in F$. The mapping $x \otimes f \mapsto x.f := \chi(x)f\chi^{-1}(x)$ defines a module algebra action of $F$ on $\mathbb{k}^G$ and the function $\sigma : F \times F \to \mathbb{k}^G, \sigma(x, y) = \chi(x)\chi(y)\chi^{-1}(xy)$ is a left, normalized 2-cocycle for that action [17, 7.2.3]. We recall that definition of action is independent of the choice of section, see e.g. [17, 7.3.5].
We consider the dual of the above action of $\mathbb{k}F$ on $\mathbb{k}^G$. For any finite group $G$ we identify $(\mathbb{k}^G)^*$ with $\mathbb{k}G$ by treating $r \in \mathbb{k}G$ as the functional $f \mapsto f(r), f \in \mathbb{k}^G$. By general principles the transpose of a left module action of $\mathbb{k}F$ on $\mathbb{k}^G$ is a right module coalgebra action, denoted $\triangleleft$ of $\mathbb{k}F$ on $(\mathbb{k}^G)^* = \mathbb{k}G$. Under this action $a \triangleleft x$ is that element of $G$ for which
$$
(1.3) \quad (a \triangleleft x)(f) := f(a \triangleleft x) = (x.f)(a), \text{ for all } f \in \mathbb{k}^G, a \in G, x \in F.
$$
This definition makes sense as $\Delta_{\mathbb{k}G}$ is a $\mathbb{k}F$-linear map, hence there holds $\Delta_{\mathbb{k}G}(a \triangleleft x) = a \triangleleft x \otimes a \triangleleft x$, whence $a \triangleleft x$ is a grouplike, hence in $G$. We note that, in general, $\triangleleft$ is a permutation action on $G$. Let $\{p_a | a \in G\}$ be a basis of $\mathbb{k}^G$ dual to the basis $\{a|a \in G\}$ of $\mathbb{k}G$. One can see easily that in the basis $\{p_a\}$ the two actions are related by the formula
$$
(1.4) \quad x.p_a = p_{ax^{-1}}
$$
Theory of extensions has a fundamental duality expressed by the fact that for each sequence $(E)$ its companion sequence
$$
(E^*) \quad B^* \xrightarrow{\pi^*} C^* \xrightarrow{\iota^*} A^*
$$
is also an extension, see [5, 4.1] or [1, 3.3.1]. Since for any finite group $F$, $(\mathbb{k}F)^* = \mathbb{k}^F$ and $(\mathbb{k}F)^* = \mathbb{k}F$, every diagram (A) induces a diagram
$$
(A^*) \quad \mathbb{k}F \to H^* \to \mathbb{k}G
$$
A crossed product structure on $H^*$ is effected by a section
$$
(1.5) \quad \omega : \mathbb{k}G \to H^*
$$
We choose to write $H^* = \omega(G)\mathbb{k}F$ with the multiplication
$$
(1.6) \quad (\omega(a)\beta)(\omega(b)\beta') = \omega(ab)\tau(a, b)(\beta.b)\beta',
$$
where for $a, b \in G$, $\beta, \beta' \in \mathbb{k}F$
$$
(1.7) \quad \beta.b = \omega^{-1}(b)\beta\omega(b), \text{ and }
$$
$$
(1.8) \quad \tau(a, b) = \omega^{-1}(ab)\omega(a)\omega(b).
$$
We note that $\tau : G \times G \to k^F$ is a right, normalized 2-cocycle for the action $\beta \otimes b \mapsto \beta.b$. As above the right action of $G$ on $k^F$ induces a left action of $G$ on $F$ by permutations denoted by $a \triangleright x$, and the two actions are related by
$$(1.9) \quad p_x.a = p_{a^{-1} \triangleright x}$$
We fuse both actions into the definition of a product on $F \times G$ via
$$(1.10) \quad (xa)(yb) = x(a \triangleright y)(a \triangleleft y)b$$
It was noted by M. Takeuchi [22] that the composition 1.10 defines a group structure on $F \rtimes G$ provided the actions $\triangleleft, \triangleright$ satisfy the conditions
$$(1.11) \quad ab \triangleleft x = (a \triangleleft (b \triangleright x))(b \triangleleft x)$$
$$(1.12) \quad a \triangleright xy = (a \triangleright x)((a \triangleleft x) \triangleright y)$$
We use the standard notation $F \triangleright \triangleleft G$ for the set $F \times G$ endowed with multiplication (1.10). We will also adopt the notation $\overline{\tau}$ for $\chi(x)$ and $\overline{a}$ for $\omega(a)$.
The above discussion enables us to associate a datum $\{\sigma, \tau, \triangleleft, \triangleright\}$ to every Hopf algebra $H$ in an extension of type (A), and we write $H = H(\sigma, \tau, \triangleleft, \triangleright)$ and $H^* = H^*(\sigma, \tau, \triangleleft, \triangleright)$ for $H$ and its dual.
1.3. Cocentral Extensions. An extension (A) is called cocentral [8] if $k^F$ is a central subalgebra of $H^*$. We record two properties of cocentral extensions needed below
**Lemma 1.2.** (1) An extension (A) is cocentral iff $\triangleright$ is trivial, or equivalently $G$ is a normal subgroup of $F \triangleright \triangleleft G$ in which case $F \triangleleft \triangleright G$ is a semidirect product $F \ltimes G$.
(2) If (A) is cocentral, then $\Delta_{k^G}$ is $F$-linear.
**Proof:** (1) It is well known [16, (4.10)] that $F \triangleright \triangleleft G$ is a group for any two actions $\triangleleft, \triangleright$ arising from an abelian extension. By (1.10) $x^{-1}ax = x^{-1}(a\triangleright x)(a\triangleleft x)$, hence $x^{-1}ax \in G$ for all $a \in G, x \in F$ iff $x^{-1}(a\triangleright x) = 1$, that is $a\triangleright x = x$. On the other hand $k^F$ is cocentral iff $p_x.a = p_{a^{-1} \triangleright x} = p_x$ by (1.9). The rest of part (1) is immediate from (1.11).
(2) We must show the equality $\Delta_{k^G}(x.p_a) = x.\Delta_{k^G}(p_a)$. On the one hand we have
$$x.\Delta_{k^G}(p_a) = \sum_{bc=a} x.p_b \otimes x.p_c = \sum_{bc=a} p_{bcx^{-1}} \otimes p_{cax^{-1}}.$$
In the second place
$$\Delta_{k^G}(x.p_a) = \Delta_{k^G}(p_{a\triangleright x^{-1}}) = \sum_{ef=a\triangleright x^{-1}} p_e \otimes p_f$$
It remains to notice that the mappings \((b, c) \mapsto (b \triangleleft x^{-1}, c \triangleleft x^{-1}), (e, f) \mapsto (e \triangleleft x, f \triangleleft x)\) give a bijective correspondence between the sets \(\{(b, c) | bc = a\}\) and \(\{(e, f) | ef = a \triangleleft x^{-1}\}\) as the action \('\triangleleft'\) is by group automorphisms.
Below we will write an extension datum \(\{\sigma, \tau, \triangleleft\}\) when \(\triangleright\) is trivial. We will need explicit formulas for coalgebra structure mappings on \(H\) and \(H^*\) expressed in terms of their datum. These are the duals of the algebra structures (1.2) and (1.6), and follow from \([16, (4.5)]\).
**Proposition 1.3.** Let \(H\) and \(H^*\) be defined by a datum \(\{\sigma, \tau, \triangleleft\}\). The coalgebra structure of \(H\) and \(H^*\) is given by the mappings
\[
\Delta_H(fx) = \sum_{a,b \in G} \tau(x, a, b)f_1p_a\bar{x} \otimes f_2p_b\bar{x},
\]
\[
\epsilon_H(fx) = f(1_G).
\]
\[
\Delta_{H^*}(ag) = \sum_{x,y \in F} \sigma(x, y, a)\bar{\sigma}_x g_1 \otimes (a \triangleleft y)p_y g_2,
\]
\[
\epsilon_{H^*}(ag) = g(1_F),
\]
where \(f \in \mathbb{k}^G, g \in \mathbb{k}^F\).
For discussion of cohomology of abelian extensions we introduce the subgroup \(\text{Map}(F^n \times G^m, \mathbb{k}^\bullet)\) of \(\text{Fun}(F^n \times G^m, \mathbb{k}^\bullet)\) of normalized \(n + m\)-dimensional cochains, i.e. functions satisfying \(f(x_1, \ldots, x_n, a_1, \ldots, a_m) = 1\) if at least one component of \((x_1, \ldots, x_n, a_1, \ldots, a_m)\) is the identity. Suppose \(F\) acts on \(G\) via \(\triangleleft\). We extend this action to \(\text{Map}(F^n \times G^m, \mathbb{k}^\bullet)\) by the rule
\[
y.f(x_1, \ldots, x_n, a_1, \ldots, a_m) = f(x_1, \ldots, x_n, a_1 \triangleleft y, \ldots, a_m \triangleleft y).
\]
Identifying \(\text{Map}(F^n \times G^m, \mathbb{k}^\bullet)\) with either \(\text{Map}(F^n, (\mathbb{k}G^m)^\bullet)\) or \(\text{Map}(G^m, (\mathbb{k}^F)^\bullet)\) (see \([11]\)) we denote by \(\delta_F, \delta_G\), respectively, the standard differentials of group cohomology. Finally we state conditions for equivalence \([16, 3.4]\) of two extensions in the form needed below. They are a particular case of\([16, 5.2]\).
**Lemma 1.4.** Two extensions \(H\) and \(H'\) defined by data \(\{\sigma, \tau, \triangleleft\}\) and \(\{\sigma', \tau', \triangleleft'\}\) are equivalent if and only if \(\triangleleft = \triangleleft'\) and there exists \(\zeta \in \text{Map}(F \times G, \mathbb{k}^\bullet)\) satisfying
\[
\sigma' = \sigma \delta_F \zeta^{-1} \text{ and } \tau' = \tau \delta_G \zeta
\]
If so, an isomorphism \(\psi : H \rightarrow H'\) defined by \(\psi(f\bar{x}) = f\zeta(x)\bar{x}, f \in \mathbb{k}^G, x \in F\) carries out the equivalence.
1.4. **Cohomology Groups** $H^2(kF, k^G, \triangleleft)$. We describe in some detail cohomology theory of abelian extensions in the special case studied below. In the rest of the paper we consider cocentral extensions (A) satisfying the condition
(1.17) \[ H^2(F, (k^G)^*, \triangleleft) = \{1\} \] for every action $\triangleleft$.
We observe a simple
**Lemma 1.5.** Under the assumption (1.17) every extension $H(\sigma, \tau, \triangleleft)$ is equivalent to an extension $H(1, \tau', \triangleleft)$
**Proof:** The condition (1.17) means $\sigma = \delta_F \zeta, \zeta \in \text{Map}(F \times G, k^*)$. Then by Lemma 1.4 the mapping $\psi : H(\sigma, \tau, \triangleleft) \to H(1, \tau', \triangleleft), \psi(f \tau) = f \zeta(x) \tau, f \in k^G, x \in F$ with $\tau' = \tau \delta_G \zeta$ is the required equivalence. \(\Box\)
Below we will write $H = H(\tau, \triangleleft)$ for an extension with a datum $\{\sigma, \tau, \triangleleft\}$ and $\sigma$ trivial. We let $\text{Ext}(kF, k^G)$ stand for the set of equivalence classes of extensions with fixed action $\triangleleft$.
Cocentral extensions satisfying (1.17) have been studied in [11]. It is shown there [11, 4.4] that the standard second cohomology group of abelian extensions [7] coincides with the one in the next definition.
**Definition 1.6.** We let $Z^2_{c}(kF, k^G, \triangleleft)$ denote the subgroup of all elements $\tau$ of $Z^2(G, (k^F)^*, \text{id})$ satisfying $\delta_F(\tau) = \epsilon$. We let $B^2_{c}(kF, k^G, \triangleleft)$ stand for the subgroup of 2-cocycles $\delta_G \eta, \eta \in \text{Map}(F \times G, k^*)$ satisfying $\delta_F \eta = 1$. We define the second degree Hopf cohomology group by
$$H^2_{c}(kF, k^G, \triangleleft) = Z^2_{c}(kF, k^G, \triangleleft)/B^2_{c}(kF, k^G, \triangleleft).$$
Explicitly both conditions $\delta_F \tau = \epsilon$ and $\delta_F \eta = \epsilon$ are expressed by:
\begin{align*}
\tau(xy) &= \tau(x) (x. \tau(y)) \\
\eta(xy) &= \eta(x) (x. \eta(y))
\end{align*}
for all $x, y \in F$.
We call elements of $Z^2_{c}(kF, k^G, \triangleleft)$ and $B^2_{c}(kF, k^G, \triangleleft)$ Hopf 2-cocycles and 2-coboundaries, respectively. We will use abbreviated symbols $Z^2_{c}(kF, k^G, \triangleleft), B^2_{c}(kF, k^G, \triangleleft)$, etc. for $Z^2(\triangleleft), B^2(\triangleleft)$, etc when the groups $G$ and $F$ are fixed. The restriction $B^2(G, (k^F)^*) \cap Z^2(\triangleleft)$ of the group of coboundaries to $Z^2(\triangleleft)$ will be denoted by $B^2_{cc}(\triangleleft)$. As $B^2_{cc}(\triangleleft) \subseteq B^2(\triangleleft)$ we can form the subgroup $H^2_{cc} = B^2_{cc}(\triangleleft)/B^2(\triangleleft)$ of $H^2(\triangleleft)$. Explicitly,
$$H^2_{cc}(kF, k^G, \triangleleft) := \{\delta_G \eta B^2_{c}(\triangleleft)|\eta \in \text{Map}(F \times G, k^*) \text{ with } \delta_F(\delta_G \eta) = 1\}.$$
Lemma 1.7. If \( F \) is abelian, then groups \( Z^2(F,\langle \cdot \rangle) \), \( B^2_0(\langle \cdot \rangle) \), and \( B^2_0(\langle \cdot \rangle) \) are \( F \)-invariant.
Proof: Suffices to show that for any \( f \in \text{Map}(F \times G^m, k^*) \) and \( g \in \text{Map}(F^n \times G, k^*) \) there holds
\[
(1.20) \quad x.\delta_F f = \delta_F(x.f),
\]
\[
(1.21) \quad x.\delta_G g = \delta_G(x.g)
\]
For, setting \( m = 1, 2, f = \eta, \tau \) and \( n = 1, g = \eta \) in (1.20) and (1.21), respectively we get our statement.
(1.21) is immediate from definitions in view of \( G \) acting trivially on \( F \). To show (1.20) we calculate
\[
(x.\delta_F f)(y, z, a_1, \ldots, a_m) = (\delta_F f)(y, z, a_1 \triangleleft x, \ldots, a_m \triangleleft x) =
\]
\[
f(y, a_1 \triangleleft x, \ldots, a_m \triangleleft x)(y.f)(z, a_1 \triangleleft x, \ldots, a_m \triangleleft x)
\]
\[
f(yz, a_1 \triangleleft x, \ldots, a_m \triangleleft x)^{-1} = f(y, a_1 \triangleleft x, \ldots, a_m \triangleleft x)
\]
\[
(xy.f)(z, a_1 x, \ldots, a_m f(y, a_1 \triangleleft x, \ldots, a_m \triangleleft x)^{-1}
\]
Switching around \( x \) and \( y \) in the middle term we get exactly \( \delta_F(x.f) \).
\[\square\]
2. Structure of \( H^2_c(\mathbb{k}C_p, \mathbb{k}G, \prec) \)
Unless stated otherwise \( G \) is a \( p \)-group and \( F = C_p \). The group \( C_p \triangleleft G \) is a \( p \)-group as well, hence nilpotent. As \( G \) has index \( p \) in \( C_p \triangleleft G \), \( G \) is normal in \( C_p \triangleleft G \). By Lemma 1.2(1) the action \( \triangleright \) is trivial. In addition, as \( \mathbb{k}^* \) is a divisible group the group \( H^2(C_p, (\mathbb{k}G)^*), \prec \) vanishes by e.g. [11, 4.4]. Thus the results of the preceding section are applicable. We note a simple fact.
Lemma 2.1. Let \( \tau \in Z^2(G, (\mathbb{k}F)^*) \). Then for every \( x \in C_p \) \( \tau(x) \) is a 2-cocycle for \( G \) with coefficients in \( \mathbb{k}^* \) with the trivial action of \( G \) on \( \mathbb{k}^* \).
Proof: The 2-cocycle condition for the trivial action is
\[
(2.1) \quad \tau(a, bc)\tau(b, c) = \tau(ab, c)\tau(a, b).
\]
Expanding both sides of the above equality in the basis \( \{p_x\} \) and equating coefficients of \( p_x \) proves the assertion. \[\square\]
Consider group \( F \) acting on an abelian group \( A \), written multiplicatively, by group automorphisms. Let \( ZF \) be the group algebra of \( F \) over \( \mathbb{Z} \). \( ZF \) acts on \( A \) via
\[
(\sum c_i x_i).a = \prod x_i.(a^{c_i}), \quad c_i \in \mathbb{Z}, \quad x_i \in F.
\]
For $F = C_p$ pick a generator $t$ of $C_p$ and set $\phi_i = 1 + t + \cdots + t^{i-1}$, $i = 1, \ldots, p$. Choose $\tau \in Z^2(G, (k^C)^*)$ and expand $\tau$ in terms of the standard basis $p_i$ for $k^C$, $\tau = \sum \tau(t^i)p_i$ with $\tau(t^i) \in Z^2(G, k^*)$. An easy induction on $i$ shows that condition (1.18) implies
$$\tau(t^i) = \phi_i \tau(t), \text{ for all } i = 1, \ldots, p$$
For $i = p$ we have
$$\phi_p \tau(t) = 1$$
in view of $t^p = 1$ and $\tau(1) = 1$.
Let $M$ be a $ZC_p$-module. Following [12] we define the mapping $N : M \rightarrow M$ by $N(m) = \phi_p(t).m$. We denote by $M_N$ the kernel of $N$ in $M$. For $M = Z^2(G, k^*)$, $B^2(G, k^*)$ or $H^2(G, k^*)$ we write $Z^2_N(G, k^*)$ for $Z^2(G, k^*)_N$ and similarly for the other groups. We abbreviate $Z^2_N(G, k^*)$ to $Z^2_N(\langle \rangle)$ and likewise for $B^2_N(G, k^*)$ and $H^2_N(G, k^*)$.
**Definition 2.2.** We call a 2-cocycle $s \in Z^2(G, k^*)$ admissible if $s$ satisfies the condition
$$\phi_p.s = 1$$
Thus by definition the set of all admissible cocycles is $Z^2_N(\langle \rangle)$. We note that $Z^2_N(\langle \rangle)$ is a subgroup of $Z^2(G, k^*)$ as $ZC_p$ acts by endomorphisms of $Z^2(G, k^*)$. We want to compare abelian groups $Z^2_\langle \rangle(\langle \rangle)$ and $Z^2_N(\langle \rangle)$. This is done via the mapping
$$\Theta : Z^2(G, (k^C)^*) \rightarrow Z^2(G, k^*), \Theta(\tau) = \tau(t).$$
**Lemma 2.3.** The mapping $\Theta$ induces a $C_p$-isomorphism between $Z^2_\langle \rangle(\langle \rangle)$ and $Z^2_N(\langle \rangle)$.
**Proof:** We begin with an obvious equality $x.(\tau(y)) = (x.\tau)(y)$. Taking $y = t$ we get $\Theta(x.\tau) = x.\Theta(\tau)$, that is $C_p$-linearity of $\Theta$. The relations (2.2) show that $\Theta$ is monic. It remains to establish that $\Theta$ is epic.
Suppose $s$ is an admissible 2-cocycle of $G$ in $k^*$. Define $\tau : G \times G \rightarrow (k^C)^*$ by setting $\tau(t^i) = \phi_i(t).s$, $1 \leq i \leq p$. The proof will be complete if we demonstrate that $\tau$ satisfies (1.18).
For any $i, j \leq p$ we have
$$\tau(t^i)(t^i.\tau(t^j)) = (\phi_i(t).s)(t^i.\phi_j(t).s) = (\phi_i(t) + t^i \phi_j(t)).s$$
One sees easily that $\phi_i(t) + t^i \phi_j(t) = \sum_{k=0}^{i+j-1} t^k$. Hence if $i+j < p$ we have
$$\phi_i(t) + t^i \phi_j(t) = \phi_{i+j}(t)$$
and so $\tau(t^i)(t^i.\tau(t^j)) = \tau(t^{i+j})$. If $i+j = p+m$
with \( m \geq 0 \), then \( \sum_{k=0}^{p+m-1} t^k = \phi_p(t) + t^p(1 + \cdots + t^{m-1}) \) which implies
\[
( \sum_{k=0}^{p+m-1} t^k ).s = \phi_p(t).s \cdot t^p \phi_m(t).s = \phi_m(t).s = \tau(t^{i+j}) \text{ by (2.4)} \text{ and as } t^p = 1.
\]
The next step is to describe structure of \( H^2_{cc}(<) \). We need some preliminaries. First, we write \( x.f \) for the left action of \( C_k \) on \( k^G \) dual to \( < \) as in (1.3). Since \( \hat{G} \) is the group of grouplikes of \( k^G \), \( \hat{G} \) is \( C_p \)-stable by Lemma 1.2(2). Further, we use \( \delta \) for the differential on the group of 1-cochains of \( G \) in \( k^\bullet \). We also note \( B^2_N(<) = B^2(G, k^\bullet) \cap Z^2_N(<) \). By (2.4) \( \delta f \in B^2_N(<) \) iff \( \phi_p(t).\delta f = \delta \chi \) which, in view of \( \delta \) being \( C_p \)-linear, is the same as \( \delta(\phi_p(t).f) = 1 \). Since \( (\delta f)(a,b) = f(a)f(b)f(ab)^{-1} \), \text{Ker} \( \delta \) consists of characters of \( G \), whence \( \delta f \in B^2_N(<) \) iff \( \phi_p(t).f \) is a character of \( G \). Say \( \chi = \phi_p(t).f \in \hat{G} \). Then as \( t\phi_p(t) = \phi_p(t) \), \( \chi \) is a fixed point of the \( C_p \)-module \( \hat{G} \). Letting \( \hat{G}^{c_p} \) stand for the set of fixed points in \( \hat{G} \) we have by [12, IV.7.1] an isomorphism \( H^2(C_p, \hat{G}, \bullet) \approx \hat{G}^{c_p}/N(\hat{G}) \).
We connect \( B^2_N(<) \) to \( H^2(C_p, \hat{G}) \) via the homomorphism
\[
(2.5) \quad \Phi : B^2_N(<) \to H^2(C_p, \hat{G}, \bullet), \delta f \mapsto (\phi_p.f)N(\hat{G})
\]
**Lemma 2.4.** The following properties holds
- (i) \( \Theta(B^2_N(<)) = B^2_N(<) \),
- (ii) \( \Theta(B^2(<)) = \text{Ker} \Phi \),
- (iii) \( B^2_N(<)/\text{Ker} \Phi \simeq H^2(C_p, \hat{G}, \bullet) \),
- (iv) \( H^2_{cc}(<) \simeq H^2(C_p, \hat{G}, \bullet) \).
**Proof:** First we show that \( \Phi \) is well-defined. For, \( \delta f = \delta g \) iff \( fg^{-1} = \chi \in \hat{G} \), hence
\[
\Phi(\delta f) = (\phi_p.f)N(\hat{G}) = (\phi_p.g\chi)N(\hat{G}) = (\phi_p.g)N(\hat{G}) = \Phi(\delta g)
\]
(i) Take some \( \delta(\eta) \in B^2_N(<) \). Evidently for every \( x \in C_p (^x) \delta(\eta)(x) = \delta(\eta(x)) \), hence \( \Theta(\delta(\eta)) = \delta(\eta(t)) \) is a coboundary, and \( \phi_p(\delta(\eta) = 1 \) by (2.3), whence \( \Theta(\delta(\eta)) \in B^2_N(<) \). Conversely, pick \( \delta f \in B^2_N(<) \) and define \( \omega = \sum_{i=1}^{p} (\phi_i.f)p_{i^\ell} \). The argument of Lemma 2.3 shows \( \omega \) lies in \( Z^2_N(<) \). Set \( \eta = \sum_{i=1}^{p} (\phi_i.f)p_{i^\ell} \). Using \(^x\) again we derive
\[
\delta G\eta = \sum_{i=1}^{p} (\phi_i.\delta f)p_{i^\ell} = \omega,
\]
hence \( \delta G\eta \in B^2_{cc}(<) \). Clearly \( \Theta(\delta G\eta) = \delta f \).
(ii) The argument of Lemma 2.3 is applicable to 1-cocycles satisfying (1.19). It shows that \( \eta \) satisfies (1.19) iff
\[
\eta(t^i) = \phi_i \eta(t)
\]
For \( i = p \) we get \( \phi_p, \eta(t) = \epsilon \), hence the calculation
\[
\Phi(\Theta(\delta_G \eta)) = \Phi(\delta(\eta(t))) = (\phi_p, \eta(t))N(\hat{G}) = N(\hat{G}).
\]
gives one direction. Conversely, \( \Phi(\delta f) \in N(\hat{G}) \) means \( \phi_p, f = \phi_p, \chi \)
which implies \( \phi_p, f \chi^{-1} = \epsilon \). Set \( g = f \chi^{-1} \) and define 1-cocycle \( \eta_g = \sum_{i=1}^p (\phi_i, g) p_i \). Since \( \phi_p, g = \epsilon \), \( g \) satisfies (1.19), whence \( \delta G \eta_g \in B^2_G(\chi) \).
As \( (\delta G \eta_g)(t) = \delta g = \delta f \) by construction, \( \Theta(\delta G \eta_g) = \delta f \).
(iii) We must show that \( \Phi \) is onto. For every character \( \chi \) in \( \hat{G}^C_p \) we want to construct an \( f : G \to \mathbb{k}^* \) satisfying \( \phi_p, f = \chi \). To this end we consider splitting of \( G \) into the orbits under the action of \( C_p \). Since every orbit is either regular, or a fixed point under the action by \( C_p \). Thus every orbit is either regular or a fixed point we have
\[
G = \bigcup_{i=1}^r \{ g_i \triangleleft t^i, \ldots, g_i \triangleleft t^{p-1} \} \cup G^C_p
\]
For every \( s \in G^C_p \) we pick a \( \rho_s \in \mathbb{k} \) satisfying \( \rho_s^p = \chi(s) \). We define \( f \) by the rule
\[
f(g_i) = \chi(g_i), \quad f(g_i \triangleleft t^j) = 1 \quad \text{for all} \quad j \neq 1 \quad \text{and all} \quad i = 1, \ldots, r, \quad \text{and} \quad f(s) = \rho_s \quad \text{for every} \quad s \in G^C_p
\]
By definition \( (\phi_p, f)(g) = \prod_{i=0}^{p-1} f(g \triangleleft t^i) \). Therefore \( (\phi_p, f)(s) = \rho_s^p = \chi(s) \) for every \( s \in G^C_p \). If \( g = g_i \triangleleft t^j \) for some \( i, j \), then a calculation \( (\phi_p, f)(g) = f(g_i) = \chi(g_i) = \chi(g_i \triangleleft t^j) = \chi(g) \), which uses the fact that \( \chi \) is a fixed point under the action by \( C_p \), completes the proof.
(iv) follows immediately from \( H^2_{cc}(\chi) = B^2_{cc}/B^2_c(\chi) \) and parts (i)-(iii). \( \square \)
**Corollary 2.5.** There is a \( C_p \) isomorphism \( H^2_c(\chi) \cong Z^2_N(\chi)/\ker \Phi \).
**Proof:** Combining Lemmas 2.3 and 2.4 with the natural epimorphism \( Z^2_N(\chi) \to Z^2_N(\chi)/\ker \Phi \) proves the Corollary. \( \square \)
We proceed to the main result of the section.
**Proposition 2.6.** Suppose \( G \) is a finite abelian \( p \)-group. If \( p \) is odd, or \( p = 2 \) and either \( C_2 \)-action is trivial, or \( G \) is an elementary \( 2 \)-group, there exists a \( C_p \)-isomorphism
\[
H^2_c(\chi) \cong H^2(C_p, \hat{G}, \bullet) \times H^2_N(G, \mathbb{k}^*)
\]
**Proof:** (1) First we take up the odd case. By the preceding Corollary we need to decompose \( Z^2_N(\chi)/\ker \Phi \). We note that for any \( p \) there is a
group splitting $Z^2(G, \mathbb{k}^*) = B^2(G, \mathbb{k}^*) \times H^2(G, \mathbb{k}^*)$ due to the fact that the group of 1-cocycles $\mathbb{k}^*G$ is injective, and hence so is $B^2(G, \mathbb{k}^*)$. We aim at finding a $C_p$-invariant complement to $B^2(G, \mathbb{k}^*)$. To this end we recall a well-known isomorphism $a : H^2(G, \mathbb{k}^*) \rightarrow \text{Alt}(G)$, see e.g. [23, §2.3]. There $\text{Alt}(G)$ is the group of all bimultiplicative alternating functions
$\beta : G \times G \rightarrow \mathbb{k}^*$, $\beta(ab, c) = \beta(a, c)\beta(b, c)$, and $\beta(a, a) = 1$ for all $a \in G$. For future applications we outline the construction of $a$. Namely, $a$ is the antisymmetrization mapping sending $z \in Z^2(G, \mathbb{k}^*)$ to $a(z)$ defined by $a(z)(a, b) = z(a, b)z^{-1}(b, a)$. One can check that $a$ is bimultiplicative (cf. [23, (10)]) and it is immediate that $a$ is $C_p$-linear. Another verification gives $\text{im } a = \text{Alt}(G)$ and, moreover, $\ker a = B^2(G, \mathbb{k}^*)$, see [23, Thm.2.2]. Thus we obtain a $C_p$-isomorphism $H^2(G, \mathbb{k}^*) \cong \text{Alt}(G)$.
For every $\beta = a(z)$ a simple calculation gives $a(\beta) = \beta^2$. Since elements of $\text{Alt}(G)$ are bimultiplicative mappings, they have orders dividing the exponent of $G$. Thus $a(\beta) \neq 1$ for all $\beta \in \text{Alt}(G)$. It follows $B^2(G, \mathbb{k}^*) \cap \text{Alt}(G) = \{1\}$. We arrive at a splitting of abelian groups
$$Z^2(G, \mathbb{k}^*) = B^2(G, \mathbb{k}^*) \times \text{Alt}(G)$$
But now both subgroups $B^2(G, \mathbb{k}^*)$ and $\text{Alt}(G)$ are $C_p$-invariant hence there holds $Z^2_N(G, \mathbb{k}^*) = B^2_N(G, \mathbb{k}^*) \times \text{Alt}_N(G)$ which, in view of $\text{Alt}(G) = H^2(G, \mathbb{k}^*)$, is the same as
$$Z^2_N(a) = B^2_N(a) \times H^2_N(G, \mathbb{k}^*).$$
Now part (iii) of Lemma 2.4 completes the proof of part (1).
(2) Here we prove the second claim of the Proposition. We decompose $G$ into a product of cyclic groups $\langle x_i \rangle$, $1 \leq i \leq m$. For every $\alpha \in \text{Alt}(G)$ we define $s_\alpha \in Z^2(G, \mathbb{k}^*)$ via
$$s_\alpha(x_i, x_j) = \begin{cases} \alpha(x_i, x_j), & \text{if } i \leq j \\ 1, & \text{else.} \end{cases}$$
The set $S = \{s_\alpha | \alpha \in \text{Alt}(G)\}$ is a subgroup. One can see easily that $a(s_\alpha) = \alpha$, hence $S$ is isomorphic to $\text{Alt}(G)$ under $a$. Let us write $G_{(p)}$ for the set of elements of order $p$. We observe that $Z^2_N(\text{triv}) = Z^2(\text{triv})_{(2)}$, hence $S_{(2)} \subset Z^2_N(\text{triv})$. For every $z \in Z^2_N(\text{triv}), a(z) \in \text{Alt}(G)_{(2)}$, and therefore $a(z) = a(s)$ for some $s \in S_{(2)}$. We have $zs^{-1} \in B^2(G, \mathbb{k}^*)$, and, as $zs^{-1}$ has order 2, $zs^{-1} \in B^2_N(\text{triv})$. Thus $Z^2_N(\text{triv}) = B^2_N(\text{triv}) \times S_{(2)}$ which implies (2.7) as $S_{(2)} \cong \text{Alt}(G)_{(2)} \cong H^2_N(\text{triv})$.
(3) We prove the last claim of the Proposition. Below $G$ is an elementary 2-group, and action of $C_2$ is nontrivial. First we establish an intermediate result, namely
**Lemma 2.7.** If action $\triangleleft$ is nontrivial, then $Z^2_N(\triangleleft)$ is a nonsplit extension of $\text{Alt}_N(G)$ by $B^2_N(\triangleleft)$.
**Proof:** This will be carried out in steps.
(i) We aim at finding a basis for $\text{Alt}_N(G)$. We begin by noting that as $\text{Alt}(G)$ has exponent 2, $\text{Alt}_N(G)$ is the set of all fixed points in $\text{Alt}(G)$. Put $R = \mathbb{Z}_2C_2$. One can see easily that $R$-module $G$ decomposes as
$$G = R_1 \times \cdots \times R_m \times G_0$$
where $R_i \simeq R$ as a right $C_2$-module, and $G_0 = G^{C_2}$. Denote by $t$ the generator of $C_2$. For each $i$ let $\{x_{2i-1}, x_{2i}\}$ be a basis of $R_i$ such that $x_{2i-1} \triangleleft t = x_{2i}$. We also fix a basis $\{x_{2m+1}, \ldots, x_n\}$ of $G_0$.
We associate to every subset $\{i, j\}$ the bilinear form $\alpha_{ij}$ by setting
$$\alpha_{ij}(x_i, x_j) = \alpha_{ij}(x_j, x_i) = -1, \text{ and } \alpha_{ij}(x_k, x_i) = 1 \text{ for any } \{k, l\} \neq \{i, j\}.$$
The set $\{\alpha_{ij}\}$ forms a basis of $\text{Alt}(G)$. One can check easily that $t$ acts on basic elements as follows
$$t.\alpha_{ij} = \alpha_{kl} \text{ if and only if } \{x_i, x_j\} \triangleleft t := \{x_i \triangleleft t, x_j \triangleleft t\} = \{x_k, x_l\}. $$
Recall the element $\phi_2 = 1 + t \in \mathbb{Z}C_2$. We define forms $\beta_{ij}$ via
$$\beta_{ij} = \phi_2.\alpha_{ij} \text{ if } t.\alpha_{ij} \neq \alpha_{ij}, \text{ and } \beta_{ij} = \alpha_{ij}, \text{ otherwise.}$$
The label $ij$ on $\beta_{ij}$ is not unique as $\beta_{ij} = \beta_{kl}$ whenever $\{x_i, x_j\} \triangleleft t = \{x_k, x_l\}$. Of the two sets $\{i, j\}$ and $\{k, l\}$ labeling $\beta_{ij}$ we agree to use the one with the smallest element, and call such minimal. We claim:
$$\beta_{ij} \text{ the one with the smallest element, and call such minimal. We claim:}$$
(ii) We want to show $\text{Alt}_N(G)$ is an epimorphic image of $Z^2_N(\triangleleft)$.
The restriction $\hat{\alpha}^* \otimes \hat{\alpha}^*$ of $\hat{\alpha}$ to $Z^2_N(\triangleleft)$ induces a $C_2$-homomorphism $Z^2_N(\triangleleft) \xrightarrow{\hat{\alpha}^*} \text{Alt}_N(G)$. We have ker $\hat{\alpha}^* = B^2(G, k^*) \cap Z^2_N(\triangleleft) = B^2_N(\triangleleft)$. First we show $\phi_2.\text{Alt}(G) \subset \text{im} \hat{\alpha}^*$. For, if $\beta = \phi_2.\alpha$, pick an $s \in Z^2(G, k^*)$ with $\hat{\alpha}(s) = \alpha$. Then $(t-1).s \in Z^2_N(\triangleleft)$, and $\hat{\alpha}((t-1).s) = (t-1).\hat{\alpha}(s) = (t-1).\alpha = \phi_2.\alpha = \beta$, as $\alpha^2 = 1$, which gives the inclusion.
By step (i) and definition (2.11) it remains to show that all fixed points $\alpha_{ij}$ lie in $\text{im} \hat{\alpha}^*$. By formula (2.10) $\alpha_{ij}$ is a fixed point if and only if either (a) $\{i, j\} \subset \{2m+1, \ldots, n\}$ or (b) $\{i, j\} = \{2k-1, 2k\}$ for some $k, 1 \leq k \leq m$. Below we find it convenient to write $s_{ij}$ for $s_{\alpha_{ij}}$.
\begin{thebibliography}{99}
\end{thebibliography}
Consider case (a). We claim \( s_{i,j} \) is a fixed point. For, \( t.s_{i,j} \) is bi-
multiplicative, hence is determined by its values at \((x_k, x_l)\). It is im-
mediate that \( t.s_{i,j}(x_k, x_l) = s_{i,j}(x_k, x_l) \) for all \((x_k, x_l)\), whence the as-
sertion. Since \( s_{i,j}^2 = 1 \) for all \( i, j \), \( \phi_2.s_{i,j} = 1 \), hence \( s_{i,j} \in \mathbb{Z}_N^2(\langle \rangle) \). As
\( g(s_{i,j}) = \alpha_{ij} \), this case is done.
We take up (b). Say \( z = s_{2i-1,2i} \) for some \( i, 1 \leq i \leq m \). An easy
verification gives \( \phi_2.z = \alpha_{2i-12i} \neq 1 \). Thus \( z \notin \mathbb{Z}_N^2(\langle \rangle) \). To prove
(ii) we need to find a coboundary \( \delta g \) such that \( z\delta g \in \mathbb{Z}_N^2(\langle \rangle) \). Since
\( g(\alpha_{2i-12i}) = 1, \alpha_{2i-12i} = \delta f_i \) for some \( f_i : G \to \mathbb{k}^* \). Put \( G_i \) for
the subgroup of \( G \) generated by all \( x_j, j \neq 2i-1, 2i \). We assert that one
choice is the function \( f_i \) defined by
\[
(2.13) \quad f_i(x_{2i-1}^{j_1} x_{2i}^{j_2} x') = (-1)^{j_1+j_2+j_1j_2} \text{ for all } x' \in G_i
\]
For, on the other hand it is immediate that for any \( x', x'' \in G_i \)
\[
\alpha_{2i-12i}(x_{2i-1}^{j_1} x_{2i}^{j_2} x', x_{2i-1}^{k_1} x_{2i}^{k_2} x'') = (-1)^{j_1k_2+j_2k_1}
\]
On the other hand the definitions of \( f_i \) and differential \( \delta \) give
\[
\delta f_i(x_{2i-1}^{j_1} x_{2i}^{j_2} x', x_{2i-1}^{k_1} x_{2i}^{k_2} x'') = (-1)^{j_1+k_1+j_2+k_2} (-1)^{j_1+k_1+j_2} = (-1)^{j_1+j_2+j_1j_2}
\]
Define the function \( g_i : G \to \mathbb{k}^* \) by \( g_i(x_{2i-1}^{j_1} x_{2i}^{j_2} x') = i^{j_1+j_2+j_1j_2} \) where
\( i^2 = -1 \). One can check easily the equalities \( f_i^2 = 1 \) and \( t.g_i = g_i, g_i^2 = f_i \). Hence we have \( f_i(\phi_2.g_i) = f_i g_i^2 = f_i^2 = 1 \), and then a calculation
\[
\phi_2(z\delta g_i) = (\phi_2.z)(\phi_2.\delta g_i) = \delta f_i \cdot \delta(\phi_2.g_i) = \delta(f_i(\phi_2.g_i)) = 1
\]
completes the proof of (ii).
(iii) Suppose \( \mathbb{Z}_N^2(\langle \rangle) = B_N^2(\langle \rangle) \times C \) where \( C \) is a \( C_2 \)-invariant subgroup.
Then \( C \) is mapped isomorphically on \( \text{Alt}_N(G) \) under \( g \) and so there is
a unique \( z \in C \) such that \( g(z) = \alpha_{12} \). Since \( g(s_{1,2}) = \alpha_{12} \), \( z = s_{1,2}\delta g \)
for some \( g : G \to \mathbb{k}^* \). Further, as \( \alpha_{12} \) is a fixed point \( g(t.z) = \alpha_{12} \)
as well, hence \( t.z = z \). In addition, since \( \text{Alt}(G) \) is an elementary
2-group, \( 1 = z^2 = (s_{1,2}\delta g)^2 = (\delta g)^2 = \delta(g^2) \). It follows that \( g^2 \) is a
character of \( G \). Moreover, \( t.z = z \) is equivalent to \( t.s_{1,2}(t.\delta g) = s_{1,2}\delta g \)
which in turn gives \( s_{1,2}(t.s_{1,2}(t.\delta g) = \delta g \). As \( \phi_2.s_{1,2} = \alpha_{12} = \delta f_1 \)
we have \( \delta f_1(t.\delta g) = \delta g \) which implies \( \delta f_1 = \delta g(t.\delta g) \) on the account of \( (\delta g)^2 = \delta(g^2) = 1 \) as \( g^2 \) is a character. Equivalently we have the equality
\[
(2.14) \quad f_1 = g \cdot (t.g) \cdot \chi \text{ for some } \chi \in \hat{G}.
\]
Noting that \( f_1 \) is defined up to a character of \( G \) we can assume that
\( f_1(x_1) = 1 = f_1(x_2) \) and \( f_1(x_1x_2) = -1 \). For, \( f_1 \) is defined as any
function satisfying $\delta f_i = \alpha_{12}$. As $\delta(f_1 \chi) = \delta f_1$ for any $\chi \in \hat{G}$, $f_1$ can be modified by any $\chi$. By (2.13) $f_1(x_j) = -1 = f_1(x_1x_2)$, $j = 1, 2$ so we can take $\chi$ such that $\chi(x_1) = \chi(x_2) = -1$. The equality (2.14) implies that for some $\chi \in \hat{G}$ there holds
\[
(*) \quad 1 = f_1(x_j) = g(x_1)g(x_2)\chi(x_j), \quad j = 1, 2, \text{ and}
\]
\[
(**) \quad -1 = f_1(x_1x_2) = g(x_1x_2)^2\chi(x_1x_2)
\]
as $t$ swaps $x_1$ and $x_2$. Since $g^2$ is a character, $g^2(a) = \pm 1$ for every $a \in G$. It follows that $g(x_1) = \iota^m$ and $g(x_2) = \iota^k$ for some $0 \leq m, k \leq 3$. Then equation (*) gives $1 = \iota^{m+k}\chi(x_j)$. This equality shows that $\chi(x_1) = \chi(x_2)$ and $m + k$ is even, because $\chi(a) = \pm 1$ for all $a$. Now (**), and the fact that $g^2$ is a character, gives $-1 = g^2(x_1)g^2(x_2)x_1x_2 = \iota^{2(m+k)}\iota^{-2(m+k)} = 1$, a contradiction. This completes the proof of the Lemma.
Finally we prove (3). Let $G$ be a group with a decomposition (2.9). Set $C$ to be the subgroup of $Z_N^2(<a>)$ generated by the set $B = B' \cup B'' \cup B'''$ where
\[
B' = \{\phi_2, s_{i,j} | \alpha_{ij} \text{ is not a fixed point, and } \{ij\} \text{ is minimal}\}
\]
\[
B'' = \{s_{i,j} | i < j \text{ and } \{i,j\} \subset \{2m+1, \ldots, n\}\}
\]
\[
B''' = \{s_{2i-1,2i} \delta g_i | i = 1, \ldots, m\}
\]
There $\delta g_i$ is chosen as in the proof of the case (ii) of Lemma 2.7. Passing on to $Z_N^2(<a>/\ker \Phi$ we denote by $\overline{B'_N(<a>)}$ and $\overline{C}$ images of these subgroups in $Z_N^2(<a>/\ker \Phi$. Pick a $v \in B$. If $v \in B' \cup B''$ then $v^2 = 1$ because the corresponding $s_{i,j}$ has order 2. For $v = s_{2i-1,2i} \delta g_i$, $v^2 = \delta g_i^2 = \delta f_i$. We know $t.f_i = f_i$ and $f_i^2 = 1$ and therefore $\phi_2.f_i = 1$, whence $\delta f_i \in \ker \Phi$ by definition (2.5). It follows that $\overline{v} = 1$ for all $\overline{v} \in \overline{B}$. Furthermore, by Lemma 2.7 the mapping $\overline{a}$ sends $\overline{B}$ to the basis (2.12) of Alt$_N(G)$. Therefore $\overline{C}$ is isomorphic to Alt$_N(G)$ at least as an abelian group and forms a complement to $\overline{B'_N(<a>)}$ in $Z_N^2(<a>/\ker \Phi$. Since Alt$_N(G)$ consists of fixed points the proof will be completed if we show the same for $\overline{C}$. The fact that $B' \cup B''$ consists of fixed points follows from $t.\phi_2 = \phi_2$ and the case (i) of Lemma 2.7. For an $s_{2i-1,2i} \delta g_i$, the equality $\phi_2.s_{2i-1,2i} = s_{2i-1,2i}(t.s_{2i-1,2i}) = \alpha_{2i-1,2i} = \delta f_i$ gives $t.s_{2i-1,2i} = s_{2i-1,2i} \delta f_i$. Since $\delta f_i \in \ker \Phi$ and $t \delta g_i = \delta g_i$ we see that $s_{2i-1,2i} \delta g_i$ is a fixed point in $Z_N^2(<a>/\ker \Phi$ which completes the proof. \qed
3. The Isomorphism Theorems
We begin with a general observation. Let $H$ be an extension of type (A). The mapping $\pi$ induces a $kF$-comodule structure $\rho_\pi$ on $H$ via
\[(3.1) \quad \rho_\pi : H \to H \otimes kF, \quad \rho_\pi(h) = h_1 \otimes \pi(h_2).\]
$H$ becomes an $F$-graded algebra with the graded components $H_f = \{ h \in H | \rho_\pi(h) = h \otimes f \}$. Let $\chi : kF \to H$ be a section of $kF$ in $H$. By definition $\chi$ is a convolution invertible $kF$-comodule mapping, that is
\[(3.2) \quad \rho_\pi(\chi(f)) = \chi(f) \otimes f, \quad \text{for every } f \in F.\]
Set $f = \chi(f)$. The next lemma is similar to [16, 3.4] or [17, 7.3.4].
**Lemma 3.1.** For every $f \in F$ there holds $H_f = kGf$.
**Proof:** By definition of components $H_1 = H^\text{coG}$ which equals to $kG$ by the definition of extension. By the equation (3.2) $\rho_\pi(f) = f \otimes f$, hence $kGf \subset H_f$. Since the containment holds for all $f$, the equalities $H = \bigoplus_{f \in F} H_f = \bigoplus_{f \in F} kGf$ force the equalities $H_f = kGf$ for all $f \in F$. $\square$
**Definition 3.2.** Given two $F$-graded algebras $H = \bigoplus H_f$ and $H' = \bigoplus H'_f$ and an automorphism $\alpha : F \to F$ we say that a linear mapping $\psi : H \to H'$ is an $\alpha$-graded morphism if $\psi(H_f) = H'_\alpha(f)$ for all $f \in F$.
**Lemma 3.3.** Suppose $H$ and $H'$ are two extensions of $kF$ by $kG$ and $\psi : H \to H'$ a Hopf isomorphism sending $kG$ to $kG$. Then $\psi$ is an $\alpha$-graded mapping for some $\alpha$.
**Proof:** Suppose $H$ and $H'$ are given by sequences
\[
\begin{align*}
kG & \xrightarrow{\iota} H \xrightarrow{\pi} kF, \quad \text{and} \quad kG & \xrightarrow{\iota'} H' \xrightarrow{\pi'} kF.
\end{align*}
\]
By definition of extension $\text{Ker } \pi = H(kG)^+$ and likewise $\text{Ker } \pi' = H'(kG)^+$. By assumption $\psi(kG) = kG$, hence $\psi$ induces a Hopf isomorphism $\alpha : H/H(kG)^+ \to H'/H'(kG)^+$. Replacing $H/H(kG)^+$ and $H'/H'(kG)^+$ by $kF$ we can treat $\alpha$ as a Hopf isomorphism $\alpha : kF \to kF$. $\alpha$ is in fact an automorphism of $F$. We arrive at a commutative diagram
\[
\begin{array}{ccc}
kG & \xrightarrow{\iota} & H \xrightarrow{\pi} kF \xrightarrow{\alpha} kF \\
\psi & & \downarrow \psi \quad \downarrow \alpha \\
kG & \xrightarrow{\iota'} & H' \xrightarrow{\pi'} kF
\end{array}
\]
Since $\psi$ is a coalgebra mapping for every $f \in F$ we have
$$\Delta_{H'}(\psi(\overline{f})) = (\psi \otimes \psi)\Delta_{H}(\overline{f}) = \psi((\overline{f})_1) \otimes \psi((\overline{f})_2),$$
hence
$$\rho_{\pi'}(\psi(\overline{f})) = \psi((\overline{f})_1) \otimes \pi'\psi((\overline{f})_2) = \psi((\overline{f})_1) \otimes \alpha\pi((\overline{f})_2)$$
On the other hand, applying $\psi \otimes \alpha$ to the equality
$$\rho_{\pi}(\overline{f}) = (\overline{f})_1 \otimes \pi((\overline{f})_2) = \overline{f} \otimes f$$
gives
$$\psi((\overline{f})_1) \otimes \alpha\pi((\overline{f})_2) = \psi(\overline{f}) \otimes \alpha(f)$$
whence we deduce $\rho_{\pi'}(\psi(\overline{f})) = \psi(\overline{f}) \otimes \alpha(f)$. Thus $\psi(\overline{f}) \in H'_{\alpha(f)}$ which shows the inclusion
$$\rho_{\pi}(\overline{f}) = \psi(\overline{f}) \otimes \alpha(f) \subseteq \psi(\overline{f}) \otimes \alpha(f)$$
Since both sides of the above inclusion have equal dimensions, the proof is complete.
From this point on $F = C_p$. Let $\triangleleft$ and $\triangleright$ be two actions of $C_p$ on $G$. We denote $(G, \triangleleft)$ and $(G, \triangleright)$ the corresponding $C_p$-modules and we use the notation ‘$\bullet$’ and ‘$\circ$’ for the actions of $C_p$ on $\mathbb{K}^G$ corresponding by (1.3) to $\triangleleft$ and $\triangleright$, respectively. We let $I(\triangleleft, \triangleright)$ denote the set of all automorphisms of $G$ intertwining actions $\triangleleft$ and $\triangleright$, that is automorphisms $\lambda : G \to G$ satisfying
$$(a \triangleleft x)\lambda = a\lambda \triangleright x, \quad a \in G, \quad x \in C_p$$
We make every $\lambda$ act on functions $\tau : C_p \times G^2 \to \mathbb{K}^{C_p}$ by
$$(\tau.\lambda)(x, a, b) = \tau(x, a\lambda^{-1}, b\lambda^{-1}).$$
**Lemma 3.4.** (i) The group $Z^2(G, (\mathbb{K}^{C_p})^\bullet)$ is invariant under the action induced by any automorphism of $G$.
(ii) A $C_p$-isomorphism $\lambda : (G, \triangleleft) \to (G, \triangleright)$ induces $C_p$-isomorphisms between the groups $Z^2_c(\triangleleft), B^2_c(\triangleleft), H^2_c(\triangleleft)$ and $Z^2_c(\triangleright), B^2_c(\triangleright), H^2_c(\triangleright)$, respectively.
**Proof:** (i) is immediate.
(ii) We must check condition (1.18) for $\tau.\lambda$ and $\mathbb{Z}C_p$-linearity of the induced map. First we note $\lambda^{-1}$ is a $C_p$-isomorphism between $(G, \triangleright)$ and $(G, \triangleleft)$, as one can check readily. For, set $b = a\lambda$ in (3.3). Then we have $(b\lambda^{-1} \triangleleft x)\lambda = (b \triangleright x)$ hence $b\lambda^{-1} \triangleleft x = (b \triangleright x)\lambda^{-1}$.
Next we verify (1.18) and $C_p$-linearity in a single calculation
\[
(\tau.\lambda)(xy)(a, b) = \tau(xy, a\lambda^{-1}, b\lambda^{-1})
= \tau(x, a\lambda^{-1}, b\lambda^{-1})(x \bullet \tau(y, a\lambda^{-1}, b\lambda^{-1}))
= \tau(x, a\lambda^{-1}, b\lambda^{-1})\tau(y, a\lambda^{-1} < x, b\lambda^{-1} < x)
= \tau(x, a\lambda^{-1}, b\lambda^{-1})\tau(y, (a \triangleleft x)\lambda^{-1}, (b \triangleleft x)\lambda^{-1})
= (\tau.\lambda)(x)(x \circ (\tau.\lambda)(y))(a, b).
\]
In the case of $B^2_2(\triangleleft)$, first one checks the equality
\[
(\delta_G \eta).\lambda = \delta_G(\eta.\lambda) \text{ for any } \eta : C_p \times G \to k^*.
\]
It remains to verify the condition (1.19) for $\eta.\lambda$. That is done similarly to the calculation in (ii). \qed
Let $(G, \triangleleft)$ be a $C_p$-module. We denote by $A(\triangleleft)$ the group of $C_p$-automorphisms of $(G, \triangleleft)$. By the above Lemma $Z^2_c(\triangleleft)$ is an $A(\triangleleft)$-module. Symmetrically, we introduce the group $A_p = \text{Aut}(C_p)$ of automorphisms of $C_p$. We define an action of $A_p$ on $\text{Map}(C_p \times G^2, k^*)$ via
\[
\tau.\alpha(x, a, b) = \tau(\alpha(x), a, b)
\]
We want to know the effect of this action on $Z^2_c(\triangleleft)$. Let $(G, \triangleleft)$ be a $C_p$-module. For $\alpha \in A_p$ we define a $C_p$-module $(G, \triangleleft')$ via
\[
a \triangleleft' x = a \triangleleft \alpha(x), \quad a \in G, \quad x \in C_p
\]
Similarly, an action $\cdot'$ of $C_p$ on $k^G$ can be twisted by $\alpha$ into $\cdot'^\alpha$ by
\[
x \cdot'^\alpha r = \alpha(x) \cdot r, \quad r \in k^G
\]
One can see easily that if $\cdot'$ and $\triangleleft'$ correspond to each other by (1.3), then so do $\cdot'^\alpha$ and $\triangleleft'^\alpha$.
**Lemma 3.5.** (i) If $\lambda \in I(\triangleleft, \triangleleft')$, then $\lambda \in I(\triangleleft', \triangleleft'^\alpha)$ for every $\alpha \in A_p$.
(ii) The mapping $\tau \mapsto \tau.\alpha$ induces an $A(\triangleleft)$-isomorphism between $Z^2_c(\triangleleft), B^2_c(\triangleleft), H^2_c(\triangleleft)$ and $Z^2_c(\triangleleft'^\alpha), B^2_c(\triangleleft'^\alpha), H^2_c(\triangleleft'^\alpha)$, respectively for every $\alpha \in A_p$.
**Proof:** (i) For every $a \in G, x \in C_p$, we have
\[
(a \triangleleft'^\alpha)x = (a \triangleleft \alpha(x))x = a\lambda \triangleleft' \alpha(x) = a\lambda \triangleleft'^\alpha x
\]
(ii) First we note that $A(\triangleleft)$ can be identified with $A(\triangleleft'^\alpha)$ for any $\alpha$ by the folllowing calculation
\[
(g \triangleleft'^\alpha x)\phi = (g \triangleleft \alpha(x))\phi = (g\phi) \triangleleft \alpha(x) = g\phi \triangleleft'^\alpha x \text{ for every } \phi \in A(\triangleleft).
\]
Thus we will treat every $Z^2_c(\mathcal{A}^\alpha)$ as an $\mathcal{A}(\mathcal{A})$-module. Our next step is to show that for every $\tau \in Z^2_c(\mathcal{A})$, $\tau \alpha$ lies in $Z^2_c(\mathcal{A})$. This boils down to checking (1.18) for $\tau \alpha$ with the $\mathcal{A}(\mathcal{A})$-action:
\[
(\tau \alpha)(xy) = \tau(\alpha(x)\alpha(y)) = \tau(\alpha(\alpha(x))(\alpha(x) \bullet \alpha(\alpha(y))) = \tau(\alpha(x)(x \bullet \alpha(\alpha(y)) = (\tau \alpha)(x)(x \bullet \alpha(\alpha(y))) = (\tau \alpha)(x)(x \bullet \alpha(\alpha(y))).
\]
As for $\mathcal{A}(\mathcal{A})$-linearity, for every $\phi \in \mathcal{A}(\mathcal{A})$, we have
\[
((\tau \alpha) \phi)(x, a, b) = (\tau \alpha)(x, a\phi^{-1}, b\phi^{-1}) = \tau(\alpha(x), a\phi^{-1}, b\phi^{-1}) = (\tau \phi)(\alpha(x), a, b) = ((\tau \phi)(\alpha)(x, a, b).
\]
We need several short remarks.
**Lemma 3.6.** Suppose $\tau$ is a 2-cocycle. Assume $r \in (kG)^\bullet$ is such that $r = \epsilon$. Set $r_i = \phi_i r$, $1 \leq i \leq p$. Define a 1-cocycle $\zeta : G \rightarrow (kG)^\bullet$ by $\zeta(t^i) = r_i$ and a 2-cocycle $\tau' = \tau(\delta_G \zeta)$. Then the mapping
\[
i : H(\tau, \mathcal{A}) \rightarrow H(\tau', \mathcal{A}), i(p_a t^i) = p_a r_i t^i, a \in G, 1 \leq i \leq p
\]
is an equivalence of extensions.
**Proof:** We need to show $\delta_G \zeta \in B^2$ which means that $\zeta$ satisfies (1.19). The argument of Lemma 2.3 used to derive (1.18) from the condition (2.4) works verbatim for $\zeta$.
**Lemma 3.7.** $H(\tau, \mathcal{A})$ is cocommutative iff $\tau$ lies in $H^2_c(\mathcal{A})$.
**Proof:** $H^*(\tau, \mathcal{A})$ is commutative iff $a b = b a$ which is equivalent to $\tau(a, b) = \tau(b, a)$. The latter implies that $\tau(t) : G \times G \rightarrow k^\bullet$ is a symmetric 2-cocycle, hence a coboundary, that is an element of $B^2_N$. A reference to Lemma 2.4(i) completes the proof.
Unless stated otherwise, $H(\tau, \mathcal{A})$ is a noncocommutative Hopf algebra. We pick another algebra $H(\tau', \mathcal{A}')$ isomorphic to $H(\tau, \mathcal{A})$ via $\psi : H(\tau, \mathcal{A}) \rightarrow H(\tau', \mathcal{A}')$. The next observation is noted in [14, p. 802].
**Lemma 3.8.** Mapping $\psi$ induces an Hopf automorphism of $kG$.
Let $G$ be a finite group and $\text{Aut}_{HF}(kG)$ be the group of Hopf automorphisms of $kG$. For $\phi \in \text{Aut}_{HF}(kG)$ we denote by $\phi^*$ the mapping of $G$ induced by $\phi$ via
\[
(a\phi^*)(f) := f(a\phi^*) = \phi(f)(a), f \in kG.
\]
**Lemma 3.9.** Let $G$ be a finite abelian group. The mapping $\phi \mapsto \phi^*$ is an isomorphism between $\text{Aut}_H(\mathbb{k}G)$ and $\text{Aut}(G)$. $\phi$ is a $C_p$-isomorphism $(\mathbb{k}G, \bullet) \to (\mathbb{k}G, \circ)$ if and only if $\phi^*$ is a $C_p$-isomorphism $(G, \triangle) \to (G, \triangle)$.
**Proof:** In general $\phi^*$ is a permutation of the set $G$. When $G$ is abelian and $\mathbb{k}$ contains a $|G|$th root of 1, we have $\mathbb{k}G = \mathbb{k}G$. Then $\phi(G) = G$, as $\phi$ preserves grouplikes. It follows from a straightforward calculation that $\phi^*$ is a group automorphism and $\phi \mapsto \phi^*$ is an isomorphism.
We proceed to formulation of isomorphism theorems. We need several preliminary remarks. First off, let $\triangle$ be a $C_p$-action on $G$. We denote by $[\triangle]$ the class of $C_p$-actions $\triangle'$ isomorphic to $\triangle^\alpha$ for some $\alpha \in A_p$, that is such that $I(\triangle', \triangle^\alpha)$ is nonempty. We let $\text{Ext}_{\triangle}(\mathbb{k}C_p, \mathbb{k}G)$ stand for all equivalence classes of extensions whose $C_p$-action on $G$ lies in $[\triangle]$.
In the second place we construct groups $G(\triangle)$ that control isomorphism types of extensions. For the trivial action we set $G(\text{triv}) = \text{Aut}(G) \times A_p$. Else, we observe that by Lemma 3.5(i) if $\lambda \in I(\triangle, \triangle^\alpha)$, $\mu \in I(\triangle, \triangle^\beta)$, then $\lambda \mu \in I(\triangle, \triangle^{\alpha \beta})$. Therefore the set of all $\alpha \in A_p$ such that $I(\triangle, \triangle^\alpha) \neq \emptyset$ is a subgroup of $A_p$ denoted by $C(\triangle)$. Let us select an element $\lambda_\alpha \in I(\triangle, \triangle^\alpha)$ for every $\alpha \in C(\triangle)$. We define $G(\triangle)$ as the subgroup of $\text{Aut}(G)$ generated by $\mathbb{A}(\triangle)$ and the elements $\lambda_\alpha, \alpha \in C(\triangle)$.
**Proposition 3.10.** If action $\triangle$ is nontrivial, then $G(\triangle)$ is a crossed product of $\mathbb{A}(\triangle)$ with $C(\triangle)$.
**Proof:** It is evident that $\lambda \mathbb{A}(\triangle) \lambda^{-1} = \mathbb{A}(\triangle)$ for every $\lambda \in I(\triangle, \triangle^\alpha)$. In addition, for every $\lambda, \mu \in I(\triangle, \triangle^\alpha)$, $\lambda^{-1} \mu \in \mathbb{A}(\triangle)$. Thus we have $I(\triangle, \triangle^\alpha) = \mathbb{A}(\triangle) \lambda_\alpha$. It follows that $\lambda_\alpha : \lambda_\beta = \phi(\alpha, \beta)\lambda_{\alpha \beta}$ for some $\phi(\alpha, \beta) \in \mathbb{A}(\triangle)$. It remains to show that the kernel of $\pi : G(\triangle) \to C(\triangle)$, $\pi(\phi \lambda_\alpha) = \alpha$ equals $\mathbb{A}(\triangle)$. Pick $\alpha : x \to x^k, k \neq 1$. Clearly $\lambda \in I(\triangle, \triangle^\alpha)$ iff $t \lambda = \lambda t$ where we treat $t \in C_p$ as automorphism of $G$. Since elements of $\mathbb{A}(\triangle)$ commute with $t$, $I(\triangle, \triangle^\alpha) \cap \mathbb{A}(\triangle) = \emptyset$.
Our next goal is to define a $G(\triangle)$-module structure on $H^2_c(\triangle)$. For every $\lambda \in I(\triangle, \triangle^\alpha)$ Lemmas 3.4(ii), 3.5(ii) show that the mapping
\begin{equation}
(3.5) \quad \omega_{\lambda, \alpha} : \tau \mapsto \tau.\lambda \alpha^{-1}, \tau \in H^2_c(\triangle)
\end{equation}
is an automorphism of $H^2_c(\triangle)$. For $\lambda = \lambda_\alpha$ we write $\omega_\alpha = \omega_{\lambda, \alpha}$. $\mathbb{A}(\triangle)$ also acts on $H^2_c(\triangle)$, and we denote by $\overline{\phi}$ the automorphism of $H^2_c(\triangle)$ induced by $\phi \in \mathbb{A}(\triangle)$.
**Lemma 3.11.** The mapping $\phi \lambda_\alpha \mapsto \overline{\phi} \omega_\alpha, \phi \in \mathbb{A}(\triangle), \alpha \in C(\triangle)$ defines $\mathbb{G}(\triangle)$-module structure on $H^2_c(\triangle)$.
Proof: $H^2_c(\langle \rangle)$ is a subquotient of $Z^2(G, (kC_p)^*)$, and actions of $A(\langle \rangle)$ and $\omega_A$ on $H^2_c(\langle \rangle)$ are induced from their actions on $Z^2(G, (kC_p)^*)$. By Lemma 3.4(i) $Z^2(G, (kC_p)^*)$ is an $\text{Aut}(G)$-module, hence it is a $G(\langle \rangle)$-module as well. On the other hand, it is elementary to check that every $\lambda \in \text{Aut}(G)$ commutes with every $\beta \in A_p$ as mappings of $Z^2(G, (kC_p)^*)$. It follows that the equalities $\omega_A \omega_B = \overline{\phi(\alpha, \beta)} \omega_{\alpha \beta}$ and $\omega_A \phi \omega_{\alpha}^{-1} = \lambda_{\alpha} \phi \lambda_{\alpha}^{-1}$ hold in $\text{Aut}(Z^2(G, (kC_p)^*))$. This shows that the mapping of the Lemma is a homomorphism, as needed.
Theorem 3.12. (I) Noncocommutative extensions $H(\tau, \langle \rangle$ and $H(\tau', \langle \rangle$ are isomorphic if and only if
(i) There exist $\alpha \in A_p$ and $C_p$-isomorphism $\lambda : (G, \langle \rangle) \to (G, \langle \rangle^\alpha)$ such that
(ii) $\tau' = \tau . (\lambda \alpha^{-1})$ in $H^2(\langle \rangle$.
(II) There is a bijection between the orbits of $G(\langle \rangle$ in $H^2_c(\langle \rangle$ not contained in $H^2_c(\langle \rangle$ and the isomorphism classes of noncocommutative extensions in $\text{Ext}_{G}(kC_p, kG)$.
Proof: (I). In one direction, suppose $\psi : H(\tau, \langle \rangle) \to H(\tau', \langle \rangle$ is an isomorphism. By Lemma 3.8 $\psi$ induces an automorphism $\phi : [kG] \to [kG]$, and from Lemma 3.3 we have the equality $\psi(t) = rt^k$ for some $k$ and $r \in kG$. The equality $\psi(t^p) = 1$ implies $(rt^k)^p = \phi_p(t^k) \circ r = 1$ and, as $\phi_p(t^k) = \phi_p(t)$, we have $\phi_p \circ r = 1$. This shows $r \in (kG)^*$. Let $\alpha : x \mapsto x^k, x \in C_p$ be this automorphism of $C_p$, and set $\phi = \psi|_{kG}$. Then the calculation
$$\phi(t \cdot f) = \psi(tft^{-1}) = r\alpha(t)\phi(f)\alpha(t)^{-1}r^{-1} = \alpha(t) \circ \phi(f), f \in kG$$
shows $\phi : (kG, \cdot) \to (kG, \circ^\alpha)$ is a $C_p$-isomorphism. It follows by Lemma 3.9 that $(G, \langle \rangle^\alpha)$ is isomorphic to $(G, \langle \rangle$ under $\phi^*$, hence $\lambda = (\phi^*)^{-1} : (G, \langle \rangle) \to (G, \langle \rangle^\alpha)$ is a required isomorphism.
It remains to establish the second condition of the theorem. Set $s = \phi^{-1}(r)$ and observe that, as $\phi^{-1}$ is a $C_p$-mapping, $\phi_p \cdot s = 1$. For $\phi_p \circ r = \phi_p \circ^\alpha r = 1$. Hence $\phi^{-1}(\phi_p \circ^\alpha r) = \phi_p \circ^{-1}(r) = \phi_p \circ s = 1$, and therefore by Lemma 3.6 there is an equivalence $\iota : H(\tau, \langle \rangle) \to H(\tilde{\tau}, \langle \rangle$ with $\iota(t) = st$.
By construction $\iota$ is an algebra map with $\iota(s) = s$ for all $s \in kG$. Hence $t = \iota(st) = st^{-1}(t)$ whence $\iota^{-1}(t) = s^{-1}t$. Thus we have $(\psi \iota^{-1})(t) = t^k$ by the choice of $s$. It follows we can assume $\psi(t) = t^k$ hence $\psi(x) = x^k$ for all $x \in C_p$.
Abbreviating $H(\tau, \langle \rangle, H(\tau', \langle \rangle$ to $H, H'$, respectively, we take up the identity.
$$\Delta_H'(\psi(x)) = (\psi \otimes \psi) \Delta_H(x), x \in C_p.$$
expressing comultiplicativity of $\psi$ on elements of $C_p$. By (1.13) this translates into
\[
(3.6) \quad \sum_{a,b} \tau'(x^k, a, b)p_a x^k \otimes p_b x^k = \sum_{c,d} \tau(x, c, d)\phi(p_c)x^k \otimes \phi(p_d)x^k.
\]
Next we connect $\phi(p_b)$ to the action of $\phi^*$. The argument used to prove (1.4) yields
\[
(3.7) \quad \phi(p_b) = p_b(\phi^*)^{-1}.
\]
For, since $\phi$ is an algebra map, $\phi(p_b) = p_c$ where $c$ is such that $\phi(p_b)(c) = 1$. By definition of action $\phi^*$, $\phi(p_b)(c) = (c\phi^*)(p_b) = p_b(c\phi^*)$, hence $c\phi^* = b$, whence $c = b(\phi^*)^{-1}$.
Switching summation symbols $c, d$ to $l = c(\phi^*)^{-1}$ and $m = d(\phi^*)^{-1}$, the right-hand side of (3.6) takes on the form
\[
\sum_{l,m} \tau(x, l\phi^*, m\phi^*)p_l x^k \otimes p_m x^k
\]
Thus $\psi$ is comultiplicative on $C_p$ iff
\[
(3.8) \quad \tau'(\alpha(x), a, b) = \tau(x, a\phi^*, b\phi^*) = \tau(\phi^*)^{-1}(x, a, b) = \tau.\lambda(x, a, b).
\]
Applying $\alpha^{-1}$ to the last displayed equation we arrive at
\[
(3.9) \quad \tau'(x, a, b) = \tau.\lambda\alpha^{-1}(x, a, b).
\]
as needed.
Conversely, let us assume hypotheses of part (I). Using Lemma 3.9 we infer that $\lambda^{-1}$ induces a Hopf $C_p$-isomorphism $\phi : (kG, \bullet) \to (kG, c^\alpha)$. We define
\[
\psi : H(\tau, \cdot, \cdot) \to H(\tau', \cdot, \cdot) \text{ via } \psi(f x) = \phi(f)\alpha(x), f \in kG, x \in C_p.
\]
A routine verification using $\phi(x \bullet f) = \alpha(x) \circ \phi(f)$ shows $\psi$ is an algebra mapping.
\[
\psi((f x)(f' x')) = \psi(f x \bullet f' x') = \phi(f)\phi(x \bullet f')\alpha(x)\alpha(x') = \phi(f)\alpha(x)\phi(f')\alpha^{-1}(x)\alpha(x)\alpha(x') = (\phi(f)\alpha(x))(\phi(f')\alpha(x') = \psi(f x)\psi(f' x').
\]
To see comultiplicativity of $\psi$ we need to verify
\[
(3.10) \quad \Delta_H(\psi(f x)) = (\psi \otimes \psi)\Delta_H(f x).
\]
By multiplicativity of $\Delta_H$, $\psi, \Delta_H$ it suffices to check (3.10) for $\phi$ and for every $\psi(x)$. Now the first case holds as $\phi$ is a coalgebra mapping, and the second follows from $\tau' = \tau.\lambda\alpha^{-1}$ by calculations (3.6) and (3.9).
(II). Pick an algebra $H(\tau', \delta')$ in $\text{Ext}_{\langle \alpha \rangle}(\mathbb{k}C_p, \mathbb{k}G)$. Let us define the set $\mathcal{C} = \mathcal{C}(\tau', \delta')$ by the formula
\[
\mathcal{C}(\tau', \delta') = \{(\tau'', \delta'')| H(\tau'', \delta'') \simeq H(\tau', \delta')\}.
\]
Clearly the family of sets $\{\mathcal{C}\}$ is identical to the set of isoclasses of extensions in $\text{Ext}_{\langle \alpha \rangle}(\mathbb{k}C_p, \mathbb{k}G)$. We look at the intersection $\mathcal{C} \cap H^2_c(\langle \alpha \rangle)$ as $\mathcal{C}$ runs over $\{\mathcal{C}\}$. First, we claim that $\mathcal{C}(\tau', \delta') \cap H^2_c(\langle \alpha \rangle) \neq \emptyset$ for every $(\tau', \delta')$. To this end we note that as $\delta' \in [\delta]$ there exists $\mu : (G, \delta') \to (G, \delta'' \alpha)$, and then setting $\tau = \tau', \mu \alpha^{-1}$ we have $(\tau, \langle \alpha \rangle \in \mathcal{C}(\tau', \delta')$ by part (I). Next we show the equality $\mathcal{C}(\tau', \delta') \cap H^2_c(\langle \alpha \rangle) = \tau\mathcal{G}(\langle \alpha \rangle)$. For, by definition $(\sigma, \langle \alpha \rangle) \in \mathcal{C}(\tau', \delta')$ iff $H(\sigma, \langle \alpha \rangle) \simeq H(\tau, \langle \alpha \rangle)$ which by part (I) implies $\sigma = \tau, \omega_{\lambda, \alpha}$ for some $\alpha \in A_p$ and $\lambda : (G, \langle \alpha \rangle) \to (G, \delta'')$. It follows that the mapping
\[
\mathcal{C} \to \mathcal{C} \cap H^2(\langle \alpha \rangle), \mathcal{C} \in \{\mathcal{C}\}
\]
is an injection from the set of isoclasses of noncocommutative extensions in $\text{Ext}_{\langle \alpha \rangle}(\mathbb{k}C_p, \mathbb{k}G)$ to the set of orbits of $\mathcal{G}(\langle \alpha \rangle)$ in $H^2_c(\langle \alpha \rangle)$ not contained in $H^2_c(\langle \alpha \rangle)$. This mapping is also a surjection as for every $\tau \in H^2_c(\langle \alpha \rangle), \mathcal{C}(\tau, \langle \alpha \rangle) \cap H^2_c(\langle \alpha \rangle) = \tau\mathcal{G}(\langle \alpha \rangle)$. □
**Corollary 3.13.** For every $\tau \in H^2_c(\langle \alpha \rangle)$ the cardinality of the orbit $\tau\mathcal{G}(\langle \alpha \rangle)$ satisfies
\[
|\tau\mathcal{A}(\langle \alpha \rangle)| \leq |\tau\mathcal{G}(\langle \alpha \rangle)| \leq |\mathcal{C}(\langle \alpha \rangle)||\tau\mathcal{A}(\langle \alpha \rangle)|.
\]
**Proof:** Let $X(\langle \alpha \rangle)/\mathcal{A}(\langle \alpha \rangle)$ be the set of $\mathcal{A}(\langle \alpha \rangle)$-orbits in $X(\langle \alpha \rangle)$. Since $\mathcal{A}(\langle \alpha \rangle)$ is normal in $\mathcal{G}(\langle \alpha \rangle)$, there is an induced action of $\mathcal{C}(\langle \alpha \rangle) = \mathcal{G}(\langle \alpha \rangle)/\mathcal{A}(\langle \alpha \rangle)$ on $X(\langle \alpha \rangle)/\mathcal{A}(\langle \alpha \rangle)$. An orbit of $\mathcal{G}(\langle \alpha \rangle)$ is union of points of some orbit of $\mathcal{C}(\langle \alpha \rangle)$. The latter has size $\leq |\mathcal{C}(\langle \alpha \rangle)|$ whence the Corollary. □
The second isomorphism theorem concerns cocommutative extensions in $\text{Ext}_{\langle \alpha \rangle}(\mathbb{k}C_p, \mathbb{k}G)$ under a stricter condition on $G$, namely we assume $G$ to be an elementary $p$-group.
**Theorem 3.14.** Let $G$ be a finite elementary $p$-group. Then there is a bijection between the set of orbits of $\mathcal{A}(\langle \alpha \rangle)$ in $H^2_{cc}(\langle \alpha \rangle)$ and the set of isoclasses of cocommutative Hopf algebras in $\text{Ext}_{\langle \alpha \rangle}(\mathbb{k}C_p, \mathbb{k}G)$.
**Proof:** By Lemma 3.7 $\tau = \delta\eta \in H^2_{cc}(\langle \alpha \rangle)$. A proof of the Theorem comes down to the statement
\[
(3.11) \quad H(\delta\eta, \langle \alpha \rangle) \simeq H(\delta\zeta, \delta') \text{ iff } \delta\zeta = (\delta\eta) \cdot (\phi^*)^{-1}
\]
for a $C_p$-isomorphism $\phi : (\widehat{G}, \bullet) \to (\widehat{G}, \circ)$. This makes sense as $\phi : (\mathbb{k}^G, \bullet) \to (\mathbb{k}^G, \circ)$ restricts to $\phi : (\widehat{G}, \bullet) \to (\widehat{G}, \circ)$ by Lemma 3.9 and $\widehat{G}$ is $C_p$-stable by Lemma 1.2(2). The proof of (3.11) will be based on several intermediate results.
By general principles a cocommutative Hopf algebra $H(\tau, \langle \rangle)$ is a Hopf group algebra of some group $L$. Our first step is to identify that group.
**Lemma 3.15.** A cocommutative extension $H(\tau, \langle \rangle)$ is isomorphic as a Hopf algebra to a group algebra $kL$ with $L \in \text{Opext}(C_p, \hat{G}, \bullet)$.
**Proof:** Let $H \sim G(H)$ be the functor of taking the group of grouplikes of $H$. Applying $G(\cdot)$ to an extension $k^G \to kL \to kC_p \in \text{Ext}(kC_p, k^G, \langle \rangle)$ yields an extension $\hat{G} \to L \to C_p \in \text{Opext}(C_p, \hat{G}, \bullet)$.
On the other hand, by Lemma 2.4 we have a group isomorphism
$$H^2_G(\langle \rangle)/B^2_G(\langle \rangle) \simeq \hat{G}^{C_p}/N(\hat{G})$$
under the mapping $\delta \eta \mapsto \Phi(\delta \eta) = \phi_p \cdot \eta(t)N(\hat{G})$. We will write $L(\chi)$ when the cohomology class of $L$ is $\chi := \chi N(\hat{G})$, $\chi \in \hat{G}^{C_p}$. We want to construct an explicit isomorphism $H(\delta \eta, \langle \rangle) \simeq kL(\Phi(\delta \eta))$.
We will use the notation $\chi(t) = \hat{G} \to \hat{G}G$, $\eta(t) \to \chi N(\hat{G})$. Thus $\hat{G}$ is a Hopf coboundary. In this case $H(\delta \eta, \langle \rangle) \simeq H(\epsilon \otimes \epsilon, \langle \rangle)$, where $\epsilon \otimes \epsilon$ is the trivial 2-cocycle. By (1.13) we have in $H(\epsilon \otimes \epsilon, \langle \rangle)$
$$\Delta_H(t) = \sum_{a,b \in G} f(a) f(b) f(ab)^{-1} p_a t \otimes p_b t$$
Thus $\hat{G} \times C_p$ consists of grouplikes, hence $H(\epsilon \otimes \epsilon, \langle \rangle) = k(\hat{G} \times C_p)$. In general, that is if $\chi(t) \neq t$, $t$ can be twisted into a grouplike.
In the foregoing notation, let $f = \eta(t)$. We claim the element $ft$ is a grouplike in $H(\delta \eta, \langle \rangle)$. First, since $\eta : G \to (k^C)^\bullet$, $\eta(t) \in k^G$, and $ft$ makes sense. By (1.13)
$$\Delta_H(f) = \sum_{a,b} (\delta f)(a,b) p_a t \otimes p_b t$$
Next apply $\Delta_H$ to the standard expansion $f = \sum_a f(a)p_a$. We get
$$\Delta_H(f) = \sum_a f(a) \sum_{b,c = a} p_b \otimes p_c = \sum_{b,c} f(\eta(b) \otimes p_c$$
All in all we have
$$\Delta_H(ft) = \Delta_H(f) \Delta_H(t)$$
$$= \sum_{a,b} f(ab)p_a \otimes p_b \sum_{a,b} f(a) f(b) f(ab)^{-1} p_a t \otimes p_b t$$
$$= \sum_{a,b} f(a) f(b)p_a t \otimes p_b t = \sum_a f(a)p_a t \otimes (\sum_b f(b) p_b) t = ft \otimes ft,$$
as needed.
Set $x = ft, \chi = \chi_\eta$ and observe that $x^p = \phi_p \cdot f = \chi$. We see $x$ is a unit in $H(\delta \eta, \langle \rangle)$. The action of $x$ on $\hat{G}$ by conjugation coincides with the action of $t$. Let $G(\overline{\chi}, \bullet)$ be the subgroup of $H(\delta \eta, \langle \rangle)$ generated by $\hat{G}$ and $x$. Clearly $G(\overline{\chi}, \bullet)/\hat{G} = C_p$, hence $G(\overline{\chi}, \bullet)$ is an extension of $C_p$ by $\hat{G}$ associated to the datum $\{\chi, \bullet\}$. There $\overline{\chi}$ represents the cohomology class of $G(\overline{\chi}, \bullet)$ as an element of $\text{Opext}(C_p, \hat{G}, \bullet)$, since $H^2(C_p, \hat{G}, \bullet) = \hat{G}^{C_p}/N(\hat{G})$. From $|G(\overline{\chi}, \bullet)| = \dim H(\delta \eta, \langle \rangle)$ we conclude $H(\delta \eta, \langle \rangle) = kG(\overline{\chi}, \bullet)$.
It becomes apparent that we have reduced the isomorphism problem for Hopf algebras to the same problem for groups $G(\overline{\chi}, \bullet)$. We need to translate condition (3.11) into a condition for the data $\{\overline{\chi}, \bullet\}$ and $\{\overline{\omega}, \circ\}$. In keeping with our convention we treat a coboundary $\delta \eta$ as an element of either $H^2_c(\langle \rangle)$ or $H^2_c/B^2_c(\langle \rangle)$.
**Lemma 3.16.** Let $\phi : (\hat{G}, \bullet) \rightarrow (\hat{G}, \circ)$ be a $C_p$-isomorphism, and $\delta \eta \in H^2_c(\langle \rangle), \delta \zeta \in H^2_c(\langle \rangle)$. Put $\overline{\chi} = \Phi \Theta(\delta \eta)$ and $\overline{\omega} = \Phi \Theta(\delta \zeta)$. Then $\delta \zeta = (\delta \eta)(\phi^*)^{-1} \iff \phi(\overline{\chi}) = \overline{\omega}$.
**Proof:** In the above statement we used the same letter $\phi$ for the induced isomorphism $\hat{G}^{C_p}/N(\hat{G}, \bullet) \rightarrow \hat{G}^{C_p}/N(\hat{G}, \circ)$. By definition of $(\phi^*)^{-1}$, $(\delta \eta)(\phi^*)^{-1}(a, b) = \eta(a \phi^*)\eta(b \phi^*)\eta((ab)\phi^*)^{-1}$. As $\eta(a \phi^*) = \phi(\eta)(a)$ by (3.4), it follows that $(\delta \eta)(\phi^*)^{-1} = \delta(\phi(\eta))$, hence the condition of the Lemma says $\delta \zeta = \delta(\phi(\eta))$. Applying $\Phi \Theta$ to the last equation, and using $C_p$-linearity of $\phi$ we derive $\phi_p \circ \zeta(t)N(\hat{G}, \circ) = \phi(\phi_p \cdot \eta(t))N(\hat{G}, \bullet)$, that is $\overline{\omega} = \phi(\overline{\chi})$. Since all steps of the proof are reversible, the proof is complete.
The final step of the proof is
**Proposition 3.17.** $G(\overline{\chi}, \bullet) \simeq G(\overline{\omega}, \circ)$ if and only if $\exists C_p$-isomorphism $\phi : (\hat{G}, \bullet) \rightarrow (\hat{G}, \circ)$ such that $\phi(\overline{\chi}) = \overline{\omega}$.
**Proof:** The proof of the proposition will be carried out in steps.
(1) We assume action `$\bullet$' to be nontrivial which is equivalent to assuming $H(\delta \eta, \langle \rangle)$ is a noncommutative algebra. We simplify notations by replacing $\hat{G}$ with $G$, and $\overline{\chi}$ by $\overline{a}$ where $a \in G^{C_p}$ and $\overline{a} = a N(G)$. An extension of $C_p$ by $G$ defined by some $\overline{a}$ and `$\bullet$' will be denoted by $G(\overline{\pi}, \bullet)$. Recapping Lemma 3.15 we note that the group $G(\overline{\pi}, \bullet)$ is generated by $G$ and an element $x \notin G$ such that $x^p = a$ and the action of $x$ in $G$ by conjugation coincides with the action of a generator of $C_p$.
We note that if $\overline{a} = \overline{T}$ then $x$ can be chosen so that $x^p = 1$. For, from $x^p = \phi_p \cdot b$ we have $(b^{-1}x)^p = 1$. It follows each $G(\overline{\tau}, \bullet) = G \rtimes C_p$.
26 LEONID KROP
1. We need only to show the necessary part, proof of elements of \( \psi \) does not exist. Hence \( \psi \) is an isomorphism. Let \( x, y \) be elements of \( G(\overline{\pi}, \bullet) \) and \( G(\overline{\pi}, \circ) \), respectively, with \( x^p = 1 \) and \( y^p = a \). Were \( \psi(g) = h g^k \) for some \( g, h \in G \), we would have \( 1 = \psi(g^p) = (\phi_p(y^k) \circ h) a^k = (\phi_p(y) \circ h) a^k \) contradicting to \( \overline{\pi} \neq \overline{\pi} \). Thus \( \psi(G) = G \), hence \( \psi(x) = cy^k, c \in G, 1 \leq k \leq p - 1 \). But then the preceding argument gives \( 1 = \psi(x^p) = (\phi_p(y) \circ c) a^k \) whence \( \overline{\pi} = \overline{\pi} \), a contradiction. Thus such \( \psi \) does not exist.
3. Here we show that \( C_p \)-modules \( (G, \bullet^a) \) and \( (G, \bullet) \) are isomorphic for every \( \alpha \in A_p \). Let us write \( G \) additively. Set \( R = \mathbb{Z}_p C_p \) and \( R_l = R/J \) where \( J_l = \langle (t - 1)^l \rangle, 1 \leq l \leq p \) with \( \langle u \rangle \) denoting the submodule generated by \( u \). The action of \( C_p \) in \( G \) induces an \( R \)-module structure in \( G \). Every indecomposable \( R \)-module is isomorphic to some \( R_l \) with the action of \( R \) by the left multiplication. Therefore the Krull-Schmidt decomposition of \( (G, \bullet) \)
\[
(G, \bullet) = B_1 \oplus \cdots \oplus B_p,
\]
consists of blocks \( B_l = R_{m_l} \) of direct sums of modules \( R_l \). There the action \( \bullet \) is taken to be the left multiplication. The sequence \( \{m_l\} \) determines the isomorphism type of \( (G, \bullet) \). An automorphism \( \alpha : x \mapsto x^k, x \in C_p \) induces the automorphism of \( R \) which sends \( J_l \) to itself. Therefore \( \alpha \) induces an automorphism of \( R_l \), hence the \( R \)-module isomorphism \( (R_l, \bullet) \sim (R_l, \bullet^a) \). This proves our claim.
4. Here we prove the proposition for groups \( G(\overline{\pi}, \bullet) \) and \( G(\overline{\delta}, \circ) \) with \( \overline{\pi} \neq \overline{\pi} \) and \( \overline{\delta} \neq \overline{\pi} \). We need only to show the necessary part, proof of sufficiency is fairly straightforward.
Suppose \( \psi : G(\overline{\pi}, \bullet) \to G(\overline{\delta}, \circ) \) is an isomorphism. Let \( x, y \) be elements of those groups such that \( x^p = a \) and \( y^p = b \). By the argument used in (2) there holds: \( \psi(G) = G \) and \( \psi(x) = cy^k \) for some \( c \in G \) and \( 1 \leq k \leq p - 1 \). We derive the equality
\[
\psi(x \bullet g) = \psi(x gx^{-1}) = y^k gy^{-k} = y^k \circ g.
\]
Note (3.13) shows the restriction \( \phi = \psi|_G \) to be a \( C_p \)-isomorphism \( \phi : (G, \bullet) \to (G, \circ^a) \) where \( \alpha : x \mapsto x^k \). Furthermore \( \psi(x) = cy^k \) implies \( \phi(a) = \psi(x^p) = (\phi_p(y^k) \circ c)y^{pk} = (\phi_p(y) \circ c)b^k \) as \( \phi_p(y^k) = \phi_p(y) \).
Say \( \lambda : (G, \circ^a) \to (G, \circ) \) is a \( C_p \)-isomorphism guaranteed by part (3). One can see easily that \( \phi_p(t)R = J_{p-1} \), hence \( N(G, \circ) = J_{p-1} \circ G \) for any action \( \circ \). Therefore \( N(G, \circ^a) = J_{p-1} \circ^a G = \alpha(J_{p-1} \circ G = J_{p-1} \circ G = N(G, \circ) \). As \( \lambda \) is \( R \)-isomorphism, \( \lambda(N(G, \circ^a)) = N(G, \circ) \), that is \( \lambda(N(G, \circ)) = N(G, \circ) \). Therefore as \( b \) is a fixed point, so is \( s = \lambda(b^k) \). Let \( b_i, s_i \) be the \( B_i \) components of \( b, s \) from a decomposition
(3.12) for \((G, \circ)\). Since \(b\) and \(s\) are fixed points, so are \(b_l\) and \(s_l\) for all \(l\). Therefore they lie in the socle of \(B_l\) and are simultaneously equal to 0, or distinct from 0, hence there is an automorphism of the socle mapping \(s_l\) to \(b_l\). Since each \(B_l\) is a free \(R_l\)-module there exists a \(C_{p^l}\)-automorphism \(\sigma_l\) such that \(\sigma_l(s_l) = b_l\). It follows that there exists a \(C_{p^l}\)-automorphism \(\sigma\) of \((G, \circ)\) with \(\sigma(s) = b\).
Indeed, suppose \(B_l = R_l^{(1)} \times \cdots \times R_l^{(m)}\). Let \(\overline{1} = 1 + J_l\) be a generator of \(R_l\) as a \(C_p\)-module, and \(g_j\) be a copy of \(\overline{1}\) in \(R_l^{(j)}\). Since \(b_l\) is a fixed point, \(b_l \in (t-1)^{l-1}B_l\), hence \(b_l = ((t-1)^{l-1}(\sum k_jg_j), k_j \in \mathbb{Z}_p\).
The mapping \(\beta : g_1 \mapsto k_1g_1 \cdots kmg_m, g_i \mapsto g_i, i > 1\) extends to a \(C_{p^l}\)-automorphism with \(\beta((t-1)^{l-1}g_1 = b_l\). If \(s_l\) is another element of \((t-1)^{l-1}B_l\), then there exists a \(C_{p^l}\)-automorphism \(\gamma : (t-1)^{l-1}g_1 \rightarrow s_l\). But then \(\beta\gamma^{-1}(s_l) = b_l\).
Since \(\sigma\) commutes with the action of \(C_{p^l}\), \(\sigma\lambda(N(G, \circ)) = N(G, \circ)\).
The mapping \(\phi = \sigma\lambda\) is a \(C_{p^l}\)-automorphism \((G, \bullet) \rightarrow (G, \circ)\) with the property \(\phi(a) = (\sigma\lambda(\phi_p \circ c))b, \) hence \(\phi(\overline{a}) = \overline{b}\). This completes the proof of (4).
(5) We consider an isomorphism \(\psi : G(\overline{T}, \bullet) \rightarrow G(\overline{T}, \circ)\). We need only to show the modules \((G, \bullet)\) and \((G, \circ)\) are isomorphic. Put \(G = G(\overline{T}, \bullet)\) and \(G_1 = G(\overline{T}, \circ)\). For a group \(F\) we let \(\{\gamma_r(F)\}\) denote the lower central series of \(F\) [6]. A routine calculation yields \(\gamma_r(G) = (t-1)^{r-1}\bullet G\). One can see easily \(\dim_{\mathbb{Z}_p} \gamma_l(G)/\gamma_{l+1}(G) = m_l + \cdots + m_p\). It becomes evident that the multiplicities \(m_j\) are determined by the lower central filtration. Since an isomorphism \(\psi : G \rightarrow G_1\) induces isomorphism between the lower central series in \(G\) and \(G_1\), the sequence \(m_1, \ldots, m_p\) is an isomorphism invariant. This proves (5).
(6) It remains to settle the case of the trivial action. Now \(G(\overline{a}) := G(\overline{a}, \text{triv})\) is abelian. We have \(N(G) = C_p = 1\), hence \(\overline{a} = a\). If \(a = 1, G(a) = G \times \langle x \rangle\) is an elementary \(p\)-group. Else, \(a \neq 1, x^p = a\) which shows \(x\) has order \(p^2\). It is clear \(G(1) \neq G(a)\) for every \(a \neq 1\). Furthermore, if \(a = 1\), let \(\overline{G}\) be a complement of \(a\) in \(G\). Evidently \(G(a) = \overline{G} \times \langle x \rangle\), hence if \(b \neq 1\) is another element of \(G\), \(G(a) \simeq G(b)\).
On the other hand, for every \(a, b \neq 1\) there is an automorphism \(\phi\) of \(G\) with \(\phi(a) = \phi(b)\). This completes the proof of the proposition. \(\square\)
For \(p = 2\) the isomorphism theorems yield
**Corollary 3.18.** Let \(G\) be an elementary 2-group. Then there is a bijection between the orbits of \(A(\langle \cdot \rangle)\) in \(H^2_c(\langle \cdot \rangle)\) and the isoclasses of extensions in \(\text{Ext}_{[\square]}(kC_p, k^G)\).
4. Commutative Extensions
An algebra $H(\tau, \cdot)$ is commutative iff the action ‘\cdot’ is trivial. Below we omit the symbol ‘\cdot’ and write $H(\tau)$ for $H(\tau, \text{triv})$. Every commutative finite-dimensional Hopf algebra over an algebraically closed field is of the form $k^L$ ([10], [17, 2.3.1]) for some finite group $L$. We will identify groups $L$ appearing in that formula for algebras $H(\tau)$. It is convenient to introduce the group $\text{Cext}(G, C_p)$ of central extensions of $C_p$ by $G$ [2].
**Proposition 4.1.** The group $\text{Ext}_{\text{triv}}(kC_p, k^G)$ of equivalence classes of commutative extensions is isomorphic to the group $\text{Cext}(G, C_p)$. The isomorphism is given by $H(\tau) \simeq k^G(\tau)$ where $G(\tau)$ is the central extension defined by the 2-cocycle $\tau$.
**Proof:** In one direction, pick $\tau \in H^2(\text{triv})$. We have by Proposition 1.3 for the trivial action that for every $a \in G$
$$\Delta_H(\tau) = \sum_{x, y \in C_p} \Delta p_x \otimes \Delta p_y = (\tau \otimes \tau)(\sum x p_x \otimes \sum y p_y) = \tau \otimes \tau$$
Thus $\tau$ is a grouplike for every $a \in G$. Let $\theta$ be a generator of $\hat{C}_p$. Since $k^C_{p}$ is a Hopf subalgebra of $H^*(\tau)$, $\theta$ is a grouplike of $H^*(\tau)$. We see that the set $G(\tau) = \{\Delta a|a \in G, 0 \leq i \leq p - 1\}$ consists of grouplikes. Moreover, $|G(\tau)| = \dim H^*(\tau)$, hence $G(\tau)$ is a basis of $H^*(\tau)$. Therefore $G(\tau) = \tau(\tau) = \text{G}(\tau)$ is a group and $H^*(\tau) = k\text{G}(\tau)$, whence $H(\tau) = k^G(\tau)$.
Since $\tau$ is a Hopf 2-cocycle it satisfies (1.18) which for the trivial action of $C_p$ turns into $\tau(xy) = \tau(x)\tau(y)$. Thus $\tau(a, b) : C_p \to k^*$ is a character for any choice of $a, b \in G$. We see that $\tau : C \times G \to \hat{C}_p$ is a 2-cocycle of $G$ in $\hat{C}_p$, hence $G(\tau)$ is a central extension of $G$ by $\hat{C}_p$ defined by $\tau$. It remains to notice that the subgroup $B^2_c$ consists of coboundaries in the group $Z^2(G, \hat{C}_p)$. For, by Definition 1.6 $\delta \eta \in B^2_c$ iff $\eta$ satisfies the condition (1.19), hence $\eta : G \to \hat{C}_p$.
The opposite direction is trivial. \qed
For calculations of orbits of $G(\cdot)$ in $H^2_c(\cdot)$ we prefer to use a much smaller space
$$\mathbb{X}(\cdot) = H^2(C_p, \hat{G}, \cdot) \times H^2_N(G, k^*)$$
(4.1)
We make several remarks regarding $\mathbb{X}(\cdot)$. Let $C_p$ act on $k^C_*$ by $\bullet$ with the induced action $\cdot$ on $G$. Then $C_p$ acts on $Z^2(G, (k^C_*))$ via $x \bullet \tau(y, a, b) = \tau(y, a < x, b < x), x \in C_p, a, b \in G$. Recall $Z^2_N(G, k^*)$ is the subgroup of $Z^2(G, k^*)$ of all $s \in Z^2(G, k^*)$ subject to $\phi_p \bullet s = 1$,
where $\phi_p \circ s = \prod(t^i \circ s)$, and $\phi_p = 1 + t + \cdots + t^{p-1}$. The next lemma is a strengthening of Lemma 3.4.
**Lemma 4.2.** (i) For every $\lambda \in I(\triangle, \triangle')$ the mapping $s \mapsto s.\lambda$ is a $C_p$ isomorphism $X(\triangle) \simeq X(\triangle')$.
(ii) $X(\triangle)$ is invariant under action by elements of $I(\triangle, \triangle')$ for every $\alpha \in A_p$.
**Proof:** (i) Let $\circ$ denote the action of $C_p$ on $Z^2(G, k^*)$ induced by $\triangle'$, i.e. $(x \circ s(a, b) = s(a \triangle' x, b \triangle' x)$. We need to show $\phi_p \circ (s.\lambda) = 1$. Since $\lambda^{-1} \in I(\triangle', \triangle)$ there holds $(a \triangle' x).\lambda^{-1} = a\lambda^{-1} \triangle x$. Therefore $t^i \circ (s.\lambda) = (t^i \circ s).\lambda$ as the following calculation shows:
$$t^i \circ (s.\lambda)(a, b) = (s.\lambda)(a \triangle' t^i, b \triangle' t^i) = s((a \triangle' t^i).\lambda^{-1}, (b \triangle' t^i).\lambda^{-1})$$
$$= s(a.\lambda^{-1} \triangle t^i, b.\lambda^{-1} \triangle t^i) = (t^i \circ s).\lambda(a, b).$$
We conclude that $\lambda$ induces a $C_p$-linear map $X(\triangle) \to X(\triangle')$, and also $\phi_p \circ (s.\lambda) = \prod(t^i \circ (s.\lambda)) = (\prod(t^i \circ s)).\lambda = 1$
(ii) We must show the equality $\phi_p \circ (s.\lambda) = 1$ for every $s \in Z^2_N(\triangle)$. By part (i) with $\circ = \bullet^\alpha$ there holds $\phi_p \circ (s.\lambda) = 1$. Assuming $\alpha : x \mapsto x^k$ and noting $\phi_p(t^k) = \phi_p(t)$ this gives
$$1 = \phi_p \circ (s.\lambda) = \phi_p(t^k) \circ (s.\lambda) = \phi_p \circ (s.\lambda)$$
Since $\lambda$ sends $\ker \Phi$ in $Z^2_N(\triangle)$ to $\ker \Phi$ in $Z^2_N(\triangle')$ the proof is complete. \qed
We turn $X(\triangle)$ into a $G(\triangle)$-module by transferring its action from $H^2_c(\triangle)$ to $Z^2_N(\triangle)$ along $\Theta$. Pick $\omega_{\lambda, \alpha}$ and suppose $\alpha^{-1} : x \mapsto x^t, x \in C_p$. For $s \in Z^2_N(G, k^*)$ we set
$$(4.3) \quad s.\omega_{\lambda, \alpha} = (\phi_t \circ s).\lambda.$$
Let $\Theta_*$ be the isomorphism of Corollary 2.5.
**Lemma 4.3.** (i) For every prime and any action ‘$\triangle$’ isomorphism $\Theta_* : H^2_c(\triangle) \simeq Z^2_N(G, k^*)/\ker \Phi$ is $G(\triangle)$-linear.
(ii) For every odd $p$ the isomorphism $Z^2_N(G, k^*)/\ker \Phi \simeq H^2(C_p, \tilde{G}) \times H^2_c(\triangle)$ is $G(\triangle)$-linear.
**Proof:** (i). For every $\tau \in Z^2_c(\triangle)$ we have by (2.2)
$$\Theta(\tau.\omega_{\lambda, \alpha}) = (\tau.\omega_{\lambda, \alpha})(t) = (\tau.\lambda)(t^i) = \phi_t \circ (t^i.\lambda(t)) = \phi_t \circ \alpha(\tau(t).\lambda)$$
(by (4.2)) = $(\phi_t \circ \tau(t)).\lambda = \Theta(\tau).\omega_{\lambda, \alpha}$
This equation demonstrates that (4.3) turns $\mathbb{Z}_2^N(\triangleright)$ into a $\mathcal{G}(\triangleright)$-module. It is immediate that $B^2_c(\triangleright)$ is a $\mathcal{G}(\triangleright)$-subgroup of $Z^2_c(\triangleright)$. By Lemma 2.4(ii) $\ker\Phi$ is a $\mathcal{G}(\triangleright)$-subgroup, which proves part (i).
(ii). For an odd $p$ splitting (2.8) is carried out by the mapping $s \mapsto s(s^2) \times g(s^2)$ which is clearly a $\mathcal{G}(\triangleright)$-map. It remains to note that homomorphism $\Phi$ is also a $\mathcal{G}(\triangleright)$-map. □
The next result gives the number of isotypes of commutative extensions in Ext($kC_p,kG$) for odd primes $p$ and elementary $p$-groups. By Proposition 4.1 this is also the number of nonisomorphic groups in $C_{ext}(G,C_p)$ which can be derived by group-theoretic methods. Our proof avoids group theory and sets up framework for generalization to non-elementary abelian groups. However, it does not cover 2-groups.
**Proposition 4.4.** Let $G$ be a finite elementary $p$-group of order $p^n$ for an odd $p$. There are $\left\lfloor \frac{3n+2}{2} \right\rfloor$ isotypes of commutative Hopf algebra extensions of $kC_p$ by $kG$ for any odd prime $p$.
**Proof:** Write $\mathcal{G}$ for $\mathcal{G}$(triv) and likewise $\mathbb{A} = \mathbb{A}$(triv). By Theorems 3.12, 3.14 and the preceding lemma the isotypes in question are in a bijection with the set of $\mathcal{G}$-orbits in $X$(triv). We observe that for every trivial $C_p$-module $M$, $N(M) = M^p$. Therefore, if $M$ has exponent $p$, $N(M) = 1$ and $M^p = M$. From these remarks, in view of $\hat{\mathcal{G}}$ and $\text{Alt}(G)$ having exponent $p$, we derive by Lemma 4.3 a $\mathcal{G}$-isomorphism
\[
H^2_c(\triangleright) \simeq \hat{\mathcal{G}} \times \text{Alt}(G).
\]
By definition $\mathcal{G} = \mathbb{A} \times A_p$ with elements $\alpha_k : x \mapsto x^k$ of $A_p$ acting on $X$(triv) by (4.3) as
\[
z.\alpha_k = \phi_k \bullet z = z^k \text{ as } \bullet \text{ is trivial}
\]
We proceed to description of orbits of $\mathbb{A}$ in $H^2_c(\triangleright)$. This description will show that every $\mathbb{A}$-orbit is closed to action by $A_p$, hence $\mathcal{G}$- and $\mathbb{A}$-orbits coincide. We switch to the additive notation in our treatment of $\hat{\mathcal{G}} \times \text{Alt}(G)$ and view the latter as a vector space over the prime field $\mathbb{Z}_p$.
We note $\mathbb{A}$ acts in $\hat{\mathcal{G}} \oplus \text{Alt}(G)$ componentwise. For a $\chi, \beta \in \hat{\mathcal{G}} \times \text{Alt}(G)$ we let $(\chi, \beta)\mathbb{A}$ denote the orbit of $(\chi, \beta)$. For every $\chi \in \hat{\mathcal{G}}$ we let $K_\chi$ denote $\ker \chi$.
Classification of orbits of $\mathbb{A}$ in $\hat{\mathcal{G}} \oplus \text{Alt}(G)$ relies on the theory of symplectic spaces. A symplectic space $(V, \beta)$ is a vector space with an alternating form $\beta$. We need a structure theorem for such spaces (see e.g. [9]). For a subspace $X$ of $V$ we denote by $X^\perp$ the subspace consisting of all $v \in V$ such that $\beta(x, v) = 0$ for all $x \in X$. We call $V^\perp$ the radical of $\beta$ and denote it by $\text{rad } \beta$. We say that two elements $x, y \in$
V are orthogonal if $\beta(x, y) = 0$. We call subspaces $X, Y$ orthogonal if $X \subset Y^\perp$, and we write $X \perp Y$ in this case. A symplectic space $(V, \beta)$ is an orthogonal sum of subspaces $U_1, \ldots, U_k$ if $V = U_1 \oplus \cdots \oplus U_k$ and $U_i \perp U_j$ for all $i \neq j$. We use the symbol $V = U_1 \perp \cdots \perp U_k$ to denote an orthogonal decomposition of $(V, \beta)$. A hyperbolic plane $P$ is a 2-dimensional subspace of $V$ such that $\beta(x, y) = 1$ relative to a basis $\{x, y\}$ of $P$. The elements $x, y$ are called a hyperbolic pair. The structure theorem states
\begin{equation}
V = P_1 \perp \cdots \perp P_r \perp \text{rad } \beta.
\end{equation}
We call this splitting of $V$ a complete orthogonal decomposition of $(V, \beta)$. The number $r$ will be referred to as the width of $\beta$, denoted by $w(\beta)$.
Let us agree to write $\text{Alt}_r(G)$ for the set of alternating forms of width $r$. We identify $\widehat{G} \oplus \text{Alt}_0(G)$ with $\widehat{G}$. The set $\widehat{G} \oplus \text{Alt}_r(G)$ is visibly stable under $\mathbb{A}$. Using (4.5) one can see easily $\mathbb{A}$ acts transitively on $\text{Alt}_r(G)$ for every $r$. It follows that every orbit of $\mathbb{A}$ lies in $\widehat{G} \oplus \text{Alt}_r(G)$ for some $r$. A refinement of $\widehat{G} \oplus \text{Alt}_r(G)$ gives all orbits of $\mathbb{A}$.
**Proposition 4.5.** The orbits of $\mathbb{A}$ in $\widehat{G} \oplus \text{Alt}_r(G)$ are as follows:
(i) $\{0\}$ and $\widehat{G} \setminus \{0\}$ if $r = 0$;
(ii) $\{(0, \beta)\}$, $\{(\chi, \beta) | \text{rad } \beta \subset K_\chi\}$, $\{(\chi, \beta) | \text{rad } \beta \not\subset K_\chi\}$ for every $1 \leq r \leq \lfloor n/2 \rfloor$ for an odd $n$, or $1 \leq r < n/2$ for an even $n$, where $\beta$ runs over $\text{Alt}_r(G)$;
(iii) $\{(0, \beta)\}$ and $\{(\chi, \beta) | 0 \neq \chi\}$, where $\beta$ runs over $\text{Alt}_{n/2}$ if $n$ is even.
**Proof:** Pick $\chi \in \widehat{G}$. Let $x \in G$ be an element, unique modulo $K_\chi$, such that $\chi(x) = 1$ where 1 is the unity of $\mathbb{Z}_p$. Clearly $\chi$ is uniquely determined by a pair $(K_\chi, x)$. For any $\lambda \in \widehat{G}$ with an associated pair $(K_\lambda, z)$ the equality $\chi.\phi = \lambda.\phi \in \mathbb{A}$ holds iff $K_\chi.\phi = K_\lambda$ and $x.\phi = k + z$ for some $k \in K_\lambda$. On the other hand, $\beta, \gamma \in \text{Alt}(G)$ are related by $\beta.\phi = \gamma$ iff there is a decomposition (4.5) of $(V, \beta)$ satisfying $P_i.\phi$ is a hyperbolic plane for $\gamma$ for all $i$ and $(\text{rad } \beta).\phi = \text{rad } \gamma$.
Let $\langle X \rangle$ denote the subspace spanned by a subset $X \subset G$. Note $\mathbb{A}$ acts transitively on the set of pairs $(L, x)$ such that $G = L \oplus \langle x \rangle$ whence $\mathbb{A}$ acts transitively on $\widehat{G} \setminus \{0\}$ which proves (i). (iii) is a special case of the second set in (ii) as $\text{rad } \beta = 0$ for every $\beta$ of width $n/2$.
We take up part (ii). First, we show that all sets there are $\mathbb{A}$ invariant. It suffices to consider the property $\text{rad } \beta \subset \ker \chi$ of $(\chi, \beta)$. Let $(\lambda, \gamma) = (\chi, \beta).\phi$. Then $\beta.\phi = \gamma$ implies $(\text{rad } \beta).\phi = \text{rad } \gamma$. The
second condition $\lambda = \chi.\phi$ yields the equality $K_\chi \phi = K_\lambda$. Therefore $\text{rad} \gamma = (\text{rad} \beta)\phi \subset K_\chi \phi = K_\lambda$.
Second, we prove that each set in (ii) is a single orbit. We begin with \{$(\chi, \beta)$|rad $\beta \subset K_\chi$\}. Let $\chi$ denote the restriction of $\beta$ to $K_\chi$. Take a complete orthogonal decomposition $(K_\chi, \beta) = P_1 \perp \cdots \perp P_m \perp \text{rad} \beta$. Suppose $w(\beta) = r$. Then $\dim \text{rad} \beta = n - 2r$ while $\dim \text{rad} \beta_\chi = n - 1 - 2m$. Since rad $\beta \subset$ rad $\beta_\chi$ it follows that $m < r$. Therefore $\dim \text{rad} \beta_\chi \geq n - 1 - 2(r - 1) = n - 2r + 1 > \dim \text{rad} \beta$. Further select an $x \in \text{rad} \beta_\chi \setminus \text{rad} \beta$ and some $y \notin K_\chi$. Notice $x$ is not orthogonal to $y$ for else, as $G = K_\chi \langle y \rangle$, $x \in \text{rad} \beta$, a contradiction. Let $R = \text{rad} \beta_\chi$. Since $\beta(x, y) \neq 0$ the functional $\beta(-, y) : R \to \mathbb{Z}_p$, $r \mapsto \beta(r, y)$, $r \in R$ is nonzero. Therefore $R$ splits up as $R = \langle x \rangle \oplus \ker \beta(-, y)$. It is clear that $\ker \beta(-, y) = \text{rad} \beta$ which implies $\dim R = n - 1 - 2m = n - 2r + 1$ hence $m = r - 1$. Put $P = P_1 \oplus \cdots \oplus P_{r-1}$ and observe that the restriction of $\beta$ to $P$ is nondegenerate forcing $P \cap P_\perp = 0$. From this we obtain a decomposition $G = P \perp P_\perp$. Since the number $w(\beta)$ is an invariant of decompositions (4.5) and $\text{rad} \beta|_{P_\perp} = \text{rad} \beta$, we conclude that there is a single hyperbolic plane $P_r$ such that $P_\perp = P_r \perp \text{rad} \beta$. In consequence $R \cap P_\perp = (R \cap P_r) \perp \text{rad} \beta$ as rad $\beta \subset R$. Let $u, v$ be a hyperbolic pair in $P_r$ with $u \in R$. Then $v \notin K_\chi$, for otherwise $K_\chi \supset P_r$, and then $K_\chi = G$. We see that $G$ decomposes in two ways
\begin{align*}
(4.6) & \quad (G, \beta) = K_\chi \perp \langle v \rangle, \text{ and} \\
(4.7) & \quad (G, \beta) = P_1 \perp \cdots \perp P_{r-1} \perp P_r \perp \text{rad} \beta
\end{align*}
with $K_\chi = P_1 \oplus \cdots \oplus P_{r-1} \oplus \langle u, \text{rad} \beta \rangle$ and $P_r = \langle u, v \rangle$. Pick another element $(\lambda, \gamma)$ of the set. By (4.6),(4.7) $(G, \gamma) = Q_1 \perp \cdots \perp Q_r \perp \text{rad} \gamma = K_\lambda \perp \langle w \rangle$ with $Q_r = \langle z, w \rangle$ and $K_\lambda = Q_1 \oplus \cdots \oplus Q_{r-1} \oplus \langle z, \text{rad} \gamma \rangle$. Then any automorphism $\phi$ sending $P_i$ to $Q_i$ for $i = 1, \ldots, r - 1$, rad $\beta$ to rad $\gamma$, and $u \mapsto z, v \mapsto w$ carries $(\chi, \beta)$ to $(\lambda, \gamma)$.
Finally we show that any set \{$(\chi, \beta)$|rad $\beta \notin K_\chi$\} is a single orbit. Pick $(\chi, \beta)$ from the set, and let $(K_\chi, \beta) = P_1 \perp \cdots \perp P_m \perp \text{rad} \beta_\chi$ be a complete orthogonal decomposition of $(K_\chi, \beta)$. Select some $y \in \text{rad} \beta \setminus K_\chi$. Then $G = K_\chi \perp \langle y \rangle$, hence rad $\beta = \text{rad} \beta_\chi \oplus \langle y \rangle$. We see $(G, \beta) = P_1 \perp \cdots \perp P_m \perp (\text{rad} \beta_\chi \oplus \langle y \rangle)$ is a complete orthogonal decomposition of $G$. It becomes evident that $m = r$ and for any other pair $(\lambda, \gamma)$ from the set $(\chi, \beta), \phi = (\lambda, \gamma)$ for some $\phi \in \mathbb{A}$.
A simple count of the number of orbits yields the formula. \hfill \Box
5. Some Extensions of Dimension $p^4$
In this section $p$ is an odd prime and $G$ is an abelian group of order $\leq p^3$. When $|G| = p$, any action of $C_p$ on itself is trivial, hence
Ext($k^p, kC_p$) = Ext_{triv}($k^p, kC_p$) which by Theorem 4.4 has two isoclasses. Moreover, as Alt($C_p$) = 1 every $H \in$ Ext_{triv}($kC_p, k^p$) is cocommutative. By Proposition 3.17 part (6) $H = kC_p^2$ or $H = k(C_p \times C_p)$, and we derive part of [15, Theorem 2]. The case $|G| = p^2$, also due to A. Masuoka [14], will be dealt with below as specialization of a more general theory for $|G| = p^3$.
We assume that, unless stated otherwise, $|G| = p^3$. In the additive notation $G = \mathbb{Z}_p^3$ or $G = \mathbb{Z}_p^2 \oplus \mathbb{Z}_p$, and the theory splits into two parts.
(A) Suppose $G = \mathbb{Z}_p^3$. There are up to isomorphism two nontrivial $\mathbb{Z}_p C_p$-module structures on $G$. Let $R_i = \mathbb{Z}_p C_p / \langle (t - 1)^i \rangle$, $0 \leq i \leq p - 1$. Then either $G \simeq R_2 \oplus R_1$ or $G \simeq R_3$. Before proceeding to cases we make a notational change. We write $\alpha_k$ for the mapping $x \mapsto x^k$, $x \in C_p$ and $\alpha_k^{\circ}$ for $x^{p^k}$.
(I) Suppose $G \simeq R_2 \oplus R_1$, and let $\triangleleft$ be the action of $C_p$ on $G$ composed of regular actions of $C_p$ on $R_2$ and $R_1$. We aim to prove
**Theorem 5.1.** Ext_{\triangleleft}($k^p, kC_p$) contains $2p + 11$ isoclasses of extensions.
We break up proof in steps.
(1) Here we compute $\mathcal{X}(\triangleleft)$. Select a basis $\{e, g, f\}$ for $G$ where $\{e, f\}$ span $R_2$, and $R_1 = \mathbb{Z}_p g$ with the action
$$
e \triangleleft t = e + f, \; g \triangleleft t = g, \; f \triangleleft t = f.
$$
Clearly the matrix $T$ of $t$ in that basis is $T = \begin{pmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}$. Let
$$\{e^*, g^*, f^*\}$$
be the dual basis for $\widehat{G}$, and let $\wedge$ denote the multiplication in the Grassman algebra over $\widehat{G}$. We fix a basis $\{e^* \wedge g^*, e^* \wedge f^*, g^* \wedge f^*\}$ for $\widehat{G} \wedge \widehat{G}$, hence a basis $\{e^*, g^*, f^*, e^* \wedge g^*, e^* \wedge f^*, g^* \wedge f^*\}$ for $\widehat{G} \oplus \widehat{G} \wedge \widehat{G}$. We refer to the above bases as standard.
**Proposition 5.2.** $\mathcal{X}(\triangleleft) = \widehat{G}^p \oplus \widehat{G} \wedge \widehat{G} = \langle e^*, g^* \rangle \oplus \widehat{G} \wedge \widehat{G}$.
**Proof:** Recall $\mathcal{X}(\triangleleft) = \widehat{G}^p \cap \widehat{G} \wedge \widehat{G} / \forall(G) \oplus \text{Alt}_N(G)$. We use the well known identification Alt($G$) = $\widehat{G} \wedge \widehat{G}$. One can see easily that action of $t$ in $\widehat{G}$ is described by $T^t$ in the standard basis of $\widehat{G}$. By general principles [4, III, 8.5] the matrix of $t$ in the standard basis of $\widehat{G} \wedge \widehat{G}$ is $T^t \wedge T^{t^*} = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ -1 & 0 & 1 \end{pmatrix}$. It follows that $(t - 1)^{p - 1} \bullet \widehat{G} = 0$ and $(t - 1)^{p - 1} \bullet \widehat{G} \wedge \widehat{G} = 0$, and
that is \( N(\hat{G}) = 0 \) and \((\hat{G} \wedge \hat{G})_N = \hat{G} \wedge \hat{G}\). Further, one can see easily \( \hat{G}^{C_p} = \langle e^*, g^* \rangle \).
(2) Group \( A(\langle \rangle) \). Identifying \( \phi \in A(\langle \rangle) \) with its matrix \( \Phi \) one has \( \Phi \in A(\langle \rangle) \) iff \( \Phi T = T \Phi \). This condition leads up to a determination of \( A(\langle \rangle) \), viz.
\[
(5.2) \quad A(\langle \rangle) = \left\{ \Phi \mid \Phi = \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ 0 & a_{22} & a_{23} \\ 0 & 0 & a_{11} \end{pmatrix}, \ a_{ij} \in \mathbb{Z}_p, \ a_{11}a_{22} \neq 0 \right\}
\]
(3) Orbits of \( A(\langle \rangle) \) in \( X(\langle \rangle) \). Since \( A(\langle \rangle) \) acts on \( \hat{G} \) by \((v^* \phi)(a) = v^*(a \phi^{-1}), v^* \in \hat{G} \), the matrix of \( \phi \) in the standard basis for \( \hat{G} \) is \((\Phi^{-1})^\text{tr}\). We prefer to use coordinates \( u, v, q, r, s \) for \( \Phi^{-1} \) where \( u = a_{11}^{-1}, v = a_{22}^{-1} \) and \( q = ua_{12}, r = ua_{13}, s = va_{23} \). A routine calculation gives
\[
(5.3) \quad (\Phi^{-1})^\text{tr} = \begin{pmatrix} u & 0 & 0 \\ -vq & v & 0 \\ u(qs - r) & -us & u \end{pmatrix}
\]
We treat the tuple \((u, v, q, r, s)\) as coordinates of either \( \phi \) or \( \Phi \). On general principles [4, III,8.5] the matrices of \( \phi \) in the standard bases for \( \hat{G} \) and \( \hat{G} \wedge \hat{G} \) are \((\Phi^{-1})^\text{tr} \) and \((\Phi^{-1})^\text{tr} \wedge (\Phi^{-1})^\text{tr}\), respectively. For \( \Phi \) defined by \((u, v, q, r, s)\) the result is
\[
(5.4) \quad (\Phi^{-1})^\text{tr} \wedge (\Phi^{-1})^\text{tr} = \begin{pmatrix} uv & 0 & 0 \\ -u^2s & u^2 & 0 \\ uvr & -uvq & uv \end{pmatrix}
\]
Regarding \( \mathbb{Z}_p \) as field we let \( \zeta \) denote a generator of \( \mathbb{Z}_p^* \). We observe a simple lemma
**Lemma 5.3.** There are two and four nonzero orbits of \( A(\langle \rangle) \) in \( \hat{G}^{C_p} \) and \( \hat{G} \wedge \hat{G} \), respectively.
**Proof:** We assign a vector \((a_1, a_2)\) to the element \( a_1e^* + a_2g^* \) of \( \hat{G}^{C_p} \) and likewise \((b_1, b_2, b_3)\) to \( b_1e^* \wedge g^* + b_2e^* \wedge f^* + b_3g^* \wedge f^* \). By (5.3) \((0, 1).A(\langle \rangle) = \{(a_1, a_2|a_2 \neq 0\}, \) and \((1, 0).A(\langle \rangle) = \{(a_1, 0)|a_1 \neq 0\} \). This proves the first claim.
Similarly, using (5.4) one can derive readily the equalities
\[
(0, 0, 1).A(\langle \rangle) = \{(b_1, b_2, b_3)|b_3 \neq 0\}, \ (1, 0, 0).A(\langle \rangle) = \{(b_1, 0, 0)|b_1 \neq 0\}.
\]
However, the set \( \{(b_1, b_2, 0)|b_2 \neq 0\} \) is union of two orbits. Namely, if \( b_2 \in \mathbb{Z}_p^* \), then by (5.4) \((b_1, b_2, 0) \in (0, 1, 0).A(\langle \rangle) \). But if \( b_2 \notin \mathbb{Z}_p^* \), then \( b_2 \in \zeta \mathbb{Z}_p \) which implies \((b_1, b_2, 0) \in (0, \zeta, 0).A(\langle \rangle) \). \( \square \)
We introduce notation
\[ \Omega'_0 = \{(0, 0)\}, \Omega'_1 = (1, 0).\mathbb{A}(\phi), \Omega'_2 = (0, 1).\mathbb{A}(\phi), \]
\[ \Omega''_0 = \{(0, 0)\}, \Omega''_1 = (1, 0, 0).\mathbb{A}(\phi), \Omega''_{2,0} = (0, 1, 0).\mathbb{A}(\phi), \]
\[ \Omega''_{2,1} = (0, \zeta, 0).\mathbb{A}(\phi), \Omega''_3 = (0, 0, 1).\mathbb{A}(\phi). \]
Some of products \( \Omega'_i \times \Omega''_j \) are orbits itself. We list those that are in
**Lemma 5.4.** The following sets are orbits
\[ \begin{align*}
(0) & \quad \Omega'_0 \times \Omega''_0 \quad \text{and} \quad \Omega'_i \times \Omega''_j, \quad j = 0, 1, (2, 0), (2, 1), 3, \quad i = 1, 2. \\
(1) & \quad \Omega'_1 \times \Omega''_1 \quad \text{and} \quad \Omega'_1 \times \Omega''_3. \\
(2) & \quad \Omega'_2 \times \Omega''_1, \quad \Omega'_2 \times \Omega''_{2,0} \quad \text{and} \quad \Omega'_2 \times \Omega''_{2,1}.
\end{align*} \]
**Proof:** Vectors \((a_1, a_2)\) and \((b_1, b_2, b_3)\) give rise to a concatenated vector \((a_1, a_2; b_1, b_2, b_3)\). The claim is that concatenating generators of \( \Omega'_i, \Omega''_j \) for \( i, j \) as in the Lemma we get a generator for \( \Omega'_i \times \Omega''_j \). We give details for \( \Omega'_1 \times \Omega''_3 \). Other cases are treated similarly. Combining (5.3) with (5.4) we obtain
\[ (1, 0; 0, 0, 1).\mathbb{A}(\phi) = \{(u, o; uv, −uv, uv)|uv \neq 0, q, r, s \text{ arbitrary}\} \]
Now for every element \((a_1, 0; b_1, b_2, b_3)\) \( \in \Omega'_1 \times \Omega''_3 \) the equations \( u = a_1, uv = b_3, uvr = b_1, −uvq = b_2 \) are obviously solvable, which completes the proof. \( \square \)
We pick up \( p - 1 \) additional orbits in
**Lemma 5.5.** Each set \( \Omega'_i \times \Omega''_{2,i}, i = 0, 1 \) is union of \((p - 1)/2 \) orbits.
**Proof:** Say \( i = 0 \). By definition \( \Omega'_1 \times \Omega''_{2,0} = \{(a_1, 0; b_1, b_2, 0)|a_1 \in \mathbb{Z}_p^*, b_2 \in \mathbb{Z}_p^2, b_1 \text{ arbitrary}\} \). For every \( m \in \mathbb{Z}_p^2 \) we let \( z_m = (1, 0; 0, m, 0) \). By (5.3) and (5.4) \( z_m.\phi = (u, 0; −u^2sm, u^2m, 0) \) where \( u, s \) are among parameters of \( \phi \). It is immediate that \( |z_m.\mathbb{A}(\phi)| = (p - 1)p, \) and one can verify equally directly that \( z_m.\mathbb{A}(\phi) \cap z_n.\mathbb{A}(\phi) = \emptyset \) for \( m \neq n \). Since \( |\Omega'_1 \times \Omega''_{2,0}| = \frac{(p-1)}{2}(p-1)p \) this case is done. For \( i = 1 \) one should take \( z'_m = (1, 0; 0, \zeta m, 0) \).
We summarize
**Lemma 5.6.** There are \( 2p + 11 \) orbits of \( \mathbb{A}(\phi) \) in \( \mathbb{X}(\phi) \).
**Proof:** The previous two lemmas give \( p + 11 \) orbits. The rest will come from splitting of the remaining set \( \Omega''_2 \times \Omega''_3 \). The latter is defined as \( \{(a_1, a_2; b_1, b_2, b_3)|a_2, b_3 \in \mathbb{Z}_p^*, a_1, b_1, b_2 \text{ arbitrary}\} \). For every \( k \in \mathbb{Z}_p \) we define \( w_k = (k, 1; 0, 0, 1) \). Again by (5.3) and (5.4) we have
\[ w_k.\mathbb{A}(\phi) = \{(uk − vq, v; uvr, −uvq, uv)\}. \]
There \( u, v \) run over \( \mathbb{Z}_p^* \) and \( r, q \) run over \( \mathbb{Z}_p \). One can see easily that
\[
|w_k.\mathcal{A}(\prec)| = (p - 1)^2 p^2.
\]
Furthermore, we claim that \( w_k.\mathcal{A}(\prec) \cap w_l.\mathcal{A}(\prec) = \emptyset \) for \( k \neq l \).
For, suppose
\[
(u^k - vq, v; uwr, -uvq, uv) = (u'l - v'q', v'; u'v'r', -u'v'q', u'v')
\]
for some \((u, v, q, r)\) and \((u', v', q', r')\). Then \( v = v' \) and \( uv = u'v' \) give \( u = u' \). This implies \( q = q' \), \( r = r' \), and finally \( uk = ul \) yields \( k = l \), a contradiction. We conclude that \( |\bigcup_{0 \leq k \leq p-1} w_k.\mathcal{A}(\prec)| = p^3(p - 1)^2 \). As this is the number of elements in \( \Omega_2' \times \Omega_2' \), the proof is complete. \( \square \)
(4) Orbits of \( \mathcal{G}(\prec) \). By definition \( \mathcal{G}(\prec) \) is generated by \( \mathcal{A}(\prec) \) and a select set \( \{\lambda_k|2 \leq k \leq p - 1\} \) of automorphisms of \( G \). There \( \lambda_k \in I(\prec, \prec^k) \), and by (3.3) \( \lambda \in I(\prec, \prec^k) \) iff its matrix \( \Lambda \) satisfies
\[(5.5)\]
\[T\Lambda = \Lambda T^k.\]
Set \( \Lambda_k = \text{diag}(1, 1, k) \) (that is the diagonal matrix with entries 1, 1, \( k \)), and observe that \( \Lambda_k \) satisfies (5.5). We denote by \( \lambda_k \) the automorphism whose matrix is \( \Lambda_k \), and we set \( \omega_k = \lambda_k^-1 \). We move on to calculation of matrices of automorphisms \( \omega_k \). We set \( l = k^{-1} \pmod{p} \).
**Lemma 5.7.** Action of \( \omega_k \) is described by
\[
e^* \omega_k = le^*, \ g^* \omega_k = lg^*
\]
\[
e^* \wedge g^* \omega_k = le^* \wedge g^*
\]
\[
e^* \wedge f^* \omega_k = l^2 e^* \wedge f^*
\]
\[
g^* \wedge f^* \omega_k = -\left(\frac{1}{2}\right) e^* \wedge g^* + l^2 g^* \wedge f^*
\]
**Proof:** By (4.3) for \( \tau \in X(\prec) \), \( \tau.\omega_k = (\phi_i \bullet \tau).\lambda_k \). For \( \tau = e^*, g^*, e^* \wedge g^*, e^* \wedge f^* \phi_i \bullet \tau = l\tau \) as such \( \tau \) is fixed by \( C_p \). Because \( (t-1)^2 \tilde{G} \wedge \tilde{G} = 0 \) we expand \( \phi_i \) in powers of \( t - 1 \), namely \( \phi_i = l + \left(\frac{1}{2}\right)(t - 1) \) \( + \) higher terms.
We deduce
\[
\phi_i \bullet g^* \wedge f^* = lg^* \wedge f^* + \left(\frac{1}{2}\right)(t - 1) \bullet g^* \wedge f^* = lg^* \wedge f^* - \left(\frac{1}{2}\right) e^* \wedge g^*
\]
Further \( (\Lambda_k^{-1})^\text{tr} = \text{diag}(1, 1, k^{-1}) \) and \( (\Lambda_k^{-1})^\text{tr} \wedge (\Lambda_k^{-1})^\text{tr} = \text{diag}(1, k^{-1}, k^{-1}) \). These matrices describe action of \( \lambda_k \). Applying \( \lambda_k \) to \( \phi_i \bullet \tau \) as \( \tau \) runs over the standard basis of \( X(\prec) \) we complete the proof of the Lemma. \( \square \)
The next Proposition completes the proof of the Theorem.
**Proposition 5.8.** The set of \( \mathcal{G}(\prec) \)-orbits coincides with the set of \( \mathcal{A}(\prec) \)-orbits.
Proof: By Corollary 3.13 for every \( \tau \in \mathcal{X}(\vartriangle) \), \( \tau \mathcal{G}(\vartriangle) \) is union of orbits \( \tau \omega_k \mathcal{A}(\vartriangle) \) for \( 1 \leq k \leq p - 1 \). Thus it suffices to show \( \tau \omega_k \in \tau \mathcal{A}(\vartriangle) \) for every \( k \). We note that Lemma 5.7 implies that \( \omega_k \not\in \mathcal{A}(\vartriangle) \). Nevertheless, the inclusion \( \tau \omega_k \in \tau \mathcal{A}(\vartriangle) \) holds for generators \( \tau \) of every orbit described in Lemmas 5.4, 5.5, 5.6. We give a sample calculation for \( \tau = w_m = me^* + g^* + g^* \wedge f^* \) of Lemma 5.6. By Lemma 5.7
\[
w_m \omega_k = lme^* + lg^* - \left( \frac{l}{2} \right) e^* \wedge g^* + l^2 g^* \wedge f^*
\]
Now take \( \phi \) with coordinates \( u = l, v = l, r = -l^2 \left( \frac{l}{2} \right), q = s = 0 \). By (5.3) and (5.4) one sees immediately that \( w_m \phi = w_m \omega_k \).
We can quickly dispose of the case \( G = C_p \times C_p \) as promised above. Let \( \triangle \) denote the right regular action of \( C_p \) on \( R_2 \).
**Proposition 5.9.** ([14]) There are up to isomorphism \( p + 7 \) Hopf algebras in \( \text{Ext}(kC_p \times C_p, kC_p) \).
Proof: Since all nontrivial actions of \( C_p \) form a single isomorphism class we have
\[
\text{Ext}(kC_p \times C_p, kC_p) = \text{Ext}_{\triangle}(kC_p \times C_p, kC_p) \cup \text{Ext}_{\text{triv}}(kC_p \times C_p, kC_p).
\]
By Proposition 4.4 \( \text{Ext}_{\text{triv}}(kC_p \times C_p, kC_p) \) contributes four nonisomorphic algebras. It remains to show that \( \text{Ext}_{\triangle}(kC_p \times C_p, kC_p) \) contains \( p + 3 \) isoclasses.
Setting \( g = 0 \) in the definition of \( G \) reduces it to \( G = \mathbb{Z}_p \times \mathbb{Z}_p \) with \( G \simeq R_2 \) as \( C_p \)-module. Further reductions are as follows. The classifying space is \( \mathcal{X}(\triangle) = \langle e^* \rangle \oplus \langle e^* \wedge f^* \rangle \),
\[
\mathcal{A}(\triangle) = \left\{ \Phi \in \text{GL}(G) \mid \Phi = \begin{pmatrix} a_{11} & a_{12} \\ 0 & a_{11} \end{pmatrix}, a_{11} \not= 0 \right\},
\]
and automorphisms \( \lambda_k \in I(\triangle, \mathcal{A}) \) are defined by \( \Lambda_k = \begin{pmatrix} 1 & 0 \\ 0 & k \end{pmatrix}, 1 \leq k \leq p - 1 \). It becomes apparent that elements \( \phi \) and \( \omega_k \) act on \( \mathcal{X}(\triangle) \) by
\[
(a, b) \phi = (ua, u^2b)
\]
\[
(a, b) \omega_k = (la, l^2b)
\]
where \( ae^* + be^* \wedge f^* \) is identified with \((a, b)\) and \( l = k^{-1} \) (mod \( p \)) as above. Thus the orbits of \( \mathcal{G}(\triangle) \) in \( \mathcal{X}(\triangle) \) coincide with those of \( \mathcal{A}(\triangle) \). For the latter we note that the \( \mathcal{A}(\triangle) \)-orbit of every vector \((a, b)\) with \( a, b \not= 0 \) has \( p - 1 \) elements, hence there are \( p - 1 \) orbits of this kind. The set \( \{(0, b) \mid b \not= 0\} \) is the union of two orbits, viz. \( \{(0, m) \mid m \in \mathbb{Z}_p \wedge 2\} \) and \( \{(0, \zeta m) \mid m \in \mathbb{Z}_p \wedge 2\} \), and two more orbits \( \{(0, 0)\}, \{(a, 0) \mid a \not= 0\} \) are supplied by the set \( \{(a, 0) \mid a \in \mathbb{Z}_p\} \).
We return to algebras of dimension \( p^4 \). We consider the case
(II) $G \simeq R_3$. We denote by $\triangleleft_r$ the right multiplication in $R_3$. This case is sensitive to prime $p$. Let us agree to write $\mathbb{X}(\triangleleft_r)$ as $\mathbb{X}_p$ if $G$ is a $p$-group. For $r \in \mathbb{Z}_pC_p$ we denote by $\pi$ the image of $r$ in $R_3$. The elements $e = 1, f = (t - 1), g = (t - 1)^2$ form a basis for $R_3$ in which action of $t$ is defined by $T = \begin{pmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{pmatrix}$. Let $\{e^*, f^*, g^*\}$ be the dual basis for $\hat{G}$, and $\{e^* \wedge f^*, e^* \wedge g^*, f^* \wedge g^*\}$ the induced basis for $\hat{G} \wedge \hat{G}$. We call all these bases standard. We aim to prove
**Theorem 5.10.** $\text{Ext}_{\mathbb{Z}_p}(\mathbb{C}_p, \mathbb{C}_p)$ contains $p + 9$ isoclasses, if $p > 3$, and four isoclasses if $p = 3$.
Proof will be carried out in steps.
(1) Space $\mathbb{X}_p(\triangleleft_r)$.
**Lemma 5.11.** If $p = 3$, then
$$\mathbb{X}_3 = \langle e^* \wedge f^*, e^* \wedge g^* \rangle$$
For every $p > 3$
$$\mathbb{X}_p = \mathbb{Z}_p e^* \oplus \hat{G} \wedge \hat{G}$$
**Proof:** The matrices of $t$ in the standard bases of $\hat{G}$ and $\hat{G} \wedge \hat{G}$ are $T_{tr}$ and $T_{tr} \wedge T_{tr}$, respectively, with $T_{tr} \wedge T_{tr} = \begin{pmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{pmatrix}$. From this one computes directly $(t - 1)^3 \bullet \hat{G} = (t - 1)^3 \bullet \hat{G} \wedge \hat{G} = 0$. Since $\phi_p(t) = (t - 1)^p - 1$, it follows that $N(G) = 0$ and $(\hat{G} \wedge \hat{G})_N = \hat{G} \wedge \hat{G}$ for any $p > 3$. Furthermore $\hat{G}^C_r = \mathbb{Z}_p e^*$ for every $p$. Thus as $\mathbb{X}_p = \hat{G}^C_r / N(G) \oplus (\hat{G} \wedge \hat{G})_N$ the second statement of the Lemma follows.
Say $p = 3$. Then $N(\hat{G}) = (t - 1)^2 \bullet \hat{G} = \mathbb{Z}_3 e^*$, hence $\hat{G}^C_r / N(\hat{G}) = 0$. Another verification gives $(\hat{G} \wedge \hat{G})_N = \langle e^* \wedge f^*, e^* \wedge g^* \rangle$. \hfill \Box
(2) Group $\mathbb{A}(\triangleleft_r)$. For any ring $R$ with a unity viewed as a right regular $R$-module and any right $R$-module $M$ the mapping $\lambda_M : M \rightarrow \text{Hom}_R(R, M)$ defined by $\lambda_M(m)(x) = mx, x \in R$ is an $R$-isomorphism. Set $M = R = R_3$, and pick $r = a_1 e + a_2 f + a_3 g$. The matrix of $\lambda_R(r)$ in the standard basis is $\Phi = \begin{pmatrix} a_1 & a_2 & a_3 \\ 0 & a_1 & a_2 \\ 0 & 0 & a_1 \end{pmatrix}$. From this it is evident that
$$\mathbb{A}(\triangleleft_r) = \left\{ \Phi \in GL(G) | \Phi = \begin{pmatrix} a_1 & a_2 & a_3 \\ 0 & a_1 & a_2 \\ 0 & 0 & a_1 \end{pmatrix}, a_i \in \mathbb{Z}_p, a_1 \neq 0 \right\}$$
Take $\phi = \lambda_{R_3}(r)$. Action of $\phi$ in $\hat{G}$ and $\hat{G} \wedge \hat{G}$ is described by $(\Phi^{-1})^\text{tr}$ and $(\Phi^{-1})^\text{tr} \wedge (\Phi^{-1})^\text{tr}$. Set $u = a_1^{-1}, q = ua_2, r = ua_3$. A routine calculation gives
\begin{equation}
(\Phi^{-1})^\text{tr} = \begin{pmatrix}
u & 0 & 0 \\
uq & u & 0 \
u(q^2 - r) & -uq & u
\end{pmatrix}
\end{equation}
\begin{equation}
(\Phi^{-1})^\text{tr} \wedge (\Phi^{-1})^\text{tr} = \begin{pmatrix}
u^2 & 0 & 0 \\
u^2q & u^2 & 0 \\
u^2r & -u^2q & u^2
\end{pmatrix}
\end{equation}
At this point it is convenient to determine a family of isomorphisms $\lambda_k : (G, q_r) \to (G, q_k)$. To this end, let us take $M = (R_3, q_k^R)$ with $2 \leq k \leq p - 1$. We set $\lambda_k = \lambda_M(e)$. By definition of $\lambda_k$ we have
$\lambda_k(e) = e, \lambda_k(f) = e(t^k - 1), \lambda_k(g) = e(t^k - 1)^2$
Using the expansion $t^k - 1 = k(t - 1) + \binom{k}{2}(t - 1)^2 \pmod{(t - 1)^3}$ we conclude that $\Lambda_k = \begin{pmatrix}1 & 0 & 0 \\0 & k & \binom{k}{2} \\0 & 0 & k^2\end{pmatrix}$ is the matrix of $\lambda_k$ in the standard basis. We shall need an explicit form of the associated matrices describing the action of $\lambda_k$ in $\hat{G}$ and $\hat{G} \wedge \hat{G}$, respectively. Put $l = k^{-1} \pmod{p}$ as usual. Then an easy calculation gives
\begin{equation}
(\Lambda_k^{-1})^\text{tr} = \begin{pmatrix}1 & 0 & 0 \\0 & l & 0 \\0 & \binom{l}{2} & l^2\end{pmatrix},
\end{equation}
\begin{equation}
(\Lambda_k^{-1})^\text{tr} \wedge (\Lambda_k^{-1})^\text{tr} = \begin{pmatrix}l & 0 & 0 \\\binom{l}{2} & l^2 & 0 \\0 & 0 & l^3\end{pmatrix}.
\end{equation}
Unless stated otherwise we assume below that $p > 3$. The degenerate case $p = 3$ follows easily from the general one.
(3) Orbits of $\mathbb{A}(q_r)$ in $\mathbb{X}_p$. We identify an element of $\mathbb{X}_p$ with its coordinate vector $(a; b_1, b_2, b_3)$ relative to the standard basis of $\mathbb{X}_p$. We start by fixing a family of orbits separately in $\hat{G}^{C_p}$ and $\hat{G} \wedge \hat{G}$.
These are
$\Omega'_0 = \{(0)\}, \Omega'_1 = \{(a)|a \neq 0\}, \Omega''_0 = \{(0, 0, 0)\}$, $\Omega''_i = \{(*, \ldots, *, \zeta^j b_i, 0, \ldots, 0)|b_i \in \mathbb{Z}_p^\ast\}, i = 1, 2, 3; j = 0, 1$
where the \( * \) denotes an arbitrary element of \( \mathbb{Z}_p \). For more complex orbits we need vectors \( v_i(m) = (m; 0, \ldots, m, 0, \ldots, 0) \) with the second \( m \) filling the \( i \)th slot, and \( m \) running over \( \mathbb{Z}_p^* \).
**Lemma 5.12.** There are \( 3p + 5 \) orbits of \( A(\omega) \) in \( X_p \). These are
\[
\Omega'_0 \times \Omega''_0, \quad \Omega'_1 \times \Omega''_0, \quad \Omega'_0 \times \Omega''_1, \quad \text{and} \quad v_i(m)A(\omega), \quad i = 1, 2, 3, \quad j = 0, 1; \quad m \in \mathbb{Z}_p^*
\]
**Proof:** It is obvious that \( \Omega'_1 = (1)A(\omega) \). By (5.7) \( (0, \ldots, \zeta^j, 0, \ldots, 0) \phi = (\ast, \ldots, \ast, \zeta^j u^2, 0, \ldots, 0) \) for all \( i, j \) with the \( \ast \) denoting an arbitrary element of \( \mathbb{Z}_p \). This shows \( \Omega''_i = (0, \ldots, \zeta^j, 0, \ldots, 0)A(\omega) \), hence an orbit. Similarly, by (5.6) and (5.7) we have
\[
(5.10) \quad v_i(m)\phi = (um; \ast, \ldots, \ast, u^2m, 0, \ldots, 0).
\]
From this one can see easily that \( v_i(m)A(\omega) \) has \( (p - 1)p^{i-1} \) elements. Another verification gives \( v_i(m)A(\omega) \cap v_i(n)A(\omega) = \emptyset \) for \( m \neq n \). Set \( \Omega''_i = \Omega''_0 \cup \Omega''_1 \) and observe that \( |\Omega''_i| = (p - 1)p^{i-1} \) which gives \( |\Omega'_1 \times \Omega''_i| = (p - 1)^2p^{i-1} \). Evidently \( v_i(m) \in \Omega'_1 \times \Omega''_i \) for all \( m \) and therefore comparing cardinalities we arrive at the equality \( \Omega'_1 \times \Omega''_i = \bigcup_m v_i(m)A(\omega) \). But clearly \( X_p = \bigcup k \Omega'_k \times \Omega''_i, \quad k = 0, 1; 0 \leq i \leq 3 \) which completes the proof.
(4) Orbits of \( G(\omega) \). These are listed in
**Proposition 5.13.** In the foregoing notation the orbits of \( G(\omega) \) in \( X_p \) are as follows.
\[
\Omega'_0 \times \Omega''_0, \quad \Omega'_1 \times \Omega''_0, \quad \Omega'_0 \times \Omega''_1, \quad \Omega'_1 \times \Omega''_2, \\
\Omega'_0 \times \Omega''_3, \quad v_i(m)A(\omega), \quad \Omega'_1 \times \Omega''_2, \quad \Omega'_1 \times \Omega''_3
\]
where \( j = 0, 1 \) and \( m \) runs over \( \mathbb{Z}_p^* \).
**Proof:** In view of Corollary 3.13 we need to determine the \( A(\omega) \)-orbit containing \( v\omega_k \) where \( v \) runs over a set of generators of \( A(\omega) \)-orbits of Lemma 5.12, and \( \omega_k = \lambda_k \alpha_k^{-1}, 2 \leq k \leq p - 1 \), as usual.
(i) For \( A(\omega) \)-orbits \( \Omega'_1 \times \Omega''_0 \) and \( \Omega'_1 \times \Omega''_1 \) generators can be chosen as \( v_1 = (1; 0, 0, 0) \) and \( v_{ij} = (0; 0, \ldots, \zeta^j, 0, \ldots, 0) \), respectively. In view of \( e^* \) and \( f^* \) being fixed points for the action of \( t \), and by (5.8), (5.9) it is immediate that
\[
(5.11) \quad v_1 \omega_k = lv_1 \quad \text{and} \quad v_{1j} \omega_k = t^2v_{1j},
\]
hence those sets are \( G(\omega) \)-orbits.
Next we take \( v_{20} = e^* \wedge g^* \). Noting that \( (t - 1)^2 \cdot e^* \wedge g^* = 0 \), we use the expansion \( \phi_1 = l + \left( \frac{1}{2} \right)(t - 1) \mod (t - 1)^2 \) to derive
\[
\phi_1 \cdot e^* \wedge g^* = ce^* \wedge f^* + le^* \wedge g^*, \quad c \in \mathbb{Z}_p.
\]
Applying $\lambda_k$ to the last equation we find with the help from (5.9)
\begin{equation}
(5.12) \quad e^* \wedge g^* \omega_k = c'e^* \wedge f^* + l^3 e^* \wedge g^*, \text{ for some } c' \in \mathbb{Z}_p.
\end{equation}
The last equation shows that $\nu_{20}.\omega_k \in \nu_{21}.A(\zeta_r)$ if $l$, hence $k$, is not a square, and $\nu_{20}.\omega_k \in \nu_{20}.A(\zeta_r)$, otherwise. This means $\nu_{20}G(\zeta_r) = \Omega'_0 \times (\Omega''_{20} \cup \Omega''_{21})$, that is $\Omega'_0 \times \Omega''_2$ as needed.
(ii) For a generator $\nu_{3j} = (0; 0, 0, \zeta^j) = \zeta^j f^* \wedge g^*$ of $\Omega'_0 \times \Omega''_{3j}$, we claim that $\nu_{3j}.\omega_k \in \nu_{3j}.A(\zeta_r)$ for all $k$. Using the expansion $\phi_l = l + c_1(t - 1) + c_2(t - 1)^2 \pmod{(t - 1)^3}$ we derive $\phi_l \bullet f^* \wedge g^* = (c_1 + c_2)e^* \wedge f^* + c_1e^* \wedge g^* + lf^* \wedge g^*$. Applying $\lambda_k$ we have by (5.9)
\begin{equation}
(5.13) \quad f^* \wedge g^*.\omega_k = c'_1e^* \wedge f^* + c_1l^2 e^* \wedge g^* + l^4 f^* \wedge g^*, \quad c'_1, c_1 \in \mathbb{Z}_p.
\end{equation}
which shows $f^* \wedge g^*.\omega_k \in \Omega_{3j}$. As $\Omega_{3j} = \nu_{3j}.A(\zeta_r)$ by part (3) the claim follows.
(iii) We pause to mention that the above arguments settle the $p = 3$-case. For, since $X_3 = \langle e^* \wedge f^*, e^* \wedge g^* \rangle$, by part (i) it has three nonzero orbits, namely $\Omega''_{1j}$, $\Omega''_1$, $j = 0, 1$.
(iv) Here we take $\nu_1(m) = (m; m, 0, 0)$. Calculations in part (i) give $\nu_1(1).\omega_k = (lm; l^2m, 0, 0) \in \nu_1(m)A(\zeta_r)$ by (5.10). That is, $\nu_1(m)A(\zeta_r)$ is a $G(\zeta_r)$-orbit for every $m \in \mathbb{Z}_p^*$.
It remains to show that the last three sets of the Proposition are $G(\zeta_r)$-orbits.
(v) $\Omega'_{1} \times \Omega''_3$ is an orbit. By Lemma 5.12 $\Omega'_{1} \times \Omega''_3 = \bigcup_m \nu_2(m).A(\zeta_r)$ where $\nu_2(m) = me^* + me^* \wedge g^*$. Note that by (5.11) and (5.12) there holds $\nu_2(m).\omega_k = (lm; c', l^3m, 0)$. On the other hand we have by (5.10) $\nu_2(n).\phi = (un; a, u^2n, 0)$ where $u, a$ run over $\mathbb{Z}_p^*$ and $\mathbb{Z}_p$, respectively. For every $l$ choosing $n = l^{-1}m, u = l^2$ and $a = c'$ we obtain $\nu_2(m).\omega_k \in \nu_2(n)A(\zeta_r)$. Letting $l$ run over $\mathbb{Z}_p^*$ we see that $\bigcup_n \nu_2(n)A(\zeta_r) = \nu_2(m)A(\zeta_r)$ which completes the proof.
(vi) Here we show that each $\Omega'_{1} \times \Omega''_{3j}$ is an orbit. By (5.12) and (5.13)
\begin{equation}
(5.14) \quad \nu_3(m).\omega_k = \nu_3(n).\phi \text{ for some } \phi \in A(\zeta_r).
\end{equation}
We seek an $n$ such that
By (5.10) $\nu_3(n).\phi = (un; a, b, u^2n)$ with $a, b$ and $u$ taking arbitrary values in $\mathbb{Z}_p$ and $\mathbb{Z}_p^*$, respectively. Setting $u = l^3, n = l^{-2}m, a = c'$ and $b = c''$ fullfils (5.14). We see $\nu_3(m)G(\zeta_r) = \bigcup_{n \in m\mathbb{Z}_p^*} (n; 0, 0, 0)A(\zeta_r)$.
On the other hand $\Omega'_1 \times \Omega''_{3j} = \bigcup_{n \in \mathbb{Z}_p^2} (n; 0, 0, n) \mathbb{A}(\varsigma_r)$ by comparing cardinalities of both sides.
Case (B) $G = \mathbb{Z}_p^2 \oplus \mathbb{Z}_p$ is more involved. There are 6 classes $[\varsigma]$ of actions each one with its own extension theory. The final result is that $\text{Ext}(kC_p, k^G)$ contains $3p + 19$ nonisomorphic algebras $2p + 7$ of which are neither commutative, nor cocommutative. The details of the proof will appear elsewhere.
Appendix: Crossed product splitting of $H$
**Proposition.** Let $H$ be an extension of $kF$ by $k^G$. Then $H$ is a crossed product of $kF$ over $k^G$.
**Proof:** First observe that $H$ is a Hopf-Galois extension of $k^G$ by $kF$ via $\rho_{\pi} = (\text{id} \otimes \pi)\Delta_H : H \to H \otimes kF$, see e.g. the proof of [17, 3.4.3], hence by [17, 8.1.7] $H$ is a strongly $F$-graded algebra. Setting $H_x = \{h \in H|\rho_{\pi}(h) = h \otimes x\}$ we have $H = \bigoplus_{x \in F} H_x$ with $H_1 = k^G$ and $H_xH_{x^{-1}} = k^G$ for all $x \in F$. Next for every $a \in G$ we construct elements $u(a) \in H_x$, $v(a) \in H_{x^{-1}}$ such that
$$u(a)v(a) = p_a, p_au(a) = u(a), v(a)p_a = v(a), \text{ and}$$
$$u(a)v(b) = 0 \text{ for all } a \neq b.$$
Indeed, were all $uv, u \in H_x, v \in H_{x^{-1}}$ lie in span$\{p_b|b \neq a\}$, then so would $H_xH_{x^{-1}}$, a contradiction. Therefore for every $a \in G$ there are $u \in H_x, v \in H_{x^{-1}}$ such that $uv = \sum c_b p_b, c_a \neq 0$. Setting $u(a) = \frac{1}{c_a} p_a u, v(a) = v p_a$ we get elements satisfying the first three properties stated above. Furthermore, the last property also holds because $u(a)v(b) = p_a u(a)v(b)p_b = p_a p_b u(a)v(b) = 0$. It follows that the elements $u_x = \sum_{a \in G} u(a), v_x = \sum_{a \in G} v(a)$ satisfy $u_x v_x = 1$ hence, as $H$ is finite-dimensional, $v_x u_x = 1$ as well. Thus $u_x$ is a 2-sided unit in $H_x$.
Now define $\chi : kF \to H$ by $\chi(x) = \frac{1}{\epsilon_H(u_x)} u_x$. One can see immediately that $\chi$ is a convolution invertible mapping satisfying $\rho_{\pi} \circ \chi = \chi \otimes \text{id}, \chi(1_F) = 1$ and $\epsilon_H \circ \chi = \epsilon_F$. Thus $\chi$ is a section of $kF$ in $H$, which completes the proof. \qed
**References**
[1] N. Andruskiewitsch, Notes on extensions of Hopf algebras, *Can. J. Math.* 48(1)(1996), 3-42.
[2] F. R. Beyl and J. Tappe, Group Extensions, Representations, and the Schur Multiplier, Lecture Notes in Mathematics 958, Springer-Verlag, 1982.
[3] R.J. Blatttner, M. Cohen and S. Montgomery, Crossed Product and Inner Actions of Hopf Algebras, *Trans. Amer. Math. Soc* **298**(2)(1986),671-711.
[4] N. Bourbaki, Elements of Mathematics, Algebra I, Springer-Verlag, 1989.
[5] N.P. Byott, Cleft extensions of Hopf algebras, *J. Algebra* **157**(1993),405-429.
[6] M. Hall, Jr., “The Theory of Groups”, The Macmillan Company, New York, 1959.
[7] I. Hofstetter, Extensions of Hopf algebras and their cohomological description, *J. Algebra* **164**(1994), 264-298.
[8] Y. Kashina, G. Mason, S. Montgomery, Computing the Frobenius-Schur indicator for abelian extensions of Hopf algebras, *J. Algebra* **251**(2002), 888-913.
[9] S. Lang, “Algebra”, Addison-Wesley, 1993.
[10] R.G. Larson and D.E. Radford, Semisimple cosemisimple Hopf algebras, *Amer. J. Math.* **110**(1988), 187-195.
[11] M. Mastnak, Hopf algebra extensions arising from semi-direct products of groups, *J. Algebra* **251**(2002), 413-434.
[12] S. MacLane, “Homology”, Die Grundlehren der Mathematischen Wissenschaften **114**, Springer-Verlag, 1963.
[13] A. Masuoka and Y. Doi, Generalization of cleft comodule algebras, *Comm. Algebra* **20**(1992), 3703-3721.
[14] A. Masuoka, Self-dual Hopf algebras of dimension $p^3$ obtained by extensions, *J. Algebra* **178**(1995), 791-806.
[15] A.Masuoka, The $p^n$ theorem for semisimple Hopf algebras, *Proc. Amer. Math. Soc.*, **124**(3)(1996), 735-737.
[16] A. Masuoka, Extensions of Hopf algebras (Lecture Notes, University of Cordoba, 1997) Notas Mat.No. 41/99, FaMAF Uni. Nacional de Cordoba, 1999.
[17] S. Montgomery, Hopf Algebras and their Actions on Rings, in: *CMBS Reg. Conf. Ser. Math.* **82**, AMS, 1993.
[18] C. Nastasescu and F. Van Oystaeyen, On strongly graded rings and crossed products, *Comm. Algebra* **10** (1982), 2085-2106.
[19] H.-J. Schneider, Some remarks on exact sequences of quantum groups, *Comm. Algebra* (9)**21**(1993), 3337-3358.
[20] H.-J. Schneider, A normal basis and transitivity of crossed products for Hopf algebras, *J. Algebra* **152**(1992), 289-312.
[21] D. Stefan, The set of Types of $n$-dimensional semisimple and cosemisimple Hopf algebras is finite, *J. Algebra* **193**(1997), 571-580.
[22] M. Takeuchi, Matched pairs of groups and bismash products of Hopf algebras, *Comm. Algebra* **9**(1981), 841-882.
[23] K. Yamazaki, On projective representations and ring extensions of finite groups, *J. Fac. Science Univ. Tokyo, Sect. I* **10**(1964), 147-195.
DePaul University, Chicago, IL 60614
E-mail address: [email protected] | 2025-03-06T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2260,
1
],
[
2260,
5515,
2
],
[
5515,
8578,
3
],
[
8578,
10956,
4
],
[
10956,
13761,
5
],
[
13761,
16502,
6
],
[
16502,
19278,
7
],
[
19278,
22136,
8
],
[
22136,
24738,
9
],
[
24738,
27148,
10
],
[
27148,
29982,
11
],
[
29982,
32964,
12
],
[
32964,
36110,
13
],
[
36110,
39143,
14
],
[
39143,
42533,
15
],
[
42533,
45395,
16
],
[
45395,
47791,
17
],
[
47791,
50491,
18
],
[
50491,
53242,
19
],
[
53242,
55774,
20
],
[
55774,
59681,
21
],
[
59681,
62930,
22
],
[
62930,
65088,
23
],
[
65088,
69349,
24
],
[
69349,
71802,
25
],
[
71802,
75506,
26
],
[
75506,
79100,
27
],
[
79100,
82533,
28
],
[
82533,
85317,
29
],
[
85317,
88106,
30
],
[
88106,
91359,
31
],
[
91359,
94723,
32
],
[
94723,
98579,
33
],
[
98579,
101534,
34
],
[
101534,
104494,
35
],
[
104494,
107540,
36
],
[
107540,
110549,
37
],
[
110549,
113858,
38
],
[
113858,
116548,
39
],
[
116548,
118818,
40
],
[
118818,
122071,
41
],
[
122071,
125058,
42
],
[
125058,
127609,
43
],
[
127609,
130149,
44
]
]
} |
51777fae05d7b19d16b0b317584270e4173032b7 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 6,
"total-fallback-pages": 0,
"total-input-tokens": 17197,
"total-output-tokens": 4793,
"fieldofstudy": [
"Medicine"
]
} | Resistance of a novel denture identification system to various assault: An in‑vitro study
Vishwas Narang, Harinder Kuckreja, Naveen Oberoi, Jaswinder Kaur, Navneet Kaur Birdi, Santosh Mahajan
Departments of Prosthodontics and Crown and Bridge and Departments of Biochemistry, Baba Jaswant Singh Dental College, Hospital and Research Institute, Ludhiana, Punjab, India
INTRODUCTION
Forensic odontology is the branch of dentistry, that in the interest of justice, involves the management, examination, evaluation, and presentation of dental evidence in criminal or civil proceedings. Forensic odontology can help identification of individuals in mass disasters, detecting domestic violence in suspicious cases, and recognition of victims in situations where other evidence for identification are deliberately tampered. Various methods used in forensic odontology
Abstract
Aim: Denture marking has been advocated and recommended by many forensic organizations. The prosthodontists can play a significant role in the identification of geriatric population by adopting denture marking as a routine procedure. These stickers are easily readable and can be connected to smartphone devices without the need of specific equipment, store information in variety of ways, and cost-effective. The purpose of this study is to evaluate NFC stickers against physical insult; acid, base, and heat.
Settings and Design: In‑vitro evaluation study.
Materials and Methods: Denture bases were fabricated, using chemical and heat-cured acrylic resin. NFC stickers were incorporated using postfabrication inclusion method for chemically cured resin base and prefabrication inclusion method for heat-cured acrylic resin base. These bases were subjected to acid, alkali, and thermal insults.
Statistical Analysis Used: Descriptive statistics.
Results: Both pre and postfabrication inclusion NFC stickers were capable of withstanding various chemical and thermal assaults.
Conclusion: NFC stickers could be used as an adjunct to radio frequency identification (RFID) tags for denture identification. NFC stickers appear to be easy to use and more cost-effective than RFID tags.
Keywords: Denture labeling, forensic identification, near-field communication, radio frequency identification
Address for correspondence: Dr. Vishwas Narang, Department of Prosthodontics and Crown and Bridge, Baba Jaswant Singh Dental College, Hospital and Research Institute, Sector 39, Moti Nagar, Ludhiana - 141 010, Punjab, India.
E-mail: [email protected]
Submitted: 18-Jan-2021, Accepted: 23-Mar-2021, Published: 28-Apr-2021
How to cite this article: Narang V, Kuckreja H, Oberoi N, Kaur J, Birdi NK, Mahajan S. Resistance of a novel denture identification system to various assault: An in‑vitro study. J Indian Prosthodont 2021;21:180-5.
are previous dental records, bite marks, radiographs, denture ID tags, etc.
Denture identification has been around for many years. There are documented cases of dentures being used in postmortem identification from as early as 1835. Apart from their advantage in forensic odontology, denture identification can help solve the ownership problem of lost dentures in long-term care facilities and hospitals. Multiple different techniques and methods are practised that include surface engraving or embossing and incorporation of bar codes, photographs, PIN or radio frequency identification (RFID) tags, but none of them fulfills the “ideal” of being simple, practical, affordable and universally acceptable.
Near field communication (NFC) is a type of RFID technology that operates at a frequency of 13.56 MHz. They have a short distance of communication which is in range of 10 cm. The major advantage of NFC is that no specific interrogator AKA reader and controller is required (used in case of RFID) as peer-to-peer (P2P) communication can be established between a smartphone and NFC tag.
NFC technology is used in medical science as monitoring and home-based management system for variety of chronic disease. MiniME® by Ergonomidesign is one such device that monitors various parameters such as electrocardiography, heart rate, pulse and transmits the data to cloud through NFC. Another such device is FITBIT® which uses NFC to transfer details such as calories burned, number of steps taken. Literature also mentions some recent concept about miniature NFC sensors that can be either implanted on skin, fingernails, teeth, or eyes to collect information from body fluids.
Practical application of NFC in the field of dentistry is not limited to identification of complete dentures, removable prosthesis, orthodontic appliances, etc., or in forensic odontology as an aid for postmortem identification of deceased. However, they can also be used in finding lost dentures which will be discussed further in this article.
The purpose of this study is to evaluate NFC stickers against physical insult; acid, base, and heat.
MATERIALS AND METHODS
The study was approved by Institutional review board. One hundred denture bases were fabricated, fifty with chemically cured acrylic resin (DPI, India) and other 50 using heat-cured acrylic resin (Pyrax, India) [Flow Chart 1]. Commercially available NFC stickers (LINQS®, India) NTAG216 NFC tag measuring 8 mm × 18 mm [Figure 1] were incorporated into denture bases.
Prefabrication inclusion technique
Used for heat-cured acrylic resin, Tags were incorporated while packing. Small rectangle of 10 mm × 20 mm was cut from baseplate wax of 1 mm thickness. This wax piece was further wrapped in aluminum foil and placed in the flask along with heat-cured polymethyl-meth acrylate (PMMA) in dough stage. A damped cellophane sheet was then placed and trial closure was performed. The flask was opened, wax-aluminum spacer was retrieved and NFC tag was placed along with heat-cured PMMA. Finally, the flask was closed, allowed to bench set and was cured at 100°C for 90 min [Figure 3a].
Postfabrication inclusion technique
Used for chemically cured acrylic resin, a channel was cut at the palatal area of denture base of dimension 10 mm × 20 mm × 1 mm using a small round bur. NFC tag was placed, covered with self-cure clear acrylic (DPI, India), and cured under 30 psi pressure for 20 min [Figure 3b].
These bases were divided into five groups to check for different types of physical insult [Table 1].
Group 1: Samples were immersed in 90% concentrated sulphuric acid (H₂SO₄) for 24 h [Figure 4a].
Group 2: Samples were immersed in 98% concentrated sulphuric acid (H₂SO₄) and evaluated after 24 h [Figure 4b].
Group 3: Samples were kept in 60% concentrated sodium hydroxide (NaOH) for 24 h [Figure 4c].
Group 4: Incineration at 200°C for 20 min, followed by raising the temperature to 400°C and maintaining for 10 min [Figure 4d].
Group 5: Direct flaming of denture bases was done using a butane microtorch (Roburn, Taiwan) for 1 min, samples were allowed to burn for 3 min and then extinguished and assessed [Figure 4e].
After incorporating the tags using prefabrication and postfabrication inclusion technique, they were programmed with OnePlus 7T smartphone device (One Plus Tech. Co. Ltd., China) using NFC Tools application (downloaded from Google Play). Information fed to NFC tag included: (1) Sample number; (2) Type of PMMA used for fabricating base; (3) Physical insult performed on sample [Figure 5].
**RESULTS**
The results of all groups are shown in Tables 1 and 2. Group 1 [Figure 6a], where the specimens were placed in 90% conc. H$_2$SO$_4$ for 24 h showed complete deterioration of acrylic surface, however, the NFC tags were readable when tested after completely neutralizing the acid. Increased conc. of H$_2$SO$_4$ in Group 2 (98% conc.) lead to nonresponding NFC tags after 24 h. Only 2 out of 10 tags responded in heat-polymerizing PMMA group and none of the tags responded in self-polymerizing PMMA group. Group 2 [Figure 6b] depicted 20% positive result for heat acrylizing PMMA.
Group 3 [Figure 6c] involved placing NFC tags in 60% conc. NaOH. No physical change was seen on the surface of acrylic after a period of 24 h and all NFC tags were easily readable. For Group 4 [Figure 6d], Denture bases were placed in a preheated furnace at 200°C for 20 min, temperature was then raised to 400°C and maintained for another 10 min. Both denture bases suffered significant
| Group | Type of assault | Self-cure PMMA | Heat-cure PMMA |
|-------|--------------------------------------|----------------|----------------|
| 1 | 90% concentrated H$_2$SO$_4$ for 24 h | 10/10 | 10/10 |
| 2 | 98% concentrated H$_2$SO$_4$ for 24 h | 0/10 | 2/10 |
| 3 | 60% concentrated NaOH for 24 h | 10/10 | 10/10 |
| 4 | Incineration in a furnace | 8/10 | 9/10 |
| 5 | Direct flaming (3 min) | 10/10 | 10/10 |
Result: NFC tags working out of total samples tested. PMMA: Poly-methyl meth acrylate, H$_2$SO$_4$: Sulphuric acid, NaOH: Sodium hydroxide, NFC: Near-field communication
| Group | Type of assault | Self-cure PMMA | Heat-cure PMMA |
|-------|--------------------------------------|----------------|----------------|
| 1 | 90% concentrated H$_2$SO$_4$ for 24 h | ✓ | ✓ |
| 2 | 98% concentrated H$_2$SO$_4$ for 24 h | X | X |
| 3 | 60% concentrated NaOH for 24 h | ✓ | ✓ |
| 4 | Incineration in a furnace | ✓ | ✓ |
| 5 | Direct flaming (3 min) | ✓ | ✓ |
✓: Functioning tags, X: Nonfunctioning tags (group with at-least 80% of result is considered functioning). H$_2$SO$_4$: Sulphuric acid, NaOH: Sodium hydroxide, PMMA: Poly-methyl meth-acrylate
damage of the surface but the NFC tags were in their functional state. Nine out of 10 tags were found functional in heat-polymerized PMMA group and 8 out of 10 tags were working in self-polymerizing PMMA group. For Group 3, 100% samples were in functional state and for group 4, 90% samples of heat-polymerized group and 80% for self-polymerizing group were found working at the end of the experiment.
For direct flaming: Group 5 [Figure 6e], Denture bases were set on fire with a butane-based torch by direct flaming for 1 min. After which, samples were left to burn. All tags were functioning well after a period of 3 min. 100% samples responded for both PMMA material.
### DISCUSSION
An attempt is made by the authors to use commercially available NFC stickers and incorporating them to dentures to facilitate their identification.
Forensic odontology demands a denture identification method that is not only easy to access but also resistant to thermal and chemical insults that otherwise make it difficult to identify deceased individuals. In this study, NFC tags has been put to various thermal and chemical assaults. Similar study was performed by Richmond and Pretty with ten different denture marking systems incorporated in a large PMMA block at a depth of 2 mm. Although, NFC, in particular, was not used; the RFID tags tested in their study...
performed well in terms of acid and base assaults but failed to respond after placing in a furnace at 800°C for 20 min.\cite{4} To increase the clinical applicability of this study, denture bases were used instead of a large PMMA block while preparing samples. For placement of tag at an appropriate depth, a modified technique of one demonstrated by Reeson and Venkat Nag & Shenoy was used.\cite{14,15} To attain correct vertical depth, a small wax-aluminum spacer was incorporated at the stage of trial closure, which was later replaced with tag and filled with PMMA before final closure. This could be a simple and more accurate technique for placing any denture identification material of choice. Although, the inability of RFID to withstand extreme temperatures had been mentioned in literature.\cite{4} However, Thomas et al. observed that dentures, if present in the mouth at the time of incineration are well protected from direct fire by the surround soft tissue.\cite{4,16} Furthermore, it has been reported that under such conditions, one-half to one-third of dentures will survive.\cite{4,17} Hence, NFC tags can be expected to survive incineration in an unfortunate situation as long as they are located in the oral cavity.
NFC stickers are passive tags that are powered externally by NFC reader modules. These modules were first introduced as shells for cell phones by Nokia in 2004, These specifically designed covers would clip over Nokia 5140 devices to read and write NFC tags.\cite{18} Currently, there are >500 commercially available smart devices that support reading/writing of NFC tags worldwide.
Apart from simply storing information, these tags can be programmed to initiate certain tasks on smart devices that include sending text messages and sharing GPS coordinates. This feature can help locate lost dentures, when scanned these tags can initiate location sharing via text message to any registered number. Once the details of reader are shared to registered number, patient or clinician can easily contact the reader device and locate lost denture.
Alternatively, patients home location and other relevant details can be stored on tags and once found, dentures can be safely returned to patient. Intelligence and ease of connection (through smartphone, which is commonly available) play a major role in making this possible.
Almost all denture labeling systems have some drawback. While many including limited amount of storage, are solved by RFID tags; The price and availability of RFID reader have always been an issue.\cite{8,19} Apart from managing this, these NFC stickers allow complete control over information, i.e., information can be added, removed, amended, or even locked by reader device. NFC stickers are extremely thin, flexible, and resistant to heat at denture curing temperatures, making them a potential material to be used in denture labeling.
**CONCLUSION**
Within the limitations of this study, it can be concluded that NFC stickers have a better potential to be an ideal material for denture labeling than currently available methods. NFC stickers can overcome disadvantages of RFID system including cost factors, difficulty in rewriting/adding information, and requirement of additional equipment.\cite{8,11}
Further studies are required to evaluate the efficacy of these stickers under *in-vivo* conditions with a significant clinical period of use.
Studies are also required to check the effect of normal denture cleaning procedures on these stickers.
**Financial support and sponsorship**
Nil.
**Conflicts of interest**
There are no conflicts of interest.
**REFERENCES**
1. Avon SL. Forensic odontology: The roles and responsibilities of the dentist. J Can Dent Assoc 2004;70:453-8.
2. Luthra R, Arora S, Meshram S. Denture marking for forensic identification using memory card: An innovative technique. J Indian Prosthodont Soc 2012;12:231-5.
3. Reid R. On application of dental science in the direction of crime. Br Dent J 1884;5:556.
4. Richmond R, Pretty IA. A range of postmortem assault experiments conducted on a variety of denture labels used for the purpose of identification of edentulous individuals. J Forensic Sci 2009;54:411-4.
5. Kareker N, Aras M, Chitre V. A review on denture marking systems: A mark in forensic dentistry. J Indian Prosthodont Soc 2014;14:4-13.
6. Mohan J, Kumar CD, Simon P. “Denture Marking” as an aid to forensic identification. J Indian Prosthodont Soc 2012;12:131-6.
7. Madrid C, Korsvold T, Rochar A, Abare M. Radio frequency identification (RFID) of dentures in long-term care facilities. J Prosthet Dent 2012;107:199-107.
8. Millet C, Jeannin C. Incorporation of microchips to facilitate denture identification by radio frequency tagging. J Prosthet Dent 2004;92:588-90.
9. Bali SK, Naqash TA, Abdullah S, Mir S, Nazir S, Yaqooh A. Denture identification methods: A review. Int J Health Sci Res 2013;3:100-3.
10. Rathee M, Yadav K. Denture identification methods: A review. J Med Dent Sci 2014;13:58-61.
11. Richmond R, Pretty IA. The use of radio-frequency identification tags for labeling dentures-scanning properties. J Forensic Sci 2009;54:664-54.
12. Cao Z, Chen P, Ma Z, Li S, Gao X, Wu RX, et al. Near-field communication sensors. Sensors (Basel) 2019;19:3947. Available from: https://www.mdpi.com/1424-8220/19/18/3947/htm. [Last accessed on 2020 Mar 27].
13. Gautam J, Kumar Y, Jhamb S. Current near field identification (NFC) trends in medical sector. Int J Eng Res Tech 2013;2:1948-53.
14. Reeson MG. A simple and inexpensive inclusion technique for denture identification. J Prosthet Dent 2001;86:441-2.
15. Venkat Nag PR, Shenoy KK. Dentures in forensic identification: A simple and innovative technique. J Indian Prosthodont Soc 2006;6:75-7.
16. Thomas CJ, Mori T, Miyakawa O, Chung HG. In search of a suitable denture marker. J Forensic Odontostomatol 1995;13:9-13.
17. Olsson T, Thureson P, Borrman H. Denture marking. A study of temperature resistance of different metal bands for ID-marking. J Forensic Odontostomatol 1993;11:37-44.
18. “Nokia’s NFC Phone History”. Microsoft Devices Blog; April 11, 2012. Available from: http://blogs.windows.com/devices/2012/04/11/nokias-nfc-phone-history. [Last accessed on 2020 Mar 27].
19. Charles DP, Nandini VV, Rengasamy S, Kumar MD, Rajendran A. A study on the incorporation of radiofrequency identification strips in implant and tooth supported over dentures for treatment information and denture identification. J NTR Univ Health Sci 2017;6:103-6. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2819,
1
],
[
2819,
6582,
2
],
[
6582,
9906,
3
],
[
9906,
11266,
4
],
[
11266,
15480,
5
],
[
15480,
17789,
6
]
]
} |
e3b781df389e7a6ffc61f8ba561fdeedb520a2e0 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 11,
"total-fallback-pages": 0,
"total-input-tokens": 38008,
"total-output-tokens": 11833,
"fieldofstudy": [
"Physics"
]
} | Coupled KIPP-EDGE2D modelling of parallel transport in the SOL and divertor of inter-ELM JET high radiative H-mode plasma
A V Chankin1,∗, G Corrigan2, D P Coster1 and JET Contributors3,4
1 Max Planck Institut für Plasmaphysik, Garching bei München, Boltzmannstr. 2, 85748, Germany
2 CCFE, Culham Science Centre, Abingdon OX13 3DB, United Kingdom
3 EUROfusion Consortium, JET, Culham Science Centre, Abingdon OX14 3DB, United Kingdom
E-mail: [email protected]
Received 10 March 2022, revised 12 May 2022
Accepted for publication 6 July 2022
Published 20 July 2022
Abstract
The Kinetic Code for Plasma Periphery (KIPP) models parallel (along magnetic field lines) propagation of charged particles in the scrape-off layer (SOL) and divertor of tokamaks. An iterative coupling between KIPP and a 2D edge fluid code EDGE2D, which in turn is coupled to the Monte-Carlo solver EIRENE for neutrals, was used to achieve a converged KIPP-EDGE2D-EIRENE solution. The original EDGE2D-EIRENE solution simulated SOL and divertor of JET high radiative inter-edge localized mode H-mode plasma conditions with strong nitrogen injection, leading to partial detachment at divertor targets. This work is a continuation of earlier studies of modelling kinetic electrons (Chankin et al 2018 Plasma Phys. Control. Fusion 60 115011) and ions (Chankin et al 2020 Plasma Phys. Control. Fusion 62 105022) with KIPP. For numerical reasons caused by large cell-to-cell plasma parameter variations near entrances to divertors, multipliers for parallel electron and ion conductive power fluxes (KIPP/EDGE2D ratios) which are passed onto EDGE2D, could only be used in the main SOL, outside divertors. There, the heat flux limiting effect led to an increase in maximum plasma temperatures in the main SOL and a decrease in power fluxes to divertor targets. Results of the coupling studies are consistent with earlier studies, suggesting that under investigated JET plasma conditions kinetic effects of charged particle parallel propagation do not drastically change target power deposition at divertor targets calculated by EDGE2D-EIRENE along.
Keywords: coupled, KIPP-EDGE2D, modellings, parallel, transport, SOL
(Some figures may appear in colour only in the online journal)
4 See the author list of ‘Overview of the JET preparation for Deuterium-Tritium Operation’, by Joffrin et al 2019 Nucl. Fusion 59 112021.
∗ Author to whom any correspondence should be addressed.
1. Introduction
The Kinetic Code for Plasma Periphery (KIPP) is a continuum Vlasov–Fokker–Planck code for parallel plasma transport (along magnetic field lines) in the scrape-off layer (SOL) and divertor. The main equations, including the normalization of parameters, are described in [1]. The code combines an implicit 2nd order scheme for a full non-linear Coulomb collision operator with an explicit 2nd order scheme for the parallel free-streaming. Results of the code benchmarking can be found in [2] and references therein. In the present paper the code was run in the 1D2V mode, with one spatial coordinate (along magnetic field lines) and two velocity variables: parallel and gyro-averaged perpendicular velocities.
The present paper is a continuation of two earlier studies on the modelling kinetic electrons [3] and ions [4] with KIPP. In both studies the EDGE2D-EIRENE solution simulating SOL and divertor of JET high radiative H-mode inter-edge localized mode (ELM) plasma conditions with 8 MW of input power into the computational grid and strong nitrogen (N₂) injection, leading to the partial detachment at divertor targets [5], was used as a starting point for KIPP runs. Distribution functions (f_e and f_i), analysed in [3,4], reveal that non-Maxwellian features range from high energy tails in the main SOL to bump-on-tail features owing to strongly non-local transport.
The Kinetic Code for Plasma Periphery (KIPP) is a continuum Vlasov–Fokker–Planck code for parallel plasma transport (along magnetic field lines) in the scrape-off layer (SOL) and divertor. The main equations, including the normalization of parameters, are described in [1]. The code combines an implicit 2nd order scheme for a full non-linear Coulomb collision operator with an explicit 2nd order scheme for the parallel free-streaming. Results of the code benchmarking can be found in [2] and references therein. In the present paper the code was run in the 1D2V mode, with one spatial coordinate (along magnetic field lines) and two velocity variables: parallel and gyro-averaged perpendicular velocities.
The present paper is a continuation of two earlier studies on the modelling kinetic electrons [3] and ions [4] with KIPP. In both studies the EDGE2D-EIRENE solution simulating SOL and divertor of JET high radiative H-mode inter-edge localized mode (ELM) plasma conditions with 8 MW of input power into the computational grid and strong nitrogen (N₂) injection, leading to the partial detachment at divertor targets [5], was used as a starting point for KIPP runs. Distribution functions (f_e and f_i), analysed in [3,4], reveal that non-Maxwellian features range from high energy tails in the main SOL to bump-on-tail features owing to strongly non-local transport. The latter are caused by very high Maxwelization rates for the bulk of charged particles under high density and low temperature conditions. Here only macroscopic plasma parameters obtained from EDGE2D-EIRENE solutions and extracted from KIPP runs are presented. By ‘plasma temperature’ in KIPP runs one understands 2/3’s of energy content ⟨v||e,i⟩^2 (with … denoting averaging over the distribution function) divided by density n_e,i in the reference frame moving with the plasma species at velocity ⟨v||e,i⟩.
Here the aim was to apply an iterative coupling scheme successfully tested earlier (KIPP-scrape-off layer plasma simulation (SOLPS) coupling, see [6]) to JET radiative divertor conditions. In [6] only ~5 iterative steps, with KIPP supplying SOLPS with kinetic transport coefficients and SOLPS returning to KIPP plasma parameter profiles maintained by sources, were sufficient to reach a steady state coupled KIPP-SOLPS solution. In the present work, due to numerical problems caused ultimately by very large cell-to-cell parameter variations near entrances to, and inside divertors (see details in section 3), applying such an iterative coupling scheme in divertor regions was impossible. At the same time, the scheme worked well in the main SOL, outside of divertors, where conductive electron and ion power fluxes are known to be lower than those calculated by fluid codes (‘heat flux limiting’).
In this paper, the setup of EDGE2D-EIRENE cases and the KIPP-EDGE2D-EIRENE (referred to as KIPP_EDGE2D) iterative coupling algorithm is described in section 2. Challenges to the implementation of the iterative KIPP-EDGE2D coupling scheme in divertor regions are described in section 3. Parallel power flux and temperature profiles are presented in section 4. Power balance in EDGE2D solutions corresponding to progressing KIPP-EDGE2D iterations is considered in section 5. The results of the work are summarized in section 6.
2. Setup of EDGE2D-EIRENE cases and KIPP-EDGE2D iterative coupling
Figure 1 shows an expanded view of the EDGE2D grid in the divertor region, indicating numbered cells: only odd numbers out of total 16 cells in the radial direction are indicated. These cells belong to ‘poloidal rings’ in the SOL, labelled s01 to s16, according to EDGE2D nomenclature. Arrows indicate the direction of counting parallel distances, from the inner to outer target. Note that such a counting is opposite to that adopted in EDGE2D (from the outer to inner target). The KIPP grid is based on the EDGE2D grid. However, for the sake of obtaining smoother profiles in KIPP solutions, each EDGE2D cell is divided into two in the poloidal/parallel direction, with the corresponding interpolation for plasma parameters onto the new, finer grid. The number of cells in KIPP is therefore doubles that of EDGE2D. The reader is referred to [3,4] for details of KIPP kinetic calculations along magnetic field lines.
The latest EDGE2D version allows the introduction of 2D arrays specifying KIPP/EDGE2D multipliers for parallel transport coefficients for electrons and ions, different in each cell. As pointed out above, in this work the multipliers were applied only to EDGE2D transport coefficients for cells in the main SOL. The transport coefficients affected by the multipliers were heat conductivities for electron and main ion (deuterium) parallel conductive power fluxes. As explained in [4], impurities (seven nitrogen and four beryllium species) were not treated kinetically, their distribution functions were assumed to be drifting Maxwellian. They were accounted for in the calculation of Rosenbluth potentials, which in turn were used to calculate transport coefficients is velocity space for electrons and main ions. The multipliers were calculated by dividing conductive power fluxes obtained in KIPP runs by those obtained in preceding EDGE2D-EIRENE runs.
Near stagnation points in the main SOL, where electron and ion temperatures, T_e and T_i, reached maxima, the multipliers could have negative numbers for some cells. This can be explained by differences in calculations of power fluxes in EDGE2D and KIPP. In EDGE2D analytical formulas for electron and main ion conductive power flux coefficients χ_e and χ_i, where used, yielding conductive power fluxes in the direction opposite to parallel T_e and T_i gradients. In KIPP due to non-local effects of the power transport, T_e,maxima did not necessarily coincide with locations of zero conductive power fluxes. Therefore, in some cells the multipliers had negative values. It was, however, found in EDGE2D runs that negative χ_e and χ_i values quickly lead to instabilities and failure of cases. For this reason negative multipliers were not applied to such cells, that is, they were set to 1. Away from stagnation points, where strong parallel T_e and T_i gradients develop, the calculated multipliers were always positive and therefore were fully applied. The consequence of effectively not applying the multipliers to some cells near stagnation points can be seen
Figure 1. Expanded view of the EDGE2D grid in the divertor region, showing numbered cells (only odd numbers) and the direction of counting distances. The divertor entrance is indicated by the bold line. See text for details.
Figure 2. OMP profiles for 0th and 5th EDGE2D-EIRENE iterations cases. See text for details. Vertical dashed line indicates the separatrix position.
The first EDGE2D case, with all multipliers set to 1, served as the 0th iteration EDGE2D case, which is essentially the original case in [5], but continued under the newer EDGE2D and EIRENE versions. Based on this, the KIPP run generates KIPP/EDGE2D multipliers for the next, 1st iteration EDGE2D run, and so on. As in [6], only five KIPP-EDGE2D iterations were sufficient to reach converged solutions.
Figure 2 shows radial profiles of \( T_e, T_i \) and electron density \( n_e \) across cells at the outer midplane (OMP) for the 0th iteration EDGE2D-EIRENE case (solid lines with points) and for the 5th iteration EDGE2D-EIRENE case (solid lines without points). Almost no difference between profiles of the two iterations can be seen in the figure, except for the 5th iteration \( T_i \) profiles having higher values in the outer core and in the SOL. A significant difference between \( T_i \) profiles belonging to different iterations, compared to a much smaller difference between \( T_e \) profiles, is attributed to a much lower ion than electron dimensionless collisionality in the SOL due to much higher upstream \( T_i \) (plots of the dimensionless collisionalities can be found in figure 3 of [4]).
Figure 3 shows parallel profiles of \( T_i \), main ion density \( n_i \), and ion conductive power flux \( q_{i\text{cond}} \) (which is \( =0 \) at targets in EDGE2D), for poloidal ring s01 just outside of the separatrix, for various EDGE2D-EIRENE iteration numbers. Heat flux limits push maximum upstream \( T_i \) values higher by factor 1.20, from 164.3 eV for the 0th iteration to 197.4 eV for the 5th iteration, in response to falling \( \chi_i \). In the zones of highest \( q_{i\text{cond}} \), multipliers used for \( \chi_i \) values in EDGE2D were \( \approx 0.22 \) and \( \approx 0.13 \) at high field side (closer to the inner divertor) and at the low field side (closer to the outer divertor), respectively, in the 5th iteration case. Parallel ion conductive power fluxes to divertors are lower in the 5th iteration case, while \( n_i \) at entrances to divertors are higher. Power balance in the SOL including target powers and volume radiation will be discussed in section 5.
For electron parameters, parallel profiles look qualitatively similar to the ions’, but owing to lower dimensionless electron upstream collisionality, \( T_e \) and \( q_{e\text{cond}} \) variations among different iterations are smaller. In particular, maximum \( T_e \) values rise only by factor 1.10, from 90.44 to 99.37 eV. In the zones of highest electron conductive power fluxes multipliers used for \( \chi_e \) values in EDGE2D were \( \approx 0.60 \) and \( \approx 0.45 \) at high and low field sides, respectively, in the 5th iteration case. These profiles are not shown here.
The same profiles as shown in figure 3 for ions, but at the poloidal ring s11, are shown in figure 4. This ring corresponds to a position inside the SOL where the maximum, or close to maximum, target power loads are obtained, as will be shown below in this section. In difference to the ring s01, maximum $T_i$ gradients are formed further away from divertors in the main SOL. Maximum upstream $T_i$ values rise by factor 1.36, from 96.0 to 130.8 eV, from 0th to 5th iterations in response to falling $\chi_i$ caused by heat flux limiting. In the zones of highest $q_{\text{cond}}^i$, multipliers used for $\chi_i$ values in EDGE2D were $\approx 0.26$ and $\approx 0.10$ at the high and low field sides, respectively, in the 5th iteration case. Similar to the ring s01, $q_{\text{cond}}^i$ to divertors are lower in the 5th iteration case, while $n_i$ in divertors are higher. Stronger upstream $T_i$ rise from the 0th to 5th iteration cases than at ring s01: despite lower upstream $T_i$, the effect of a much lower plasma density at ring s11 compared to ring s01 results in lower dimensionless collisionality, as can be seen from figure 3 of [4] (note that ring s01 in this reference is denoted as position $i = 6$). At the same time, electron dimensionless collisionality, unlike ion’s, is higher at ring s11 compared to ring s01. Correspondingly, electron kinetic effects at this ring are weaker than at ring s01. Such a disparity between ion and electron profiles can be explained by electron dimensionless collisionality weakly rising from the ring s01 to ring s11, while for ions it is sharply falling. This is related to flatter $T_i$ than $T_e$ profile across the SOL. Electron profiles, similar to those plotted in figure 4 for ions, are not shown here.
Qualitatively similar effects of kinetics on temperature profiles as those shown in figures 3 and 4, with upstream temperatures rising and downstream falling, were found in earlier kinetic calculations, for example in the particle in cell (PIC) code modelling, when comparing them to fluid code calculations, see figure 6 in [7].
Figure 5 shows $T_e$, $n_e$, and total, ion plus electron, conductive plus convective, parallel power flux profiles to divertor targets for EDGE2D-EIRENE iterations 0 and 5. The effect of the heat flux limiting upstream, partly compensated by the rise in upstream temperatures, has a net effect of the reduction of the total target power flux. The reduction is achieved mostly by the target $T_e$ reduction. The input power into the EDGE2D grid is the same for all iterations, hence, a drop in the target power must be compensated by the rise of volumetric power losses. The detailed analysis of the power balance in these EDGE2D-EIRENE cases will be discussed in section 5.
3. Challenges to the iterative KIPP-EDGE2D coupling
Success in testing the algorithm of the iterative KIPP-SOLPS coupling in [6] for kinetic electrons can be attributed to relatively smooth profiles of plasma parameters along the field line (a 1D SOLPS version was used in [6]), with not very large $T_e$ drops at targets and relatively small cell-to-cell variations of plasma parameters in this reference. These are conditions where KIPP, whose parallel free-streaming scheme is based on the high resolution 2nd order explicit scheme with monotonic central-difference flux limiter (‘MC limiter’), can give reliable results. The scheme uses reconstruction-evolution-averaging (REA) finite volume algorithm described in [8]. In edge 2D fluid codes, at the same time, the situation is often quite different, with significant cell-to-cell parameter variations. This is also the case with EDGE2D-EIRENE solutions analysed here, with plasma parameters close to entrances to divertors exhibiting large cell-to-cell variations. The ‘evolution’ part of the REA algorithm describes advection of a piece wise interpolated distribution function $f$. The slope of segments inside of a velocity cell is equated to the spatial derivative of $f$ calculated
inner divertor, the power flux profile is non-monotonic, with its absolute value increasing from the cell face in the main SOL to the adjacent cell face at the entrance to the divertor. The later feature is impossible to justify physically, and it demonstrates that the EDGE2D solver struggles to deliver correct profiles near divertor entrances.
Strongly non-rectangular cells, in particular, EDGE2D grid cells around the X-point (see figure 1), may have contributed to large $T_e$, $n_e$ and total power flux variation seen in figure 6. They also present an additional numerical problem for KIPP whose equations employ the philosophy of a flux tube. When reading EDGE2D-EIRENE output data into KIPP, it is implicitly assumed that an infinitely narrow flux tube passes through centres of EDGE2D cells. In reality, EDGE2D solves equations in flux coordinates, so their reconstruction in the Cartesian coordinate system leads to inaccuracies in the mapping, resulting in wiggles in the profiles. The mapping accuracy depends on the local change of the grid size which is the largest near the X-point.
Large cell-to-cell plasma parameter variations are, however, not limited only to the ring s01, despite strongly shaped non-rectangular cells are only present on this ring. On ring s02, the steep $T_e$ drop starts from the 1st cell already in the outer divertor, where $T_e = 33.1$ eV, and following cells (the first of which is indicated in figure 1), with $T_e$ for the next three cells being 22.40, 6.35 and 3.13 eV. For the next ring, s03, the steepest $T_e$ drop occurs between the 6th and 7th (indicated in figure 1) cells counting from the cell just before the entrance to the outer divertor on the main SOL side, from 9.46 to 4.70 eV. These features are caused by sharp ionization fronts taking place at different locations in the divertor at different rings.
Discussion about challenges facing KIPP cases under conditions of strong cell-to-cell plasma parameter variations will be continued in the next section.
4. Parallel power flux and temperature profiles along field lines
In this section parallel profiles of plasma temperature, density and parallel power fluxes for the two selected poloidal rings, s01 and s11, are presented. These are the same rings as were chosen for the analysis in the two earlier papers [3, 4], in which, however, they were labelled as slice numbers $i = 1$ and 6, with slice numbers $i = 1–6$ representing only a fraction of the total 16 poloidal rings covering the EDGE2D grid in the SOL and divertor.
All profiles in this section are plotted along the spatial grid used by KIPP, which, as was pointed out above, for numerical reasons of smoothness of KIPP solutions, has evolved out of the EDGE2D grid by dividing each EDGE2D cell into two equal size cells and interpolating parameters onto the new, finer grid. The final EDGE2D iteration 5 case is used here for plotting conductive power fluxes extracted from EDGE2D, as well as for convective power fluxes, which depend on profiles of plasma temperatures, densities and parallel electron and main ion velocities obtained in EDGE2D cases. Conductive power fluxes from KIPP also refer to the last, 5th iteration.
Figure 6. Profiles of $T_e$, $n_e$, and total parallel power flux (ion plus electron, conductive plus convective) on ring s01 for the EDGE2D-EIRENE 0th iteration case. Vertical dashed lines indicate entrances to divertors.
KIPP run. Since the outer target receives higher power flux than the inner target, only zoomed up profiles near this target will be presented, as in [3, 4].
4.1. Profiles along ring s01
Figure 7 shows electron temperature, \( T_e \), and parallel power flux profiles from the inner to outer target: electron conductive power flux \( q_{e,cond,EDGE2D}^{\text{conv}} \) from the EDGE2D-EIRENE solution, electron convective power flux \( q_{e,conv}^{\text{cond, KIPP}} \) (the same in KIPP and in EDGE2D) and electron conductive power flux \( q_{e,cond, KIPP}^{\text{conv}} \) from KIPP. A good match between \( q_{e,cond, KIPP}^{\text{conv}} \) and \( q_{e,cond, EDGE2D}^{\text{cond}} \) in the main SOL, as a result of the iterative KIPP-EDGE2D coupling, can be seen. The only exception is around the stagnation point at maximum \( T_e \) values where, due to different signs of EDGE2D and KIPP conductive power fluxes, KIPP/EDGE2D multipliers were not applied (they were specified as unities in EDGE2D) and the two conductive power fluxes strongly diverge, see section 2 for explanations. Note that, since the KIPP/EDGE2D multipliers were not applied to EDGE2D cells in the divertor, convergence between KIPP and EDGE2D cases was not reached in this region, and KIPP and EDGE2D power fluxes may differ. KIPP results in the divertor should be considered as representing kinetic solutions for given background (thermal) plasma parameter profiles.
Large spikes of \( q_{e,cond, KIPP}^{\text{conv}} \) at divertor entrances should be considered as artefacts of the numerical scheme for the free-streaming used in KIPP, as was discussed in section 3. The scheme is based on the linear interpolation of cell centre electron and ion distribution functions, \( f_e \) and \( f_i \), onto cell faces, at which power fluxes are calculated. With large \( T_e \) and \( q_{e,cond,EDGE2D}^{\text{conv}} \) cell-to-cell variations, such an interpolation becomes imprecise. Perhaps, more physically adequate would have been an interpolation using exponents, which are expected to yield much smaller values of \( q_{e,cond, KIPP}^{\text{conv}} \) under such conditions. Apart from \( q_{e,cond, KIPP}^{\text{conv}} \) spikes, one can also see spikes in \( q_{e,cond, EDGE2D}^{\text{conv}} \), albeit to a much smaller extent. Such spikes are seen in all EDGE2D-EIRENE solutions except for the original, 0th iteration, case. For calculations of fluxes through cell faces EDGE2D uses extrapolations of transport coefficients calculated at cell centres, onto cell faces, which should further reduce accuracy of fluxes’ calculations under conditions of very large cell-to-cell parameter variations.
Note that \( T_e \) and power flux oscillations in figure 7 are smoothed by the procedure of doubling the number of EDGE2D cells to obtain the KIPP grid, with a consequent interpolation of plasma parameters, see section 2. This explains, in particular, why \( q_{e,cond, EDGE2D}^{\text{conv}} \) spikes near divertor entrances cover two cell faces instead of one.
Figure 8 shows the same quantities as shown in figure 7, but at distances near the outer divertor target, to provide good spatial resolution. \( q_{e,cond, EDGE2D}^{\text{conv}} \) values are extremely low in the divertor, since they scale with \( T_e^{5/2} \) \( \nabla T_e \), with \( T_e \) being very low near the target. At the same time, \( q_{e,cond, KIPP}^{\text{conv}} \) is much higher, being only a factor 2 lower than \( q_{e,conv}^{\text{cond, EDGE2D}} \). The relatively flat \( q_{e,cond, KIPP}^{\text{conv}} \) profile when approaching the divertor is explained by this power flux being carried mostly by superthermal electrons originating from regions far upstream in the main SOL [3]. Since these electrons are much less collisional than thermal electrons, the heat flux they carry is strongly non-local and not being much affected by a steep \( T_e \) drop right at the target. Lower \( q_{e,cond, KIPP}^{\text{conv}} \) than \( q_{e,conv}^{\text{cond, EDGE2D}} \) at the target implies that kinetic effects cannot strongly increase electron power deposition at the target calculated by EDGE2D-EIRENE.
Figure 9 shows ion temperature \( T_i \) and parallel power flux profiles from the inner to outer target: ion conductive power flux \( q_{i,cond,EDGE2D}^{\text{cond}} \) from the EDGE2D-EIRENE output, ion convective power flux for main ions \( q_{i,conv}^{\text{cond, KIPP}} \) (the same in KIPP and EDGE2D) and ion conductive power flux \( q_{i,cond, KIPP}^{\text{cond}} \) from KIPP. As in figure 8 for electrons, a good match between \( q_{i,cond, KIPP}^{\text{cond}} \) and \( q_{i,cond, EDGE2D}^{\text{cond}} \) in the main SOL, except for the
Figure 9. Profiles of ion temperature, parallel ion conductive power flux from EDGE2D-EIRENE and KIPP runs and parallel ion convective power flux along ring s01. See text for details.
Figure 10. Profiles of the same quantities as shown in figure 9, zoomed up near the outer target (ring s01).
region around the stagnation point at maximum $T_i$ values, can be seen, for the same reason as explained for electron profiles above. A sharp increase in $q_{i,\text{cond,KIPP}}^{\text{conv}}$ and a simultaneous sharp drop in $q_{i,\text{cond,KIPP}}^{\text{cond}}$ at the entrance to the outer divertor can be explained by the sharp increase in the main ion velocity towards the divertor entrance, as follows from the EDGE2D-EIRENE solution.
Figure 10 shows the same quantities as shown in figure 8, but at distances near the outer divertor target. Qualitatively, they show the same features as can be seen in figure 9 for electrons. In particular, the relatively flat $q_{i,\text{cond,KIPP}}^{\text{cond}}$ profile approaching the divertor is explained by this power flux being carried mostly by super-thermal ions originating from the main SOL [4]. As for electrons, target $q_{i,\text{cond,KIPP}}^{\text{cond}}$ values are somewhat lower than $q_{e,\text{cond,KIPP}}^{\text{cond}}$. Note that $q_{i,\text{cond,KIPP}}^{\text{cond}}$ values are comparable to $q_{e,\text{cond,KIPP}}^{\text{cond}}$ (see figure 8) in the divertor. This is despite the factor $\sim \sqrt{m_e/m_i}$ of reduction of classical collisional conductive ion power fluxes compared to electron power fluxes caused by lower ion velocities (for equal ion and electron temperatures). Apparently, much lower ion dimensionless collisionality caused by much higher $T_i$ than $T_e$ upstream ($T_{i,\text{max}} = 160.3$ eV, $T_{e,\text{max}} = 88.8$ eV) leads to a very significant increase in the ion parallel power flux in the divertor due to much less collisional (compared to electrons) non-local transport of super-thermal ions.
Overall, results of this sub-section show that for the given JET experimental conditions kinetic effects of the parallel charged particle transport do not critically influence target power load along the ring s01 with large temperature variations and partially detached plasma near the targets.
4.2. Profiles along ring s11
Figure 11 shows parallel profiles of the same quantities as shown in figure 7, but for the poloidal ring s11. Compared to ring s01, the plasma is well attached to divertor targets, and the $T_e$ variation along field lines is quite moderate, from the maximum of 36.5 eV to 5.82 and 11.7 eV at inner and outer targets, respectively. As for the ring s01, good agreement between $q_{e,\text{cond,KIPP}}^{\text{cond}}$ and $q_{e,\text{cond,EDGE2D}}^{\text{cond}}$ can be seen in the main SOL, except for the region surrounding the stagnation point with maximum $T_e$. The convective power flux $q_{e,\text{conv}}^{\text{conv}}$ plays a secondary role in the total electron power flux, which is almost always the case for electrons, except for very cold (low $T_e$) and dense (high $n_e$) regions in the divertor. The negative value of $q_{e,\text{conv}}^{\text{conv}}$ almost along the entire ring reflects the plasma (ion) flow from the outer to inner target in the EDGE2D-EIRENE solution.
Figure 12 shows zoomed up parallel profiles of the same quantities as shown in figure 11, for the region near the outer target. A relatively modest $T_e$ variation along field lines,
power profiles in the main SOL presented above, good agreement between $q_{\text{cond,KIPP}}^i$ and $q_{\text{cond,EDGE2D}}^i$ in the main SOL can be seen, except for the region around the stagnation point with the highest $T_i$. Ion temperature along field lines is substantially higher than electron, varying between $T_{i,\text{max}} = 130.8$ eV and 19.0 and 8.54 eV near inner and outer targets, respectively. A strong decoupling between $T_i$ and $T_e$ is caused by low dimensionless collisionalities of both species, including in the divertor region. An unusual situation with the substantially lower $T_i$ at the outer than at the inner target, following from the EDGE2D-EIRENE solution, must be caused by the reversal of $q_{i,\text{conv}}^i$ inside of the outer divertor, transferring thermal energy $3/2n_iT_i$ to kinetic energy $n_i m_i v_{\parallel i}^2/2$. Equipartition energy exchange between ions and electrons, on the other hand, cannot be responsible for lower $T_i$ at the outer target due to $T_e > T_i$ near the outer target, as can be seen from figures 12 and 14 (see below). Note that in the main SOL the convective power flux $q_{i,\text{conv}}^i$ plays a much larger role in the total ion power flux than for electrons, as expected from relatively low ion parallel velocities compared to electron velocities (factor $\sim \sqrt{m_e/m_i}$ for comparable $T_e$ and $T_i$).
Figure 14 shows zoomed up parallel profiles of the same quantities as shown in figure 13, for the region near the outer target. The dominant role of ion convection in the total parallel target ion power flux can be seen. The much higher $q_{i,\text{cond,KIPP}}^i$ compared to $q_{i,\text{cond,EDGE2D}}^i$ must be caused by a much lower ion dimensionless collisionality at this ring, leading to a large contribution of ion non-local kinetic effects to the conductive power flux. This is related both to a very high $T_{i,\text{max}} = 130.8$ eV (compared to $T_{e,\text{max}} = 36.5$ eV) and to a very low upstream dimensionless collisionality. According to the ion and electron upstream (at the OMP position) dimensional collisionality profiles, which can be found in figure 3 of [4], the ion dimensionless collisionality on ring s11 is lower than the electron dimensionless collisionality by factor $\approx 10$.
Despite very strong heat flux enhancement (a very large contribution of ion non-local kinetic transport effects leading
to a much higher parallel ion conductive power flux compared to that calculated in EDGE2D according to a strongly collisional fluid model) the total ion power flux to the outer target, with the inclusion of the convective power flux contribution, appears to be not too much affected by ion kinetic effects, as was the case with the ion target power flux for ring s01 and for electron power fluxes for both rings s01 and s11.
5. Power balance in KIPP-EDGE2D solutions
Contributions of electron and main ion conductive and convective parallel power fluxes at the outer target, with the exception of the ion conductive power flux from EDGE2D, \( q_{\text{cond,EDGE2D}} \), which is zero, for the 5th iteration of both EDGE2D-EIRENE and KIPP runs, are plotted in figure 15. This figure can be compared with figure 6 of [4], which shows some of the fluxes presented here for selected rings for what is here referred to as the 1st KIPP iteration (following the 0th EDGE2D-EIRENE iteration). It has to be pointed out, however, that in the legend of figure 6 of [4] a mistake was made: instead of ‘\( q_{\text{conv}} / 5 \)’ it should read ‘\( q_{\text{conv}} \).
Comparing contributions from individual power fluxes shown in figure 15, it is useful to consider three main distinct regions: near the strike point, near the maximum target power load, and in the outer SOL. Relative contributions of individual power fluxes for these three regions are considered below.
In the region near the strike point with partial detachment and very low target \( T_e \), which in figure 15 covers rings with almost negligible \( q_{\text{e,cond,EDGE2D}} \), dominant contributions to the target power load are electron and ion convective power fluxes, \( q_{\text{e,conv}} \) and \( q_{\text{i,conv}} \). At the same time, kinetic conductive power fluxes calculated by KIPP, \( q_{\text{e,cond,KIPP}} \) and \( q_{\text{i,cond,KIPP}} \), cannot be neglected in this region.
In the region of highest target power loads the largest power flux is kinetic conductive electron power flux \( q_{\text{e,cond,KIPP}} \). It exceeds the fluid power flux \( q_{\text{e,cond,EDGE2D}} \) by factor \( \approx 2 \) owing to the contribution from the non-local transport of super-thermal electrons. Indicating ‘heat flux enhancement’ due to the contribution from the non-local transport of super-thermal electrons. Note however, that \( q_{\text{e,cond,EDGE2D}} \) is lower than the sum of other power flux contributions.
In the outer SOL/divertor region the largest power flux comes from ion convection, \( q_{\text{i,conv}} \). The dominance of this term, and in particular, its access over \( q_{\text{e,conv}} \), is caused by much higher \( T_i \) than \( T_e \) in the whole SOL and divertor region owing to much flatter upstream \( T_i \) profiles. This region is also characterized by small \( T_{e,i} \) variations along field lines, leading in particular to fairly close values of electron conductive power fluxes calculated by KIPP, \( q_{\text{e,cond,KIPP}} \), and EDGE2D, \( q_{\text{e,cond,EDGE2D}} \).
In none of the above regions ion conductive power flux, even with inclusion of effects of non-local transport of super-thermal ions, \( q_{\text{i,cond,KIPP}} \), plays any significant role.
As was discussed in section 2, kinetic effects in the main SOL (leading to ‘heat flux limiting’) reduce the total target power flux, as was demonstrated by comparing total power fluxes extracted from 0th and 5th iterations of EDGE2D-EIRENE cases shown in figure 5, with the exception of power fluxes at the outer target on rings s12–s16 (the last five points in figure 5) connected to the outer SOL. At these outer rings small \( T_{e,i} \) variations along field lines and, consequently, small contributions of kinetic effects to power fluxes follow from KIPP. Lower total target power load, by factor \( \approx 1.4 \), in the 5th iteration EDGE2D-EIRENE case, 0.771 MW, compared to the 0th iteration case, 1.09 MW, is confirmed by the EDGE2D output. Lower power load in the 5th iteration EDGE2D-EIRENE case is compensated by higher volumetric power losses, mainly from higher electron power loss on radiation and higher ion power loss on charge exchange. These increased volumetric power losses must be caused by higher plasma density in zones of maximum radiation. Higher \( n_i \) in the 5th iteration EDGE2D-EIRENE case can be seen around the X-point for ring s01 (figure 3), and closer to the target for ring s11 (figure 4), with higher plasma densities in these regions in turn being caused by lower ion and electron temperatures.
In the iterative KIPP-EDGE2D-EIRENE modelling described here non-Maxwellian features of the electron distribution function in the calculation of rate constants for atomic physics processes contributing to particle and power sources were not taken into account, despite a significant impact of high energy tail electrons on the rates in the divertor was reported (see e.g. [7, 9–11]). The main trends in adding kinetin atomic rates to fluid code plasma solutions in high recycling plasmas are summarized in [12], where 1% population of high energy super-thermal electrons was artificially added to SOLPS (a 2D edge fluid code) modelling into detached divertor plasma. It was shown that the presence of high energy electrons in the low \( T_e \approx 1 \) eV thermal population, high density plasma caused an enhanced ionization rate; then, since the recombination rate was essentially unchanged, ions...
recombined. Thus, a new ‘volume recycling’ zone was established, with enhanced energy losses, and ultimately, less ions reached the target, assisting the detachment process.
In KIPP calculations presented here energies of superthermal electrons on field lines with detachment are extremely high, \( \sim \) few 100’s of eV, since they mostly originate from the regions of the main SOL with highest \( T_e \), with their energies being \( \sim 6T_e \), as was estimated in [3]. At the same time, the rate coefficients for atomic and molecular hydrogen ionization have a maximum at or below \( T_e \approx 100 \) eV (see e.g. [13], figure 1.25). The cross-section for nitrogen ionization also peaks at \( T_e \approx 100 \) eV ([14], figure 3). Hence, no particularly strong impact of ionization/attaching processes on super-thermal bump-on-tail electrons is expected. And in any case, such processes are expected to increase the ionization rate and detachment in the divertor. The results obtained in the present study, pointing to only a moderate increase in target power fluxes caused by kinetic effects, can therefore be regarded as conservative in the sense that the proper description of the atomic rates may only increase the volumetric power loss and the degree of detachment, thereby reducing the target power load.
6. Summary
Owing to large \( T_e \) and \( T_i \), variations along field lines close to the separatrix and partial detachment at divertor targets, the JET H-mode radiative divertor conditions analysed in this paper may to some extent be considered reactor relevant. Further away from the separatrix conditions change, from strongly attached, with high power flux conducted to the target, to low recycling conditions in the outer SOL, with much lower upstream \( T_{e,i} \) and relatively flat temperature profiles along field lines.
The main progress achieved in this work compared to earlier studies [3, 4] is in the iterative coupling between KIPP and EDGE2D, and with KIPP cases running for both ions and electrons simultaneously, resulting in the converged KIPP-EDGE2D-EIRENE solution. Despite the failure of the iterative coupling scheme between KIPP and EDGE2D in the divertor region owing to very high \( T_e \), \( T_i \) and \( n_e \) cell-to-cell variations in EDGE2D-EIRENE solutions, some conclusions, based on the successful performance of the iterative scheme in the main SOL, can be made. The results of this work, combined with those of earlier studies in [3, 4], for JET conditions analysed here can be summarized as follows:
- On field lines with large \( T_e \) and \( T_i \), variations in the main SOL, kinetic effects of non-local parallel transport of superthermal electrons and ions reduce conductive power flows, leading to ‘heat flux limiters’ with reduced parallel conductive power flux coefficients compared to fluid code solutions. This is a well-known result of kinetic calculations (see e.g. [3] and references therein). As a result, maximum upstream temperatures, \( T_{e,i,max} \), increase, but this does not restore original (following from fluid calculations) parallel power fluxes. This in turn leads to the reduction of power fluxes to the divertor, the reduction of \( T_{e,i} \), and the increase of plasma density and volumetric power losses due to plasma interactions with neutrals and impurities in the divertor.
- In the near SOL, on field lines just outside of the separatrix, with partial detachment near strike points, owing to very low target \( T_{e,i} \), dominant contributions to the outer target power flux come from electron and ion convection. High heat flux enhancement factors for conductive power fluxes caused by kinetic effects of parallel propagation of super-thermal electrons and ions do not make these fluxes large enough to compete with convective power fluxes, as classical collisional conductive power fluxes are almost negligible due to very low \( T_{e,i} \) in the divertor. The electron conductive power flux calculated by KIPP may, however, be close to the electron convective power flux, which is attributed to the power flux carried by a tiny minority of super-thermal electrons originating from locations in the main SOL with highest \( T_e \).
- In the middle of the SOL, on field lines with attached divertor conditions and with highest target power loads, the dominant contribution to the outer target power load comes from electron conduction, which, due to kinetic effects, is higher by factor \( \sim 2 \) compared to that following from EDGE2D-EIRENE, which, in turn, is close to convective power fluxes of both electrons and ions. The contribution from the ion conductive power flux, even despite its strong enhancement by kinetic effects, is insignificant.
- In the outer SOL the predominant contribution to the outer target power load is from the ion convective power flux, which is factor \( \sim 2 \) higher than the electron convective power flux owing to much higher \( T_i \) than \( T_e \). Conductive and convective electron power fluxes are close to each other. Ion conductive power flux is negligible.
A very important conclusion from results of this work, which is in line with earlier studies [3, 4], is that under inter-ELM H-mode JET radiative divertor conditions analysed, kinetic effects of parallel charged particle propagation do not significantly increase the total outer target power load near the strike point. The kinetic effects are unlikely to cause a power flux ‘burnthrough’ leading to a substantial increase in the target power load at locations where the fluid code (EDGE2D-EIRENE) predicts partial divertor detachment. On the contrary, the impact of a minority of super-thermal electrons on atomic rate coefficients can only increase the volumetric power loss in the divertor, leading to stronger detachment, as pointed out in section 4.
For field lines with attached plasma and a relatively high power flux to the divertor target (in the middle of the SOL), kinetic effects of parallel electron transport may raise the conductive electron power flux by factor \( \sim 2 \), which then becomes the dominant contribution to the total target power flux. But even there, the total target power flux is increased by only factor \( \sim 1.5 \) compared to the total target power flux predicted by EDGE2D-EIRENE calculations, when contributions
of convective electron and ion power fluxes are taken into account.
Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.
Acknowledgments
This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under Grant Agreement No. 633053. KIPP calculations were supported by the EUROfusion cycle 5 HPC project ‘KIPPSOL’ enabling calculations on Marconi high performance computer. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
ORCID IDs
A V Chankin https://orcid.org/0000-0002-7016-6829
D P Coster https://orcid.org/0000-0002-2470-9706
References
[1] Chankin A V, Coster D P and Meisl G 2012 Contrib. Plasma Phys. 52 500
[2] Chankin A V and Coster D P 2015 J. Nucl. Mater. 463 498
[3] Chankin A V, Corrigan G and Jaervinen A E (JET Contributors) 2018 Plasma Phys. Control. Fusion 60 115011
[4] Chankin A V, Corrigan G and Jaervinen A E (JET Contributors) 2020 Plasma Phys. Control. Fusion 62 105022
[5] Jaervinen A E et al 2016 Plasma Phys. Control. Fusion 58 045011
[6] Zhao M, Chankin A V and Coster D P 2019 Comput. Phys. Commun. 235 133
[7] Popova L, Tsakakaya D, Kuhn S, Nickolov T, Hristov S, Hristov V, Kamberov G, Marichkova H, Tomova Z and Vasileva D 2004 Contrib. Plasma Phys. 44 252
[8] LeVeque R J 2004 Finite-Volume Methods for Hyperbolic Problems (Cambridge: Cambridge University Press)
[9] Batishchev O V et al 1997 Phys. Plasmas 4 1672
[10] Allais F, Matte J P, Alouani-Bibi F, Kim C G, Stotler D P and Rognlien T D 2005 J. Nucl. Mater. 337–339 246
[11] Tsakakaya D 2017 Plasma Phys. Control. Fusion 59 114011
[12] Coster D P 2011 J. Nucl. Mater. 415 S545
[13] Stangeby P C 2000 The Boundary of Magnetic Fusion Devices (Bristol: IOP Publishing)
[14] Kim Y-K and Desclaux J-P 2002 Phys. Rev. A 66 012708 | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2452,
1
],
[
2452,
10266,
2
],
[
10266,
13442,
3
],
[
13442,
17457,
4
],
[
17457,
20891,
5
],
[
20891,
25610,
6
],
[
25610,
29105,
7
],
[
29105,
31537,
8
],
[
31537,
37063,
9
],
[
37063,
43449,
10
],
[
43449,
45420,
11
]
]
} |
818fbe7b7dadd14e47ddd70d330e1fb0be33f132 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 10,
"total-fallback-pages": 0,
"total-input-tokens": 24839,
"total-output-tokens": 8198,
"fieldofstudy": [
"Economics"
]
} | Implementation of the Far Eastern Hectare program as a tool to improve land management in the Khabarovsk Territory
A A Murasheva, V N Khlystun, V M Stolyarov, N A Ivanova and E M Chepurin
State University of Land Use Planning, 15, Kazakova Str., Moscow, 105064, Russia
E-mail: [email protected]
Abstract. By the end of the first decade of the 21st century, an extremely serious migration situation had developed in the Far Eastern region of the Russian Federation, which was characterized by the alarming rate of population outflow from this already sparsely populated region of the country. Between 1991 and 2010, according to various estimates, the population of the Far East decreased by 1.8 million people or by 22%. Of all the constituent entities of the Russian Federation that are part of the Far Eastern Federal District, not one is characterized by positive population growth rates. In this regard, the Government has developed a number of measures aimed at breaking the tense migration situation. The so-called “Far Eastern hectare” has become the main instrument for the implementation of the new migration and economic policies in this region. The article sets forth material related to the development of proposals to ensure the sustainable development of rural territories of the Far Eastern Federal District of the Russian Federation through the implementation of the Far Eastern Hectare program. The practical significance lies in the fact that the results of the study can be useful in identifying and forming land for the Far Eastern Hectare program.
1. Introduction
At present, with trends in the development of the Russian national economy, as well as global economic relations, it is especially important to resolve issues related to the efficient use of agricultural land by increasing the profitability of agricultural production and ensuring sustainable development of rural areas. One of the goals of this work is to develop proposals for ensuring the sustainable development of rural territories of the Far Eastern Federal District of the Russian Federation on the basis of increasing the profitability and efficiency of regional agricultural production. The development of proposals was carried out within the framework of the adopted State Program for the Development of Agriculture in the Far Eastern Federal District by implementing the “Far Eastern Hectare” program.
In the process, the agricultural sector of the Far Eastern rural territories was analyzed, including the state of agricultural land use, information support and the quality of information in generating data for the Far Eastern Hectare program. The research regions are the regions of the Far East, examples are considered on materials of the Khabarovsk Territory.
Previously, the study of the research object, rendered in this article’s title, were accessed by authors such as the ZI Sidorkina (2009), A.N. Demyanenko (2017), D.A. Izotov (2017), S.A. Lipsky (2017), I.N. Kustysheva (2018).
2. Materials and methods
When developing the proposals, the adopted incentive programs were analyzed, which are an important
lever of the state’s influence on the economy, since they allow comprehensively and systematically solving the problems of the country's economic and social policy in areas where other methods are ineffective or unacceptable. In this case, the balance method was used on materials obtained from publicly available sources (reports, statistical material). As a result of the application of these methods, the main problems of the implementation of the Far Eastern Hectare program in the Far Eastern Federal District were identified and suggestions were made to improve the effectiveness of its implementation.
3. A study of the implementation of the Far Eastern Hectare program in the Far Eastern Federal District
The agricultural industry of the Far East operates in difficult climatic and socio-economic conditions. The main reasons for this are the geographical location, climate features and remoteness from large industrial centers and agricultural areas. More than 80% of the region’s territory belongs to the Far North and equivalent areas [1].
The severe climatic conditions in the Far East and the aggressive economic environment created a situation threatening agriculture in the Far East.
Positive results cannot be achieved without comprehensive state support. At present, the Federal Law "On the Development of Agriculture" dated December 29, 2006 N 264-FL as amended on December 2018 is in force, which defines the main provisions and vectors of development of the state agricultural policy [2]. In this law, agricultural policy is interpreted as “an integral part of the state socio-economic policy aimed at the sustainable development of agriculture and rural territories”.
Federal Law dated 01.05.2016 N 119-FL “On the Peculiarities of Providing Citizens with State or Municipal Land Plots in the Territories of the Subjects of the Russian Federation that Are Part of the Far Eastern Federal District, and Amending Certain Legislative Acts of the Russian Federation” provided for a program supporting the settlement of the Far East and the development of local infrastructure, titled the "Far Eastern Hectare".
Initially, only local residents could receive land in their areas for development, but already on February 1, such permission was given to all citizens of the country. As of September 2019, more than 141 thousand people exercised their right, and about 68 thousand applicants have already received their allotment.
The total area planned to be distributed exceeds 130,000 hectares. The program will run until 2035. The most important conditions of this program are as follows:
- The maximum size of the development plot is 1 ha;
- When combining several citizens, not necessarily related by kinship, you can get an area of maximum 10 ha;
- The size of the allotment may be less than the established norm; the area, configuration and location of the site is determined by the applicant;
- Land distribution is done online on an interactive map on the official website (“To the Far East”).
- Allocation of the site is completely free.
In accordance with the provisions of the Far Eastern Hectare campaign, the following can claim rights to receive their land: Citizens of Russia; Foreigners participating in the program "Relocation of compatriots"; Associations consisting of several citizens of the Russian Federation or immigrants.
The program is designed for sustainable development of rural areas, that is: stable socio-economic development; increase in agricultural production; improving agricultural efficiency; achieving full employment of the rural population and improving their living standards; rational use of land.
In order to weaken negative phenomena as much as possible or more systematically control them, implementation of the program shall take into account the regional characteristics of the Far East, including its economic branch structure, features of the social sphere and others. Therefore, the study of trends, factors and conditions that determine the results of the agricultural sector in a particular region is of not only scientific, but also practical importance and economic entities will be able to more reasonably approach the improvement of business and increase the production of competitive products.
In this work, we set such a goal as conducting research on the implementation of the Far Eastern
Hectare program, identifying factors that have both positive and negative effects on the results of the program, justifying a system of measures and conditions for its sustainable development, which ultimately should lead to increasing incomes of the population and the region of the Far Eastern Federal District, solving economic and social problems in the Far East.
We believe that the effectiveness of program implementation correlates with indicators such as:
- tax rate;
- cadastral value, which depends on timely updating of land and appraisal information and differentiation of the cadastral value of land plots, taking into account their quality, location, and national economic significance;
- Providing relevant information on the state of land offered by the «Far Eastern Hectare» program, etc.
It should be noted that rural areas exist and work in difficult conditions - as already mentioned, adverse climatic and geographical factors have a significant impact on the results and quality indicators of activity. It is worth noting that agricultural lands of the Far East are characterized by rather low natural fertility, and the organizational scheme of agriculture is complicated by the remoteness of the supply centers of both production resources and finished agricultural products. An important aspect is also the state of the material and technical base of enterprises and the labor potential of the rural population [3].
Nevertheless, taking into account all of the above, it can be said that the State Program “Far Eastern Hectare” provided for all citizens of the Russian Federation new tools and technologies for obtaining land and effective ways of state support; as well as a number of regional programs that create conditions for suspending population outflow and attracting initiative people from all over the country to distant regions of a number of constituent entities of the Russian Federation with a low population density, which will create new industries and jobs in these territories, including for local residents.
In the early stages of the program, the constituent entities of the Russian Federation included in the Far Eastern Federal District decided on the land plots allocated to citizens participating in the project. The Far Eastern Federal District is the largest district of Russia, its area is 6,217 thousand km2 or 36.4% of the country's territory. In the region's land reserve, agricultural land occupies 1.1% of the territory, and arable land - only 0.4%.
Table 1. Comparative characteristics of the regions participating in the Far Eastern Hectare program
| Municipal District | The subject of the Russian Federation | Distance from the center of the subject, km | Population at the beginning of the project, people |
|--------------------|--------------------------------------|-------------------------------------------|-------------------------------------------------|
| Khankai district | Primorsky Krai | 204 | 22992 |
| Amur District | Khabarovsk region | 431 | 61338 |
| Oktyabrsky District| Jewish Autonomous Region | 215 | 10068 |
| Arkharin district | Amur region | 269 | 15496 |
| Namsky ulus | The Republic of Sakha (Yakutia) | 84 | 23887 |
| Olsky district | Magadan Region | 36 | 9992 |
| Ust-Bolsheretsky | Kamchatka Krai | 216 | 7944 |
| district | | | |
| Tymovsky district | Sakhalin region | 494 | 14956 |
| Anadyrsky district | Chukotka Autonomous Okrug | 0 | 8788 |
The main agricultural territories of the Far Eastern Federal District are Amur Region, Primorsky and Khabarovsk Territories, these territories are shown in color; they are commonly called the southern territories of the Far Eastern Federal District. In these regions, 4,244 thousand hectares of agricultural land are concentrated, or 78.7% of all farmland in the Far East.
As can be seen from the data in Table 1, in the Chukotka Autonomous Region, the Republic of Sakha (Yakutia) and the Magadan Region, land plots were allocated for the implementation of the project.
within a radius of less than 100 kilometers from the center of the region.
As of February 1, 2019 (two years from the beginning of the implementation of the Far Eastern Hectare program), more than 73 thousand citizens of the Russian Federation became participants in the program, and the area of the provided plots is about 47 thousand hectares. During the implementation of the program, about 17% of applications were received from residents of non-Far Eastern regions (Moscow and Moscow Region, St. Petersburg and the Leningrad Region, Sverdlovsk Region, Krasnodar Territory, Irkutsk Region and others).
In all other constituent entities of the Russian Federation, land was allocated at a great distance, which causes additional difficulties for project participants at all stages of its implementation, since all issues related to the provision of public services are resolved in the capital of the subject, and not in the center of the municipality [4].
Note that this situation arose in connection with the state program, according to which the plots are distributed far from settlements - no closer than 10 km from a city with a population of 50 thousand people and at least 20 km from a city with a population of 300 thousand people or more. Moreover, even in the most attractive part for resettlement in the Far Eastern Federal District - Amur Region - more than 500 settlements have no gas supply. In some villages there is no water supply, drinking water can only be obtained from a depth of 100 meters, and there are problems with the power supply. To a greater extent, there are problems with infrastructure and not with obtaining land.
For example, in the Amur Region, not only the Far Eastern hectare program is being implemented, but there is also the possibility of obtaining land in accordance with the current law No. 422-OZ “On the grounds (cases) for the free provision and the maximum size of land plots to be granted to citizens in the territory of the Amur Region”.
It should be noted that in accordance with the legislative acts, during the first year after the registration of the site provided under the Far Eastern Hectare program, the user must determine the direction of its use. At the same time, after 3 years the user is obliged to report on the use of the site. In accordance with the norm of Law No. 119-FL, a corresponding Declaration will be submitted as a report, in which, in addition to the general sections, it is necessary to describe the actions and measures taken by the citizen for the intended use of the land plot provided to him.
If the allocated site is not being developed or the program participant does not invest in the development of the region, then the site is returned to the state.
Due to the fact that the allocation of a site under the Far Eastern Hectare program takes place upon mandatory development, and, accordingly, its involvement in economic turnover, there is a need to carry out a procedure for registering a legal entity and determining a taxation system. In some regions, a reduced tax rate is calculated using the simplified tax system. So, most regions of the Far Eastern Federal District have adopted local laws that provide for lowering tax rates for the simplified tax system (the relevant legislative acts are listed in table 2).
The exception is Primorsky Krai, where reduced tax rates are not set. We draw attention to the fact that in many cases differentiated tax rates are set. As a rule, the basis for this approach is the main type of activity. When studying these legislative acts, we came to the conclusion that for most types of activities that theoretically can be developed on the Far Eastern hectare, the indicated tax rates can be applied. Legislative acts of the Chukotka Autonomous Okrug provide for lowering rates for all program participants, without exception, in comparison with federal legislation. We consider it appropriate to use a similar approach in economic activity.
In order for the Program to function fully, it needs to be improved. For example, the mandatory connection of infrastructure to areas suitable for agriculture. At the same time, the state can put forward the following condition - certain areas can only be used for their intended purpose and impose sanctions in the form of fines for non-use of land or its use for other purposes. This will force citizens to take a more responsible approach to choosing a site and realistically assess their capabilities.
The state could provide material support to program participants who proposed the most successful and promising business plans, requesting in return the provision of full reports on the use of the funds provided.
It will also be prudent to provide participants with more detailed information on the status of hectares participating in the program and an approximate list of activities that can be carried out in such areas. For these purposes, land quality assessment is carried out as a result of receiving digital information on the properties of land as a means of production in agriculture. Assessment of the quality of land that is the original habitat of the indigenous peoples of the North, Siberia and the Far East of the Russian Federation is carried out in order to establish the productivity of deer pastures and the availability of biological resources necessary to ensure the traditional way of life of the indigenous peoples of the North, Siberia and the Far East of the Russian Federation [5].
Table 2. Tax rate reduction in the regions participating in the Far Eastern Hectare program
| The subject of the Russian Federation | Object of taxation | Regional legislative act |
|-------------------------------------|--------------------|-------------------------|
| Amur region | 1 and 3 - for individual activities | The law of the Amur Region dated 10.10.2015 No. 592-OZ |
| | 5 - for individual activities | Law of the Jewish Autonomous Region of December 24, 2008 No. 501-OZ |
| Jewish Autonomous Region | 6 | The law of the Kamchatka Krai dated March 19, 2009 No. 245 |
| | 5, 8 and 10 - for individual activities | Law of the Magadan Region of November 27, 2015 No. 1950-OZ and dated July 29, 2009 No. 1178-OZ |
| Kamchatka Krai | 1, 2, 3, 4 and 5 - for individual activities | The Law of the Republic of Sakha (Yakutia) dated 07.11.2013 1231-3 No. 17-V |
| Magadan Region | 3 - for individual activities | Law of the Sakhalin Region dated 10.02.2009 No. 4-OZ |
| | 7, 5 - for individual activities | The law of the Khabarovsk Territory dated 10.11.2005 No. 47-OZ |
| The Republic of Sakha (Yakutia) | 2 and 4 - for individual activities | Law of the Chukotka Autonomous Okrug of May 18, 2015 No. 47-OZ |
| | 5 - for individual activities | Article 346.20 of the Tax Code of the Russian Federation |
| Sakhalin Oblast | 3 - for individual activities | |
| | 5 - for individual activities | |
| | 8 - for certain types of activities specified in the law | |
| | 10 - for all other activities | |
| Khabarovsk region | 6 | Article 346.20 of the Tax Code of the Russian Federation |
| | 5 - for certain types of activities specified in the law | |
| | 10 - for all other activities | |
| Chukotka Autonomous Okrug | 4 - for individual activities | Article 346.20 of the Tax Code of the Russian Federation |
| | 10 - for all other activities | |
Without obtaining reliable data on the actual use of land, the legal status of land used by agricultural enterprises and organizations, the identification and establishment of the area of land unused, irrationally
used, or used for other purposes and not in accordance with the permitted use of land, the possibility of development and implementation of actions aimed at the development and improvement of agricultural land is excluded. The original data must be contained, first of all, in the Unified State Register of Real Estate (USRRE).
As a result of the study, using the example of the Khabarovsk Territory, the information recorded in the USRRE on the provided land plots as part of the implementation of the Federal Law dated 05/01/2016 No. 119-FL was analyzed (Fig. 1).
From the diagram it is seen that:
- for the period of 2019 (as of 04/17/2019), the branch of the Federal State Budgetary Institution “Federal Registration Service Rosreestr” (FSBI FRS Rosreestr) received 285 applications for cadastral registration of land plots sent to the Branch by authorized bodies. Of these, 249 land plots were registered;
- for the period of 2018, a branch of the FSBI FRS Rosreestr received 801 applications for cadastral registration of land plots sent to the Branch by authorized bodies. Of these, 764 land plots were registered;
- for the period of 2017, the branch of the FSBI FRS Rosreestr received 7413 applications for registration of land plots sent to the Branch by authorized bodies. Of these, 7226 land plots were registered;
- for the period of 2016 (from June 1, 2016 to December 31, 2016), 1406 applications for registration of land plots sent to the Branch by authorized bodies were received at the branch of the FSBI FRS Rosreestr. Of these, 1356 land plots were registered.
In accordance with the law on the Far Eastern Hectare, the application will be considered within 10 business days. Then the recipient will have another 30 days to sign the contract. Table 3 shows the dynamics of processing applications in the branch of FSBI “FRS Rosreestr”.
The problems associated with obtaining a hectare are analyzed - these are previously registered land plots that do not have borders in the state real estate cadastre, as well as land plots arbitrarily occupied by local residents that are not reflected in the state federal information system (FIS), through which the “Far Eastern hectare” is provided”. Accordingly, upon receipt or allocation of plots, controversial situations arise between potential recipients of the “hectare” and local residents [6].
The recipients of the “Far Eastern Hectare” highlight the longest paperwork and the fact that most of the land, for various reasons, is in the “gray” zone, which is forbidden to be issued, as the most important and acute problems. This applies in particular to hunting grounds.
There are several typical mistakes due to which the provision of one hectare is delayed for a long time:
- the format of the documents does not correspond to the format established by the regulatory authority (provided in the format Doc, Jpeg);
- documents submitted in electronic form are not signed by an enhanced qualified electronic signature (EQES) of the authorized body;
- documents required for state cadastral registration or registration of rights are not presented: in particular, there is no scheme for placing a land plot on a public cadastral map (when submitting an application for land plot civil registration), there is no contract for gratuitous use (when submitting an application for registration);
| Table 3. Dynamics of processing applications of participants in the Far Eastern Hectare program |
|-----------------------------------------------|
| 01.06.2016 - 31.12.2016 | 01.01.2017 - 31.12.2017 | 01.01.2018 - 31.12.2018 | 01.01.2019 - 17.04.2019 |
| Received applications for state cadastral registration (SCR) | 1408 | 7413 | 1009 | 285 |
| Registered at SCR | 1345 | 7238 | 963 | 249 |
| SCR terminated upon application | 40 | 82 | 1 | 0 |
| Decisions made to refuse to conduct SCR | 10 | 102 | 35 | 0 |
| Decision made to suspend SCR | 0 | 0 | 0 | 19 |
- the contract for gratuitous use in the form of an electronic image of the document was not signed by all parties: in particular, there is no signature of the representative of the authorized body or the signature of the citizen who is granted the land plot, or the contract is not signed by all citizens who submitted a collective application for the provision of the land;
- the area of the formed land plot according to the document differs significantly from the area on the cadastral map with the coordinates presented in the scheme; Also, when submitting an application for accounting for changes in connection with a change in the boundaries of the land plot in the title document, there is no cadastral number of the land plot [7].
The majority of users of the Far Eastern Hectare, about 25% of the participants in the Far Eastern Hectare program, plan to build housing for themselves; 15% - to set up a personal plot for personal subsidiary plots, to build a country or garden house. Also, 13.5% of residents of the Far East plan to use the land for the implementation of tourism projects or for recreation. Other types of entrepreneurship - including trade, hotel services, entertainment, catering and motor vehicle servicing, account for 7% of the total number of applications sent to the Federal Information System (FIS) (Fig. 2) [8].
Taking into account the requirements of the Order of the Government of the Russian Federation to improve the investment and business climate of the Khabarovsk Territory, remove legal, administrative, economic and organizational barriers to business development, the Governor of the Khabarovsk Territory has approved “road maps” for introducing targeted models to simplify business processes and increase the investment attractiveness of Khabarovsk Territory, including: “Cadastral registration of land plots and real estate” and “Registration of ownership rights to land plots and real estate objects” [9].
Figure 2. Types of use of the Far Eastern Hectare
Now more than 73,200 Russians are participating in the Far Eastern Hectare program. The area of the provided plots is more than 48 thousand hectares, and the authorized bodies made a positive decision on the provision of land for another 6 thousand hectares (Fig. 3).
Figure 3. The number of applications for the provision of land plots under the program "Far Eastern hectare" in the subjects of the Far East
The most popular land is in Primorsky Krai - 16.5 thousand land plots are approved here (free use agreements were signed with citizens or approval of authorized bodies was obtained). 9.6 and 9.5 thousand applications were approved in the Khabarovsk Territory and the Republic of Sakha (Yakutia), respectively. 8.5 thousand sites approved in Sakhalin Oblast [10].
It should be noted that for operational work with applicants for the provision of the Far Eastern hectare, the Federal Service for State Registration, Cadastre and Cartography (hereinafter referred to as Rosreestr) acted as the operator of the federal information system (FIS) “НаДальнийВосток.РФ”. Rosreestr keeps statistics including on the "Far Eastern hectare". FIS provides an opportunity using the official website to:
1) to prepare the layout of the land on the public cadastral map in the form of an electronic document;
2) to prepare and send citizen’s application to the authorized body (in the form of an electronic document) for provision of a land plot for gratuitous use, rental or ownership, as well as other documents and information, the submission of which by a citizen to the authorized body is required by Federal Law No. 119-FL;
3) to prepare and send to the authorized body documents and information at the request of a citizen interested in providing land for gratuitous use, rental or ownership by a federal executive body authorized by the Government of the Russian Federation to carry out the functions of registering rights to real estate and transactions with it and providing public services in the field of cadastral registration of real estate, land management, state monitoring of land, geodesy and cartography (hereinafter referred to as the registration authority);
4) to receive information from the authorized body on decisions taken in connection with a citizen’s application for the provision of a land plot for free use, rental or ownership;
5) receive from the authorized body the draft contract for the gratuitous use of the land plot, the draft lease agreement or the draft contract for the sale of the land plot, as well as the decision to grant the land plot ownership free of charge or other documents and information the provision of which to the citizen by the authorized body is provided for by Federal Law No. 119-FL [11].
The requirements for the procedure for updating, forming and using basic state information resources are determined by the Government of the Russian Federation. These requirements should contain a list of measures aimed at ensuring the observance of the rights of subjects of personal data, as well as provide for measures to protect information in accordance with the legislation of the Russian Federation. Information on basic State information resources and on the procedure for access to information on basic State information resources are included in the register of basic State information resources, the procedure for the formation, updating and use of which is determined by the Government of the Russian Federation.
4. Conclusion
Taking into account the requirements of the Order of the Government of the Russian Federation to improve the investment and business climate of the Khabarovsk Territory, as well as remove legal, administrative, economic and organizational barriers to business development, the Governor of the Khabarovsk Territory approved “road maps” for introducing targeted models to simplify business processes and increase investment attractiveness of the Khabarovsk Territory.
The introduction of FSIS USRRE on the territory of the Khabarovsk Territory will automate the processing of incoming applications, as well as reduce the processing time of incoming applications and reduce the timing of accounting and registration actions. At the same time, applications can be accepted at any office of the MFC (multifunctional centers), including on an extraterritorial basis - regardless of the location of the facility.
The main purpose of the information system is to ensure automation of the processes of providing land plots to citizens for free use in the territory of the Far Eastern Federal District in accordance with the legislation of the Russian Federation;
An interdepartmental request for the submission of documents and information should contain an identifier of information about an individual.
Thanks to the interagency cooperation of the authorized bodies, information on land plots under the Far Eastern Hectare program was optimized and improved, which reduced the time for making a decision on granting or refusing to give one hectare.
In order to improve the investment climate in the region, the Government of the Khabarovsk Territory has implemented a number of important decisions for investors:
- a procedure has been established for supporting investment projects on the basis of the “one-stop-shop” principle in order to provide information, consulting and organizational assistance to investors;
- A specialized organization for attracting investments and working with investors was created - ANO "Agency for Investment and Development of the Khabarovsk Territory";
- Created an investment map of the Khabarovsk Territory;
- a specialized bilingual Internet portal on investment activity in the Khabarovsk Territory has been created - Investment portal of the Khabarovsk Territory.
6) In the structure of the land fund of the Khabarovsk Territory, 93.6% are the lands of the forest fund, 1.2% are the lands of the water fund, 1.8% are the lands of the reserve, 0.5% are the lands of agricultural purpose, 0.5% are the lands of settlements, 0.3% - lands of industrial and other special purposes, 2.1% - lands of specially protected territories and objects.
7) The Far Eastern hectare program is designed to attract settlers to the relatively uninhabited region of Russia; at present, the multiplier effect of its implementation is noted.
8) Taking into account the requirements of the Order of the Government of the Russian Federation in order to improve the investment and business climate of the Khabarovsk Territory, the Governor of the Khabarovsk Territory approved “road maps” for introducing targeted models to simplify business processes and increase the investment attractiveness of the Khabarovsk Territory.
9) The introduction of FSIS USRRE on the territory of the Khabarovsk Territory will automate the processing of incoming applications, as well as reduce the processing time of incoming applications and reduce the timing of accounting and registration actions. At the same time, applications can be accepted at any office of the MFC (multifunctional centers), including on an extraterritorial basis - regardless of the location of the facility.
10) Based on the analysis of the work of the FIS “НадальнийВосток.рф”, a requirement is formulated to display the recommended types of permitted use (TPU) of land plots in the information system by establishing the boundaries of zones with special ones recommended by TPU.
11) Thanks to the interagency cooperation of the authorized bodies, information on land plots under the Far Eastern Hectare program was optimized and improved, which reduced the time for making a decision on granting or refusing to give one hectare.
References
[1] Sidorkina Z I and Tsitsiashvili G Sh 2009 Determination of stability factors in the dynamics of the number of population of the cities of the Far East Geography and Natural Resources 30(4) 383–387
[2] The State Program for the Development of Agriculture and Regulation of Agricultural Products, Raw Materials and Food Markets for 2013–2020 (Moscow)
[3] Murasheva A A 2005 The development of the territories of the Far Eastern region and ways to solve the environmental problem Cadastru, organizateritorialului, ingineriamediului 13 80–85 (Chisinau: Volumul)
[4] Khlystun V N and Alakoz V V 2016 Mechanisms for the inclusion of unused land in agricultural turnover Economics of agricultural and processing enterprises 11 38-42
[5] Shelepa A S 2013 Agrarian sector of the Far East: problems and development prospects (Khabarovsk: GNU DVNIIEP AIC of the Russian Agricultural Academy)
[6] Lipski S A 2017 Far Eastern hectare: features of the provision and use Citizen and Law 5 11-16
[7] Shapovalov D A, Klyushin P V, Murasheva A A et al 2017 Current problems of the efficient operation of the agro-industrial complex of the Russian Federation Problems of the development of the agricultural sector in the region 31(3) 152-157
[8] Demyanenko A N 2017 About the “Far Eastern hectare”, or How do we attract the population to the Far East: historical experience Regional Studies 4(3) 5-13
[9] Murasheva A A 2006 The effectiveness of environmental management in the region (on example of the Far Eastern Federal District) (Moscow: State university of land use planning)
[10] Kustysheva I N and Ostarkova D A 2018 Implementation of the Far Eastern Hectare program as a way to develop the territory of the Far East International Agricultural Journal 2 69-71
[11] Izotov D A 2017 Far East: innovations in public policy ECO journal 4 27-44 | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3116,
1
],
[
3116,
7489,
2
],
[
7489,
12561,
3
],
[
12561,
17262,
4
],
[
17262,
20642,
5
],
[
20642,
23171,
6
],
[
23171,
26692,
7
],
[
26692,
27943,
8
],
[
27943,
32316,
9
],
[
32316,
36281,
10
]
]
} |
bacf0bccc86fd7eaa4dccbfa798a3c1ad65aacd4 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 22,
"total-fallback-pages": 0,
"total-input-tokens": 93061,
"total-output-tokens": 26193,
"fieldofstudy": [
"Physics"
]
} | The CARMENES search for exoplanets around M dwarfs
LP 714-47 b (TOI 442.01): populating the Neptune desert*,**,***
S. Dreizler¹, I. J. M. Crossfield², D. Kossakowski³, P. Plavchan⁴, S. V. Jeffers¹, J. Kemmer⁵, R. Luque⁶,⁷, N. Espinoza⁸, E. Pallé⁹, K. Stassun⁹, E. Matthews¹⁰, B. Cale⁴, J. A. Caballero¹¹, M. Schlecker⁵, J. Lillo-Box¹¹, M. Zechmeister¹, S. Lalitha¹, A. Reiners¹, A. Soubkiou¹², B. Bitsch³, M. R. Zapatero Osorio¹³, P. Chaturvedi¹⁴, A. P. Hatzes¹⁴, G. Ricker¹⁰, R. Vandenspeck¹⁰, D. W. Latham¹⁵, S. Seager¹⁰,¹⁶,¹⁷, J. Winn¹⁸, J. M. Jenkins¹⁹, J. Aceituno²⁰,²¹, P. J. Amado²¹, K. Barkaoui²²,²³, M. Barbieri²³, N. M. Batalha²⁴, F. F. Bauer²⁵, B. Benneke²⁵, Z. Benkhaldoun²⁶,²⁷, J. Berberian⁶, J. Burt²⁸, R. P. Butler²⁹, D. A. Caldwell³⁰,³¹, A. Chintada³¹,³²,³³, J. L. Christiansen³³, D. R. Ciardi³³, C. Cifuentes¹¹, K. A. Collins⁵, K. I. Collins⁴, D. Combs⁴, M. Cortés-Contreras¹¹, J. D. Crane³⁴, T. Daylan¹⁰, D. Dragomir³⁵, E. Esparza-Borges³, P. Evans³⁶, F. Feng³⁹, E. E. Flowers¹⁸,²⁹,³⁰, A. Fukui³⁷,²⁶, B. Fulton³⁸,²⁶,²⁷, E. Furlan²⁷, E. Gaidos³⁹, C. Geneser⁴⁰, S. Giacalone⁴¹, M. Gillon²², E. Gonzales²⁴,³⁰, V. Gorjian³⁸, C. Hellier⁴², D. Hidalgo⁶,⁷, A. W. Howard²⁶, S. Howell¹⁹, D. Huber¹², H. Isaacson¹¹,¹²,¹³, E. Jehin⁴⁴, E. L. N. Jensen⁴⁵, A. Kaminski⁵, S. R. Kane⁴⁶, K. Kawatha³⁷, J. F. Kielkopf⁴⁷, H. Klahr³, M. R. Kosiarek²⁴,³⁰,³¹, L. Kreidberg¹⁵,³, M. Kürster³, M. Lafarga³⁸,³⁹,⁴⁰, J. Livingston⁴⁰, D. Louie⁵², A. Mann⁵³, A. Madrigal-Aguado¹, R. A. Matson⁵⁴, T. Mocz⁴⁶, J. C. Morales⁴⁶,⁴⁷, P. S. Muirhead⁵⁵, F. Murgas⁶,⁷, S. Nandakumar²², N. Narita⁶,⁵⁶,⁵⁷,⁵⁸, G. Nowak⁶,⁷, M. Oshagh⁶,⁷, H. Parviainen⁶,⁷, V. M. Passegger⁵⁹,⁶⁰, D. Pollacco⁶¹, F. J. Pozuelos⁴,³², A. Quirrenbach⁸, M. Reede⁴, I. Ribas⁴⁸,⁴⁹, P. Robertson⁶², C. Rodríguez-López²¹, M. E. Rose¹⁹, A. Roy³⁶, A. Schweitzer⁶⁰, J. Schlieder⁶³, S. Shectman³⁴, A. Tanner⁴⁰, H. V. Şenavc⁵⁶, J. Teges⁵⁴,⁶⁰, J. D. Twicken³⁰, J. Villasenor¹⁰, S. X. Wang³⁴, L. M. Weiss³²,⁶⁰, J. Wittrock⁴, M. Yilmaz⁶⁴, and F. Zohrabi⁴⁰
(Affiliations can be found after the references)
Received 25 March 2020 / Accepted 8 October 2020
ABSTRACT
We report the discovery of a Neptune-like planet (LP 714-47 b, \( P = 4.05204 \, \text{d}, m_b = 30.8 \pm 1.5 \, M_{\oplus}, R_b = 4.7 \pm 0.3 \, R_{\oplus} \)) located in the “hot Neptune desert.” Confirmation of the TESS Object of Interest (TOI 442.01) was achieved with radial-velocity follow-up using CARMENES, ESPRESSO, HIRES, iSHELL, and PFS, as well as from photometric data using TESS, Spitzer, and ground-based photometry from MuSCAT2, TRAPPIST-South, MONET-South, the George Mason University telescope, the Las Cumbres Observatory Global Telescope network, the El Sauce telescope, the TÜBİTAK National Observatory, the University of Louisville Manner Telescope, and WASP-South. We also present high-spatial resolution adaptive optics imaging with the Gemini Near-Infrared Imager. The low uncertainties in the mass and radius determination place LP 714-47 b among physically well-characterised planets, allowing for a meaningful comparison with planet structure models. The host star LP 714-47 is a slowly rotating early M dwarf \( (T_{\text{eff}} = 3950 \pm 51 \, \text{K}) \) with a mass of \( 0.59 \pm 0.02 \, M_{\odot} \) and a radius of \( 0.58 \pm 0.02 \, R_{\odot} \). From long-term photometric monitoring and spectroscopic activity indicators, we determine a stellar rotation period of about 33 d. The stellar activity is also manifested as correlated noise in the radial-velocity data. In the power spectrum of the radial-velocity data, we detect a second signal with a period of 16 days in addition to the four-day signal of the planet. This could be shown to be a harmonic of the stellar rotation period or the signal of a second planet. It may be possible to tell the difference once more TESS data and radial-velocity data are obtained.
Key words. methods: data analysis – planetary systems – stars: late-type – stars: individual: LP 714-47 – planets and satellites: individual: LP 714-47 b
* RV data are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/644/A127.
** Based on observations carried out at the Centro Astronómico Hispano Alemán (CAHA) at Calar Alto, operated jointly by the Junta de Andalucía and the Instituto de Astrofísica de Andalucía (CSIC), on observations carried out at the European Southern Observatory under ESO programme 0103.C-0152(A), and data collected with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile.
*** National Science Foundation Graduate Research Fellow.
**** NASA Hubble Fellow.
***** Beatrice Watson Parrent Fellow.
1. Introduction
Currently, approximately 4000 planets have been detected using the transit method, primarily with the *Kepler* space telescope. A statistical analysis of these detections indicates that at short orbital periods, there is a bimodal distribution of planets, characterised by a population of Earth-sized planets (including super-Earths) and a population of larger Jupiter-sized planets (Szabó & Kiss 2011; Mazeh et al. 2016). While intermediate Neptune-mass planets have been detected at longer orbital periods, there is a distinct lack of Neptune-mass planets at short orbital periods. The rarity of planets with masses of approximately 0.1 $M_{\text{Jup}}$ and periods of less than about 4 d is referred to as the “hot Neptune desert”.
Deliberations on the cause of the hot Neptune desert have been addressed in several papers involving photo-evaporation (e.g. Owen & Wu 2013; Lopez & Fortney 2014), the preferential formation of Jupiter-sized rather than Neptune-sized planets, as a consequence of core accretion (e.g. Ida & Lin 2008; Mordasini et al. 2009), the early migration of low-mass planets (e.g. Flock et al. 2019), or core-powered mass loss (Gupta & Schlichting 2020). In an investigation of possible formation mechanisms, and to explain the distinctive triangular shape of the desert in the mass-period diagram, Owen & Lai (2018) showed that photo-evaporation of Neptune-mass planets occurs very close to the host stars.
Photo-evaporation may not necessarily be required in this process. Instead, atmospheric mass-loss can be driven by the release of the primordial energy from the formation, which is comparable to the atmospheric binding energy (Ginzburg et al. 2016, 2018; Gupta & Schlichting 2019). With this scenario, it is possible to explain the radius valley spanning between Earth-sized and sub-Neptune-sized planets. Properties of the radius valley are predicted to show a different dependence on age and metallicity between the photo-evaporation and the core-powered mass-loss scenario. Another possibility is that of scattering onto high-eccentric orbits followed by a circularisation (high-eccentricity migration). This could explain the lower and upper boundary of the Neptune desert (Matsakos & Königl 2016).
A few planets or planet candidates have been detected in the hot Neptune desert. These include K2-100b (Mann et al. 2017), NGTS-4-b (West et al. 2019), TOI-132 b (Díaz et al. 2020), TOI-824 b (Burt et al. 2020), LTT 9779 b (Jenkins 2019), and TOI-849 b (Armstrong et al. 2020). The latter two are extreme cases with orbital periods shorter than one day. More planets close to or inside the Neptune desert with precise mass and radius determinations would help to shed more light on the distinction between the various explanations for the existence of the Neptune desert.
The Transiting Exoplanet Survey Satellite (TESS, Ricker et al. 2014), launched in April 2018, aims to detect close-in planets transiting bright and nearby stars. Such transiting systems are ideal for ground-based follow-up observations focused on the study of the atmospheres of exoplanets by using transmission or emission spectroscopy. Given its instrument characteristics, TESS is ideal for the detection of hot Neptunes. In this paper, the TESS Object of Interest TOI-442.01 is confirmed to be a 30-Earth-mass planet orbiting its late-type host star LP 714-47 with an orbital period of 4.05 d. From the radial velocity measurements, as well as the TESS, Spitzer, and ground-based photometry, presented in Sect. 3, we conclude that LP 714-47 b is a transiting Neptune-like planet close to the lower edge of the hot Neptune desert, presented in Sect. 5. Adding a new planet with precise mass and radius determination is, therefore, helpful in shedding more light on the origins of the hot Neptune desert, which may, in turn, place constraints on planet formation scenarios, as discussed in Sect. 6.
2. TESS photometry
LP 714-47 was observed in TESS sector 5 in two-minute cadence mode between 15 November and 11 December 2018 (see Figs. 1 and 2). The planet candidate TOI442.01 was announced on 31 January 2019. The TESS Data Validation diagnostic (DV) (Twicken et al. 2018; Li et al. 2019) revealed a planet candidate at a period of 4.05 d (TOI 442.01) with depths of $5685 \pm 134$ ppm ($S/N = 45.3$), the planet radius of the candidate was determined as $4.7 \pm 0.7 R_{\oplus}$, slightly different values are reported on the ExoFOP web page\(^1\). The DV difference image centroid offsets for TOI 442.01 indicate that the source of the transit signature is within 2 arcsec (0.1 TESS pixels). The TESS lightcurves produced by the Science Process Operation Centre (SPOC, Jenkins et al. 2016) are available at the Mikulski Archive
\(^1\) [https://exofop.ipac.caltech.edu/tess/target.php?id=70899085](https://exofop.ipac.caltech.edu/tess/target.php?id=70899085)
for Space Telescopes\textsuperscript{2}. For our analysis, we used the de-trended pre-search data conditioning simple aperture photometry (PDC-SAP) lightcurve (Stumpe et al. 2012, 2014; Smith et al. 2012). The total time-span of the observation covered seven transits, although one of them occurs during a gap in the data caused by the re-orientation of the spacecraft needed for the data downlink.
We independently searched for a transit signal in the light curve using the transit-least-squares method with a signal detection efficiency of 19.8 (TLS, Hippke & Heller 2019) and the box-least-squares algorithm (BLS, Kovács et al. 2002). We recovered the 4.05 d signal in both cases with a depth of 4.8 ± 0.3 ppt. After removing the transits, the strongest peak in the periodogram of the residuals was a modulation with a period of 9.2 d and an amplitude of 230 ppm.
The announcement of TOI442.01 as a potential planet host star initiated a series of follow-up observations: space and ground based transit photometry, high-resolution and low-resolution spectroscopy, and high-contrast imaging. Between the various teams, we decided to analyse all available data jointly.
3. Follow-up observations
3.1. Spitzer photometry
We observed a transit of the system with the Spitzer Space Telescope’s IRAC instrument (Fazio et al. 2004), as part of Spitzer GO 14084 (PI Crossfield). The observations on 21 May 2019 used the channel 2 (4.5\textmu m) broadband filter and we acquired 228 sets of 64 sub-array frames with integration times of 2 s. The observations used the standard Spitzer approach to observing, with an initial peak-up observation to place the target near the well-calibrated sweet spot of the IRAC2 detector. Because our target is fainter than the recommended brightness level for peak-up observations, we used the brighter, nearby star HD 27112 for peak-up. In total, the Spitzer observations spanned 8.3 h and covered a full transit (Sect. 5).
In order to account for the intra-pixel variations, we used the pixel-level de-correlation method developed by Deming et al. (2015). This method reconstructs the observed transit signal from a linear combination of the varying contributions from the nine pixels covered by the instrument point spread function (PSF) and a transit model. The linear fit of the correlation coefficients is part of the optimisation procedure.
3.2. Ground-based photometry
We acquired ground-based, time-series follow-up photometry of TOI-442 as part of the TESS Follow-up Observing Program\textsuperscript{3} to attempt to: (i) rule out nearby eclipsing binaries as potential sources of the TESS detection, (ii) detect the transit-like event on target to confirm the event depth and, thus, the TESS photometric deblending factor, (iii) refine the TESS ephemeris, (iv) provide additional epochs of transit centre time measurements to supplement the transit timing variation (TTV) analysis, and (v) place constraints on transit depth differences across optical filter bands. We used the TESS Transit Finder, which is a customised version of the Tapir software package (Jensen 2013), to schedule our transit observations. Unless otherwise noted, the transit follow-up data were extracted using the
\begin{table}[h]
\centering
\caption{Summary of radial-velocity data sets.}
\begin{tabular}{|l|c|c|}
\hline
Observatory & Instrument & Spectral resolution & Observing season (2019) \\
\hline
Calar Alto & CARMENES VIS & 94 600 & Spring + autumn & 33 \\
& CARMENES NIR & 80 400 & Autumn & 21 \\
Paranal & ESPRESSO & 140 000 & September & 19 \\
Keck & HIRES & 60 000 & Autumn & 14 \\
Las Campanas & PFS & 127 000 & Autumn & 6 \\
iRTF & iSHELL\textsuperscript{4} & 75 000 & December 2019–January 2020 & 9 \\
\hline
\end{tabular}
\end{table}
\textbf{Notes.} \textsuperscript{4}For iSHELL, we list the number of epochs, which consist of multiple co-added exposures.
\begin{table}[h]
\centering
\caption{Summary of radial-velocity data sets.}
\begin{tabular}{|l|c|c|}
\hline
Instrument & Spectral resolution & Observing season (2019) \\
\hline
CARMENES VIS & 94 600 & Spring + autumn & 33 \\
CARMENES NIR & 80 400 & Autumn & 21 \\
ESPRESSO & 140 000 & September & 19 \\
HIRES & 60 000 & Autumn & 14 \\
PFS & 127 000 & Autumn & 6 \\
iSHELL\textsuperscript{4} & 75 000 & December 2019–January 2020 & 9 \\
\hline
\end{tabular}
\end{table}
3.3. High resolution spectroscopy
As a summary of the various instruments used for radial velocity follow-up of TOI 442.01, we list the basic properties of the radial-velocity data and the number of observations from each instrument in Table 1 (see also Fig. D.1), followed by a more detailed description below. With CARMENES, we started the RV follow-up after the candidate alert in February 2019 and re-started in October 2019. HIRES and PFS observations started in August 2019, and those with iSHELL in November 2019.
3.3.1. CARMENES spectra
The CARMENES spectrograph consists of a red-optical (VIS) channel and a near-infrared (NIR) channel, covering a wide
---
\textsuperscript{2}https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html
\textsuperscript{3}https://tess.mit.edu/followup/
\textsuperscript{4}http://tug.tubitak.gov.tr/en
wavelength range of 550–960 nm and 960–1700 nm, and achieving spectral resolutions of 94 600 and 80 400, respectively (Quirrenbach et al. 2014, 2018). The average sampling per resolution element is 2.8 px. The spectra were processed by the standard pipeline caracal (CARMENES reduction and calibration software; Zechmeister et al. 2014) and went through the guaranteed observation time data flow (Caballero et al. 2016).
Triggered by the TESS alert, we monitored LP 714–47 with CARMENES from February 2019 to November 2019. We collected 33 spectra, each with an exposure time of 30 min (Table 1). The median typical signal-to-noise ratio (S/N) per pixel of the observations was ~63 at 746 nm. The RVs were computed with serval5 (Spectrum radial-velocity analyzer Zechmeister et al. 2018); the uncertainties range from about 2–4 m s\(^{-1}\), with a median of 2.6 m s\(^{-1}\).
The python code serval also provides spectroscopic activity indicators and the equivalent widths of key diagnostic photospheric and chromospheric lines, such as the differential line width, dLW, and the chromatic index, CRX (Zechmeister et al. 2018). Due to an apparently systematic offset, the CARMENES NIR data from the first season were excluded from the fit.
3.3.2. ESPRESSO spectra
ESPRESSO is a new high-resolution spectrograph at the ESO Very Large Telescope (Pepe et al. 2010). It covers the wavelength range 380–788 nm with a resolution of 140 000 and sampling of 4.5 px per resolution element.
We obtained 19 spectra of LP 714–47 in September 2019 in the single-telescope high-resolution mode with 2×1 binning (HR21). The exposure times were at least 10 min, and the S/N was about 30 pixel at 573 nm. The spectra were processed with the standard ESO pipeline. The RVs were calculated with serval.
3.3.3. HIRES spectra
We acquired 14 spectra with the HIRES spectrograph with the standard CPS setup (Howard et al. 2010): the C2 decker, the usual HIRES iodine cell (used to measure precise RVs; Marcy & Butler 1992; Butler et al. 1996), and exposures of 10–30 min (depending on seeing conditions). The HIRES observations began on 14 Aug. 2019 and ended on 15 Nov. 2019. As part of the HIRES analysis, we also acquired an iodine-free observation to serve as a template spectrum on 31 October 2019 using the B3 decker and an exposure time of 45 min.
3.3.4. PFS spectra
LP 714–47 was observed on six nights with the Carnegie Planet Finder Spectrograph (PFS; Crane et al. 2006, 2008, 2010) mounted on the Magellan 2 (Clay) 6.5 m telescope at Las Campanas Observatory in Chile. Two consecutive exposures were taken each night. The individual exposure times ranged from 15 to 20 min, depending on the conditions. Due to the faintness of this star, the CCD was 3×3 binned to minimise readout noise. The spectral resolution of all observations was 127 000 and the typical S/N of the individual observations was 25. Target stars are routinely observed through a custom built iodine cell, which was scanned by the NIST Fourier transform spectrometer at a resolution of 10\(^6\) (Nave 2017) and provides a rich embedded reference from 5000 to 6200 Å. As with the HIRES spectra, the velocity reduction used the approach described by Butler et al. (1996).
3.3.5. iSHELL spectra
We obtained 198 spectra of LP 714–47 on nine nights, spanning a 53 d interval with the iSHELL spectrometer on the NASA Infrared Telescope Facility (IRTF, Rayner et al. 2016). The exposure times were 5 min, repeated 17–22 times over a single a night to reach a cumulative photon S/N per spectral pixel at about 2.2 μm (at the approximate centre of the blaze for the middle order) varying from 107 to 171 to achieve a per-night RV precision of 3–10 m s\(^{-1}\) (median 6 m s\(^{-1}\)). Spectra were reduced and RVs extracted using the methods outlined in Cale et al. (2019).
3.4. Low-resolution spectroscopy
On 3 December 2019 (UT), we collected low-resolution optical spectra of LP 714–47 using the Alhambra Faint Object Spectrograph and Camera (ALFOSC) mounted on the Cassegrain focus of the 2.56 m Nordic Optical Telescope (NOT), located at the Observatorio del Roque de los Muchachos on La Palma island. ALFOSC is equipped with a 2k×2k pixel e2v detector providing a plate scale of 0.2138 arcsec pixel\(^{-1}\) on the sky. We used the grism number 5 and a long slit with a width of 1.0 arcsec, which delivered spectral data with a nominal dispersion of 3.55 Å pixel\(^{-1}\) (resolution of 17 Å; resolving power of R ≈ 420 at 700 nm) and a wavelength coverage of 500–1000 nm. A total of four exposures of 300 s each were obtained at parallactic angle and at airmass of 1.33. The observations were hampered by thin cirri and a poor seeing of about 3.0 arcsec.
The raw data were reduced following standard procedures for long-slit spectra within the IRAF environment, including debiasing and flat-fielding. The spectra were optimally extracted and wavelength calibrated using Th–Ar arc lamp exposures obtained at the beginning of the night. The dispersion of the wavelength calibration was 1.3 Å. The spectra were corrected for instrumental response using the spectrophotometric standard star G 191–B2B (white dwarf), which was observed on the same night and with an identical instrumental configuration as our target, but with a different airmass. This and the poor weather conditions prevented us from removing the telluric contribution from the ALFOSC spectra. All four individual spectra were combined to produce a final spectrum (cosmic rays were removed in the process). The ALFOSC spectrum of LP 714–47 is shown in Fig. B.1. It has a S/N higher than 200. This spectrum is used in Sect. 4.1 to derive the stellar parameters. A comparison of this spectrum with stellar templates as well as model atmospheres is presented in Appendix B.
3.5. High-contrast imaging
We obtained diffraction-limited infrared images of LP 714–47 on 18 March 2019 with the NIRI instrument at the Gemini Observatory (Hodapp et al. 2003, Program GN-2019A-LP-101, PI Crossfield). We used the NIRI camera behind the ALTAIR adaptive optics (AO) system. Nine dithered exposures of 3 s each were acquired, using the Br-y filter to approximate the K band while avoiding saturation. A sky background image was constructed from the dithered science frames. The data were reduced using a custom code that corrects for bad pixels, flatfields, subtracts the sky background, aligns the star between images, and coadds data. Sensitivity to faint companions was calculated by injecting fake PSFs and scaling them to
---
5 https://github.com/mzechmeister/serval
the magnitude at which they are detected at 5σ. No companions were seen anywhere in the field of view, which extends at least 13 arcsec from the target in all directions, and we were sensitive to candidates 7 mag fainter than the star beyond a few tenths of arcseconds. Our sensitivity to companions is shown in Fig. 3 along with a thumbnail image of the target. The candidate planet is, therefore, highly unlikely to be a false positive from a blended eclipsing binary.
Additional high-contrast imaging (Fig. C.1) was obtained on 14 January 2020 using the Zorro speckle instrument on Gemini-South6. The results are reported in Appendix C. Both direct imaging observations with high contrast and high spectral resolution exclude a companion which could either lead to a false positive transit detection as background binary or would lead to a third light contribution for the transit light curve.
4. Host star
4.1. Basic stellar parameters
The host star LP 714-47 was a poorly investigated, late-type, high-proper-motion star tabulated first by Luyten (1963) and Giclas et al. (1971), and later by Salim & Gould (2003), Lépine & Gaidos (2011), Frith et al. (2013), and Kirkpatrick et al. (2016). The TESS Input Catalog Version 8 (Stassun et al. 2019) lists TOI 442 = TIC 70899085 as a star with an effective temperature of 3779 ± 157 K, a mass of 0.59 ± 0.02 M⊙, and a radius of 0.61 ± 0.02 R⊙. The entry in the ExoFOP database also lists user-uploaded analyses by Jason Eastman and Abderrahmane Soubkiou (A.S.). Both used exofastv2 (Eastman et al. 2019), which fits planetary and stellar parameters simultaneously using MIST isochrones (Dotter 2016; Choi et al. 2016), the spectral energy distribution (Fig. 4) and the Gaia DR2 distance (Table 2). A.S. used Gaussian priors on the effective temperature and metallicity from the CARMENES spectral analysis as well as Gaussian priors on the Gaia DR2 parallax (adding 82 μas to the reported value and adding 33 μas in quadrature to the reported error, following the recommendation of Stassun & Torres 2018). An upper limit on the extinction of A V = 0.15 from the Schlafly & Finkbeiner (2011) dust maps was enforced. The exofastv2 fit without priors results in a slightly higher effective temperature (4200 ± 160 K) and lower mass (0.58 ± 0.03 M⊙), the metallicity being slightly sub-solar. The one with priors is in very good agreement with the values reported in Table 2.
We re-determined the stellar parameters from CARMENES spectra of LP 714-47 taken during the radial-velocity follow-up (Sect. 3.3.1). As explained by Passegger et al. (2018, 2019), we used a χ2 method together with a downhill simplex to obtain Teff, log g, and [Fe/H] by fitting the most recent PHOENIX spectra (Hauschildt 1992, 1993; Passegger et al. 2019) to the co-added CARMENES spectra in both VIS and NIR channels. The luminosity, radius, and mass were determined following
| Parameter | Value | Reference |
|-----------|-------|-----------|
| Name | LP 714-47 | Luy63 |
| Name | G 160-62 | Gic78 |
| TOI | 442 | TESS alerts |
| TIC | 70 899 085 | Sta19 |
| Karmn | J04167-120 | Cab16 |
| α (J2000) | 04:16:45.65 | Gaia DR2 |
| δ (J2000) | -12:05:05.5 | Gaia DR2 |
| d (pc) | 52.70 ± 0.11 | Gaia DR2 |
| G (mag) | 11.7282 ± 0.0004 | Gaia DR2 |
| TESS (mag) | 10.733 ± 0.007 | Sta19 |
| J (mag) | 9.493 ± 0.024 | 2MASS |
| Sp. type | M0.0 V | This work |
| T eff (K) | 3950 ± 51 | This work |
| log g (cgs) | 4.64 ± 0.04 | This work |
| L* (L⊙) | 0.075 ± 0.001 | This work |
| R* (R⊙) | 0.584 ± 0.016 | This work |
| M* (M⊙) | 0.59 ± 0.02 | This work |
| [Fe/H] | 0.41 ± 0.16 | This work |
| pEW (Hα) (Å) | <0.3 | This work |
| v sin i (km s⁻¹) | <2 | This work |
| P rot (d) | 33 ± 3 | This work |
Notes. (a) 2MASS: Skrutskie et al. (2006); Cab16: Caballero et al. (2016); Gaia: Gaia Collaboration (2018); Gic78: Giclas et al. (1978); Luy63: Luyten (1963); Sta19: Stassun et al. (2019). (b) Note that the Gaia DR2 coordinates are for equinox J2000 and at epoch J2015.5. (c) Metallicity is not well constrained. See Appendix B.
Schweitzer et al. (2019); that is, together with the Gaia DR2 parallactic distance, we obtained the luminosity, \( L_\star \), by integrating the broad-band spectral energy distribution from the blue optical to the mid-infrared, using the Virtual Observatory Spectral Energy Distribution Analyser (VOSA, Bayo et al. 2008, Fig. 4). After applying Stefan–Boltzmann’s law to obtain the radius, \( R_\star \), we used the linear mass-radius relation from Schweitzer et al. (2019) to arrive at a mass, \( M_\star \). The rotational velocity upper limit was determined as in Reiners et al. (2018), and the spectral type was estimated from a comparison with other early-type M dwarfs in their catalogue. All these results, as well as other basic parameters compiled from the literature, are listed in Table 2.
Using the HIRES data (Sect. 3.3.3), we also applied the SpecMatch–Empirical spectral characterisation tool (Yee et al. 2017) to the template spectrum, which yielded \( T_{\text{eff}} = 3869 \pm 70 \, \text{K}, \) \([\text{Fe/H}] = +0.38 \pm 0.09 \, \text{dex}, \) and \( R_\star = 0.60 \pm 0.10 \, R_\odot \). This is in agreement with the results from the CARMEHES data.
In the spectroscopic analysis, the CARMEHES-derived effective temperature is found to be in between the TIC v8 and exofastv2 results. However, the mass of \( 0.59 \pm 0.02 \, M_\odot \) and radius of \( 0.58 \pm 0.02 \, R_\odot \) match the previous results. As an independent check on the derived stellar parameters, we also performed a very similar analysis of the spectral energy distribution following the procedures described in Stassun et al. (2018), which resulted in \( R = 0.590 \pm 0.015 \, R_\odot \) and \( M = 0.57 \pm 0.03 \, M_\odot \). The latter mass determination is also consistent with the one that is based on the spectroscopic \( \log g \) and the photometry-based radius, \( M = 0.55 \pm 0.06 \, M_\odot \). Finally, our mass also agrees with the results from the mass-magnitude relation by Mann et al. (2019), which yields \( M = 0.595 \pm 0.015 \, M_\odot \) when applying the metallicity-independent version.
The CARMEHES and HIRES spectral analyses result in a super-solar metallicity. A note of caution on such a super-solar metallicity should be included, as a low-resolution spectrum of LP 714-47 with ALFOSC at the 2.56 m Nordic Optical Telescope points to a slightly sub-solar metallicity (see Appendix B for further details). The most accurate way to determine the metallicity of LP 714-47 is thus an unresolved issue. This is not surprising, given the intensive discussion in the literature about the best way to determine M-star metallicities (Bonfils et al. 2005; Wolff & Wallerstein 2006; Rojas-Ayala et al. 2010; Neves et al. 2013; Gaidos & Mann 2014; Mann et al. 2015; Alonso-Floriano et al. 2015; Montes et al. 2018, and references therein).
For the following analysis of the radial velocity and transit light curve data, we use the CARMEHES spectroscopically derived values. In particular, the stellar mass and radius, which are the most important parameters for exoplanet characterisation, are in good agreement with the various analysis results.
### 4.2. Stellar activity and rotation period
We investigated the stellar activity of LP 714-47 using the CARMEHES activity indicators (Sect. 3.3.1) presented by Schöfer et al. (2019). The variability across a variety of potential stellar activity indicators such as H\( \alpha \), He D3, Na I D, Ca II IRT, He I \( \lambda 10830 \, \text{Å}, \) Pa-\( \beta \), TiO bands, and the differential line width (dLW, Sect. 3.3.1), all show that LP 714-47 is a relatively inactive star. In particular, the measured pseudo-equivalent width of the H\( \alpha \) line is less than +0.3 \, \text{Å}; LP 714-47 is thus considered to be an inactive star. This is consistent with the results of Jeffers et al. (2018) and many other authors, who found that only about 10% of early-M stars are H\( \alpha \)-active. There is an indication of variability in the TiO bands, the chromatic index (CRX), and the dLW, which would indicate a very low level of spot coverage.
Using the generalised Lomb–Scargle (GLS) periodogram\(^7\) and the corresponding false-alarm probabilities (Zechmeister & Kürster 2009), we investigated the available long-term ground-based photometry (see Fig. 5). While the ASAS and NSVS data do not show significant periods, the WASP-South data show a peak at 33 d and likely the first harmonic at 16 d. We interpret the 33 d signal as the stellar rotation period, as discussed further in Sect. 5.3. Finally, the very low stellar activity of LP 714-47 is consistent with the upper limit of 2 km s\(^{-1}\) on its projected rotational velocity and with the relatively long rotation period of 33 d.
### 5. Analysis
The analysis of the various data sets was performed in a sequence of steps, with the modelling details described below. At first, we analyse the radial-velocity data and the transit photometry data separately. In the former, we focus on the planetary origin of the signals; in the latter, we focus on possible transit time variations.
#### 5.1. Method and modelling details
The analysis was done based on a collection of python scripts for fitting Keplerian orbits for the radial velocity and transit data together with Gaussian process regression (GP) accounting for correlated noise, either due to stellar activity or due to coming from an instrumental source or caused by the Earth’s atmosphere. The GP model is therefore used as a parametric noise model to account for residuals between observations and the planetary model. For the GP modelling, we used celerite (Foreman-Mackey et al. 2017), which offers a fast and reliable implementation of GP regression, and two sets of celerite kernels describing the correlation between each pair of data points, namely REAL and SHO. The former represents an exponential decay at a characteristic time scale \( \tau \), while the latter is a stochastically-driven damped harmonic oscillator with an oscillator period \( P \) and a damping time scale \( \tau \), and can describe a quasi-periodic behaviour. Mathematical details are given in Appendix E.
For the analysis of the radial-velocity data, we assume that the noise is (mostly) due to stellar activity. Sufficiently long-living active regions would cause correlations on time scale of their lifetimes and a (quasi) periodicity on the stellar rotation period or its harmonics, represented by the SHO kernel. Active regions with life times sufficiently below the rotation period or small-scale regions would cause correlated noise, which shows short-term correlations better represented by the REAL kernel. In the model, it is required for the same GP model to fit all radial-velocity data simultaneously. In order to constrain the GP regression, the fit of the GP parameters can simultaneously take the spectral activity indicators into account. We did not add a GP model for the transit data sets.
Each data set was analysed with an individual offset and with the option of a jitter, quadratically added to the measurement uncertainties, for each data set separately. We checked for a linear trend within the radial-velocity data, but found it to be consistent with zero. Therefore, we did not include a linear term in the RV fitting.
The Keplerian model had the following physical parameters: using the radial velocity we fitted the orbital period, \( P \), the eccentricity, \( e \), the longitude of periastron, \( \omega \), and the time of
\(^7\) https://github.com/mzechmeister/GLS
periapsis, $t_{\text{peri}}$, as well as a semi-amplitude of the radial velocity variation, $K$. For the analytic transit light curve model (Mandel & Agol 2002), we used the orbital period, the time of periapsis, the orbital inclination, $i$, the planet-to-star radius ratio, $R_p/R_\star$, as well as the semi-major axis in units of the stellar radius, $a/R_\star$, as fit parameters.
In the combined fit of radial-velocity data and transit photometry, we used the stellar mass and its uncertainty from Table 2 as input values and derived $a$ and $R_\star$ independently. Additionally, the planetary mass, radius, density, and equilibrium temperature could then be derived.
When investigating transit timing variations, the transit time of each transit was an additional free parameter. Depending on the limb darkening law applied, additional free parameters were needed. In particular, we used a quadratic limb darkening adding two parameters. Here, we only fitted the limb darkening parameters of the TESS light curve, but kept the others fixed using values from stellar atmosphere models for the ground-based data sets.
**Fig. 5.** Periodogram of radial-velocity data with sufficiently long coverage, spectral activity indicators, long-term photometry, and TESS light curve. The red vertical line indicates the planet period, the blue vertical lines indicate the potential rotation period at 33 d and its first harmonic, while the corresponding dashed lines mark the 1-day alias in the ground-based data sets. For CARMENES VIS and NIR, as well as for Keck/HIRES, we also show the periodogram of the residuals after subtracting the planet signal. Horizontal lines indicate the false alarm probability of 10%, 1%, and 0.1%, respectively.
(Husser et al. 2013) and Spitzer data (Claret et al. 2013) to limit the number of free parameters. Since the second coefficient of the quadratic limb darkening law was unconstrained by the TESS data, we also fixed to the value derived from the stellar atmosphere models.
The fitting procedure started with an initial guess of the planetary parameters guided by a periodogram analysis. These parameters were optimised using scipy.optimize.minimize. We then ran the Markov chain Monte Carlo (MCMC) procedure emcee (Foreman-Mackey et al. 2013) with 400 walkers and 10,000 steps after already 10,000 burn-in steps, initialised with a Gaussian distribution around the previous best fit and a standard deviation 10 times larger than that of the first optimisation. We made sure that the initial distribution was far broader than the final one from the MCMC posteriors. Boundaries for the parameters were only set to guarantee positive definite values for the amplitude \( K \), \( R_p/R_* \), and \( R_* \). The eccentricity is limited to bound orbits, the absolute value of the eccentricity was used when calculating the Keplerian models, as discussed in Eastman et al. (2013, Appendix D). We use uniform priors for all parameters within their bounds.
### 5.2. Confirmation of LP 714-47 b from radial velocity variations
For our initial values, we calculated the GLS periodogram and the corresponding false-alarm probabilities (Zechmeister & Kürster 2009) for all radial-velocity data and the spectroscopic and photometric activity indicators (Fig. 5). The CARMENES VIS and the CARMENES NIR and HIRES data sets all show a signal at the expected period of the transiting planet at 4.05 d, with daily aliasing. The structure of the peaks show the mean separation of the two runs (1/220 and 1/75 d\(^{-1}\) for CARMENES VIS and HIRES, respectively) and the run length of about 20 d as width of the alias pattern. The signal is above the 0.1% false-alarm probability (FAP) in the VIS and HIRES data, and at 1% in the NIR data. The ESPRESSO data set is by itself too limited to show the 4.05 d signal, but a broad peak in that period range is present in the periodogram of the data. Likewise, the sampling was also insufficient to detect the 4.05 d signal in the PFS data set by itself; the 4.05 d signal could not be detected in the periodogram of the iSHELL data alone.
After subtracting the signal at 4.05 d, additional power is present in the periodograms in the range of 14–16 d for VIS and HIRES, but not for NIR. The inspection of the periodograms of the spectroscopic activity indicators CRX, dLW, and Hα revealed power in the 14–16 d (dLW and Hα) and 25–40 d (CRX) ranges, respectively. While the former period range overlaps with the second highest peak in the periodogram of the radial-velocity data, the latter is about twice that period. As mentioned in Sect. 4.2, the long-term photometry of WASP-South shows a clear peak at 33 d, which we interpret as the stellar rotation period. Therefore, we used the activity indicators in order to discriminate between the signals of a true companion and of stellar activity in the radial-velocity data as discussed in the following.
For the detailed analysis, we ran a sequence of models with increasing complexity for the radial-velocity data (Table 3). For the model selection, we used the Bayesian Information Criterion (BIC) defined as \(-2 \ln L_{\text{max}} + k \ln N\) with the maximum likelihood \( L_{\text{max}} \), the number of free parameters \( k \), and the number of data points \( N \). Following Kass & Raftery (1995), we convert the difference of the BIC value of two models \( M_1 \) and \( M_2 \) into the Bayes Factor (BF) by assuming a single Gaussian posterior distribution, \( \ln BF_{21} = 1/2 (\text{BIC}_{M_1} - \text{BIC}_{M_2}) \). An appropriate threshold for the selection is \( \ln BF_{21} > 5 \) according to Kass & Raftery (1995).
### Table 3. Sequence of models for the analysis of the radial-velocity data
| \( n \) | Orbit | GP | BIC | BF |
|-------|-------|----|-----|----|
| | | No jitter | Jitter | No jitter | Jitter |
| 0 | – | 8192 | 889 | 3755 | 103.5 |
| 1 | C | 1360 | 752 | 339 | 35 |
| 1 | K | 1344 | 761 | 331 | 39.5 |
| 1 | K \ REAL | 693 | 720 | 4.5 | 18 |
| 1 | K \ SHO | 696 | 720 | 6 | 18 |
| 2 | K | 709 | 705 | 12.5 | 10.5 |
| 2 | K \ REAL | 684 | 709 | 0 | 12.5 |
| 2 | K \ SHO | 690 | 719 | 3 | 17.5 |
Notes. The BF is calculated relative to the model with the lowest BIC value. The selected model is in boldface.
Our base model was the no-planet model that allowed for instrumental offsets for the individual data sets. We then added one Keplerian signal with a period of 4.05 d (see Table 4). The eccentricity was small and compatible with zero, as expected for a close-in planet. We also checked the match between the mid transit time predicted from the fit of all radial-velocity data only with those from all transit data. From the former, the 1σ uncertainty is 0.095 d compared to 0.0003 d from the latter. From the radial-velocity data, the transit time of the first transit in the TESS data is predicted within 2σ. The improvement in the BIC value constitutes a clear detection of the transit signal period in the radial-velocity data (Table 3, Fig. 6). This improvement was complemented by the analysis of the high-spatial resolution imaging (Sect. 3.5), which excluded any background eclipsing binary. Further confirmation was obtained from the comparison of the analysis of the visual (CARMENES VIS, HIRES, PFS) versus infrared (CARMENES NIR, ISHELL) data. The radial-velocity semi-amplitudes determined from both data sets agree within the uncertainties of our preferred model listed in Table 4, showing that the strength of the signal is wavelength independent, as expected for a planetary signal.
### 5.3. Correlated noise, stellar rotation, and search for additional planets
After subtracting the Keplerian signal, a second signal at about 16 d (0.06 d\(^{-1}\)) is detected in the periodograms of the residuals of individual data sets (Fig. 5, panels 2, 5, and 7 from the top) as well as in the combined radial velocity data (Fig. 7). The GLS-periodogram in this figure was calculated from all radial velocity data, corrected for individual offsets taken from the best-fit model (Table 4).
As mentioned in Sect. 4.2, this period is close to half of the stellar rotation period of 33 d (5) and this signal could be due to stellar activity rather than to a second planet. Modelling this signal as a second planet or as correlated noise shows a significant improvement in the BIC value (bottom five rows in Table 3).
A fit with a second Keplerian signal results in a good fit for a Neptune-mass planet (Table 4, Figs. F.1 and F.2). In combination with the REAL kernel, the two-planet model has the lowest BIC value. The eccentricity of the second planet would be rather high (\( e = 0.26 \), without GP). Nonetheless, we checked
Table 4. Model and reference statistical parameters from the simultaneous fit of radial velocities and transit photometry.
| Parameter | One planet + GP(a) | Two planets | Two planets + GP |
|-----------------|-------------------|-------------|------------------|
| $P$ (d) | 4.052037 ± 0.000004 | 4.052039 ± 0.000005 | 16.04 ± 0.04 |
| $K$ (m s$^{-1}$) | 17.6 ± 0.8 | 17.5$^{+0.3}_{-0.2}$ | 6.9 ± 0.3 |
| $e$ | 0.04 ± 0.02 | 0.030$^{+0.008}_{-0.009}$ | 0.26 ± 0.06 |
| $\omega$ (deg) | 219 ± 19 | 191$^{+12}_{-12}$ | 297 ± 112 |
| $t_{pen}$ (d)$^{(b)}$ | 1.80 ± 0.23 | 1.48$^{+0.15}_{-0.10}$ | 7.3 ± 0.9 |
| $i$ (deg) | 87.3 ± 0.2 | 87.2$^{+0.2}_{-0.2}$ | ... |
| $R_p/R_*$ | 0.61 ± 0.009 | 0.67$^{+0.010}_{-0.009}$ | ... |
| $R_*$ (R$_\odot$) | 0.57 ± 0.02 | 0.58 ± 0.02 | ... |
| $u_1$ | 0.48 ± 0.08 | 0.5 ± 0.1 | ... |
| $u_2$ (c) | 0.10 ± 0.2 | 0.47 ± 0.1 | ... |
Derived parameters
| $a$ (au) | 0.0417 ± 0.0005 | 0.0417 ± 0.0005 | 0.104 ± 0.0001 |
| $\lambda$ (deg)$^{(b,d)}$ | 336.1 ± 0.8 | 337.0 ± 0.9 | 135 ± 12 |
| $t_c$ (d)$^{(b,e)}$ | 0.3842 ± 0.00025 | 0.38401 ± 0.00041 | 13.22 ± 0.92 |
| $m_p$ (M$_\oplus$) | 30.8 ± 1.5 | 30.7 ± 0.8 | 18.4 ± 1.0 |
| $a/R_*$ | 15.9$^{+1.0}_{-0.7}$ | 15.8$^{+1.2}_{-0.8}$ | 39.5$^{+3.1}_{-2.0}$ |
| $R_p$ (R$_\oplus$) | 4.7 ± 0.3 | 4.8 ± 0.3 | ... |
| $\rho_p$ (g cm$^{-3}$) | 1.7 ± 0.3 | 1.5$^{+0.3}_{-0.2}$ | ... |
| $T_{eq}$ (K)$^{(f)}$ | 700$^{+19}_{-24}$ | 70$^{+21}_{-29}$ | 444$^{+13}_{-18}$ |
Instrumental parameters offset and weighted rms
| CARMENES VIS (m s$^{-1}$) | −2.5$^{+1.3}_{-1.5}$ | 1.64 | −1.0$^{+0.5}_{-0.4}$ | 4.28 | −2.4$^{+0.8}_{-0.7}$ | 1.85 |
| CARMENES NIR (m s$^{-1}$) | 0.0$^{+2.7}_{-2.6}$ | 12.3 | 5.6$^{+0.5}_{-0.4}$ | 11.8 | −2.8$^{+0.9}_{-0.8}$ | 12.3 |
| ESPRESSO (m s$^{-1}$) | 3.6$^{+3.2}_{-3.1}$ | 0.50 | 3.1$^{+0.2}_{-0.3}$ | 1.26 | 4.8$^{+0.6}_{-0.5}$ | 0.52 |
| HIRES (m s$^{-1}$) | 2.3$^{+1.7}_{-1.6}$ | 0.44 | 1.5$^{+0.4}_{-0.5}$ | 2.80 | 3.5$^{+0.7}_{-1.0}$ | 0.42 |
| PFS (m s$^{-1}$) | −3.6$^{+2.4}_{-2.5}$ | 0.65 | −0.6$^{+0.5}_{-0.3}$ | 2.49 | −4.6$^{+1.0}_{-0.7}$ | 0.90 |
| iSHELL (m s$^{-1}$) | −0.3$^{+2.8}_{-3.0}$ | 5.03 | 0.02$^{+0.2}_{-0.1}$ | 7.61 | 0.0$^{+0.8}_{-1.0}$ | 5.49 |
GP hyper parameters
| Variance (m$^2$s$^{-2}$) | 27$^{+8}_{-6}$ | ... | 16.9$^{+5.5}_{-4.6}$ | 3.0 |
| $\tau_d$ (d) | 3.2$^{+1.9}_{-1.9}$ | ... | 2.2$^{+1.3}_{-0.7}$ |
| $-\ln L$ | 316 | 336 | 303 |
| Red. $\chi^2$ | 0.81 | 2.64 | 1.04 |
Notes. Uncertainties are given as 68% intervals. The planetary parameters of the transiting planet from the different models are within 1-$\sigma$ of each other, proving the consistency of this signal. Posterior distributions of the parameters are displayed in Fig. 11. The derived values for semi-major axis and planetary mass take the stellar mass uncertainty listed in Table 2 into account. The likelihood – $-\ln L$ and the reduced $\chi^2$ is given for the RV fit. (a) We found the best model to be the one planet + GP model. (b) Reference time is BJD = 2458438. (c) Fixed. (d) Mean longitude. (e) Time of inferior conjunction. (f) Assuming zero albedo and full heat redistribution.
the dynamical stability of this hypothetical two-planet system, which would be close to a 4:1 mean motion resonance, using the Hill stability criterion of the angular momentum deficit (AMD) framework introduced by Petit et al. (2018) implemented in the Exo-Striker package (Trifonov 2019). A second (co-planar) planet at a 4:1 period commensurability would be stable up to an eccentricity of about 0.4. The TESS data did not show indications of another transit. However, transits corresponding to most of the viable orbital solutions of this potential planet would have gone undetected due to the gap in the TESS data during the time needed for the data downlink.
Alternatively, we fit the second signal assuming it to be caused by correlated noise due to stellar activity with REAL and SHO kernels. The oscillator period of the SHO kernel representing the stellar rotation periods was constrained by the simultaneous fit of the chromatic index with a wide uniform prior
between 5 d and 200 d. Despite the simultaneous fit of the activity indicator, the fit with the SHO kernel resulted in a strongly damped oscillator equivalent to an exponential decay, which was better modelled using the REAL kernel. This is also indicated by the better BIC value of the fits with the REAL kernel (Table 3). In Fig. 7, the middle and lower panels show the subsequent removal of the two model components, that is, the one-planet and the GP model (REAL kernel). The models are sampled at the times of observation. In Fig. 8, the periodograms of these two model components are shown in comparison to the full dataset.
The two-planet model with GP has a lower BIC value compared to the one-planet model that includes a GP model, however, the Bayes factor differs slightly less than the threshold of five. This weak detection could argue for using this as our final best model, but there is currently more evidence for an interpretation of the 16 d signal as correlated noise due to stellar activity. First, the activity indicators showed periods at 33 d (Hα) and 16 d (dLW and CRX), as seen in Fig. 5. The photometric monitoring with WASP-South showed a peak at 33 d. Secondly, a given GP kernel might not adequately represent the effect of stellar activity. Therefore, we interpret the 33 d as the stellar rotation period and the 16 d signal is potentially the second harmonic. While none of these arguments rule out a second planet, its confirmation would need a longer time base to check the coherence of this signal. We show the comparison of the two-planet model with the GP in more detail in Appendix F (in particular Figs. F.1–F.4).
All the variants of the modelling do not have an impact on the parameters derived for the planet b, as demonstrated by the comparison between the parameters for the one planet + GP, the two planets, and the two planets + GP models shown in Table 4.
### 5.4. Analysis of the transit light curves
As the next step in our analysis, we performed a simultaneous fit of the transit light curves (Figs. 9, 10, and A.1) to obtain the additional planet parameters, namely the planet-to-star radius ratio and a refined orbital period (see Sect. 5.1). We first used the linear ephemeris to calculate all mid-transit times during the fit procedure. The good fit of the ground-based transit follow-up light curves additionally confirms the planetary origin of the 4.05 d signal.
We then allowed for small shifts in the mid-transit times for each transit. The very good match of all the transits with a Keplerian model indicates very small or absent TTVs and, hence, potential planet-planet interaction below the current detection.
threshold. The possible indication of a small shift in mid transit time of the TUG, GMU, and MONET data (Fig. A.1), on the order of 3 min, can be attributed to correlated noise. A small transit midpoint shift of about 2 min (1σ deviation) is also visible in the Spitzer light curve (Fig. 9). By fitting the five TESS transits individually, we also see a scatter in transit time by that amount. The transit times were also checked and confirmed independently within the team using juliet and exofast.
This marginal transit time variation in the Spitzer light curve may indicate that a less massive planet could be hidden in the data. As a result, we explored this possibility using TTVFaster (Agol & Deck 2016). At a 2:1 orbit commensurability or mean motion resonance to planet b, a low-mass planet would produce TTVs of the order of minutes, strongly depending on the period and mass ratio, while its radial velocity signal could be sufficiently low to escape detection in the current data. A more in-depth investigation of the possibility of an additional planet is beyond the scope of this paper and requires more data, in particular, more transit-time measurements for planet b.
5.5. Final model for LP 714-47b
In a final analysis step, we simultaneously fit the radial-velocity data together with the transit light curves. The simultaneous fit slightly improves the parameters. The results are listed in Table 4. In summary, we firmly detect a transiting planet with about twice the mass of Neptune (mₚ = 30.8 ± 1.5 Mₑ) orbiting the early M star LP 714-47 at the period of the signal reported for TOI 442.01. The radius of rₚ = 4.7 ± 0.3 Rₑ makes LP 714-47 b a Neptune-like planet with a mean density of ρ = 1.7 ± 0.3 g cm⁻³. We obtain the stellar radius from the stellar mass prior and the transits individually, we also see a scatter in transit time by that amount. The transit times were also checked and confirmed independently within the team using juliet and exofast.
This marginal transit time variation in the Spitzer light curve may indicate that a less massive planet could be hidden in the data. As a result, we explored this possibility using TTVFaster (Agol & Deck 2016). At a 2:1 orbit commensurability or mean motion resonance to planet b, a low-mass planet would produce TTVs of the order of minutes, strongly depending on the period and mass ratio, while its radial velocity signal could be sufficiently low to escape detection in the current data. A more in-depth investigation of the possibility of an additional planet is beyond the scope of this paper and requires more data, in particular, more transit-time measurements for planet b.
5.5. Final model for LP 714-47b
In a final analysis step, we simultaneously fit the radial-velocity data together with the transit light curves. The simultaneous fit slightly improves the parameters. The results are listed in Table 4. In summary, we firmly detect a transiting planet with about twice the mass of Neptune (mₚ = 30.8 ± 1.5 Mₑ) orbiting the early M star LP 714-47 at the period of the signal reported for TOI 442.01. The radius of rₚ = 4.7 ± 0.3 Rₑ makes LP 714-47 b a Neptune-like planet with a mean density of ρ = 1.7 ± 0.3 g cm⁻³. We obtain the stellar radius from the stellar mass prior and the transits individually, we also see a scatter in transit time by that amount. The transit times were also checked and confirmed independently within the team using juliet and exofast.
This marginal transit time variation in the Spitzer light curve may indicate that a less massive planet could be hidden in the data. As a result, we explored this possibility using TTVFaster (Agol & Deck 2016). At a 2:1 orbit commensurability or mean motion resonance to planet b, a low-mass planet would produce TTVs of the order of minutes, strongly depending on the period and mass ratio, while its radial velocity signal could be sufficiently low to escape detection in the current data. A more in-depth investigation of the possibility of an additional planet is beyond the scope of this paper and requires more data, in particular, more transit-time measurements for planet b.
5.5. Final model for LP 714-47b
In a final analysis step, we simultaneously fit the radial-velocity data together with the transit light curves. The simultaneous fit slightly improves the parameters. The results are listed in Table 4. In summary, we firmly detect a transiting planet with about twice the mass of Neptune (mₚ = 30.8 ± 1.5 Mₑ) orbiting the early M star LP 714-47 at the period of the signal reported for TOI 442.01. The radius of rₚ = 4.7 ± 0.3 Rₑ makes LP 714-47 b a Neptune-like planet with a mean density of ρ = 1.7 ± 0.3 g cm⁻³. We obtain the stellar radius from the stellar mass prior and the transits individually, we also see a scatter in transit time by that amount. The transit times were also checked and confirmed independently within the team using juliet and exofast.
This marginal transit time variation in the Spitzer light curve may indicate that a less massive planet could be hidden in the data. As a result, we explored this possibility using TTVFaster (Agol & Deck 2016). At a 2:1 orbit commensurability or mean motion resonance to planet b, a low-mass planet would produce TTVs of the order of minutes, strongly depending on the period and mass ratio, while its radial velocity signal could be sufficiently low to escape detection in the current data. A more in-depth investigation of the possibility of an additional planet is beyond the scope of this paper and requires more data, in particular, more transit-time measurements for planet b.
5.5. Final model for LP 714-47b
In a final analysis step, we simultaneously fit the radial-velocity data together with the transit light curves. The simultaneous fit slightly improves the parameters. The results are listed in Table 4. In summary, we firmly detect a transiting planet with about twice the mass of Neptune (mₚ = 30.8 ± 1.5 Mₑ) orbiting the early M star LP 714-47 at the period of the signal reported for TOI 442.01. The radius of rₚ = 4.7 ± 0.3 Rₑ makes LP 714-47 b a Neptune-like planet with a mean density of ρ = 1.7 ± 0.3 g cm⁻³. We obtain the stellar radius from the stellar mass prior and the transits individually, we also see a scatter in transit time by that amount. The transit times were also checked and confirmed independently within the team using juliet and exofast.
This marginal transit time variation in the Spitzer light curve may indicate that a less massive planet could be hidden in the data. As a result, we explored this possibility using TTVFaster (Agol & Deck 2016). At a 2:1 orbit commensurability or mean motion resonance to planet b, a low-mass planet would produce TTVs of the order of minutes, strongly depending on the period and mass ratio, while its radial velocity signal could be sufficiently low to escape detection in the current data. A more in-depth investigation of the possibility of an additional planet is beyond the scope of this paper and requires more data, in particular, more transit-time measurements for planet b.
model and the planetary model. The comparison to the radial-velocity data is shown in Fig. D.1, as well as to the phase-folded data in Fig. 6. In the latter, we omit CARMENES NIR data due to larger uncertainties as they would not contribute any additional information. A comparison of our final model to the transit photometric data sets is displayed in Figs. 9, 10, and A.1. The posterior parameter distribution is presented as a corner plot in Fig. 11.
6. Discussion and conclusions
We used radial-velocity data from CARMENES, ESPRESSO, HIRES, PFS, and iSHELL, and light curves from TESS, Spitzer, and ground-based photometry, as well as high-resolution AO imaging using Gemini/NIRI to confirm the planetary nature of LP 714-47 b and determine the parameters of the planetary system with high accuracy. The simultaneous fit of radial velocities and transits allowed a determination of the planetary mass and radius within 5% and 6%, respectively, while the planet-to-star radius ratio was determined with an even smaller fractional
---
**Fig. 11.** Posterior distribution of planetary parameters from our best-fit model.
**Fig. 12.** Mass-radius diagram for low-mass planets. Mass-radius relations for various compositions are overlayed. Coloured lines are planetary models by Zeng et al. (2016) for idealised pure compositions. Dashed lines indicate constant mean densities. The incoming stellar radiation in present terrestrial units is colour-coded.
Multiple origins of this Neptune desert have been considered:
- Photoevaporation of the planetary atmosphere once a gas-rich planet arrives close to its central star, explaining the lower boundary of the desert (Owen & Wu 2013; Lopez & Fortney 2014; Jin et al. 2014). Either additionally or alternatively, the subsequently released primordial energy from the formation may (further) clean up the Neptune desert, since this energy is comparable to the atmospheric binding energy. This core-powered mass-loss scenario was discussed later by Ginzburg et al. (2016), Gupta & Schlichting (2019, 2020);
- Interplay of gas accretion and planet migration in the core accretion scenario. Planets of low and intermediate masses undergo fast, inward type-I migration and arrive at inner orbits where they cannot accrete efficiently anymore (e.g. Cimerman et al. 2017; Lambrechts & Lega 2017). These emerging gas giants move diagonally in the radius-period diagram and arrive at the upper border of the desert. In addition, scattering events could move gas giants that remained in the outer disc close to their host star, populating that region as well (e.g. Dawson & Johnson 2018). The resulting desert has been observed in several independent planet population syntheses (e.g. Ida & Lin 2008; Mordasini et al. 2009; Bitsch & Johansen 2016; Ndugu et al. 2018);
- Migration of low-mass planets of several Earth masses to the inner regions of the disc (e.g. Flock et al. 2019). At these close orbits, further gas accretion is unlikely due to the high temperatures (Lambrechts & Lega 2017; Cimerman et al. 2017) and the planets are stuck at low masses;
---
Fig. 13. Period-radius diagrams for planets with radius precision better than 10%. The light grey shaded region represents the mean boundaries of the Neptune desert derived by Mazeh et al. (2016) and the dark grey shaded region corresponds to the interior envelope of the 1σ boundaries. The incoming stellar radiation is colour coded.
uncertainty of 1.5%. The limiting factor was the uncertainty in the host star mass. Comparing these uncertainties to those listed in the NASA Exoplanet Archive, LP 714-47 b is among the well characterised planets, allowing for a meaningful comparison with planet structure models (Fig. 12).
As discussed in Sect. 5, the signal at 16 d is significant. From the existing data, it is, however, not possible to identify this signal in the radial-velocity data as a second planet due to the proximity of the period to half of the stellar rotation period at 33 d. We therefore do not claim the detection of a second planet in a 16 d orbit based on the current data set. The transit time of the Spitzer light curve may indicate a weak TTV, which could be due to a rocky planet close to 2:1 mean motion resonance. A longer monitoring of the radial velocity variations to check the coherence of the 16 d signal, as well as the re-visit of TESS in its extended mission to check for changes in transit times and inclination, will shed new light on this issue.
As shown in Fig. 12, LP 714-47 b has the same bulk density as Neptune at twice the Neptune mass and higher equilibrium temperature. Together with its orbital period, this places LP 714-47 b as an apparently typical warm Neptune-like planet at the edge of the Neptune desert. In the orbital period range of tens of days or less, and for a given planet size, the planet occurrence density dn/d log P rises steeply at a specific period before flattening out to a roughly constant value. The position of this rise shifts to larger orbits with rising planet mass and radius (see Fig. 13), creating a diagonal boundary between a rather densely populated zone of super-Earths and an area of very low occurrence represented in grey in Fig. 13 (e.g. Szabó & Kiss 2011; Mazeh et al. 2016). The occurrence of planets such as LP 714-47 b within the Neptune desert provides constraints for the possible scenarios to explain this feature in the planetary system architectures.
---
8 https://exoplanetarchive.ipac.caltech.edu/
– High-eccentricity migration followed by circularisation (Matsakos & Königl 2016). When circularised close to the host star, planets in the intermediate mass range are preferentially subject to tidal disruption. Predictions related to the Neptune desert limits are in good agreement with the observations.
LP 714-47b is among the few objects that populate this desert, residing at its lower boundary. The low density of the planet (see mass-radius diagram Fig. 12) suggests that it hosts an atmosphere, although its composition is not yet known. This low bulk density indicates that at some point during its evolution, LP 714-47b accreted a sizeable gaseous envelope and retained parts of this atmosphere even if it was subject to photoevaporation, which is relatively low due to the late stellar type (see the colour code in Fig. 13). This scenario is supported by the mass of the planet, which is sufficiently high to prevent significant erosion through this mechanism (e.g. Owen & Wu 2013). If, however, the dissipative ESPRESSO Programme 47b showed a preferential loss of light elements, this would indicate that it experienced photoevaporative loss (Bonneke et al. 2019).
The eccentricity of LP 714-47b is very low. If it did indeed experience a high-eccentricity migration in the past, it obviously did survive the event. This is in agreement with its position in Fig. 1 of Matsakos & Königl (2016), where it is inside the stable region.
The close orbit of LP 714-47 b implies a warm environment with equilibrium temperatures of around 700 K. At such temperatures and at its current location, the contraction of an early atmosphere is hindered due to recycling flows that penetrate the planetary Hill sphere, preventing the planet from growing into an gas giant (e.g. Cimerman et al. 2017). This leads to the tentative conclusion that the planet most likely formed in colder regions further out, possibly beyond the water ice line, before migrating inwards while its atmosphere contracted. In summary, LP 714-47b adds to planets in or close to the Neptune desert and, therefore, it contributes to the building up of a sufficiently large sample that can provide constraints for the planet formation scenarios discussed above.
Acknowledgements. CARMENES is an instrument for the Centro Astronómico Hispano-Alemán de Calar Alto (CAHA, Almería, Spain). CARMENES is funded by the German Max-Planck-Gesellschaft (MPG), the Spanish Consejo Superior de Investigaciones Científicas (CSIC), the European Union through FEDER/ERF FITCS-2011-02 funds, and the members of the CARMENES Consortium (Max-Planck-Institut für Astronomie, Instituto de Astrofísica de Andalucía, Landessternwarte Königstuhl, Institut de Ciències de l’Espai, Insti- tut für Astrophysik Göttingen, Universidad Complutense de Madrid, Thüringer Landessternwarte Tautenburg, Instituto de Astrofísica de Canarias, Hamburger Sternwarte, Centro de Astrobiología and Centro Astronómico Hispano-Alemán), with additional contributions by the Spanish Ministry of Economy, the German Science Foundation through the National Research Instrumentation Program and DFG Research Unit FOR2544 “Blue Planets around Red Stars”, the Klaus Tschira Stiftung, the states of Baden-Württemberg and Niedersachsen, and by the Junta de Andalucía. Based on data from the CARMENES data archive at CAB (INTA-CSIC). We acknowledge the use of public TESS Alert data from pipelines at the TESS Science Office and at the TESS Science Processing Operations Center. This research has made use of the Exoplanet Follow-up Observation Program website, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products. Some of the observations in the paper made use of the High-Resolution Imaging instrument Zorro. Zorro was funded by the NASA Exoplanet Exploration Program and built at the NASA Ames Research Center by Steve B. Howell, Nic Scott, Elliott P. Horch, and Emmett Quagley. Zorro was mounted on the Gemini South telescope of the international Gemini Observatory, a program of NSF’s OIR Lab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. on behalf of the Gemini partnership: the NSF, AURA, Inc., the Canadian Institutes of Health Research (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea). This work makes use of observations from the TESS Science Institute network. This article is based on observations with the MuSCAT2 instrument, developed by ABC, at Telecoso Carlos Sánchez operated on the island of Tenerife by the IAC in the Spanish Observatorio del Teide. This paper is also based on observations made in the Observatorios de Canarias del IAC with the Nordic Optical Telescope operated on the island of La Palma by NOTSA in the Observatorio del Roque de los Muchachos. Data were partly obtained with the MONET/South telescope of the MMONitoring NeW-Work of Telescopes, funded by the Alfred Krupp von Bohlen and Halbach Foundation, Essen, and operated by the Georg-August-Universität Göttingen, the McDonald Observatory of the University of Texas at Austin, and the South African Astronomical Observatory. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This research made use of Lightkurve, a Python package for Kepler and TESS data analysis (Lightkurve Collaboration 2018). We acknowledge financial support from the Spanish Agencia Estatal de Inve- stigación of the Ministerio de Ciencia, Innovación y Universidades and the Euro- pean FEDER/ERF funds through projects AYA2015-69350-C3-2-P, PGC2018- 098153-B-C31/C3, AYA2016-79425-C3-1732-P, AYA2018-84089, BES-2017- 887, under the EXOAST programme, which is supported by the German Federal Ministry for Education and Research (BMBF) and the Spanish Ministerio de Economía, Industria y Competitividad through the EXOAST-2020 project. The work was also supported by the Spanish Ministry of Economy, the German Max-Planck-Gesellschaft (MPG), the Spanish Consejo Superior de Investigaciones Científicas (CSIC), the European Union through FEDER/ERF FITCS-2011-02 funds, and the members of the CARMENES Consortium (Max-Planck-Institut für Astronomie, Instituto de Astrofísica de Andalucía, Landessternwarte Königstuhl, Institut de Ciències de l’Espai, Insti- tut für Astrophysik Göttingen, Universidad Complutense de Madrid, Thürin- gier Landessternwarte Tautenburg, Instituto de Astrofísica de Canarias, Hamburger Sternwarte, Centro de Astrobiología and Centro Astronómico Hispano-Alemán), with additional contributions by the Spanish Ministry of Economy, the German Science Foundation through the National Research Instrumentation Program and DFG Research Unit FOR2544 “Blue Planets around Red Stars”, the Klaus Tschira Stiftung, the states of Baden-Württemberg and Niedersachsen, and by the Junta de Andalucía. Based on data from the CARMENES data archive at CAB (INTA-CSIC). We acknowledge the use of public TESS Alert data from pipelines at the TESS Science Office and at the TESS Science Processing Operations Center. This research has made use of the Exoplanet Follow-up Observation Program website, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products. Some of the observations in the paper made use of the High-Resolution Imaging instrument Zorro. Zorro was funded by the NASA Exoplanet Exploration Program and built at the NASA Ames Research Center by Steve B. Howell, Nic Scott, Elliott P. Horch, and Emmett Quagley. Zorro was mounted on the Gemini South telescope of the international Gemini
A&A 644, A127 (2020)
**Appendix A: Photometric facilities**
**Table A.1. Photometric facilities.**
| Instrument | Transit date | Diameter (m) | FOV (arcmin²) | CCD | Scale (arcsec pix⁻¹) | Filter(s) | N | Δt (min) |
|------------|--------------|--------------|----------------|-----|---------------------|-----------|---|----------|
| TRAPPIST-South Paranal Observatory | 2019-02-17 | 0.6 | 22 × 22 | 2k × 2k | 0.65 | z' | 506 | 190 |
| LCOGT | 2019-02-17 | 1.0 | 26 × 26 | 4k × 4k | 0.39 | z' | 156 | 184 |
| Las Cumbres Observatory Global Telescope | 2019-02-17 | 0.36 | 18.8 × 12.5 | 1.5k × 1k | 0.74 | R | 147 | 196 |
| El Sauce Observatory | 2019-02-17 | 1.2 | 12.6 × 12.6 | 2k × 2k | 0.37 | V | 236 | 130 |
| MONET-S | 2019-09-27 | 1.0 | 21.5 × 21.5 | 4k × 4k | 0.31 | R | 114 | 219 |
| South African Astronomical Observatory | 2019-10-05 | 1.0 | 25.6 × 25.6 | 4k × 4k | 0.39 | g' | 88 | 266 |
| TUG | 2019-10-30 | 1.52 | 7.4 × 7.4 | 4 × 1k × 1k | 0.44 | g', r', i', z' | 4 × 230 | 229 |
| Steward Observatory | 2019-12-17 | 0.6 | 26 × 26 | 4k × 4k | 0.39 | g' | 146 | 157 |
| MU1MT | 2019-12-21 | 0.8 | 23 × 23 | 4k × 4k | 0.34 | R_c | 186 | 257 |
| TUG | 2019-12-25 | 0.4 | 22.5 × 22.5 | 4k × 4k | 0.34 | R_c | 186 | 257 |
**WASP-South.** TOI 442 was monitored over 120 days in 2008/9 by WASP-South, the Southern station of the Wide Angle Search for Planets. WASP-South (located at SAAO, Sutherland, South Africa) was an array of 8 cameras using 200 mm, f/1.8 lenses with a broadband filter spanning 400–700 nm, equipped with 2048 × 2048 CCDs giving a plate scale of 13.7 arcsec per pixel.
**LCOGT.** We obtained a full transit on UTC 2019-02-17 from a 1 m telescope of the LCOGT node at the Cerro Tololo Inter-American Observatory. A total of 155 frames covering 190 min of the 2019-02-17 transit were obtained in z'-band. The telescope is equipped with a Siministro camera with a pixel scale of 0.389 arcsec. The PSF is 1.75 arcsec, sources are extracted with a 16 pixel aperture. The images were calibrated by the LCOGT BANZAI pipeline (McCully et al. 2018) and photometric data were extracted using AstroImageJ.
**MONET-South.** The 1.2 m MONET/South telescope (MONitoring NEtwork of Telescopes) is located at the South African Astronomical Observatory (Northern Cape, South Africa). It is equipped with a Finger Lakes ProLine 2k × 2k e2v CCD and has a 12.6 × 12.6 arcmin² field of view. We performed aperture photometry with AstroImageJ using eight comparison stars, 236 images in V have been obtained covering 130 min of the 2019-09-27 transit.
**MuSCAT2.** The Multicolour Simultaneous Camera for studying Atmospheres of Transiting exoplanets 2 (MuSCAT2; Narita et al. 2019) is mounted at Telescopio Carlos Sánchez in Teide observatory (Tenerife, Spain). MuSCAT2 observes simultaneously in the g, r, i, and z₅ bands using a set of dichroics to split the light between four separate cameras with a field of view of 7.4 × 7.4 arcmin² (0.44 arcsec pix⁻¹). MuSCAT2 is designed to be especially efficient for science related to transiting exoplanets and objects varying on short timescales around cool stellar types. Aperture photometry is calculated using a Python-based pipeline especially developed for MuSCAT2 (see Narita et al. 2019, for details).
**TRAPPIST-South.** TRAPPIST-South at ESO’s La Silla Observatory in Chile is a 60-cm Ritchey-Chrétien telescope, which has a thermo-electrically cooled 2k × 2k FLI Proline CCD camera with a field-of-view of 22′ × 22′ and resolution of 0.65 arcsec pix⁻¹. We carried out a full-transit observation of TOI 442 on 2019-02-17 with the z’ filter using an exposure time of 10 s. We took 505 images, and we made use of AstroImageJ to perform aperture photometry, where the optimum aperture was 10 pixels (6.5 arcsec) and the PSF was 3.4 arcsec. We cleaned all the stars from eclipsing binaries within the 2.5 arcmin around the target star.
**ULMT.** We obtained a full transit on UTC 2019-10-30 from the University Louisville Manner Telescope (ULMT), which is located at Steward Observatory on Mount Lemmon near Tucson, Arizona. The observations employed a 0.6 m f/8 telescope equipped with an SBIG STX-1603 CCD which has a 4k × 4k array of 9 μm pixels, yielding a 0.39 arcsec pixel scale and a 26 × 26 arcmin field of view. A total of 89 g'-band exposures were obtained covering 266 min. The images were calibrated and photometric data were extracted using AstroImageJ.
**El Sauce.** We obtained a full transit on UTC 2019-02-17 from El Sauce private observatory in Coquimbo Province, Chile. The 0.36 m telescope is equipped with an SBIG STT/1603-3 camera with a pixel scale of 0.735 arcsec resulting in an 18.8 × 12.5 arcmin field of view. In-camera binning was used at 2 × 2 giving an operating pixel scale of 1.47 arcsec. A total of 146 exposures covering 190 min were obtained in R₅-band. The PSF is 5.7 arcsec and sources were extracted with a 6 pixel aperture. The photometric data were extracted using AstroImageJ.
**TUG.** The 1m Ritchey-Chrétien T100 telescope located at TÜBİTAK (The Scientific and Technological Research Council of Turkey) National Observatory (TUG) is equipped with an SI 1100 4k × 4k CCD camera with 15 × 15 μm pixels and 21.5′ × 21.5′ FoV. The full-transit observations have been obtained in Bessell R filter using an exposure time of 60 s. We obtained 114 frames for a full-transit observation on 2019-10-05.
During the data reduction, we performed aperture photometry using AstroImageJ with an aperture radius of 24 pixels (7.7 arcsec).
**GMU.** The 0.8 m Ritchey-Chrétien Optical Guidance Systems telescope is located at and operated by George Mason University. The observations employed an $R_c$ filter equipped with a SBIG16803 4k × 4k CCD with 9 × 9 μm pixels and 23′ × 23′ FoV. The images were calibrated and photometric data were extracted using AstroImageJ.
The main information of the ground-based photometry is also summarised in Table A.1. In the main text, we show the comparison of our final model to most of our data. Here, we add the comparison to the other ground-based transit data (Fig. A.1).
**Appendix B: ALFOSC low-resolution spectrum**
We used the spectroscopic catalogue of M dwarfs by Alonso-Floriano et al. (2015) to determine the spectral type of LP 714–47 to be M2 V, with an error of half of a subtype. This classification is later than that determined by Lee (1984). However, as shown in the bottom panel of Fig. B.1, the match between our target and the M2V spectral standard is far from what is expected for a reliable classification, with significant deviations at wavelengths affected by the molecular absorption of TiO. This suggests that the metallicity of LP 714–47 is likely non-solar. We used the NEXTGEN synthetic spectra computed for different stellar parameters (Allard et al. 1997; Hauschildt et al. 1999) with a resolution degraded to the ALFOSC data, and found that when all three parameters (temperature, surface gravity, and metallicity) are free, the solution is degenerate. Models with $T_{\text{eff}}$ in the interval 3700–3900 K, atmospheric gravity $\log g = 5.0–5.5$ (cgs), and metallicity of [M/H] = +0.3 dex (metal-rich) and −0.5 dex (metal-depleted) yield acceptable fits to the ALFOSC observations.
To conclude whether LP 714–47 is a metal-rich or metal-poor star, we used data from the literature (see next), and the modelling of the CARMENES high-resolution spectra (see main text of this paper). The optical and near-infrared colours of LP 714–47 appear to be consistent with the stars of the solar neighbourhood.
with similar spectral types, which implies a metallicity close to that of the solar vicinity. Using Gaia DR2 proper motion, parallax, and radial velocity, we obtained the space motions \( U = 124.4 \pm 3.5 \), \( V = -253.2 \pm 2.8 \), and \( W = -67.6 \pm 2.0 \) km s\(^{-1}\). The equations of Johnson & Soderblom (1987) were employed, where \( U \) is defined as positive away from the Galactic centre. Following the criteria of Leggett (1992), because of its very negative \( V \) and \( W \) velocities, LP 714-47 may kinematically belong to a low-metallicity population of the Galaxy. From the extensive MaStar stellar library (described in Yan et al. 2019), we found good matches to the ALFOSC spectrum using stars with \( T_{\text{eff}} = 3750 \) K and \([\text{Fe/H}] = -0.26 \) dex (see top panel of Fig. B.1).
**Appendix C: Additional high-contrast imaging**
Direct high-resolution imaging observations of LP 714-47 were carried out on 14 January 2020 using the Zorro speckle instrument on Gemini-South\(^9\). Zorro simultaneously provides speckle imaging in two bands, 562 nm and 832 nm, with output data products including a reconstructed image, and robust limits on companion detections (Howell et al. 2011). The observations consisted of 5 sets of 1000, 0.06 s observations each obtained during a night of good seeing (0.6 arcsec). Fig. C.1 shows the speckle imaging contrast curves in both bands and the reconstructed high-resolution images for LP 714-47. Based on these observations, we find that LP 714-47 is a single star with no companion brighter than about 5–7.5 magnitudes detected within 1.2 arcsec. These limits correspond to a detection of no companion brighter than an M7-M9 main sequence star between the inner and outer working angle limits, for \( d = 52 \) pc, of 0.9 to 1.5 au.
**Appendix D: Additional model comparison to data**
In addition to the phase-folded presentation of the radial-velocity data compared to our final model (Fig. 6), here we present the entire radial-velocity data set compared to the final model over the time base of the observations. In this plot, we also show the contribution of the Keplerian model only. The modification by the added GP model is especially visible in the regions of ESPRESSO data around BJD 2458748 and HIRES data around BJD 2458788.
---
\(^9\) [https://www.gemini.edu/sciops/instruments/aloneke-zorro/](https://www.gemini.edu/sciops/instruments/aloneke-zorro/)
Appendix E: Modelling details
As mentioned in Sect. 5, we used celerite (Foreman-Mackey et al. 2017) as parametric noise model accounting for covariances between data points, which offers a fast and reliable implementation of GP regression. Covariances may be due to stellar, instrumental, or observational origin.
The likelihood function for \( N \) data points \( y_n \) at times \( t_n \), with uncertainties \( \sigma_n^2 \), and model parameters \( \theta \) (in our case the Keplerian orbital parameters) providing the residual vector \( r \) is:
\[
\ln p((y_n) | (t_n), \{\sigma_n^2\}, \theta) = - \frac{1}{2} r^T K^{-1} r - \frac{1}{2} \ln \det K - \frac{N}{2} \ln 2\pi.
\]
The covariance matrix \( K_{nm} = \sigma_n^2 \delta_{nm} + k(\tau_{nm}) \) has two terms, the uncertainties on the diagonal, which may include a quadratically added jitter \( k(\tau_{nm}) = \sigma_n^2 \delta_{nm} \), and the covariances or kernel as function of time differences \( \tau_{nm} = t_n - t_m \). For the latter, celerite restricts the parametrisation to the following sum of complex exponential functions for \( J \) kernels:
\[
k(\tau_{nm}) = \sum_{j=1}^{J} \left[ (a_j + ib_j) e^{-(c_j + id_j)\tau_{nm}} + (a_j - ib_j) e^{-(c_j - id_j)\tau_{nm}} \right].
\]
\[
k(\tau_{nm}) = \sum_{j=1}^{J} \left[ a_j e^{-\beta_j \tau} + a_j^* e^{-\beta_j^* \tau} \right].
\]
For \( b = 0 \) and \( d = 0 \), the kernel is called REAL and represents an exponential decay at a characteristic time scale \( \tau \) and has two
free parameters, the variance \( a \) and \( c = 1/\tau \):
\[
k(\tau_{nm}) = a \exp(-c \tau_{nm}).
\]
(E.3)
A kernel representing damped oscillations driven by white noise is called \( \text{SHO} \). It could represent solar-like oscillation or pseudo radial velocity variations from evolving spots on the rotating stellar surface. It has three parameters, the undamped oscillator period \( P = 2\pi/\omega_0 \), a damping time scale \( \tau \) related to the quality factor \( Q \), and the variance \( S_0 \). For more details see Eqs. (19)–(24) in Foreman-Mackey et al. (2017). It has the form:
\[
k(\tau_{nm}) = S_0 \omega_0 Q \exp -\frac{\omega_0 T_{n,m}}{2Q}
\]
\[
\begin{align*}
\cosh (\eta \omega_0 \tau_{nm}) + \frac{1}{\eta Q} \sinh (\eta \omega_0 \tau_{nm}) & \quad 0 < Q < 1/2 \\
\frac{2(1 + \omega_0 T_{n,m})}{\eta Q} & \quad Q = 1/2 \\
\cos (\eta \omega_0 \tau_{nm}) + \frac{1}{\eta Q} \sin (\eta \omega_0 \tau_{nm}) & \quad 1/2 < Q
\end{align*}
\]
with \( \eta = \sqrt{1 - (4Q^2)^{-1}} \).
Appendix F: Two-planet model
As discussed in Sect. 5, a second planet may be present. Its orbital period close to the first harmonic of the stellar rotation period requires a longer time base in order to check the coherence of that signal. We show the fit to the current data here. Additional ground-based data, especially longer coverage of a single instrument, would be necessary for discriminating between planetary origin and stellar activity.
Assuming the second signal to be of planetary origin, we show the fit to all radial velocity data in Fig. F.1, and the second phase-folded with the correlated noise and the first planet removed (Fig. F.2). The decomposition of the radial velocity data into the two planetary signals and the correlated noise is shown in Figs. F.3 and F.4.
Fig. F.1. Radial-velocity data (CARMENES VIS/NIR in light blue and orange circles, respectively, ESPRESSO in purple upper triangles, HIRES in crimson lower triangles, PFS in orange diamonds, and iSHELL in green pentagons). The two-planet model is shown in dark grey (thick line) including the variation due to the GP (light grey). The two-planet model is shown in darker grey and thin line.
Fig. F.2. Radial velocity data (grey symbols) and corrected for correlated noise (coloured symbols) phase folded to the period of the putative second planet.
Fig. F.3. Subsequent pre-whitening of the radial velocity data (top) with the signals of TOI 442.01 and the potential second planet (second panel), the Gaussian Process modelling the correlated noise (third panel), and the residuals (bottom). Horizontal lines indicate the false alarm probability of 1%, 0.11%, and 0.01%, respectively.
Fig. F.4. Periodograms of the model components: original radial-velocity data (top) the Gaussian process modelling the correlated noise (second panel), planet b (third panel), and the potential second planet (bottom). Horizontal lines indicate the false alarm probability of 1%, 0.11%, and 0.01%, respectively. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4699,
1
],
[
4699,
9594,
2
],
[
9594,
14816,
3
],
[
14816,
21411,
4
],
[
21411,
26192,
5
],
[
26192,
33779,
6
],
[
33779,
35522,
7
],
[
35522,
42592,
8
],
[
42592,
46921,
9
],
[
46921,
49596,
10
],
[
49596,
56708,
11
],
[
56708,
58168,
12
],
[
58168,
62218,
13
],
[
62218,
70797,
14
],
[
70797,
70797,
15
],
[
70797,
70797,
16
],
[
70797,
76183,
17
],
[
76183,
78352,
18
],
[
78352,
80799,
19
],
[
80799,
82311,
20
],
[
82311,
84507,
21
],
[
84507,
85313,
22
]
]
} |
222aa0b23217fcf3053e836a19272c54ab8d70bd | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 17,
"total-fallback-pages": 0,
"total-input-tokens": 46513,
"total-output-tokens": 18265,
"fieldofstudy": [
"Biology"
]
} | Viral Membrane Fusion and Nucleocapsid Delivery into the Cytoplasm are Distinct Events in Some Flaviviruses
Adel M. Nour¹, Yue Li¹, Joseph Wolenski², Yorgo Modis¹*
¹ Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, Connecticut, United States of America, ²Department of Molecular, Cellular and Developmental Biology, Yale University, New Haven, Connecticut, United States of America
Abstract
Flaviviruses deliver their genome into the cell by fusing the viral lipid membrane to an endosomal membrane. The sequence and kinetics of the steps required for nucleocapsid delivery into the cytoplasm remain unclear. Here we dissect the cell entry pathway of virions and virus-like particles from two flaviviruses using single-particle tracking in live cells, a biochemical membrane fusion assay and virus infectivity assays. We show that the virus particles fuse with a small endosomal compartment in which the nucleocapsid remains trapped for several minutes. Endosomal maturation inhibitors inhibit infectivity but not membrane fusion. We propose a flavivirus cell entry mechanism in which the virus particles fuse preferentially with small endosomal carrier vesicles and depend on back-fusion of the vesicles with the late endosomal membrane to deliver the nucleocapsid into the cytoplasm. Virus entry modulates intracellular calcium release and phosphatidylinositol-3-phosphate kinase signaling. Moreover, the broadly cross-reactive therapeutic antibody scFv11 binds to virus-like particles and inhibits fusion.
Citation: Nour AM, Li Y, Wolenski J, Modis Y (2013) Viral Membrane Fusion and Nucleocapsid Delivery into the Cytoplasm are Distinct Events in Some Flaviviruses. PLoS Pathog 9(9): e1003585. doi:10.1371/journal.ppat.1003585
Editor: Ted C. Pierson, NIH, United States of America
Received February 6, 2013; Accepted July 12, 2013; Published September 5, 2013
Copyright: © 2013 Nour et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This work was supported by NIH (nih.gov) grants P01 GM022778 and R01 GM103869 to YM and by a Burroughs Wellcome (bwfund.org) Investigator in the Pathogenesis of Infectious Disease Award to YM. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: [email protected]
Introduction
Many enveloped RNA viruses utilize the endocytic pathway to enter host cells [1,2]. Endocytosis begins at the cell membrane, where these viruses bind to their cellular receptors and ends at the lysosome, the “stomach” of the cell. Along the endocytic pathway, changes in the lipid composition and environmental pH provide a series of distinct milieus for specific cellular or viral functions to occur [3]. Enveloped viruses and bacterial toxins enter the endocytic pathway by binding receptors on the cell surface that are coupled to the endocytic machinery, in particular clathrin adaptors. These microbial cargoes undergo sorting at two different checkpoints [4,5,6]. The first is in early endosomes (EEs) where the vesicular contents are either directed back to the cell membrane via tubular structures, or targeted to the trans-Golgi network (TGN). Alternatively, the cargo contents are sorted into intraluminal vesicles and transported to late endosomes via endosomal carrier vesicles (ECVs). ECVs require functional microtubules to be transported to the second sorting station, the late endosomes. In late endosomes, cargo contents can be forwarded to the TGN, the cytoplasm, or for lysosomal degradation. ECVs originate from EEs. Both the EEs and ECVs are rich in cholesterol, phosphatidylycerine (PS) and phosphatidylinositols (PI) [7,8,9]. The level of cholesterol decreases along the endocytic pathway and is replaced with ceramide in late endosomes and lysosomes, where it maintains membrane fluidity [10]. Unlike cholesterol and PS, the anionic lipid BMP (bis(monoacylglycerol)phosphate), also known as LBPA (lysobisphosphatidic acid), is abundant in internal membranes of lysosomes and late endosomes, and depleted in the EEs [7]. BMP regulates membrane sorting and dynamics in the late endosome. Autoantibodies against this lipid result in human disorders such as Niemann-Pick type C (NPC) syndrome, characterized by dysfunctional sorting and trafficking in late endosomes [11].
The genus flavivirus includes important human pathogens such as dengue, Japanese encephalitis (JE), West Nile (WN) and yellow fever (YF) viruses. Flaviviruses contain a lipid envelope and a positive-stranded RNA genome encoding for a polyprotein that is processed by the host- and viral proteases to yield the viral proteins. Three structural proteins (C, M and E) form the virions; the nonstructural proteins (NS1-5) are required for virus replication, transcription and modulation of the host innate immune system [12]. Flaviviruses assemble in specialized structures within the endoplasmic reticulum and mature in the Golgi network [13]. Glycoprotein E forms the outer protein shell of the virion, mediates cellular attachment, and catalyzes the fusion of the viral and cellular membranes necessary to deliver the genome into the cytoplasm. The E ectodomain contains three domains (I–III) connected by hinges [14,15]. Conserved histidine residues at the domain I-domain III interface become protonated at the reduced pH of early endosomal compartments (pH 6–6.5), thereby triggering a conformational rearrangement in E that drives membrane fusion [16,17].
Although flaviviruses generally follow the clathrin-mediated endocytic pathway, other mechanisms of entry have also been proposed. Dengue virus has been reported to fuse primarily from within Rab7-positive late endosomes. However, certain dengue strains have been reported to infect cell independently of Rab7...
Author Summary
Many viruses package their genetic material into a lipid envelope. In order to deliver their genome into the host-cell cytoplasm, where it can be replicated, viruses must fuse their envelope with a cellular lipid membrane. This fusion event is therefore a critical step in the entry of an enveloped virus into the cell. In this study, we used various cell biological and biochemical approaches to map precisely the cell entry pathway of two major human pathogens from the flavivirus family, yellow fever virus and Japanese encephalitis virus. We discovered that these viruses co-opt cellular phospholipid signaling to promote the fusion of their envelope with the lipid envelope of small compartments inside the host-cell endosomes. The viral genome remains trapped in these compartments for several minutes until the compartments fuse with the surrounding endosomal membrane. It is this second membrane fusion event that delivers the viral genome into the cytoplasm. We also showed that the antibody fragment scFv11 inhibits the fusion of the viral envelope with small lipid compartments, explaining the therapeutic activity of the scFv11 antibody. Our work identifies new vulnerabilities in the entry pathway of flaviviruses, including the formation of small endosomal compartments and two distinct membrane fusion events involving these compartments.
Results
Purification of Japanese encephalitis virus-like particles and yellow fever virus
Recombinant Japanese encephalitis virus-like particles (JE-VLPs) were obtained by overexpressing the prM and E genes (see Materials and Methods) in human HEK 293T cells (Figure S1A), and in insect Tni cells using a baculovirus-based expression system (Figure S1B). JE-VLPs and YFV were purified by precipitation of secreted cellular products with polyethylene glycol, followed by sedimentation in sucrose density gradient (Figure S2). Since flaviviruses E proteins bind to heparan sulfate [34], the virus particles could alternatively be purified by affinity chromatography on a heparan sulfate column (Figure S2A-B). Both methods showed highly purified secreted VLPs. Coomassie stained SDS-PAGE confirmed that prM was cleaved to pr and M in the purified particles (Figure S2D), indicating a high degree of maturation in the JE-VLPs. The concentration of the purified VLPs was estimated by enzyme linked immunosorbent assay (ELISA- see Materials and Methods). Negatively stained electron microscopy (EM) show that the JE-VLPs have rough surfaces and diameters ranging from 30 to 40 nm (Figure S2F). Purified yellow fever virus (YFV) particles had a similar appearance but were 50 nm in diameter (Figure S2G). Dynamic light scattering (DLS) analysis indicated an average diameter of approximately 40 nm for the JE-VLPs (Figure S2E), consistent with the EM data.
JE-VLPs from insect or mammalian cells enter the endocytic pathway
Upon attachment to the plasma membrane, flaviviruses localize to clathrin-coated pits and undergo endocytosis [35,36]. Although, VLPs, like full virions, are expected to enter the endocytic pathway, this has not yet been demonstrated experimentally. We treated Vero cells, a commonly used cell line to study flaviviruses, with JE-VLPs and stained fixed cell at different time points with anti-E protein and the endosomal markers Rab5 and Rab7. VLPs attached to the Vero cells immediately. After 5 minutes, E protein colocalized with Rab5. At 15 minutes, E protein colocalized with both Rab5 and Rab7 (Figure 1A) but more so with Rab7, as indicated by the Pearson’s coefficients of 0.19 and 0.34 for colocalization with Rab5 and Rab7, respectively. By 25 minutes, most of the particles colocalized with Rab7 indicating their arrival to late endolysosomal compartments. This confirms that the secreted particles follow the same general cell entry pathway as full mature virions.
Tracking the membrane fusion of single JE-VLP and YFV particles in Vero cells
To dissect the mechanism and kinetics of JE-VLP cell entry, we tracked the membrane fusion step in real time in live cells using confocal microscopy. The lipid envelope of JE-VLPs was labeled with self-quenching concentrations of the hydrophobic dye rhodamine C18 (R18). Fusion of the VLP membrane with an endosomal membrane was detected as a sudden dequenching of R18 fluorescence as the concentrated dye was diluted with lipids from the host membrane. Fluorescent puncta that showed no dequenching were excluded from our analyses. Fusion events were first detected approximately 250 s after treatment of Vero cells, consistent with fusion occurring in early to intermediate endosomal compartments (Figure 1B-C). Notably, the R18 fluorescence signal for individual fusion events remained at its maximal level for 251 ± 97 seconds (n = 14) before starting to decay and the R18 dye remained concentrated in puncta during this fluorescence plateau (Figure 1B-D). Fluorescence was expected to decay immediately after dequenching due to continued dilution with host lipids. The consistent presence of fluorescent puncta for several minutes after fusion suggests that the R18 dye becomes trapped in an endosomal subcompartment after the initial membrane fusion event. The rate of fluorescence decay of the
Figure 1. Endocytosis, live-cell tracking and membrane fusion kinetics of JE-VLPs. (A) 15 min after treatment of Vero cells with 200 μl JE-VLPs (at 17 pM or 50 ng/ml E protein), JEV E protein (green, detected with anti-West Nile primary and fluorescein-labeled secondary antibodies) colocalizes with endocytic markers Rab5 and Rab7 (red). The Pearson colocalization coefficient was 0.19 and 0.34 for E-Rab5 and E-Rab7, respectively.
Chloroquine inhibits flavivirus membrane fusion and delivery of viral RNA into the cytoplasm
Chloroquine is a widely used lysosomotropic drug that acts by inhibiting the acidification of the endocytic pathway. Clinical studies have demonstrated the safety, tolerability, and efficacy of chloroquine as a treatment against ENRON VIRUS [38]. Treatment with 194 µM (0.1 g/l) chloroquine was toxic to Vero cells (Figure 2). In the presence of chloroquine, fluorescence quenching of R18 in R18-labeled JE-VLPs and YFV (Figure 2B-C) was completely inhibited, indicating that membrane fusion of JE-VLPs is dependent on the acidic pH of endosomal compartments. This is consistent with the inhibitory effect of chloroquine and other endosomal pH-neutralizing agents reported in other flaviviruses [35,39].
To confirm that mature flavivirus virions are also dependent on acidic endosomal pH, and that chloroquine inhibits not only fusion but also nucleocapsid delivery into the cytoplasm, we measured the effect of chloroquine on viral RNA release and infectivity of YFV. To measure delivery of YFV genomic RNA into the cytoplasm, infected Vero cells were fractionated into cytoplasmic and endosomal fractions (Figure S3), and viral RNA in the cytoplasmic fraction was detected by relative quantitative RT-PCR (Figure 2D). Chloroquine blocked 95–97% of YFV RNA release in Vero cells. Moreover, in a plaque assay for YFV infectivity in BHK cells, chloroquine completely inhibited infectivity (Figure 2E). These results confirm that the acidity of endosomal compartments is required for flavivirus infection, and that infection can be blocked by lysosomotropic drugs such as chloroquine that raise the endosomal pH.
Microtubules are required for RNA delivery into the cytoplasm and viral infectivity but not membrane fusion
In mammalian cells, endosomal carrier vesicles (ECVs) are transported from early endosomes (EEs) to late endosomes on microtubules. ECVs then dock onto and fuse with late endosomal membrane [40]. Inhibition of microtubule-dependent transport with the microtubule depolymerizing agent nocodazole inhibits West Nile virus infection [35]. Treatment with 20 µM nocodazole was not toxic to the cells, although changes in cell morphology were observed in the treated cells (Figure 3A). In cell pretreated with nocodazole, fluorescence quenching of R18 in R18-labeled JE-VLPs and YFV occurred with similar kinetics as in untreated cells (Figure 3), indicating that nocodazole does not affect membrane fusion. However, the R18 fluorescence intensity gradually increased after fusion (Figure 3B–C), rather than decaying after a 3–4 min plateau as in untreated cells (Figure 1C–D). The gradual increase in fluorescence in the presence of nocodazole may be attributed to sequential homotypic fusion events with other non-fluorescent ECVs in early endosomal compartments. The resulting vesicles would be still relatively small (hence the lack of dilution-dependent decay) but would allow additional R18 quenching (hence the gradual increase in fluorescence). Additionally, inefficient lipid mixing in the presence of nocodazole may contribute to the gradual increase in fluorescence. Consistent with this interpretation, YFV RNA release into the cytoplasm, measured by RT-PCR as described above, was inhibited by 80% in the presence of nocodazole (Figure 3D). Moreover, virus infectivity was completely inhibited by nocodazole (Figure 3E). Together, these results indicate that certain flaviviruses fuse with ECVs, and that membrane fusion and RNA delivery into the cytoplasm are two distinct events.
A lipid specific to late endosomes is required for RNA delivery into the cytoplasm and viral infectivity but not membrane fusion
Having established that membrane fusion occurs early in the endocytic pathway whereas the YFV nucleocapsid is delivered into a late endosomal compartment, we sought next to determine the importance of factors specific to late endosomal compartments for fusion and nucleocapsid delivery. BMP (also known as LBPA) is an anionic lipid that is present in internal membranes, but not the limiting membrane, of late endosomes. An antibody against BMP accumulates on these internal membranes [41] and interferes with the protein sorting and membrane transport functions of the late endosome. Treatment with anti-BMP antibody causes a phenotype characteristic of Niemann-Pick disease type C (NPC) [11,42]. To assess the role of late endosomal trafficking in flavivirus cell entry, we incubated Vero cells with an anti-BMP antibody and assay membrane fusion activity, RNA delivery and infectivity. The staining patterns of endocytosed anti-BMP antibody and of a total mouse IgG control in BHK cells are shown in Figure 4. Pretreatment with anti-BMP antibody followed by infection with R18-labeled JE-VLPs or YFV produced similar R18 fluorescence profiles as in cells pretreated with nocodazole, with normal R18 quenching kinetics but no fluorescence decay (Figure 4C–D). We conclude that membrane fusion is not inhibited by blocking the protein and lipid sorting functions of late endosomes. In contrast, the endocyotised anti-BMP antibody reduced both YFV RNA delivery to the cytoplasm of Vero cells and YFV infectivity in BHK cells by 35% (Figure 4E–F). These data suggest that BMP in internal late endosomal membranes is required for virus infectivity, either to ensure correct ECV trafficking, or possibly to promote “back-fusion” of ECVs to the limiting membrane of the late endosome.
Figure 2. Effects on chloroquine on membrane fusion of JE-VLPs and YFV in Vero cells. (A) 0.1 g/l chloroquine (194 μM) had no notable toxic effect on the cells as indicated by differential interference contrast (DIC) microscopy of untreated cells (left) and chloroquine-treated cells (right). Cells were treated with 0.1 g/l chloroquine and infected with R18-labeled JE-VLPs (200 μl at 17 pM), (B), or with YFV (MOI = 1), (C). Chloroquine blocked VLP membrane fusion, as judged by the lack of R18 fluorescence dequenching in a field of treated cells (red curve) relative to the normal dequenching of R18 in untreated cells (blue curve). (D) Relative qRT-PCR of viral RNA in untreated (mock) and chloroquine-treated Vero cells 1 h post-infection with YFV (MOI = 1). Endosomal and cytosolic fractions were separated and total RNA was extracted from the cytosolic fraction as described in the Materials and Methods. RT-PCR was used to quantify the 3’-UTR of YFV genomic RNA. Error bars represent the standard error of the mean (SEM) of three experiments. Treatment with chloroquine reduced RNA release into the cytoplasm by >95%. (E) Plaque assay with BHK cells infect with YFV (MOI = 0.1) in presence and in absence of chloroquine. BHK cells were infected with MOI 0.1 of YFV in presence and in absence of 0.1 g/l chloroquine. Chloroquine treatment completely inhibited YFV replication. See also Figure S3.
doi:10.1371/journal.ppat.1003585.g002
Figure 3. Microtubules are required for RNA delivery into the cytoplasm and viral infectivity but not membrane fusion. Cells were pretreated with 20 μM nocodazole (a microtubule polymerization inhibitor) for 1 h before treatment with R18-labeled JE-VLPs or YFV. (A) DIC micrograph of the treated cells showing that nocodazole has no toxic effect on Vero cells although the cell morphology is altered. (B) JE-VLPs (200 μl at 17 pM) and (C) YFV (MOI = 0.1–1) fused normally in Vero cells in the presence of 20 μM nocodazole, as indicated by the R18 fluorescence dequenching profiles of three representative tracked particles. (D) qRT-PCR nucleocapsid delivery assay showing that nocodazole reduced YFV nucleocapsid delivery into the cytoplasm of Vero cells by approximately 80% relative to untreated cells. Error bars represent the standard error of the mean (SEM) of three experiments. (E) Plaque assay showing that nocodazole treatment inhibited YFV replication, reducing the number of viral plaques by >97%. See also Movie S2.
doi:10.1371/journal.ppat.1003585.g003
Figure 4. BMP, a lipid specific to late endosomes, is required for nucleocapsid delivery into the cytoplasm and viral infectivity but not membrane fusion. Cells were cultured overnight in media containing 50 μg/ml anti-BMP antibody. Cells were washed and the medium was changed before immunostaining, treatment with R18-labeled JE-VLPs (200 μl at 17 pM) or with YFV (MOI = 0.1–1). (A) Immunostaining of BMP in BHK cells. Left: BMP staining (Texas Red) was mainly perinuclear. Center: NS1-GFP (green) expression in BHK cells to transcomplement the ΔNS1-YFV genome with NS1 for viral production as described in Ref. [37]. (B) BHK cells treated with total mouse IgG instead of anti-BMP antibody. No antibody staining is detectable in the cells (left panel). JE-VLPs, (C), or YFV, (D), fused normally in Vero cells pretreated with anti-BMP antibody, as indicated by the R18 fluorescence dequenching profiles of three representative tracked particles. Error bars represent the standard error of the mean (SEM) of three experiments. (E) qRT-PCR assay showing that pretreatment of Vero cells with anti-BMP antibody reduced the delivery of YFV nucleocapsid into the cytoplasm.
PI(3) kinase activity is required for RNA delivery into the cytoplasm and viral infectivity but not membrane fusion
In our emerging model of flavivirus cell-entry, viruses fuse with ECVs and the nucleocapsid is delivered into the cytoplasm when the ECVs fuse back to the limiting late endosomal membrane. To test this model, we set out to evaluate the importance of factors required for ECV formation for fusion and nucleocapsid delivery and for trafficking of ECV to the late endosome. The lipid phosphatidylinositol-3-phosphate (PI(3)P) is generated by PI(3)P kinase and is required for endocytic trafficking [43]. Vero cells infected with either fusogenic or chemically inactivated YFV or JE-VLPs induced robust activation of PI(3)P kinase as indicated by phosphorylation of AKT, also known as protein kinase B (Figure S4). The PI(3)P kinase inhibitor wortmannin inhibits ECV formation in mammalian cells [44]. PI(3)P is abundant in ECVs and early endosomes, but not in the late endosome [45]. To determine whether PI(3)P kinase activity is required for membrane fusion, we pretreated Vero cells with 60 nM wortmannin and tracked fusion of R18-labeled JE-VLPs and YFV as described above. This concentration of wortmannin was not toxic but did cause vacuoles to form inside the cells as expected (Figure 5A). The resulting R18 fluorescence profiles were similar to those with nocodazole or anti-BMIP antibody pretreatment, with the same R18 dequenching kinetics but no fluorescence decay (Figure 5B–C and Movie S3). Since wortmannin inhibits ECV formation, we attribute the gradual increase in fluorescence in the presence of wortmannin to inefficient lipid mixing. RT-PCR analysis and plaque assay showed that wortmannin pretreatment blocked RNA release into the cytoplasm of Vero cells and viral infectivity in BHK cells, respectively (Figure 5D–E). Collectively, these results suggest that in the absence of ECVs, JE-VLPs and YFV fuse with other as yet unidentified membranous structures or compartments, where the nucleocapsid remains trapped. Alternatively, the lipid composition or curvature of the limiting early endosomal membrane may preclude full membrane fusion of JE-VLPs. The observed R18 dequenching may then be attributed to transient hemifusion of the viral and endosomal membranes, which would allow lipid mixing of the proximal viral and endosomal lipid monolayers, and therefore dilution of R18, without nucleocapsid delivery into the cytoplasm.
YFV and JE-VLPs bind to phosphatidylinerine and fuse with liposomes with an EE/ECV-like lipid composition
In certain flaviviruses low pH does not appear to be sufficient to trigger fusion [21]. We note that YFV fusion is only partially inactivated by a pretreatment under conditions (pH 6.2) but that infection is nevertheless completely inhibited in acidic media (Figure S5). To determine the minimal physicochemical requirements for membrane fusion of JE-VLPs and YFV, we measured fusion of R18-labeled virus particles in vitro in a bulk fusion assay with synthetic liposomes. The liposomes were 0.1 μm in diameter (see Materials and Methods) and their lipid composition was chosen to correspond to those in EEs/ECVs: cholesterol, phosphatidylycholine (PC), phosphatidylethanolamine (PE), PI(3)P, and phosphatidylinerine (PS) at a molar ratio of 3:4:1:1:1 [7,9]. Fusion was measured by R18 dequenching. We found that both JE-VLPs and YFV fused with the liposomes at pH 5.5, but not at neutral pH (Figure 6A). In flaviviruses, a conserved cluster of histidine side chains acts as a “pH sensor”, which triggers the fusogenic conformational change in response to the reduced pH of the endosome [16,17]. The histidine modifying agent diethylpyrocarbonate (DEPC) inactivates VSV [46] and dengue virus [22] by inhibiting the fusogenic conformational change. We found that DEPC also blocked fusion of R18-labeled YFV with liposomes at pH 5.5 (Figure 6B). In conclusion, synthetic liposomes with a lipid composition similar to ECVs are sufficient to induce flavivirus fusion in vitro at low pH.
PS and PI(3)P are abundant in mammalian EEs/ECVs [7]. We found that JE-VLPs and YFV bound to PS-coated beads (Figure 6C). Similarly, heparan sulfate beads also bind the virus particles, consistent with reports that flaviviruses bind heparan sulfate through the viral envelope protein [34,47]. However, the virus particles did not bind to PI(3)P beads (Figure 6D), suggesting that the binding to PS is not due to nonspecific electrostatic interactions and that PS may act as an intracellular receptor or fusion cofactor for flaviviruses. PS and PI(3)P beads bound with equal affinity to polyarginine peptides, indicating that the surface charges of the two types of beads are comparable (Figure S6).
Calcium released into the cytoplasm during viral infection can result in the translocation of PS from cytoplasmic to extracellular lipid leaflets [48,49,50]. Imaging of cells with the calcium-dependent dye Fluo-4 showed that calcium is released into the cytoplasm within one minute of infection with YFV or JE-VLPs (Figure S7). To determine whether intracellular calcium release promotes flavivirus infection we measured the effect of the cell-permeable calcium chelator BAPTA on YFV infectivity. BAPTA reduced YFV infectivity to less than 5% of the untreated infected control (Figure S7C). We propose intracellular calcium release during flavivirus infection may cause a redistribution of PS towards extracellular or luminal leaflets, which may be important for flavivirus infectivity.
A single-chain variable region fragment of Antibody 11 (scFv11) protects Vero cells from infection by JE-VLPs but not YFV
Antibodies that inhibit fusion by targeting the fusion loop of the E protein are important determinants in the humoral response to flavivirus infection [51,52,53]. The therapeutic scFv11 antibody fragment, which recognizes the fusion loop, was selected by phage display for binding to West Nile virus E protein [54,55]. scFv11 protects mice from a lethal challenge of West Nile virus and also protects against dengue virus types 2 and 4 [54]. To probe the reactivity of scFv11 against other flaviviruses, we used an ELISA assay to measure the binding of scFv11 antibody to either JE-VLPs or YFVs. scFv11 bound tightly to JE-VLPs but did not bind to YFV (Figure 7A). These results were confirmed by co-elution of scFv11-VLP complexes in size-exclusion chromatography (Figure 7B), and by a plaque assay with YFV showing that scFv11 had no effect on YFV infectivity.
The location of the scFv11 epitope in the fusion loop of E suggests that scFv11 inhibits viral membrane fusion [55]. To test whether scFv11 inhibits fusion of JE-VLPs, we used the in vitro and in vivo fusion assays described above. Precipitation of R18-labeled JE-VLPs with scFv11 inhibited membrane fusion in Vero cells, as judged by the lack of R18 dequenching. Subsequent addition of untreated JE-VLPs produced R18 dequenching as expected (Figure 7C). In the bulk fusion assay, scFv11 reduced the...
Figure 5. PI(3) kinase activity is required for RNA delivery into the cytoplasm and viral infectivity but not membrane fusion. Cells were pretreated with 0.1 μM wortmannin for 1 h prior to treatment with JE-VLPs (200 μl at 17 pM) or infection with YFVs (MOI = 1). (A) DIC micrograph of the treated cells showing that wortmannin had no toxic effects although treated cells showed a characteristic increase in the number of intracellular vacuoles (red arrows). JE-VLPs, (B), or YFV, (C), fused normally in Vero cells pretreated with wortmannin, as indicated by the R18 fluorescence dequenching profiles of three representative tracked particles. (D) qRT-PCR assay showing that pretreatment of Vero cells with wortmannin reduced the delivery of YFV nucleocapsid into the cytoplasm by 95% relative to untreated cells. Error bars represent the standard error of the mean (SEM) of three experiments. (E) Plaque assay showing that pretreatment of BHK cells with wortmannin reduced YFV replication and viral plaque formation to background levels. See also Movie S3. doi:10.1371/journal.ppat.1003585.g005
acid-induced fusion of JE-VLPs with EE/ECV-like synthetic liposomes by 50% (Figure 7D). These data suggest that the fusion loop of JE-VLPs is accessible to scFv11, which inhibits fusion of JE-VLPs in EEs/ECVs.
The dissociation equilibrium constant of scFv11 from JE-VLPs, measured by isothermal titration calorimetry, was at 150 nM (Figure 7E). scFv11 was previously shown to bind soluble form of West Nile E with a 5 nM dissociation constant [54]. The higher affinity for West Nile E could be due to the fusion loop epitope being partially occluded in JE-VLPs, or to differences in the amino acid sequence or structure of the non-cognate JE E and the cognate West Nile E. The stoichiometry of binding was 0.648 ± 0.013 scFv11 molecules per E protein. Thus, if the JE-VLPs each contain 60 E proteins, as is the case in an electron microscopy structure of tick-borne encephalitis VLPs [56], each JE-VLP would be capable of binding approximately 40 scFv11 molecules.
The observed substoichiometric binding of scFv11 suggests that one third of the E-protein epitopes in VLPs do not bind scFv11 either because they are not fully exposed or because they are clustered too closely together to allow full occupancy by scFv11 without steric clashes. The latter is more likely given the presumed T=1 icosahedral symmetry of the VLPs, in which each E protein displays identical surface epitopes [56]. In contrast, in mature virions in the E proteins are distributed in three distinct chemical environments with slightly different surface epitopes. Two different neutralizing antibodies against dengue and West Nile viruses bind
Figure 6. JE-VLPs and YFV bind to phosphatidylycerine and fuse with liposomes with a lipid composition similar to early endosomes and ECVs. (A) Liposomes were produced from an ECV-like lipid mixture (3:1:1:4, Chol:PE:PI(3)P:PS:PC) as described in the Materials and Methods. JE-VLPs fused efficiently with the liposomes at pH 5.5 but not at pH 8.4. (B) YFV fused normally with the synthetic liposomes at pH 5.5 but pretreatment of the virus with 2 mM DEPC for 30 min blocked fusion at pH 5.5. Error bars represent the standard error of the mean (SEM) of three experiments with fluorescence measured in triplicate for each experiment. (C) Beads coated with the anionic lipid PS pulled down JE-VLPs and YFV. Beads coated with heparan sulfate (HS) were used as a positive control and uncoated beads were used as a negative control. (D) Beads coated with PI(3)P did not bind to either JE-VLPs or YFV. HS-beads and uncoated beads were used as positive and negative controls, respectively.
doi:10.1371/journal.ppat.1003585.g006
PLOS Pathogens | www.plospathogens.org 10 September 2013 | Volume 9 | Issue 9 | e1003585
Only two thirds of the E proteins in their cognate virions [57,58], providing precedents for the stoichiometry reported here for scFv11 binding to JE-VLPs.
**Discussion**
Many enveloped viruses enter the endocytic pathway and rely on specific features of the endosomal environment, in particular the reduced pH and the lipid composition, to trigger membrane fusion and productive delivery of the viral genome into the cytoplasm. Although it has been established that flaviviruses generally undergo clathrin-mediated endocytosis [35,36,59], the sequence and kinetics of the steps required for cell entry remain unclear. It has been reported that approximately 20% of dengue virions fuse early in the endocytic pathway while the rest fuse in late endosomes [60], but it is unclear whether all of these fusion events lead to productive infection. We note that diphtheria toxin, a bacterial bipartite toxin complex composed of carrier and toxin subunits, inserts its carrier subunit into early and late endosomal membranes but the active toxin subunit is only delivered to the cytoplasm from early endosomes, and most of diphtheria toxin complexes are degraded in the lysosome [4].
Little is known about the physical and biological properties of flavivirus VLPs- how and when they assemble, and what their possible roles are in infection and in virus evolution. In this study, we have dissected the cell entry steps of VLPs and virions from two different flavivirus species. Tracking of single virus particles in live cells and virus infectivity measurements in the presence of various cell biological inhibitors are consistent with an entry mechanism in which virus particles fuse preferentially with small endosomal carrier vesicles (ECVs), with nucleocapsid delivery into the cytoplasm occurring several minutes later, when the ECVs fuse with the limiting membrane of the late endosome. Alternatively, instead of fusing completely with ECVs, the virus particles may form metastable hemifusion intermediates with the ECVs, with full fusion only occurring in late endosomes, consistent with a previous report that dengue forms ‘restricted hemifusion’ intermediates [22]. Either way, we conclude that flavivirus membrane fusion and nucleocapsid delivery into the cytoplasm are distinct events in space and time (Figure 8).
While novel for flaviviruses, a sequential cell entry mechanism involving delivery into ECVs followed by back-fusion of the ECVs to the limiting late endosomal membrane is not unprecedented. VSV utilizes this mechanism of nucleocapsid delivery into the cytoplasm occurring several minutes later, when the ECVs fuse with the limiting membrane of the late endosome. Alternatively, instead of binding completely with ECVs, the virus particles may form metastable hemifusion intermediates with the ECVs, with full fusion only occurring in late endosomes, consistent with a previous report that dengue forms ‘restricted hemifusion’ intermediates [22]. Either way, we conclude that flavivirus membrane fusion and nucleocapsid delivery into the cytoplasm are distinct events in space and time (Figure 8).
While novel for flaviviruses, a sequential cell entry mechanism involving delivery into ECVs followed by back-fusion of the ECVs to the limiting late endosomal membrane is not unprecedented. VSV utilizes this mechanism of nucleocapsid delivery into the cytoplasm to reach the cytoplasm [5] although VSV does not impact PI(3)P signaling or trigger intracellular calcium release [31,32,33]. Similarly, anthrax lethal toxin (LT) from *Bacillus anthracis*, a bipartite toxin complex composed of carrier and toxin...
subunits, inserts carrier protein (protective antigen) into ECVs in response to endosomal acidification, and delivers its toxin subunit (lethal factor) into the cytoplasm upon back-fusion of the ECV with the limiting late endosomal membrane to deliver lethal factor to the cytoplasm [6].
The back-fusion of ECVs with the endosome’s limiting membrane depends on the anionic lipid BMP [5], which is found in internal membranes and vesicles within late endosomes but not in the limiting endosomal membrane [8]. Treatment of cells with anti-BMP antibody did not inhibit membrane fusion of JE-VLPs or YFV but strongly inhibited both YFV infectivity and RNA delivery into the cytoplasm. This suggests that the cell entry mechanism of these viruses is dependent on back-fusion of ECVs to the limiting late endosomal membrane. Since anionic lipids are required for efficient fusion of dengue virus [22], the presence of the anionic lipid phosphatidylserine (PS) in ECVs may be responsible for the preference of JE-VLPs and YFV to fuse with ECV membrane over limiting endosomal membranes. Additionally, the presence of cholesterol in the target membrane promotes fusion [61,62] and cholesterol chelation reduces flavivirus infectivity, although addition of exogenous cholesterol at the cellular attachment step has been reported to block JE and dengue virus cell entry [63]. Cholesterol is abundant in early endosomes and ECVs [8].
While anionic lipids are important in a general sense for cell entry of enveloped RNA viruses, PS may perform a more specific function. PS is abundant in early endosomes and ECVs, where PS represents about 9% of all phospholipids [7,9]. YFV and JE-VLPs fused with liposomes of this lipid composition. Moreover, PS-coated beads bound JE-VLPs and YFV whereas beads coated
**Figure 8. Proposed model of flavivirus cell entry.** After binding to their receptors, flaviviruses enter the clathrin-mediated endocytic pathway and are directed to early endosomes (EEs). Virus entry causes an increase in cytoplasmic calcium levels, which may cause a redistribution of phospholipids in the cellular membranes. When the pH of the early endosomal compartments is reduced to approximately 6.5, about 5 min after cellular attachment, virus particles fuse preferentially with ECVs, due to the large excess of ECV membranes over the limiting endosomal membrane. The enrichment of specific anionic lipids in ECVs such as PS may further promote fusion with ECVs over fusion with the limiting endosomal membrane. The nucleocapsid remains trapped in the ECV lumen for several minutes, until the ECV fuses back with the limiting membrane of the late endosome (LE). This back-fusion event requires microtubule transport, PI(3)P-dependent signaling, the late endosomal anionic lipid BMP, and cellular fusion proteins. The PI(3)P kinase inhibitor wortmannin inhibits the formation of ECVs. In the absence of ECVs, flaviviruses either fail to fuse completely with the EE membrane (e.g. fusion proceeds only as far as hemifusion of the proximal lipid layers) or they fuse with as yet unidentified endosomal compartments in which the nucleocapsid remains trapped.
doi:10.1371/journal.ppat.1003585.g008
with PI[3]P, which is also anionic and present in ECVs, did not bind the virus particles. Interestingly, PS is expressed on the plasma membranes of insect cells [64] and malignant and non-apoptotic cells [65,66].
The therapeutic antibody fragment scFv11 binds JE-VLPs with reasonably high affinity. Noninfectious flavivirus VLPs produced during infection [26] may thus serve as antibody decoys to promote immune evasion of the infectious virions. VLPs have recently been in focus as vaccine candidates [27]. Our study establishes that flavivirus VLPs can be used as a model for virus entry and for screening of therapeutic antibodies.
In summary, our work suggests a novel mechanism for flavivirus cell entry in which the virus fuses to ECVs and depends on a second cell-mediated membrane fusion event to deliver the viral genome from the vesicle lumen to the cytoplasm. We propose that flavivirus infection modulates PI[3]P-dependent signaling in the host and modifies host phospholipid distribution to promote fusion with endocytic compartments. Our findings provide a framework for future studies to determine the physicochemical basis of the preference for membrane fusion with ECVs, the nature of the contribution of specific lipids (BMP, PS, cholesterol) to fusion activity, and the precise sequence and kinetics of the molecular steps required for membrane fusion and nucleocapsid delivery.
Materials and Methods
Antibodies
Horse anti-WNV E antibody was a generous gift from L2 Diagnostics (New Haven). The scFv11 construct, a kind gift from Erol Fikrig, was expressed and purified as described [54]. The purified protein showed the expected purity and molecular weight in SDS-PAGE and size-exclusion chromatography (Figure S8). The following reagents were purchased from commercial sources: rabbit anti-human Rab5, Rab7, Phospho-AKT and Total-AKT antibodies (Cell Signaling), anti-LPBA (BMP) antibody (Echelon biosciences), Fluorescein (FITC)-labeled anti-horse antibody (Bethyl Labs.), horseradish peroxidase (HRP)-conjugated anti-horse (Sigma), Texas Red anti-rabbit antibody (Invitrogen), total mouse IgG (Sigma), Texas Red anti-mouse antibody (Invitrogen).
Cell biological inhibitors
All inhibitors were freshly prepared before use according to the manufacturers’ recommendations. 25 μM BAPTA (Sigma) was added to the virus, maintained during cellular attachment, and removed before addition of agaroase plugs in plaque assays. Wortmannin (Sigma) was used at a final concentration of 0.1 μM while nocodazole (Sigma) was used at 20 μM final concentration. Chloroquine (Sigma) was used at a final concentration of 194 μM (0.1 μg/ml). All inhibitors were added to the cells before starting the experiments. In the plaque assay, all of the inhibitors were diluted to their half concentrations and kept in the medium after adding the agaroase plugs as described in plaque assay method. Diethylpyrocarbonate (DEPC) (Sigma) was added at final concentration of 2 mM to purified YFVs for 30 min and then removed by buffer exchange using an ultrafiltration unit.
Expression of the JEV-VLPs
The prM-E sequence of JEV strain CH2195LA was cloned into the pAcgp67 vector (BD Biosciences). Sf9 cells were co-transfected with the linearized baculovirus genome and the pAcgp67-prM-E construct. The secreted recombinant baculovirus encoding the prM-E sequences was amplified in Sf9 cells. For protein expression, Tnl cells (Expression Systems) were infected with the baculovirus in ESF921 medium (Expression Systems) at 27°C. Alternatively, JE-VLPs were expressed in HEK293T cells transiently transfected with the pcDNA-prM-E mammalian expression vector. Cell media was clarified by centrifugation at 4°C. The VLPs were then added to the virus, maintained during cellular attachment, and the precise sequence and kinetics of the molecular steps required for membrane fusion and nucleocapsid delivery.
Production of YFV in baby hamster kidney (BHK) cells
Generation of the BHK cell line expressing the NS1-GFP fusion protein for trans-complementation of YFV 17D genome lacking NS1 has been described previously [37]. Non-infectious ANS1 viruses were collected from the cell culture medium. The YFV particles were purified by PEG6000 precipitation and sucrose gradient as described above for JE-VLPs. In the absence of an effective antibody to detect YFV structural proteins, YFV was quantified in fractions from the sucrose gradient as plaque-forming units in a plaque assay with the BHK-NS1-GFP cells (see below).
Plaque assay of YFV
Serial dilutions of YFV were added to BHK cells (5×10⁵ cells/ml) in DMEM medium. Viruses were allowed to attach to the cells for 1 h at 37°C. A 1:1 mixture of 2× DMEM medium (Gibco) and autoclaved 10% (w/v) agarose (37°C) was then layered onto the cells in 6-well plates. After 2–3 days, the wells were fixed with 7% formalin (Sigma) and the agarose plugs were removed. Cells were stained with 0.5% crystal violet (Sigma) to visualize the plagues. Excess stain was removed with water. For acid pretreatment of YFV, the buffer was exchanged to 50 mM HEPES pH 6.2 with an ultrafiltration device (Millipore), viruses were allowed to attach to cells for 15 min in DMEM pH 6.5 or 7.4, and cells were then washed with DMEM pH 7.4 before proceeding to the next step of plaque assay.
Negative staining
5 μl of JE-VLP suspension was applied for 2 min on the carbon surface of a glow-discharged carbon-coated grid (Microscopic Science). Excess sample was removed using absorbent paper and the grid was air-dried before examination. Data were collected using a Zeiss EM900 electron microscope.
R18 labeling of JE-VLPs
JE-VLPs were labeled with Rhodamine C18 (R18; Invitrogen). The dye was added to the PEG-precipitated fraction of either YFV or JE-VLPs at a final concentration of 20 ng/μl and incubated for 15 min before the sucrose gradient centrifugation step.
**Time-lapse confocal microscopy**
Vero cells were grown on a coverslip petri dish (MatTek) overnight at a density of $5 \times 10^5$ cells/ml at 37°C, 5% carbon dioxide. Before microscopic examination, the medium was changed to serum-free OptiMEM (Gibco) and cells were stained with Hoechst stain (Invitrogen). JE-VLPs were added from a stock at 17 pM (50 ng/ml E protein) and the particles were kept in the medium during data collection. Time-lapse confocal microscopy was performed using a Zeiss microscope connected to 37°C incubated and buffered with 5% CO$_2$. Time-lapse images were collected using a slice of 4 μm to avoid changes in confocal planes during data collection. Images were collected every 10 s. Data were analyzed with ImageJ [67].
**Immunostaining**
Immunostaining was performed as described [68]. Briefly, Vero cells were grown on a coverslip overnight at $5 \times 10^5$ cells/ml and treated at different time points with 34 pM JE-VLPs (50 ng/ml E protein). 1 μl of Hoechst stain (10 g/l) was added to cells for 10 min at 37°C. Cells were fixed with 4% paraformaldehyde and permeabilized with 1% Triton ×100. Cells were then blocked for 1 h with 10% fetal bovine serum (FBS) and stained with the primary anti-Rab5/7 antibody according to the manufacturer’s recommendation (Cell Signaling). The cells were washed 10 times with PBS. For BMP staining, cells were fed 50 μg/ml anti-BMP antibody overnight and the cells were washed and fixed as above. The cells were then permeabilized with 0.3% Tween-20 in PBS and blocked for 1 h in 10% PBS. Cells were blocked for 1 h with 10% PBS and then stained with secondary antibody conjugated to Texas Red (Invitrogen). Cells were washed 10 times with PBS and mounted with fluoromount G (Microscopic Science) before examination. Semi-quantitative colocalization analysis (Pearson coefficient calculation) was performed with ImageJ.
**Bulk fusion assay**
Cholesterol, phosphatidylethanolamine (PE), PI(3)P, phosphatidylserine (PS), and phosphatidylcholine (PC) were mixed in chloroform at a molar ratio of 3:1:1:1:3, respectively, and then dried with argon gas and under vacuum for 2 h. The lipids were resuspended in 3 ml TEA buffer (10 mM triethanolamine pH 8.3, 0.14 M NaCl) and subjected to 10 freeze-thaw cycles using liquid nitrogen and a 37°C water bath. The lipid suspension was then extruded through 0.1 μm membranes 21 times with a lipid extruder (Avanti Polar Lipids). The liposome suspension was added to R18-labeled virus particles. After a 5 min incubation, the pH was modified with either sodium acetate pH 5.5 buffer or with Tris pH 8.4 buffer (70 mM final concentration). R18 fluorescence was monitored after 1 min. with a QuantaMaster cuvette-based spectrofluorometer (Photon Technology International) or at a time-domain plate-based fluorimeter (HoriBa).
**ELISA**
ELISA plates were coated with 0.1 M carbonate buffer pH 9.6 and either JE-VLPs or YFV overnight at 4°C. 6 x 10$^{10}$ JE-VLPs (300 ng E protein) or 6 x 10$^7$ plaque forming units of YFV were added to each well. The coated wells were blocked with 10% FBS in PBS for 1 h at room temperature. Primary antibody was added and plates were incubated for 1 h at room temperature followed by 10 washes with PBS. Secondary antibody was added and the plate was incubated for 30 min at room temperature. Plates were then washed 10 times with PBS. HRP substrate TMB (Sigma) was added and stop solution (Sigma) was used to stop the color development. Absorbance was measured at 450 nm. Standard curves of JE-VLPs were generated by serial dilution of purified VLPs. The concentration of E protein was estimated by comparing Coomassie staining on SDS-PAGE with staining from known concentrations of bovine serum albumin (Sigma). The E protein concentration was used to determine the concentration of JE-VLPs in this study, assuming 60 copies of E per VLP.
**Pull-down assays and genomic RNA extraction**
1 ml of media from BHK cells infected with a YFV multiplicity of infection (MOI) of 0.1, or insect cells expressing prM-E were mixed with a 50 μl suspension of beads coated with heparan sulfate (HS; Sigma), phosphatidylserine (PS; Echelon biosciences), or phosphoinositol-3-phosphate (PI(3)P). The beads were pre-equilibrated with 50 mM Tris pH 7.4 and 0.1 M NaCl. Uncoated beads (Echelon biosciences) were used as a negative control. The beads were collected by centrifugation, washed with equilibration buffer and eluted with 50 mM Tris pH 7.4 and 0.5 M NaCl. Samples containing JE-VLPs were concentrated and the buffer was exchanged to 50 mM Tris pH 7.4, 0.14 M NaCl using an ultrafiltration unit (MilliPore). Samples were then analyzed by SDS-PAGE on 4–20% acrylamide gels and analyzed by Western blotting using the anti-WNV-E antibody. For samples containing YFV, RNA was extracted from the bead eluates with Trizol (Invitrogen) in the presence of 50 μg/ml yeast transfer RNA (RNase and DNase free; Sigma) as a viral RNA carrier. RNA was quantified by RT-PCR as described below. To control for the surface charges of the PI and PI(3)P beads, we tested binding of 2.5 μg/μl polyarginine (5–15 kDa, Sigma) to each types of bead, using 100 μl beads. The binding, wash, and elution steps for polyarginine were performed as described above for JE-VLPs and YFV. Polyarginine in the eluate was quantified using Bradford reagent.
**Subcellular fractionation of cytosolic and endosomal fractions**
We employed an established protocol to isolate endosomes from the cytosolic fraction [5,11,41,69]. Briefly, Vero cells (6 x 10$^6$ cells/ml) in DMEM were infected with YFV (MOI = 1) and incubated for 1 h. Cells were grown in 2 g/l HRP (Sigma) for 40 min post-infection. Cells were washed with PBS and harvested by centrifugation at 1500 rpm for 5 min at 4°C. Cells were suspended in homogenization buffer (3 mM imidazole and 8.5% sucrose pH 7.4 plus protease inhibitors (Roche)) and passed through a steel syringe needle 20 times. The nuclear fraction was isolated by centrifugation for 10 min at 1 kg and 4°C. Sucrose was added to the post-nuclear supernatant (PNS) to a final concentration of 40% (w/v). This mixture was overlaid with 35%, 27%, and 8.5% sucrose cushions in 10 mM HEPES pH 7.4. Samples were centrifuged for 1 h at 100 kg in a SW60 Ti swinging-bucket rotor. Late endosomes were collected at the 27/8.5% sucrose interface while early endosomes were collected at the 35/40% interface. Total RNA was extracted with Trizol (as described above) from the load (cytosolic) fraction. The purity and integrity of the purified RNA was determined by OD260/280 and by 1% formaldehyde agarose gel electrophoresis. To confirm that the isolated endosomes were intact, infected cells were grown with HRP for the last 20 min of the infection and the HRP activity of the endosomal or cytosolic fractions was measured after lysis with 1% Tween-20 (Figure S3A). Effective separation of the cytosolic and endosomal fractions was also confirmed by Western blotting with antibodies against Rab5 and Rab7 (Figure S3C).
RT-PCR and qRT-PCR
The 3' untranslated region downstream primer (5UTR, bases 10109–10128: 5'-AACCCACACATGCAAGCAGCAAA-3') and glycerolaldehyde-3-phosphate dehydrogenase downstream primer (GAPDH, bases 1157–1175: 5'-CCACCACCTGGTTGCTGTG-3') were used to reverse-transcribe the viral RNA and cellular housekeeping gene GAPDH, respectively. Quantitative real-time PCR (qRT-PCR) was performed using the same downstream primers and the 5UTR upstream primer (10337–10318 bases, 5'-CCACCTGGTTGCTGTG-3') and GAPDH upstream primer (bases 724–742: 5'-GCCATTCCCGGTTAGCC-3'). PCR reactions were carried out in triplicate using an RT-PCR kit (Roche) and an ABI 9700HT RT-PCR instrument (Applied Biosystems). The amplified products (228 bp for 3UTR and 450 bp for GAPDH) were identified on 2% agarose gels. RT-PCR products were relatively quantitated with the software SDS. Endogenous GAPDH was used as a control for the quality of the total extracted RNAs. Neither 3UTR nor GAPDH formed primer dimers as judged by the dissociation curve.
Isothermal titration calorimetry (ITC)
Binding of scFv11 to JE-VLPs was analyzed in 50 mM Tris pH 7.4, 0.14 M NaCl, 2 mM β-mercaptoethanol at 25°C, with an iTC200 calorimeter (MicroCal). The sample cell contained 3.1 μM JE-VLPs or buffer only, and the titrant syringe contained 40 μM scFv11. An initial injection of 1.5 μL of scFv11 was followed by 20 serial injections of 2.0 μL scFv11, each at 10 min intervals. The stirring speed was 1,000 rpm and the reference power was maintained at 11 μcal/s. The net heat absorption or release associated with each injection was calculated by subtracting the heat associated with the injection of scFv11 to buffer. Thermodynamic parameters were extrapolated from a curve fit to the data to a single-site model with Origin 7.0 (MicroCal). Experiments were performed in triplicate.
Size-exclusion chromatography binding assay
JE-VLPs, scFv11 and VLP-scFv11 complexes were separated on a Superdex 200 10/300 GL column (GE Healthcare) in 50 mM Tris pH 7.4, 0.14 M NaCl.
Visualization of intracellular calcium release
Vero cells were loaded with 5 μM of Fluo-4 (Invitrogen) for 15 min in DMEM medium. Cells were either infected with YFV (MOI = 5) or treated with 200 μL JE-VLPs (at 17 pM or 50 ng/ml E protein). As a positive control we used 10 mM iomycin (Invitrogen). As a negative control we pretreated Vero cells with 25 mM BAPTA for 30 min before loading the cells with Fluo-4. Images were collected at one frame every 2 s. Fluo-4 fluorescence was analyzed with ImageJ.
Supporting Information
Supporting Information includes seven figures and three movies and can be found with this article at the Journal’s website.
Supporting Information
Figure S1 Expression of JE-VLPs in insect and mammalian cells. (A) HEK293T cells were transfected with a construct for the expression of JE prM-E. Cells were grown on a coverslip for immunostaining. JE E expression (green) was detected only in cells successfully transfected with prM-E construct. (B) Tiat insect cells infected with a recombinant baculovirus designed to express prM-E were plated on a coverslip and subjected to immunostaining using anti-West Nile E antibody. Cells expressing prM-E are stained in red with Texas Red anti-rabbit antibody. Hoechst stain was used to stain the nucleus (blue). (TIF)
Figure S2 Purification of JE-VLPs and YFV. Purification of JE-VLPs, (A), and YFV, (B), by affinity chromatography using a heparan sulfate column. Virus particles were precipitated with PEG 6000, resuspended and loaded onto the column. A NaCl gradient was used to elute the particles (0–0.5 M for JE-VLPs and 0–2 M for YFV). (C) Dot blot detection of JE-VLPs in fractions from a 10–40% sucrose gradient. (D) Coomassie stain of VLPs purified by sucrose gradient centrifugation. Bands corresponding to pr, M and E proteins were detected (arrows). (E) Determination of the hydrodynamic radius of the purified JE-VLPs by dynamic light scattering. The JE-VLPs form a monodisperse population with a radius of approximately 20 nm. Negatively stained electron micrographs of the purified JE-VLPs, (F), and YFV, (G), using 3% uranyl acetate as the contrast agent (pH 4.2). JE-VLPs have a diameter of diameter of approximately 30 nm; YFV viruses have a diameter of 50 nm. (TIF)
Figure S3 Isolation of intact early and late endosomes from Vero cells infected with YFV and cultured in the presence of horseradish peroxidase (HRP). Vero cells infected with YFV (MOI = 1) for 1 h with addition of 2 g/ml HRP for the last 15 min of the infection. Cells were homogenized, and the post-nuclear fraction (PNS) was separated by sucrose gradient centrifugation. (A) Quantification of HRP in the cytosolic and endosomal fractions. The cytosolic fraction contained less than 5% of the HRP activity of the endosomal fraction, indicating that endosomal membranes were mostly intact in the endosomal fraction. (B) RNA extraction from the cytosolic fraction of infected and uninfected Vero cells. The integrity of the purified RNA was assessed by the presence of intact 18S and 28S ribosomal RNA. (C) Western blot of sucrose gradient centrifugation fractions containing early and late endosomes (EEs and LEs), and cytosol using anti-Rab5 or anti-Rab7 antibodies for detection. As expected, only the late endosomal fraction was positive for Rab7. Both endosomal fractions but not the cytosolic fraction were positive for Rab5. (D) RT-PCR of the 3' untranslated region of YFV RNA (left) and endogenous GAPDH (right) in the cytosolic cellular fraction in the presence of different inhibitors. GAPDH was a control for successful isolation of host transcripts and for potential effects of the inhibitors on the quality of the input RNA. The levels of YFV RNA were used to quantify delivery of the nucleocapsid into the cytoplasm. (TIF)
Figure S4 Flaviviruses activate the PI[3]P kinase signaling pathway in Vero cells. Vero cells grown in serum-free DMEM for 30 min were treated with YFV (MOI = 1) or JE-VLPs (17 pM, or 50 ng/ml E protein). Lysates were analyzed at 15, 30 and 60 min. (A) Western blot analysis using anti-Phospho-AKT (upper panel) and Total-AKT (lower panel) antibodies. As a control, serum was added in presence or absence of 60 nM wortmannin (two leftmost lanes). (B) Western blot analysis of Vero cells treated with DEPC-inactivated JE-VLPs and YFV in presence and absence of wortmannin (W). As a positive control serum was added to the leftmost lane. Cells grown in serum-free DMEM were used as a negative control (second lane from the left). (TIF)
Figure S5 Acid pretreatment only partially inactivates YFV. Plaque assay showing that acid pretreatment (incubation in 50 mM HEPES pH 6.2 for approximately 30 min) only
inactivated 40% of YFV in BHK cells in DMEM pH 7.4. Addition of acid-treated YFV to BHK cells in DMEM pH 6.5 almost completely inhibited plaque formation, suggesting that acid-inactivation of YFV is partially reversible.
**Figure S6** PS and PI(3)P beads have a comparable ionic binding capacity. To determine whether PS- and PI(3)- beads have comparable ionic binding capacity, we measured binding of both types of beads to polyarginine. The experiment was carried out as described for the JE-VLPs and YFV, except that polyarginine in the eluted samples was quantified with Bradford reagent. Two different types of beads bind with equal affinity to polyarginine, indicating that the surface charges of the beads are comparable. See also Figure 6A–B.
**Figure S7** Flavivirus infection triggers intracellular calcium release. Vero cells were incubated with 5 μM Fluo-4 for 15 min and infected with YFV (MOI = 1). (A) Snapshots of Vero cells infected with YFV at different time points showing an increase in intracellular calcium (green). Images were collected at one frame every 2 s. (B) Kinetics of intracellular calcium release upon YFV infection. Relative fluorescence intensity is expressed as the fraction of the fluorescence observed in Fluo-4-labeled Vero cells treated with ionomycin (‘% Max. Fl. Intensity’). (C) Cell-permeable calcium chelator BAPTA blocks YFV infection. BHK cells were used in a plaque assay in the presence and absence of 25 μM BAPTA.
**Figure S8** Purification of the recombinant scFv11 antibody fragment from E. coli. scFv11 was expressed and purified as described in the Materials and Methods. (A) Size-exclusion chromatography of purified histidine-tagged scFv11 was used to assess size, purity and solubility of the protein. Most of the scFv11 migrates as a monomer (‘a’). A small fraction of the protein migrates as a dimer (‘a’). (B) SDS-PAGE with Coomassie staining of the purified scFv11 was used to further assess the purity of the protein. The dimer (a) and monomer (b) peaks both contain pure scFv11.
**Movie S1** Tracking membrane fusion of R18-labeled JE-VLPs in Vero cells, monitored as dequenching of R18 dye. Frames were captured every 10 s. The movie frame rate is 7 frames per second.
**Movie S2** Tracking membrane fusion of R18-labeled JE-VLPs in Vero cells in the presence of nocodazole. Frames were captured every 10 s. The movie frame rate is 7 frames per second.
**Movie S3** Tracking membrane fusion of R18-labeled JE-VLPs in Vero cells in the presence of Wortmannin. Frames were captured every 10 s. The movie frame rate is 7 frames per second.
**Acknowledgments**
We thank Brett Lindenbach for providing the necessary reagents to produce YFV, for guidance on plaque assays and cell culture, and for his comments on the manuscript. We thank Erol Fikrig for providing the expression construct and purification protocol for scFv11, and for his comments on the manuscript. The construct for expression of JEV prM-E in mammalian cells was a kind gift from Sun-Chin Wu (National Tsing Hua University, Taiwan).
**Author Contributions**
Conceived and designed the experiments: AMN YM. Performed the experiments: AMNYL JW. Analyzed the data: AMNYL JWYM. Contributed reagents/materials/analysis tools: JW. Wrote the paper: AMN.
25. Zhu YZ, Cao MM, Wang WR, Wang W, Ren H, et al. (2012) Association of heat-shock protein 70 with lipid rafts is required for Japanese encephalitis virus infection in HuH7 cells. J Gen Virol 93: 61–71.
26. Russell PK, Brandt WE, Dalrymple JM (1980) Chemical and antigenic structure of flaviviruses. In: (ed) JEWS, editor. The togaviruses. New York, NY: Academic Press. pp. 503–529.
27. Noad R, Roy P (2003) Virus-like particles as immunogens. Trends Microbiol 11: 436–444.
28. Davis BS, Chang GJ, Cropp B, Roehrig JT, Martin DA, et al. (2001) West Nile virus recombinant DNA vaccine protects mice and horses from virus challenge and expresses in vitro a noninfectious recombinant antigen that can be used in enzyme-linked immunosorbent assays. J Virol 75: 4040–4047.
29. Konishi E, Yamada M, Khan SW, Kurane I, Mason PW (1998) Induction of protective immunity against Japanese encephalitis in mice by immunization with a plasmid encoding Japanese encephalitis virus pre-membrane and envelope genes. J Virol 72: 4923–4930.
30. Konishi E, Pincus S, Paoletti E, Shope RE, Burrage T, et al. (1992) Mice immunized with a subviral particle containing the Japanese encephalitis virus prM/E and E proteins are protected from lethal JEV infection. Virology 188: 714–720.
31. Saeed MF, Kolokoltsov AA, Freiberg AN, Holbrook MR, Davey RA (2008) Phosphoinositide-3 kinase-Akt pathway controls cellular entry of Ebola virus. PLoS Pathog 4: e1000141.
32. Dunn EF, Connor JH (2011) Dominant inhibition of Akt/protein kinase B signaling by the matrix protein of a negative-strand RNA virus. J Virol 85: 422–431.
33. Scherbik SV, Brinton MA (2010) Virus-induced Ca2+ influx extends survival of west nile virus-infected cells. J Virol 84: 4721–4731.
34. Germi R, Candiolo M, Guerin D, Guenette J, Lorret-Jacob H, et al. (2002) Heparan sulfate-mediated binding of infectious dengue virus type 2 and yellow fever virus. Virology 292: 162–168.
35. Chu JJ, Ng ML (2004) Infectious entry of West Nile virus occurs through a clathrin-mediated endocytic pathway. J Virol 78: 10545–10553.
36. Zhu YZ, Cao MM, Wang WB, Wang W, Ren H, et al. (2012) Association of heat-shock protein 70 with lipid rafts is required for Japanese encephalitis virus infection in HuH7 cells. J Gen Virol 93: 61–71.
37. Lindenbach BD, Rice CM (1997) trans-Complementation of yellow fever virus NS5 RNA replicase by early RNA replication. J Virol 71: 9608–9617.
38. Mizu T, Yamashita S, Tanida I, Takeshi Y, Ueno T, et al. (2010) Inhibition of hepatitis C virus replication by chloroquine targeting virus-associated autophagy. Journal of gastroenterology 45: 193–203.
39. Randolph GJ, Stollars V, Groenewald J, et al. (1990) Low pH-induced cell fusion in flavivirus-infected Aedes aegypti cell cultures. J Gen Virol 71 (Pt F): 1845–1850.
40. Gollins SW, Porterfield JS (1986) pH-dependent fusion between the flavivirus pH-dependent effector mechanisms. J Virol 85: 11567–11580.
41. Stiasny K, Koessl C, Heinz FX (2003) Involvement of lipids in different steps of the flavivirus fusion mechanism by using monoclonal antibodies. J Virol 81: 11526–11531.
42. Lebrand C, Corti M, Goodson H, Allsopp RE, Schalich J, et al. (2002) Molecular organization of a recombinant subviral particle from tick-borne encephalitis virus. Mol Cell 7: 593–602.
43. Gillooly DJ, Morrow IC, Lindsay M, Gould R, Bryant NJ, et al. (2000) Localization of phosphatidylinositol 3-phosphate in yeast and mammalian cells. Biological chemistry 382: 483–485.
44. Lebrant C, Corti M, Goodson H, Coston P, Cavalli V, et al. (2002) Late endosome mobility depends on lipids via the small GTPase Rab7. Embo J 21: 1280–1300.
45. Gollins SW, Porterfield JS (1986) pH-dependent fusion between the flavivirus and liposomal model membranes. J Gen Virol 67 (Pt 1): 157–166.
46. French AP, Mills S, Swarup R, Bennett MJ, Pridmore TP (2008) Colocalization of fluorescent markers in confocal microscope images of plant cells. Nat Struct Mol Biol 15: 312–317.
47. Lee CJ, Liu HR, Liao CL, Lin YL (2008) Cholesterol effectively blocks entry of dengue virus that target the fusion loop. J Virol 82: 6470–6480.
48. Miller JL, de Wet BJ, Martinez-Pouares L, Rackcliffe CM, Dwek RA, et al. (2008) The mannos e receptor mediates dengue virus infection of macrophages. PLoS Pathog 4: e17.
49. van der Schaar HM, Chen C, van der Ende-Meteaerlaar H, Wilchert J, et al. (2008) Dissecting the cell entry pathway of dengue virus by single-particle tracking in living cells. PLoS Pathog 4: e1000244.
50. Collins SW, Porterfield JS (1986) pH-dependent fusion between the flavivirus and liposomal model membranes. J Gen Virol 67 (Pt 1): 157–166.
51. Stiasny K, Koessl C, Heinz FX (2003) Involvement of lipids in different steps of the flavivirus fusion mechanism. J Virol 77: 7756–7762.
52. Miller JL, de Wet BJ, Martinez-Pouares L, Rackcliffe CM, Dwek RA, et al. (2008) The mannos e receptor mediates dengue virus infection of macrophages. PLoS Pathog 4: e17.
53. French AP, Mills S, Swarup R, Bennett MJ, Pridmore TP (2008) Colocalization of fluorescent markers in confocal microscope images of plant cells. Nat Struct Mol Biol 15: 312–317. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
6096,
1
],
[
6096,
11347,
2
],
[
11347,
11780,
3
],
[
11780,
17297,
4
],
[
17297,
18741,
5
],
[
18741,
19808,
6
],
[
19808,
20977,
7
],
[
20977,
28016,
8
],
[
28016,
29112,
9
],
[
29112,
31845,
10
],
[
31845,
35479,
11
],
[
35479,
38681,
12
],
[
38681,
44579,
13
],
[
44579,
51630,
14
],
[
51630,
58370,
15
],
[
58370,
61655,
16
],
[
61655,
66815,
17
]
]
} |
438859409c68115c70647677bbffdeb2f39e6ed6 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 6,
"total-fallback-pages": 0,
"total-input-tokens": 13978,
"total-output-tokens": 2723,
"fieldofstudy": []
} | Numerical study of Savonius wind turbine with additional fin blade using computational fluid dynamic
B Anggara*, I Widiastuti and H Saputro
Department of Mechanical Engineering Education, Sebelas Maret University, Surakarta, Indonesia
*[email protected]
Abstract. Savonius wind turbine is the wind energy conversion systems which has good potential for small-scale electrical energy source. However, standard design savonius rotor has a relatively low efficiency and rotation speed. The aim of this research is to study modification of wind turbine design of savonius type S by adding variation of fin in its turbine blades. It utilized computational fluid dynamic (CFD) using a commercial Finite Element (FEA) software. Savonius rotor employed in this research has a 1.1 m rotor diameter in 1.4 m height. The 3D model of savonius rotor was developed by a CAD Software, SolidWorks®. The wind speed utilized for simulation purpose were 3 to 5 m/s with k-epsilon turbulent model. Simulation was performed using ANSYS to generate mesh of the flow domain all of blade variant. Dynamic mesh model was used in this simulation, which then exported to FLUENT in evaluating the fluid flow for determining the aerodynamic coefficient such as drag, torque and power coefficient. This model simulated a fluid flow striking the blade and wind condition around the rotate blade. Results from this study is expected to provide an alternative evaluation of Savonius wind turbine performance in various conditions with different design parameters.
1. Introduction
Savonius wind turbines have good potential for small-scale energy resources. Potential applications of savonius turbine including: residential (lightning, air conditioning, and water pumping for irrigation. This wind turbine has an ability to operate at low wind speeds with good torque [1]. The savonius wind turbine can also receive wind from all directions and has good starting characteristics since it can spin at low wind speed. Considering its characteristic, the savonius wind turbine suitable to be implemented in Indonesia which relatively low wind speed, with the compact design and low construction cost. Savonius wind turbine has several advantages such as a compact design and low construction costs. However, savonius rotor have relatively low efficiency and rotation speed. Several studies were performed either experimentally or numerically to increase savonius rotor performance. Pamungkas and Hasan studied performance of savonius wind turbine with the addition of fin on its blade using experiment methods [2,3]. While Wijayanti studied the aerodynamic characteristic of savonius wind turbine with fin addition on its blade using numerical method [4]. The Computational of Fluid Dynamic method is used employed to estimate the aerodynamic forces acting on the rotor, torque, power absorbed by the rotor savonius. It also to analyze the influence of the variations of turbulence model [5]. Morshed, in his study numerically studied the effects of overlap ratio and Reynolds number on different type of turbine design with overlap ratio variation. It was suggested that the design without overlap ratios provide better aerodynamic coefficients at higher reynolds numbers [6].
& Petry [7] found that the moment coefficient and the wind power coefficient of the savonius rotor achieve the maximum value on the design with an overlap ratio close to 0.15. This numerical study uses a turbulence model k-\(\omega\) SST which is Reynold's simplest approach because it is considered to be in accordance with the phenomenon in this study. Another numerical study of overlap ratio was proposed by Rogowski & Maroński [5] which found that the 0.1 gap width produces higher power coefficient (Cp) compared with a gap width of 0.2. This research used two dimensional design of turbine geometry and adds variations with different turbulence models: SpalartAllmaras (SA), the k-\(\varepsilon\), the realizable k-\(\varepsilon\), the RNG k-\(\varepsilon\), and k-\(\omega\). This turbulence model SpalartAllmaras (SA) showed satisfactory results on modeling with 2 dimensional turbine geometry and the simulation results are similar with the experimental data.
In previous studies addition of fin to the Savonius S type wind turbine can increased electrical power resulted and power coefficient (Cp) [2]. Therefore this research aims to numerically study the aerodynamic behavior of savonius rotor with addition fin on its blade.
2. Method
This research utilized Computational Fluid Dynamic (CFD) method with commercial Finite Element Analysis (FEA) software ANSYS 16.2.
2.1. Geometry and computational domain
Table 1. The design of 3D savonius rotor was developed using CAD software of SolidWorks®.
| Specification | Value |
|-----------------------|----------------|
| Main shaft diameter | 20 mm |
| Rotor diameter | 1100 mm |
| Blade diameter | 600 mm |
| Blade Height | 1400 mm |
| Blade Overlap | 50 mm |
| Number of blade | 2 blade |
| Blade material | 0.3 mm aluminium plate |
Figure 1. The geometry of savonius rotor.
The simulation domain composed of two parts separated by sliding interface. The stationary boundary represents wind tunnel test environments. The stationary domain was assumed with the box shape with
the dimension 4250 mm x 3600 mm x 7600 mm. The velocity inlet was set in 4.5 m/s with the TSR (Tip Speed Ratio) of 0.8 and angular velocity of rotating boundary is 6.5 rad/s. TSR of 0.8 was choose since it was experimentally found that it produces the highest electricity power. TSR value of savonius rotor is less than 1.0, it means that the savonius rotor is a drag type wind turbine.
\[
\text{TSR (} \lambda \text{)} = \frac{\alpha DN}{60V_{\text{max}}}
\]
\[
T = \frac{P_{\text{turbine}}}{\omega}
\]
\[
CP = \frac{T_{\text{turbine}}}{T_{\text{available}}} = \frac{T_{\text{turbine}}}{\frac{1}{2} \rho A V^2 R} = \frac{F X t_p}{\frac{1}{2} \rho A V^2 R}
\]
2.2. Meshing
This research employed mesh motion to analyses the rotating domain. Mesh sizing was set as fine relevance centre and high smoothing mesh. Residual criteria used is $10^{-5}$, means that when the value has below of the criteria the solution will be convergent. Turbulence model used is standard k-ε model which relatively simple and most widely used [8].
2.3. Solving
After the mesh readings, the parameters are then determined to calculate the conditions set in the pre-processing process, boundary condition, solver value of numerical error (residual), and calculation to reach convergence value. Solver used is pressure-based type and for velocity formulation is selected as absolute. The simulation was performed in a transient fluid flow state which changed by time.
3. Discussion
From the simulation found that the drag force that work in 1 fin addition is 21,0041 N. Meanwhile drag force that work in 2 fin variation is 21.0001 N. Torque from the 1 fin addition is 14,712 N. Meanwhile torque of the 2 fin addition is 14,6658. It means that the addition of fins on the rotor blade minimizes the drag force and torque.
 
**Figure 7.** (a) Velocity distribution of 1 fin variation (b) Velocity distribution of 2 fin variation.
This simulation was set in a rotating condition or mesh motion, the velocity distribution show that variations with the addition of 2 fins make the wind speed around the turbine higher compared to 1 fin addition.
 
**Figure 8.** (a) Velocity streamline of 1 fin variation (b) Velocity streamline of 2 fin variation.
From the velocity streamline, the addition of fins on the blade turbine directing the wind flow to fills the space in blade more quickly. The addition fin will causes the blade rotate at lower velocity than without fin. Pressure along the turbine will increased because of smaller area which formed by addition of fin. Pressure of the both side of turbine area will also increase. It means pressure difference of the two blade will decreased because of both turbine area are reached higher pressure. The smaller pressure difference will make positive drag force on the blade also smaller. Torque which produce by savonius rotor will also decreased because of lower angular velocity.
4. Conclusion
The conclusion is that the addition of fin can directing the incoming turbine flow on the turbine, but the addition of the fin can reduce the torque and the drag force from the turbine, the torque variation of the addition of 1 fin higher than the addition of 2 fin at wind speed 4.5 m/s. It means that the addition of 1 fin can reached the higher power coefficient. Because the greater drag force, and torque will increased the power coefficient value [4]. This means that the simulation results support to the experimental results performed by Pamungkas et al and Hasan et al, which say the highest power coefficient is achieved by the 1 fin variation [2].
References
[1] Kamal F M and Islam M Q 2009 Aerodynamic characteristics of a stationary five bladed vertical axis vane wind turbine Journal of Mechanical Engineering, 39(2)
[2] Pamungkas S F, Wijayanto D S, Saputro H and Widiastuti I 2018 Performance ‘S’ Type Savonius Wind Turbine with Variation of Fin Addition on Blade IOP Conference Series: Materials Science and Engineering, 288
[3] Hasan O D S, Hantoro R and Nugroho G 2013 Studi Eksperimental Vertical Axis Wind Turbine Tipe Savonius dengan Variasi Jumlah Fin pada Sudu, 2(2)
[4] Wijayanti W D H, Hantoro R, Nugroho G and Hakim J A R Studi Pengembangan Model Vertical Axis Wind Turbine (VAWT) Savonius Tipe U dengan Penambahan Fin pada Sudu Menggunakan Pendekatan CFD, 6
[5] Rogowski K and Maroński R 2015) CFD computation of the Savonius rotor Journal of Theoretical and Applied Mechanics, 37
[6] Morshed K N 2010 Experimental and Numerical Investigations on Aerodynamic Characteristics of Savonius Wind Turbine with Various Overlap Ratios Electronic Theses & Dissertations,
[7] Akwa J V, Alves S J G and Petry A P 2012 Discussion on the verification of the overlap ratio influence on performance coefficients of a Savonius wind rotor using computational fluid dynamics Renewable Energy, 38(1), 141–149
[8] Debnath B K, Biswas A and Gupta R 2009 Computational fluid dynamics analysis of a combined three-bucket Savonius and three-bladed Darrieus rotor at various overlap conditions Journal of Renewable and Sustainable Energy, 1(3) | 2025-03-06T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3249,
1
],
[
3249,
5201,
2
],
[
5201,
5401,
3
],
[
5401,
6433,
4
],
[
6433,
7725,
5
],
[
7725,
10572,
6
]
]
} |
e197422ca75a08f13b17ba8ec9fd5b9d960e60ba | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 4,
"total-fallback-pages": 0,
"total-input-tokens": 13915,
"total-output-tokens": 6416,
"fieldofstudy": [
"Medicine"
]
} | Urinary Spot Albumin/Creatinine Ratio for Documenting Proteinuria in Women with Hypertensive Disorders with Pregnancy
Keywords: Proteinuria; Albumin/Creatinine ratio; 24 hour urine protein; Preeclampsia
Abstract
Background: Although, twenty-four hour urine collection was considered the gold standard for quantification of proteinuria, it has many limitations. It is cumbersome for the patient and often inaccurate because of under collection and result availability is delayed for at least 24 hours. The spot albumin creatinine (A/C) ratio use in pregnancy has been extensively studied. Its use has been adopted by some authors as they found that it had been significantly correlated to 24 hour urinary protein estimation while others did not support its use as in cases of preeclampsia kidney function may deteriorate rapidly.
Objective: To evaluate the accuracy of random urine albumin/creatinine ratio as a diagnostic method for quantitative evaluation of proteinuria in hypertensive disorders in pregnant women.
Methods: A total of 70 patients fulfilling inclusion criteria were evaluated with urine albumin/creatinine ratio performed on random voided sample. The entire 24 hour urine sample was collected and analyzed for daily protein excretion. A/C ratio was compared to the 24 hour results.
Results: There was significant positive correlation detected between A/C ratio and 24 hour protein at a cutoff value of 347.35 mg/gm. Area under curve for A/C ratio was 0.730 (P<0.001) showing sensitivity 80.6% and specificity 51.2% to detect protein excretion of ≥300 mg/gm. There was significant negative correlation detected between A/C ratio and urine creatinine.
Conclusion: Random A/C ratio could be used as a rapid, easy and reliable test for diagnosis of significant proteinuria in hypertensive disorders with pregnancy, so it can substitute 24 hour urinary protein collection.
Introduction
Preeclampsia is a multisystem disease defined as gestational hypertension with proteinuria or defective placental angiogenesis so, the quantification of proteinuria in preeclampsia is mandatory for diagnosis of the disease [1].
Significant proteinuria is defined by 24 hour urinary protein more than 300 mg/dl or persistent 30 mg/dl in random urine samples [2]. Twenty-four hour urine collection, although the gold standard for estimation of proteinuria has some constraints. It is cumbersome for the patient and often inaccurate because of under collection, and result is delayed for at least 24 hours also [3].
The degree of proteinuria show significant fluctuation throughout the day, even in severe cases. Therefore, significant proteinuria cannot be detected by a single random urinary sample [3].
The spot albumin creatinine (A/C) ratio use in pregnancy has been extensively studied. Its use has been adopted by some authors as they found that it had been significantly correlated to 24 hour urinary protein estimation and in cases of preeclampsia kidney function may deteriorate rapidly while others did not support its use [4].
Both spot albumin/creatinine ratio and spot protein/creatinine ratio had been thoroughly evaluated and used in non-pregnant women. The National Kidney Foundation adopted these tests to evaluate proteinuria in most conditions instead of 24 hour urine collection [5].
The Society of Obstetricians and Gynecologists of Canada, the Society of Obstetric Medicine of Australia and New Zealand and the International Society for the Study of Hypertension in Pregnancy have adopted the spot urine ACR as a practical method for the detection of significant proteinuria (≥0.3 gm/24 hr.) during pregnancy, but this is not proved by other international groups like the National High Blood Pressure Education Program Working Group on High Blood Pressure in Pregnancy and American Congress of Obstetricians and Gynecologists [6].
The aim of this study is to evaluate the accuracy of spot urine albumin/creatinine ratio as a diagnostic method for quantitative assessment of proteinuria in hypertensive disorders in pregnant women.
Patients and Methods
Seventy pregnant women with hypertensive disorders with pregnancy were included in the study at the department of Obstetrics and Gynecology, Zagazig University Hospitals from January 2016 to June 2017. An informed signed consent about the aim of the study, the required procedure and the follow-up plan was obtained from each woman. We exclude patients with a known kidney disease, Presence of bacteruria, Prepregestational and gestational diabetes mellitus, women delivered their babies during the urine collection day. All pregnant women who were included in the study were subjected to:
1. Full history taking, which included personal history, obstetric history, menstrual history, present history, previous and present medical diseases (cardiac, hepatic, renal, endocrinal, pulmonary) and family history of diabetes mellitus and hypertension.
2. **Physical examination:** Which included vital signs as blood pressure, heart rate, temperature and respiratory rate, abdominal examination of fundal level, Leonard’s maneuver and fetal heart sound auscultation, systemic examination of heart, lungs, lower limbs, plus ophthalmic and neurological examination.
3. **Investigations:** Full blood count, blood and Rh grouping, kidney function tests, urine analysis and culture, measurement of urine protein/creatinine ratio and ultrasound.
**Sample collection**
All women were asked to void urine into clearly labeled container over 24 hours. We excluded patients who were not able to complete 24 hour urinary collection. The 24 hour collection was started in the morning by spontaneous voiding. Then, collected samples were sent for analysis.
A single voided urine specimen (5 ml) (not first sample) was obtained randomly for the calculation of A/C ratio; they were stored at 4 °C immediately after collection and examined within 24 hours.
Urine albumin was measured in the central laboratories of Zagazig university by the Bradford method (Bio-Rad Protein Assay Kit, BioRad Laboratories) using BSA (Bio-Rad) as a calibrator. The assay was performed manually as described by the manufacturer. Briefly, in a 96-well plate the protein calibrator (BSA in 0, 1, 2, 3, and 4 µg/10 µl of isotonic saline solution) or 10 µl of sample (urine sample or a diluted sample as necessary to assess for parallelism with the calibratory curve) were mixed with 200 µl of protein assay solution diluted with 4 volumes of ultrapure water; after 5 minutes, we measured the absorbance of the assay mixture at 595 nm using an Emax precision microplate reader (molecular devices). The intra- and inter-assay imprecisions (CVs) were ≥2.3%.
Urine creatinine was measured by the modified kinetic Jaffe reaction in a 96-well plate with a filter at 490 nm using Spinreact kits. The intra- and inter-assay CVs were ≥1.2%. The urine albumin: creatinine ratio (ACR) ranged between 0.17 and 7313 with a mean of 219.3±71.2 mg/g/dl.
Principle of assessment of albumin in urine is to measure the shift in absorption spectrum from 460 to 600 nm of the complex that occurs at acid pH between Pyrogallol Red-Molibdate (PRM) and the basic amino groups of urine. The intensity of the colored complex formed with the calibratory curve were mixed with 200 µl of protein assay solution diluted with 4 volumes of ultrapure water; after 5 minutes, we measured the absorbance of the assay mixture at 595 nm using an Emax precision microplate reader (molecular devices). The intra- and inter-assay imprecisions (CVs) were ≥2.3%.
**Statistical analysis**
All data were collected, tabulated and statistically analyzed using SPSS version 20.
Continuous Quantitative variables e.g. age, laboratory characteristics were expressed as the mean±SD & median (range), and categorical qualitative variables were expressed as absolute frequencies (number) & relative frequencies (percentage). Validity of the screening test (ACR) was assessed in the terms of sensitivity, specificity, predictive value positive, predictive value negative, Likelihood ratio positive, Likelihood ratio negative and accuracy.
**Results**
Seventy pregnant women with hypertensive disorders with pregnancy were admitted to Zagazig University hospital during the period from January 2016 to June 2017. Clinical characteristics of study participants are shown in Table 1. The age of females ranged from 19 to 39 years. The gestational ages were found to be ranged between 23 and 37 weeks. It was noticed that nulliparous women were of the highest frequency represented by 61.4% among the studied group.
The mean platelet count of the study participants was 219.3±71.2 ul, the mean hemoglobin level was 11.6 mg/dl, the mean serum creatinine was 0.62 mg/dl, the mean urine volume was 1482.9 ml/24 hs, the mean uric acid was 5.90 mg/dl, the mean protein level in urine was found to be 4481.1 mg/24 hr with range of 40-13301.2 and the albumin/creatinine ratio (ACR) ranged between 0.17 and 7313 with a mean of 1977.8 mg/g. The mean ALT was 15.9 U/L with range of 3.9-62.2, the mean AST was 21.1U/L with range of 6.8-76.4 and serum albumin mean was 3 gm/dl with range of 2.0-3.92 (Table 2).
There is a significant positive strong correlation between ACR and 24 hours proteinuria (Figure 1). There is also a significant positive weak correlation between ACR and serum creatinine and uric acid. A weak negative correlation was detected between ACR and serum albumin (Table 3).
---
**Table 1:** Clinical characteristics of study participants.
| Parameter | Mean±SD | Range |
|--------------------------------|------------------|---------------------|
| Age (years) | 29.6±6.32 | 19-39 |
| Gestational age (weeks) | 32.6±3.13 | 23-37 |
| Systolic blood pressure (mmHg) | 150.7±10.26 | 130-160 |
| Diastolic blood pressure (mmHg)| 97.1±6.62 | 90-110 |
| Hemoglobin level (g/dl) | 11.6±1.22 | 9.10-14.40 |
| Serum albumin (mg/dl) | 0.62±0.19 | 0.32-1.28 |
| Urine volume (ml/24 hours) | 1482.9±1000.7 | 400-5400 |
| Proteinuria (mg/24 hours) | 4481.1±3940.2 | 40-13301.2 |
| Uric acid (mg/dl) | 5.90±1.53 | 3-9.80 |
| ACR (mg/g) | 1977.8±2129.9 | 0.17-7313 |
| ALT (U/L) | 15.9±11.9 | 3.9-62.2 |
| AST (U/L) | 21.1±14.09 | 6.8-76.4 |
| Serum albumin (g/dl) | 3±0.50 | 2.03-3.92 |
**Table 2:** Laboratory characteristics of study participants.
| Parameter | Mean±SD | Range |
|--------------------------------|------------------|---------------------|
| Platelets (10^3/ul) | 219.3±71.2 | 55-381 |
| Hemoglobin (gm/dl) | 11.6±1.22 | 9.10-14.40 |
| Serum creatinine (mg/dl) | 0.62±0.19 | 0.32-1.28 |
| Uric acid (mg/dl) | 5.90±1.53 | 3-9.80 |
| ACR (mg/g) | 1977.8±2129.9 | 0.17-7313 |
| ALT (U/L) | 15.9±11.9 | 3.9-62.2 |
| AST (U/L) | 21.1±14.09 | 6.8-76.4 |
| Serum albumin (g/dl) | 3±0.50 | 2.03-3.92 |
**Table 3:** Correlation between ACR and other parameters among the study participants.
| Variable | ACR R | ACR P |
|---------------|-------|-------|
| 24 hours proteinuria | 0.664 | <0.001 |
| Serum creatinine | 0.322 | 0.007 |
| Serum albumin | -0.513 | <0.001 |
| ALT | -0.125 | 0.304 |
| AST | -0.161 | 0.183 |
| Urine volume | -0.010 | 0.937 |
| Uric acid | 0.413 | <0.001 |
---
Citation: Abdelrahman AA, Abdou AM. Urinary Spot Albumin/Creatinine Ratio for Documenting Proteinuria in Women with Hypertensive Disorders with Pregnancy. J Androl Gynaecol. 2018;6(1): 4.
The best cutoff point of ACR to predict occurrence of preeclampsia is ≥347.35 mg/g with sensitivity of 80.6%, specificity of 51.2%, positive predictive value of 56.8% and negative predictive value of 76.9% (Table 4).
Out of 70 females included in our study, 31 patients (55.7%) had significant proteinuria (>300 mg/day), while 62.9% of females had ACR greater than 347.35 mg/g while the remaining 37.1% showed their ACR level to be <347.35 mg/g.
**Discussion**
Prevalence of preeclampsia is 12% to 22% of all pregnancies. It has many risks on both the mother and the fetus with many adverse outcomes. So, obstetricians should be aware of any sign of this dangerous complication among women in the third trimester.
The most important step in diagnosis of preeclampsia is detection of albuminuria. In preeclampsia there is glomerular endothelial dysfunction which leads to defective glomerular basement membrane that leads to leakage of protein in urine.
The quantity of protein loss has both diagnostic and prognostic implications, but what constitutes an ideal test or cut-off values still remain controversial.
Three methods of urine protein detection have been used liberally in the current obstetric practice; urine dipstick analysis, the second one is 24 hours urinary proteins and the third one is the estimation of ratio of either protein or albumin to the creatinine concentration (urinary protein/creatinine ratio (UPCR) and urine albumin/creatinine ratio (UACR)) in the random urine sample.
The dipstick method is easy to perform and cheap. However, it gives fluctuating results during the day related to changes in water intake, diet, exercise, postural changes or improper use of dipsticks. It is not a recommended test, as studies found significant false positive rates, poor sensitivity, and accuracy.
24 hour urine collection is the gold standard for detection of significant proteinuria in hypertensive women during pregnancy. However, it is time-consuming, subject to collection inaccuracy, requires good patient’s compliance and usually done on an in-patient basis. Also, if delivery was attempted before completion of 24 hour urine protein collection, there may be uncertain diagnosis of preeclampsia which may expose both mother and fetus to hazards. Also, it may increase health care costs and patient worries as there is increased hospital stay.
Urine albumin/creatinine ratio has many advantages; being a quantitative measure of protein which is not affected by different levels of urinary solutes or degree of dilution of urine. Also, being an accurate and rapid method of detection of proteinuria.
In this study, the main task was to evaluate the accuracy of albumin/creatinine ratio as a diagnostic method of proteinuria in pregnant patients with hypertensive disorders. This study included 70 pregnant women with hypertensive disorders admitted at the department of Obstetrics and Gynecology, Zagazig University Hospitals.
All included women had one form of hypertensive disorders with pregnancy (whether gestational hypertension, mild preeclampsia or severe preeclampsia). A systolic arterial blood pressure of 140 mmHg or more and a diastolic arterial blood pressure of 90 mmHg or more with or without proteinuria (detected by dipsticks) were settled as diagnostic criteria.
Our study showed that there were significant positive correlations detected between A/C ratio and 24 hour protein. While, there were significant negative correlations detected between A/C ratio and urine creatinine.
In this study we tried to get a means of quantifying proteinuria in a short period of time (spot urine Albumin/creatinine ratio). The best cutoff point of ACR to predict occurrence of preeclampsia was ≥347.35 mg/g with sensitivity of 80.6%, specificity of 51.2%, positive predictive value of 56.8% and negative predictive value of 76.9%.
The issue of reliability of measuring albumin/creatinine ratio in random urine samples as a substitute to the gold standard 24 hour urinary protein has been thoroughly studied over the last two decades; some authors showed a good correlation between them, while others found a poor correlation.
The International Society for the Study of Hypertension in Pregnancy (ISSHP) declared that random albumin/creatinine and total protein excretion in a 24 hour sample are equal in the diagnosis and classification of hypertensive disorders of pregnancy [7].
Nisell H et al. in 2006 and Rathindranath R et al. in 2015 suggested that in most cases the more cumbersome 24 hour urine collection can be replaced by the more convenient albumin/creatinine ratio on spot urine [8,9].
Amin SV et al. in 2014 showed that area under curve for urinary protein: creatinine ratio (UPCR) was 0.89 (95% CI: 0.83 to 0.95), it had sensitivity of 82% and false positive rate of 12.5% for cutoff value of 0.45 (Figure 2) [10]. They used higher cutoff values (1.46 and 1.83) for prediction of heavy proteinuria (2 g and 3 g/24 h, respectively). They concluded that random UPCR is a reliable investigation compared to dipstick method to assess proteinuria in hypertensive pregnant women. However, reference values should be standardized in clinical laboratories.
**Table 4: Performance of Albumin Creatinine Ratio (ACR) as a diagnostic tool of preeclampsia among the studied groups.**
| Cutoff Point | AUC | Sens. | Spec. | +PV | -PV | LHR* | LHR- | Accuracy | P Value |
|--------------|---------|-------|-------|-------|-------|------|------|----------|---------|
| 347.35 | 0.73 | 80.60%| 51.20%| 56.80%| 76.90%| 1.65 | 0.37 | 64.20% | 0.001 |
J Androl Gynaecol 6(1): 4 (2018)
Page - 03
Cheung HC et al. in 2016 concluded that Spot urinary protein/creatinine ratio had a positive and significant correlation with 24 hour urine results in Chinese preeclamptic women when the ratio was <200 mg/mmol [11]. Although, adverse pregnancy outcome was not predicted by this ratio.
A recent metanalysis by Sanchez-Ramos L et al. in 2013 included twenty-four trials, published between January 1966 and April 2010 with 3,186 aggregate participants [12]. Accuracy of albumin/creatinine ratio was compared to 24 hour urine collection. Pooled sensitivities were 91.0% (95% CI 87.0-93.9), pooled specificities were 86.3% (95% CI 78.4-91.7), pooled positive likelihood ratio was 6.7 (95% CI 4.1, 10.9) and pooled negative likelihood ratio was 0.10 (95%C.I 0.07, 0.16). Meta-regression analysis found that the studied co-variables did not affect test accuracy. In patients at risk for preeclampsia, random urine albumin/creatinine ratio is a useful evidence to exclude the presence of significant proteinuria. The best accuracy was found with a cut-off value of more than 0.30.
Al RA et al. in 2004 studied 185 newly diagnosed hypertensive pregnant women and concluded that random urine protein to creatinine ratio was not a good predictor of significant proteinuria in such group of women [13].
Wikström AK et al. in 2006 did not recommend random A:C ratio for quantification of proteinuria in manifest preeclampsia, as A:C ratio may variate throughout the day and poorly correlated to protein estimation in 24 hour urine collection [14]. So, they recommended 24 hour urine collection, with measurement of total albumin or protein, when quantification of proteinuria is desired in women with preeclampsia with significant proteinuria.
Conclusion
ACR in random urine correlate well with 24 hour urine protein at a cutoff value of 347.35 mg/gm with sensitivity 80.6% and specificity 51.2% to detect protein excretion of 300 mg/24 hr, Therefore random ACR could be used as a rapid, easy and reliable test for diagnosis of significant proteinuria in hypertensive disorders with pregnancy, so it can substitute 24 hour urinary protein collection.
References
1. Munir S (2013) Role of growth factors in preeclampsia: early detection and treatment. Avicenna 4: 1-9.
2. Cunningham FG, Leveno KJ, Bloom SL, Hauth JC, Rouse DJ, et al. (2010) Pregnancy hypertension. In: Williams obstetrics (23rd edn). McGraw-Hill's Access Medicine, New York, USA, pp. 708-756.
3. Maynard SE, Thadhani R (2009) Pregnancy and the Kidney. J Am Soc Nephrol 20: 14-22.
4. Wheeler TL 2nd, Blackhurst DW, Dellinger EH, Ramsey PS (2007) Usage of spot urine protein to creatinine ratios in the evaluation of preeclampsia. Am J Obstet Gynecol 196: 485.
5. Levey AS, Coresh J, Balk E, Kausz AT, Levin A, et al. (2003) National Kidney Foundation practice guidelines for chronic kidney disease: evaluation, classification, and stratification. Ann Inter Med 139: 137-147.
6. Huang Q, Gao Y, Yu Y, Wang W, Wang S, et al. (2012) Urinary spot albumin: creatinine ratio for documenting proteinuria in Women with preeclampsia. Rev Obstet Gynecol 5: 9-15.
7. Brown MA, Lindheimer MD, de Swiet M, Van Assche A, Moutquin JM (2001) The classification and diagnosis of the hypertensive disorders of pregnancy: statement from the International Society for the Study of Hypertension in Pregnancy (ISSHP). Hypertens Pregnancy 20: IX-XIV.
8. Nisell H, Trygg M, Back R (2006) Urine albumin/creatinine ratio for the assessment of albuminuria in pregnancy hypertension. Acta Obstet Gynecol Scand 85: 1327-1330.
9. Rathindranath R, Teesta B, Proloy M (2015) Evaluation of spot urine protein/creatinine ratio versus 24 hour urine protein in diagnosis of hypertensive disorders of pregnancy. IOSR J Dent Med Sci 14: 44-47.
10. Amin SV, Illipilla S, Hebbab S, Rai L, Kumar P, et al. (2014) Quantifying proteinuria in hypertensive disorders of pregnancy. Int J Hypertens 2014: 1-10.
11. Cheung HC, Leung KY, Choi CH (2016) Diagnostic accuracy of spot urine protein-to-creatinine ratio for proteinuria and its association with adverse pregnancy outcomes in Chinese pregnant patients with pre-eclampsia. Hong Kong Med J 22: 249-255.
12. Sanchez-Ramos L, Gillen G, Zamora J, Stenyakina A, Kaurnit AM (2013) The protein-to-creatinine ratio for the prediction of significant proteinuria in patients at risk for preeclampsia: a meta-analysis. Ann Clin Lab Sci 43: 211-220.
13. Al RA, Baykal C, Karacay O, Geyik PO, Altun S, et al. (2004) Random urine protein-creatinine ratio to predict proteinuria in new-onset mild hypertension in late pregnancy. Obstet Gynecol 104: 367-371.
14. Wikström AK, Wikström J, Larsson A, Olovsson M (2006) Random albumin/creatinine ratio for quantification of proteinuria in manifest pre-eclampsia. BJOG 113: 930-934.
Figure 2: Receiver Operator Curve of ACR as a predictor for occurrence of preeclampsia. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4936,
1
],
[
4936,
12166,
2
],
[
12166,
17824,
3
],
[
17824,
22695,
4
]
]
} |
85e41bec3e1af32192e042e8265fa14f35696143 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 5,
"total-fallback-pages": 0,
"total-input-tokens": 16915,
"total-output-tokens": 6459,
"fieldofstudy": [
"Medicine",
"Education"
]
} | The relationship between food frequency and menstrual distress in high school females
Soheila Mohamadirizi1, Masoumeh Kordi2
ABSTRACT
Background: Nutrition pattern is one of the important factors predicting menstrual distress, which varies among different cultures and countries. The purpose of this study is to determine the relationship between food frequency and menstrual distress in high school girls from Mashhad.
Materials and Methods: This cross-sectional study was conducted in 2012 using a two-stage sampling method on 407 high school female students from Mashhad who met the inclusion criteria. Subjects completed questionnaires of demographic characteristics, food frequency, and Menstrual Distress Questionnaire (MDQ) during three phases of the menstrual cycle (a week before bleeding, during menstrual bleeding period, and a week after menstruation). The collected data were analyzed by statistical tests such as Pearson correlation coefficient test, independent Student's t-test, and one-way analysis of variance (ANOVA).
Results: Results showed that 87.7% of the students were at moderate economic status, 82.2% were exposed to cigarette smoke, 94.8% had mothers without university education, and 9.4% had working mothers. About 71% of the students reported minor pre-menstrual distress, 81% reported minor distress during bleeding, and 39% reported minor post-menstrual distress. In addition, the mean (SD) values for sweet–fatty foods, salty–fatty foods, fast foods, and caffeine were 3.6, 3.3, 1.3, and 10.2 per week, respectively. In addition, Pearson correlation coefficient test showed no significant correlation between total menstruation distress and food frequency (P > 0.05).
Conclusions: With regard to the inappropriate food frequency and high intensity of menstrual distress among high school students and as health care and educational efforts for prevention and health promotion in society are among the duties of health workers, the results of this study can help the officials involved in education to emphasize on nutrition and the menstrual health of students.
Key words: Food frequency, menstrual distress, student
INTRODUCTION
Menstruation has been a common experience among women from the 19th century till now and has been counted as a new issue.[1] It is the only evidence proving the continuation of fertility in women's reproduction system.[2] Each woman experiences menstruation for 400 times in her fertility age.[3] It is such that one-seventh of a woman's life is accompanied with menstruation.[4] Based on some gynecologists' viewpoint, menstruation could be a sign for women's physiological status and health, and can be used as a diagnostic tool for women's problems.[5] Meanwhile, the problems related to menstruation impose high costs to the societies and affect not only the women's health but also their quality of life, body image, pregnancy, mood, as well as social economy and efficiency.[6] These disorders commonly occur at different ages among women, especially among girls who have newly passed menarche (during the first 2 years after their menarche) when many of their cycles are without anovulation.[7] Menstruation-related signs can start at any age after menarche and do not necessarily occur in each period, but exist in most of them and are manifested more severely in some months.[8] These signs have been vastly investigated in different cultures including western culture, while limited research has been conducted in the Middle
1Department of Midwifery, School of Nursing and Midwifery, Isfahan University of Medical Sciences, Isfahan, Iran, 2Department of Midwifery School of Nursing and Midwifery, Mashhad University of Medical Sciences, Mashhad, Iran
Address for correspondence: Ms. Masoumeh Kordi, Department of Midwifery School of Nursing and Midwifery, Mashhad University of Medical Sciences, Mashhad, Iran. E-mail: [email protected]
Submitted: 03-Apr-14; Accepted: 14-Mar-15
Menstrual-related signs and their severity vary in different stages of menstruation and in various cultures and societies. About 95% of women in western societies and 90% of women in Asian societies face physical and psychological changes during their menstruation period. Houston et al., in a study on difference societies, showed that 21% of American, 61.4% of Turkish, and 64.6% Japanese girls reported pre-menstrual distress. In addition, menstrual distress is one among the chronic disorders with no specific signs and causes, and cannot be explained by any one-factorial model due to the complicated process of menstruation, especially menstrual distress, and its association with external factors. Menstrual distress includes physical, psychological, and behavioral signs whose associated factors have been categorized based on a bio-psychological and social model. Based on this model, menstrual distress signs are found to be affected not only by a combination of psychological factors, including anxiety, depression, and environmental stress, and social factors such as interaction with friends, family, and colleagues and the attitude toward menstruation, but also by biological factors such as hormonal disorders and the lifestyle constituting physical activity and nutritional status. With regard to the importance of diet in adolescent period and its long-term effects that can influence menstruation signs in young women, a bulk of research has been conducted on the association between lesser or highly consumed nutritional elements and the common signs of menstruation. For instance, shortage of calcium and non-saturated fatty acids is associated with dysmenorrhea. It has been recently observed that young women who ignore eating breakfast significantly suffer from dysmenorrhea more, compared to those who eat breakfast, and a high-fiber diet is inversely associated with dysmenorrhea. As studies show the positive role of different diets on dysmenorrhea, recognition of their role is essential. On the one hand, prevalence and severity of menstrual dysmenorrhea and women’s and girls’ nutritional intake are different in various cultures and in different societies. On the other hand, nutritional disorders, especially among adolescent girls, are among major health problems and act as a risk factor for the diseases such as osteoporosis, anxiety and depression, as well as menstrual disorders such as amenorrhea. Therefore, paying attention to girls’ nutritional status is of great importance. The researcher conducted the present study since no study has been conducted on determination of the relationship between food frequency and menstrual distress in high school girls from Mashhad.
**Materials and Methods**
The study population comprised all female students in grades one to four of a high school in Mashhad during 2011–2012. The sample size was calculated to be 370 subjects after conducting a pilot study on 10 students using the sample size formula:
$$n = \frac{(z_1 + z_2)^2(1-r^2)}{r^2} + 2$$
Taking into consideration a sample size increase of 10% due to random sampling, the final sample size was estimated to be 407 subjects. Cluster random sampling was adopted to select the subjects. The city of Mashhad was divided into six districts. Then, a location was selected in each district, and from each location, one school was selected by drawing lots. As the number of high school girls in each district was different, the number of subjects in each district was determined based on the total number of students in that district. The inclusion criteria were signing an informed consent to attend the study; being the student of either the third, fourth, fifth, or sixth year of a high school; having Iranian nationality; residing in Mashhad; having at least 2 years passed after menarche; body mass index (BMI) less than 30; not having experienced an agonizing or stressful life event during 6 months prior to study (death of an immediate family member, a severe family conflict, financial problems, a major change in lifestyle); not being a professional athlete; not being married; not being on a specific diet; not being involved in a medical problem (diabetes, thyroid disorders, Cushing disease, pituitary tumors, reproductive system diseases such as myoma, endometriosis, ovarian cysts, and inflammatory pelvic diseases); not taking psychotropic medications; and having no history of mental diseases during the year prior to study (a mental disease diagnosed by a psychiatrist or taking psychotropic medications). Data collection tools included a demographic and menstruation questionnaire, Menstrual Distress Questionnaire (MDQ), and nutrition pattern questionnaire. The MDQ was designed by Randolf Moos in New York University in 1968. This questionnaire contains 16 items in four dimensions (pain, control, autonomic responses, and fluid accumulation) and is scored by a four-point Likert’s scale from 0 (no signs) to 4 (very acute) to record menstruation-related signs a week prior to menstruation, during the bleeding phase, and 1 week after menstruation during the past year. Scores less than or equal to 16 indicate minor menstruation signs, 17–32 show moderate signs, 33–48 show severe menstruation signs, and scores over 49 are considered as very severe signs. The nutrition pattern questionnaire included four main nutrients: sweet–fatty (chocolates, cake, ice cream, nuts, etc.), salty–fatty (soya, red meat, chicken meat, etc.), fast foods (hamburger, pizza, potato chips, etc.), and caffeine-containing materials (tea, coffee, etc.). The frequency of their consumption within the past year was investigated. MDQ is a valid and reliable tool which was adopted in Kordi’s study (2011) and its reliability was reported as Cronbach alpha of 0.96. The questionnaire of food material consumption was adopted in Bakhsheee’s study (2012) and is a valid tool. Its reliability was calculated by test re-test method in such a way that the
researcher administered the questionnaire for 20 students two times with a 1-week interval. Its reliability was approved by \( r = 0.89 \) and \( P = 0.01 \) in such a way that after approval of the study by ethics committee of the Mashhad University of Medical Sciences and obtaining a letter of introduction, the researcher referred to authorities of the education and training office and the selected high schools. She coordinated with them for distribution of research tools, explained the research goals to the subjects, and asked the subjects to sign an informed written consent form. Finally, keeping the ethics codes into consideration, she selected the subjects, distributed the questionnaires, and conducted the study. After consideration of the inclusion exclusion criteria and explanation of the research goals, the researcher asked the subjects to complete a three-section questionnaire including their personal and menstruation characteristics, menstrual distress, and nutrition pattern questionnaire and give it back at the end of school hours on the same day. The subjects were assured that their information would be kept confidential and the questionnaires were anonymous. Then, the researcher collected the questionnaires at the end of school hours on the same day. Data of 407 qualified students were collected and analyzed by Student’s \( t \)-test, Mann–Whitney, one-way analysis of variance (ANOVA), Chi-square, Pearson correlation coefficient, and linear regression model through SPSS14.
## Results
The mean (SD) of age at menarche was 12.78 (1.11) years, ranging from 10 to 15 years. The age, BMI, and socioeconomic status and nightly and daily sleep, physical activity and length of physical activity, and exposure to smoke have been presented in Tables 1 and 2, respectively. In addition, menstrual distress severity before menstruation, in the bleeding phase, and after menstruation was minor in 71%, 81%, and 39% of the cases, respectively. With regard to pre-menstruation signs’ dimensions, fluid accumulation (retention) was observed in 33% of the subjects. Mean weekly consumption of sweet–fatty, salty–fatty, fast food, and caffeine was 3.6, 3.3, 1.3, and 10.2 times, respectively [Table 3]. Pearson correlation coefficient test showed no correlation between the number of times the four aforementioned food substances was consumed and the total score of menstrual distress (\( P = 0.282 \)). Meanwhile, it showed a positive correlation between the number of times sweet–fatty food was consumed and the total score of post-menstrual distress signs (\( r = 0.23, P = 0.042 \)) in such a way that an increase in sweet–fatty food consumption enhanced post-menstrual distress signs. Meanwhile, there was no significant correlation between the number of times sweet–fatty food consumption and the total score of pre-menstrual phase and bleeding phase distress signs (\( P = 0.123 \) and \( P = 0.501 \), respectively). Pearson correlation coefficient test showed a positive correlation between the number of times fast food was consumed and the total score of menstrual distress in the bleeding phase (\( r = 0.41, P = 0.022 \)) in such a way that an increase in their consumption increased menstrual distress signs. Meanwhile, there was no significant correlation between the number of times fast food was consumed and the total score of menstrual distress before and after menstruation (\( P = 0.405 \) and \( P = 0.320 \), respectively). In addition, Pearson correlation coefficient test showed no significant correlation between salty–fatty food and caffeine consumption, and menstrual distress before menstruation, during the bleeding phase, and after menstruation (\( P = 0.210, P = 0.527, P = 0.300, P = 0.430, P = 0.602, \) and \( P = 0.102 \), respectively). There was a positive correlation between sweet–fatty food consumption and BMI (\( r = 1.000, P = 0.001 \)) in such a way that an increase in BMI increased sweet–fatty food consumption. There was a positive correlation between caffeine-containing food consumption and age at menarche (\( r = 1.000, \)
| Table 1: Frequency distribution of age, BMI, and socioeconomic status among female students |
|-----------------------------------------------|
| Personal characteristics | Age | \( n \) | % |
| Age (years) | 14-16 | 230 | 56.5 |
| | 17-19 | 177 | 43.5 |
| BMI | Less than 18.5 | 89 | 21.9 |
| | 18.5-24.9 | 270 | 66.3 |
| | 25-29.9 | 84 | 11.8 |
| Socioeconomic status | Poor | 20 | 4.9 |
| | Moderate | 357 | 87.7 |
| | Good | 30 | 7.4 |
BMI: Body mass index
Mohamadirizi and Kordi: Relationship between Nutrition Pattern and Menstrual Distress in high-school
Table 3: Frequency distribution of subjects’ nutritional pattern based on the number of weekly consumptions
| Nutritional pattern | n | % |
|---------------------|-----|-----|
| Sweet-fatty | | |
| 0-5 times a week | 302 | 74.2|
| 5-10 times a week | 105 | 25.8|
| Salty-fatty | | |
| 0-5 times a week | 312 | 76.7|
| 5-10 times a week | 83 | 20.4|
| More than 10 times | 12 | 2.9 |
| | | |
| Fast foods | | |
| 0-5 times a week | 391 | 96.1|
| 5-10 times a week | 9 | 2.2 |
| More than 10 times | 7 | 1.7 |
| | | |
| Caffeine | | |
| 0-5 times a week | 156 | 38.3|
| 5-10 times a week | 80 | 19.7|
| More than 10 times | 171 | 42 |
\( P = 0.004 \) in such a way that an increase in menarche age increased the consumption of caffeine-containing foods. To control the confounding factors, all variables were entered in linear regression model in such a way that the variables effective on menstrual distress and the frequency of food consumption were entered as independent variables and the two main variables were separately entered as dependent variables.
As a result, all confounding variables were controlled in this way and showed no significant association with the two main variables.
**DISCUSSION**
The present study showed no significant association between salty food consumption and menstrual distress, while Molazem et al. in Yasouj showed that there was a significant association between the number of times of salty cucumber pickle consumption and severity of girls' dysmenorrhea. However, they measured only one of the pre-menstruation signs (pain) and just investigated one type of food (salty cucumber pickle).\(^{[21]}\) Meanwhile, the present study investigated a collection of signs and a group of salty foods, which can be the reason for obtaining inconsistent results. In addition, cultural differences in consumption of salty or saltless foods can be another reason for the controversial results obtained. Our results showed no significant association between caffeine-containing foods including tea and coffee and any of menstrual distress signs, which is in line with the study of Bakhshani in which no significant association was reported between consumption of tea and menstrual distress signs.\(^{[25]}\) In addition, although some observation-based studies reported that the women complaining of more signs consumed more caffeine, the role of caffeine in menstrual distress signs is yet unclear. It needs further studies to prove whether consumption of caffeine is among the factors causing these signs or it is women’s self-therapeutic response to the usual signs of fatigue to reduce their concentration on menstrual distress signs.
In addition, Dars et al., in their study on female students in Hyderabad, Pakistan, showed a significant association between nutritional status and menstruation pattern,\(^{[26]}\) which is not in line with the present study. The reason for inconsistent results can be the difference in the evaluation of nutritional status, as BMI was considered as an index for evaluation of nutritional status in their study, while in the present study, it was evaluated using a nutrition status related tool and through consideration of main nutritious substances. Although prospective recording of the signs is more accurate due to deletion of confounding factor of memory, compared to retrospective recording, lack of students’ cooperation and interference of their school assignments with the study was one of our limitations. Among the strong points of the present study, random and multi-stage sampling, allocation of the subjects based on the target population of Mashhad, and equal chance of selection for the students can be mentioned. These strong points somehow increased generalization of our reported results and decreased the possibility of a bias. In addition, sampling was conducted among healthy students studying in the schools and not among those referring to health care centers who might have suffered from a disease. It should be noted that the study population in the present study had a better potentiality for generalization, compared to other studies.
Elimination of some questions in the questionnaire, including family history of menstrual disorders, can be mentioned as a limitation in the present study. In addition, despite confirming the subjects about confidentiality of their data, some diseases or menstrual distress signs may have been hidden due to social concerns. As the rapidest way to achieve a high level of public health is prevention and promotion of individuals’ knowledge,\(^{[27]}\) the researcher hopes that the obtained results can not only provide adequate knowledge about menstrual distress and nutritional consumption pattern among female students but also may help top health managers to make practical strategies and promote public education concerning menstrual distress signs and appropriate nutritional pattern of the students and their families.
CONCLUSION
With regard to the high level of menstrual distress, and inappropriate nutritional pattern among the students, these disorders should be detected, prevented, and treated by the authorities of Ministry of Education and Training, and related educational courses and counseling services should be held to solve these problems.
ACKNOWLEDGMENTS
This study is part of a proposal, approved and sponsored by the Research Deputy in Mashhad University of Medical Sciences, Iran (research number 88840) in 2011. The authors greatly appreciate the support and collaboration of the university Research Deputy, and education authorities and students.
REFERENCES
1. Kordi M, Mohamadirizi S, Shakeri MT. Age of menarche, Dysmenorrhea and menstrual characteristics in high school girl students in Mashhad city in the year 2011. Iran J Obstet Gynecol Infertil 2013;15:10-8.
2. Vitzthum VJ, Spielvogel H, Caceres E, Miller A. Vaginal bleeding patterns among rural highland bolivian women: Relationship to fecundity and fetal loss. Contraception 2001;64:319-25.
3. Estanislau do Amaral MC, Hardy E, Hebling Em, Faundes A. Menstrual And Amenorrhea: Opinion Of Brazilian Women. Contraception 2005;72:157-61.
4. Lee CA, Kadir RA, Kouides PA. Inherited Bleeding Disorders In Women. United Kingdom: Wiley Online Library; 2009.
5. Wyatt KM, Dimmock PW, Hayes-Gill B, Crowe J, O'brien PM. Menstrual symptomatologies: A simple computer-aided method to quantify menstrual cycle disorders. Fertil Steril 2002;78:96-101.
6. Mohamadirizi S, Kordi M, Shakeri MT, Salehi Fadardi J, Hafizi L. Relationship between Job Stress with Menstrual Bleeding Pattern among Midwives. J HAYAT 2012;18:1-11.
7. Mohamadirizi s, Kordi M. Association between menstruation signs and anxiety, depression, and stress in school girls in Mashhad in 2011-2012. Iran J Nurs Midwifery Res 2013;18:402-7.
8. Vichnin M, Freeman EW, Lin H, Hillman J, Bui S. Premenstrual Syndrome (PMS) in Adolescents: Severity and Impairment. J Pediatr Adolesc Gynecol 2006;19:397-402.
9. Mohamadirizi s, Kordi M, Shakeri MT. The Relationship between Perimenstrual Symptoms and Menstrual Attitude in high-school females in Mashhad city in the years 2011-2012. Iran J Obstet Gynecol Infertil 2012;15:25-31.
10. Kibler JL, Rhudy JL, Penzien DB, Rains JC, Meeks Gr, Bennett W, et al. Hormones, menstrual distress, and migraine across the phases of the menstrual cycle. Headache 2005;45:1181-9.
11. Kim HW, Kwon MK, Kim NS, Reame NE. Intake of dietary soy isoflavones in relation to perimenstrual symptoms of Korean women living in the USA. Nurs Health Sci 2006;8:108-13.
12. Mishell DR Jr. Premenstrual Disorders: Epidemiology and Disease Burden. Am J Manag Care 2005;11:473-9.
13. Rasheed P, Sowailen LS. Prevalence and predictors of premenstrual syndrome among college-aged women in Saudi Arabia. Ann Saudi Med 2003;23:381-7.
14. Houston AM, Abraham A, Huang Z, D’Angelo IJ. Knowledge, attitudes, and consequences of menstrual health in Urban adolescent females. J Pediatr Adolesc Gynecol 2006;19:271-5.
15. Vo HT. The effects of caffeine on premenstrual syndrome (Dissertation). USA: University of Maryland; 2007.
16. Block DJ. The biopsychosocial point of view. Healthcare outcomes management: Strategies for planning and evaluation. The United States of America: Jones And Bartlett; 2006.
17. Kordi M, Mohamadirizi S, Shakeri MT. The relationship between occupational stress and dysmenorrhea in midwives employed at public and private hospitals and health care centers in Iran ( Mashhad) in the years 2010 and 2011. Iran J Nurs Midwifery Res 2013;18:316-22.
18. Davydov DM, Shapiro D, Goldstein IB, Chicz-DeMet A. Moods in everyday situations: Effects of menstrual cycle, work, and stress hormones. J Psychosom Res 2005;58:343-9.
19. Lane T, Francis A. Premenstrual symptomatology, locus of control, anxiety and depression in women with normal menstrual cycles. Arch Women's Ment Health 2003;6:127-38.
20. Moronkola OA, Uzuegbu VU. Menstruation: Symptoms, Management And Attitude Of Female Nursing Students In Ibadan, Nigeria. Afr J Reprod Health 2007;10:84.
21. Molazem Z, Alhani F, Anooseh M, Vagharseyyedin SA. Epidemiology of dysmenorrhea with dietary habits and exercise. Zahedan J Res Med Sci (ZJRS) 2011;13:41-5.
22. Fujiwara T. Diet during adolescence is a trigger for subsequent development of dysmenorrhea in young women. Int J Food Sci Nutr 2007;58:437-44.
23. Pourghassem Gargari B, Kooshavari D, Seyed Sajadi N, Karami S, Shahrokhi H. Risk of Eating Disorders in Tabrizian High School Girls in 2007. J Tabriz Univ Med Sci Health Serv 2009;30:21-6.
24. Kordi M, Mohamadirizi S, Shakeri M-T, Salehi Fadardi Ja, Hafizi L. The Relationship between Midwives’ Work Stress and Perimenstrual Distress. Iran J Obstet Gynecol Infertil 2011;14:54-63.
25. Bakhshani N, Hasanazadeh Z. Relationship of premenstrual syndrome and nutritional style. Med J Mashhad Uni Med Sci 2012;55:151-7.
26. Dars S, Sayed K, Yousufzai Z. Relationship of menstrual irregularities to BMI and nutritional status in adolescent girls. Pak J Med Sci 2014;30:140-4.
27. Mohamadirizirzi S, Bahadoran P, Fahami F. Comparison between the impacts of e-learning and booklet education on Primigravida Women’s Satisfaction about postpartum care. Iran J Obstet Gynecol Infertil 2013;16:1-8.
How to cite: Mohamadirizi S, Kordi M. The relationship between food frequency and menstrual distress in high school females. Iranian J Nursing Midwifery Res 2015;20:689-93.
Source of Support: Mashhad University of Medical Sciences, Conflict of Interest: None declared. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3965,
1
],
[
3965,
9951,
2
],
[
9951,
14516,
3
],
[
14516,
19738,
4
],
[
19738,
25307,
5
]
]
} |
62b99c9a2aa8d15a99681ca7860f5165d6c3555f | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 8,
"total-fallback-pages": 0,
"total-input-tokens": 24782,
"total-output-tokens": 8076,
"fieldofstudy": [
"Medicine"
]
} | A novel manual therapy technique is effective for short-term increases in tibial internal rotation range of motion
Justin M. Stanek*, Bryce Brown, Jessica Barrack, Jake Parish
School of Kinesiology and Recreation, Illinois State University, Normal, IL, USA
The coupled motions of tibial internal rotation (T-IR) and ankle dorsiflexion (DF) are necessary for proper lower-limb function. Anecdotally, clinicians have been performing techniques to restore T-IR to improve ankle DF; however, no evidence exists to support their efficacy. Therefore, the two objectives were to: (a) determine the effectiveness of a manual therapy technique for improving T-IR range of motion (ROM) and (b) examine the relationship between ankle DF and T-IR ROM. Twenty-four participants qualified to participate and were randomly allocated to either the control (n = 12) or manual therapy (n = 12) group. Closed-chain ankle DF and T-IR ROM were assessed at baseline and immediately posttreatment. Control group participants sat quietly for 5 minutes. The experimental group performed 3 sets of 15 repetitions of a manual therapy, mobilization with movement technique. With the patient in a kneeling lunge position, the examiner wrapped an elastic band around the tibia and fibula and was instructed to lunge forward while the examiner simultaneously manually internally rotated the lower leg. T-IR ROM significantly increased following the intervention for the manual therapy group when compared to the control group. There were no significant changes in standing or kneeling DF ROM. No significant correlation was found between T-IR and both standing and kneeling DF ROM. No significant correlation was found between T-IR and both standing and kneeling DF ROM. A single mobilization with movement treatment is effective for improving tibial IR ROM in the short-term compared to no treatment. However, active tibial IR and end-range dorsiflexion range of motion do not appear to be correlated based on these methods.
Keywords: Ankle Joint, Articular goniometry, Dorsiflexion, Mobilization
INTRODUCTION
Clinicians routinely quantify and track joint range of motion (ROM) as part of the evaluation and rehabilitation process. Limitations in tibial ROM are often overlooked due to the difficulty in measuring transverse plane motion (Makowski et al., 2005). The embedded compass app of an iPhone (iPhone 6 model A1549, Apple, Inc., Cupertino, CA, USA) has recently been shown to reliably assess tibial internal and external rotation ROM making it convenient and easy to quantify (Stanek et al., 2020). Rotational motion at the tibia is essential for knee and ankle function and is often implicated as a compensatory strategy for various lower extremity conditions (Bell-Jenje et al., 2015; Bonci, 1999; Griffin et al., 2000; Matsumoto et al., 2000; Zhang et al., 1993). Previous authors have described tibial rotation as an important, yet often understudied (Makowski et al., 2005; Matsumoto et al., 2000; Zhang et al., 1993). A thorough understanding of rotational motion of the tibia contributes to an accurate evaluation of knee mobility, as well as provides a better understanding of function at the hip, ankle, and foot.
A previous investigation described potential complications from abnormal variations in tibial rotation (Lusin and Gajdosik, 1983). These pathologies include the development of chondromalacia patella and other degenerative joint changes. Alterations in tibial rotation have also been implicated with meniscal lesions and injuries to the cruciate ligaments (Hallen and Lindahl, 1966). Furthermore, tibial external rotation, along with anterior translation of the knee, and hindfoot eversion have been implicated with dynamic valgus...
at the knee (Bell et al., 2008; Hewett et al., 2006). This positioning has been correlated with iliotibial band syndrome (Ferber et al., 2010), patellofemoral pain syndrome (Levinger et al., 2006; Molgaard et al., 2011), tibial stress fractures (Milner et al., 2006), posterior tibial tendon dysfunction (Ness et al., 2008), anterior cruciate ligament tears (Powers, 2010), and osteoarthritis of the knee (Chang et al., 2005).
Much of the previous literature has focused on the relationship between hip and knee alignment, especially as it relates to dynamic valgus. However, a more recent study found individuals with <17° of ankle dorsiflexion (DF) exhibited 6.5° higher hip adduction angles during an elevated step down task (Bell-Jenje et al., 2015). Interestingly, the higher hip adduction angles were normalized to the group with >17° DF with a heel lift, suggesting that lost DF ROM contributed to the valgus knee positioning. During normal lower extremity biomechanics, several motions must couple in order to achieve optimal function. For example, during closed-chain activities, the tibia must internally rotate (IR) to allow ankle DF and pronation to occur (McCay and Manal, 1997). Loss of DF ROM is commonly observed in both the athletic and general population and is believed to be a predisposing factor for lower extremity injury (Backman and Danielson, 2011; Neely, 1998; Tabrizi et al., 2000; Wang et al., 2006; Willems et al., 2005; You et al., 2009). Typically, DF ROM deficits are believed to be caused by tightness of the triceps surae, a decrease in the posterior glide of the talus, and/or accessory motion loss at the tibiofibular, subtalar, and/or midtarsal joints (Denegar and Hertel, 2002; Leanderson et al., 1993). Because the motions of DF and T-IR are coupled, lost T-IR could also contribute to deficits in DF ROM. Despite wide ranges in reported normative values for T-IR (Lusin and Gajdosik, 1983; Makowski et al., 2005; Stanek et al., 2020), findings from a previous study using the compass app showed average T-IR ROM to range from 12°–14° (Stanek et al., 2020). Anecdotally, clinicians have been performing techniques to restore T-IR and potentially improve ankle DF. Several variations of the technique using elastic bands have been published in blog or online video posts (Physical Therapy Nation, YouTube, San Bruno, CA, USA) to provide guidance for how to perform the technique, however, no peer-reviewed, published literature exists to support their efficacy. Furthermore, the use of elastic bands, such as the VooDoo floss band (Rogue Fitness, Columbus, OH, USA), is scarce amongst the literature (Kiefer et al., 2017). Therefore, the purposes of this exploratory study were to determine the effectiveness of a manual therapy, mobilization with movement (MWM) technique for improving T-IR and secondarily to examine the relationship between T-IR and DF ROM. We hypothesized that the manual therapy technique would immediately improve T-IR ROM. We also hypothesized that T-IR and DF ROM would be positively correlated.
MATERIALS AND METHODS
Design
An examiner-blinded, cohort study design with randomization was used to examine the impact of the manual therapy intervention on DF ROM. Participants were required to report to the athletic training clinic for a single session. Participants were randomized into either the control or manual therapy group using block randomization. Limb dominance was self-reported by the participant as the preferred kicking limb.
Participants
Based on a data from a previous reliability study (Stanek et al., 2020), and a simple, online sample size calculator using an alpha level of 0.05 and an intraclass correlation coefficient of 0.85, an estimated sample size of 11 participants per group was recommended. Twenty-seven participants were initially recruited and screened for inclusion. A total of 24 participants (age, 20.1 ± 1.2 years; weight, 68.9 ± 13.5 kg; height, 171.3 ± 10.4 cm) met the inclusion criteria and qualified for the study (Table 1). Participants were recruited via verbal announcements and advertisements throughout the School of Kinesiology and Recreation. All participants were recreationally physically active and needed to meet the inclusion criteria. To be included in the study, participants needed to have less than 12° of T-IR, have no prior history of lower extremity surgery to the limb, and have no recent history (within the past 6 months) of lower extremity injury to the limb. The threshold of 12° was based on a previous study showing average normative values for T-IR ROM measured using a compass app ranged from 12°–14° (Stanek et al., 2020). In total, 42 limbs were randomly allocated to either the control (12 participants) or
Table 1. Demographic data for participants
| Variable | Control group (n=12) | Intervention group (n=12) |
|--------------------|----------------------|---------------------------|
| Gender, male:female| 5:7 | 5:7 |
| Limbs | 21 | 21 |
| Age (yr) | 19.9 ± 1.2 | 20.3 ± 1.2 |
| Mass (kg) | 71.0 ± 16.6 | 66.9 ± 9.7 |
| Height (cm) | 156.5 ± 36.6 | 147.4 ± 21.4 |
Values are presented as number or mean ± standard deviation.
intervention (12 participants) group. In instances when both limbs of the participant qualified, both limbs were allocated to the same group. Prior to beginning data collection, the Institutional Review Board of Illinois State University reviewed and approved the study (IRB No. 2018-93). All participants provided written informed consent prior to study participation.
**Instrumentation**
Participants’ T-IR and closed-chain ankle DF in standing and kneeling were assessed immediately before and after the intervention. To assess T-IR, the compass app on an iPhone (iPhone 6 model A1549, Apple, Inc., Cupertino, CA, USA) was secured to the lower leg using the Premium Tribe Sports Armband (Tribe Fitness, Seattle, WA, USA) following previously used methods (Stanek et al., 2020). The smartphone was secured to the lower leg so that the bottom of the device rested immediately superior to the ankle mortise.
Closed-chain ankle DF was assessed in both standing and kneeling with a digital inclinometer (SmartTool, Pro 3600, MD Building Products, Oklahoma, OK, USA) on the anterior aspect of the tibia, immediately below the tibial tuberosity. Previous authors have shown this to be a highly reliable method for evaluating DF ROM (Powden et al., 2015; Stanek et al., 2018).
**Procedures**
All procedures for evaluating T-IR followed the methods of Stanek et al. (2020) for measuring tibial rotation using a smartphone compass app and these methods showed excellent reliability. Based on this study, standard error of the measurement (SEM) for these procedures was 2.24–2.82 (Stanek et al., 2020). Participants arrived at the lab and reviewed the study purpose and procedures by reading through the informed consent document. Participants agreeing to participate signed the informed consent document and completed the preparticipation questionnaire. To standardize activity levels, all participants were instructed to ride a stationary bike with moderate resistance for 5 minutes. Participants removed shoes and socks and sat on an adjustable stool with the height adjusted so that the hip and knee angles were at 90°. The phone was secured to the lower leg with the armband so it sat immediately superior to the talocrural joint. Using a vertical plumb line, the test limb was placed in neutral by aligning the tibial tuberosity with the center of the talocrural joint. The rater stabilized the participant’s femur and taught the motions of T-IR. As the participant was taught the movement, the individual was asked to maintain the neutral, resting position of the foot in order to avoid excessive pronation and supination. The rater visually verified the movements and the test limb was returned to neutral after each movement. To assess tibial rotation ROM, the rater recorded an initial reading from the compass app while in neutral, followed by the participant moving into T-IR (Fig. 1). The rater recorded a second reading from the compass app at the end ROM, with the difference between the two positions recorded for the measurement. The average of the 3 trials for T-IR was used for analysis.
Next, the participant’s closed-chain DF was measured in standing (Fig. 2) and kneeling (Fig. 3) using a modified weight-bearing lunge test. Previous authors have shown this to be a highly reliable method for evaluating DF ROM (Bennell et al., 1998; Hall and Docherty, 2017; Powden et al., 2015; Stanek and Pieczynski, 2020). The participant stood, positioned the test leg behind the nontest leg on a strip of tape that was perpendicular to the wall, and leaned forward until the first point of stretch was felt in the calf and/or when the heel began to rise. The trial was deemed successful if the test knee remained straight and the heel-maintained contact with the floor. The digital inclinometer was placed on the anterior tibia, immediately below the tibial tuberosity. Next, participants’ kneeling DF ROM was assessed by instructing the participant to kneel on the opposite leg being tested with the test
limb visually placed in 90° of hip and knee flexion. The participant placed their front foot on the tape line as previously stated. The participant was then instructed to lunge forward while keeping their heel in contact with the ground and their foot in line with the tape. The participant was instructed to lunge forward until their first felt a stretch in their distal calf and/or the heel began to rise. The inclinometer was placed in the same position as the standing measurement. The average of three measurements was recorded.
Participants allocated to the control group were instructed to sit quietly on the exam table for 5 minutes. Experimental group participants positioned the test limb forward in a kneeling lunge. A 7-foot (2.13 m) VooDoo Floss Band (Rogue Fitness, Columbus, OH, USA) was wrapped with moderate tension from just above the ankle mortise, in the direction of IR superiorly around the lower limb. Next, the participant was instructed to lunge forward while simultaneously the clinician guided the participant into the DF position and internally rotated the tibia. Both the T-IR and DF ROM were moved to end-range with each repetition and each trial was completed to the beat of a metronome set at 45 beats per minute. A total of 3 sets of 15 repetitions of the manual therapy MWM technique were completed with 1-minute rest between sets. These methods followed a modified version of a previously used MWM technique (Collins et al., 2004). All participants had postmeasurements completed using the previously described methods.
Statistical analysis
All statistical analyses were performed using IBM SPSS Statistics ver. 24.0 (IBM Co., Armonk, NY, USA). Preliminary analyses were conducted and showed no difference between groups at baseline for demographics (age, height, and mass), T-IR, standing, or kneeling DF ROM measures (P > 0.05). To compare the effectiveness of the manual therapy intervention, change scores were calculated for T-IR, standing, and kneeling DF ROM by subtracting the postmeasurement from the premeasurement. Independent samples t-test were used to determine significant differences between groups. To determine relationships between T-IR and DF ROM, Pearson product-moment correlation coefficient were calculated. Prior to running the analyses, preliminary assumption testing for normality and homogeneity of variance were completed with no violations. Effect sizes were calculated using the Cohen d and categorized as trivial (≤ 0.20), small (0.21–0.49), moderate (0.50–0.79), or large (≥ 0.80) (Lakens, 2013). The α level was set a priori at P < 0.05.
RESULTS
Descriptive statistics for all data are included in Table 2. There was a statistically significant amount of T-IR increase following the intervention for the manual therapy group (m = 2.03° ± 2.24°) when compared to the control group (m = 0.62° ± 2.61°); t(40) = 3.53, P = 0.001, effect size = 1.09, 95% confidence interval = 0.44–
1.74. There were no significant changes in standing ($t_{40} = 0.04, P = 0.97$) or kneeling ($t_{40} = 0.81, P = 0.42$) DF ROM. No significant correlation was found between T-IR and both standing ($r = 0.20, P = 0.20$) and kneeling ($r = 0.14, P = 0.39$) DF ROM (Figs. 4, 5).
**DISCUSSION**
The purpose of this study was to investigate the effectiveness of a manual therapy technique aimed at improving T-IR ROM and examine the relationship between T-IR and DF ROM. Our hypotheses were only partially supported. Results showed a single session of manual therapy can increase T-IR ROM but it had no effect on DF ROM. Additionally, end-range T-IR and DF ROM do not appear to be associated as there were small, nonsignificant correlations between T-IR and both standing ($r = 0.20, P = 0.20$) and kneeling ($r = 0.14, P = 0.39$) DF ROM (Figs. 4, 5).
Manual therapy interventions are commonly used within rehabilitation settings, often with the goal of improving mobility. The manual therapy MWM technique employed in this study has been demonstrated online as a method for improving T-IR. Due to the nature of the technique, it is not surprising that it can increase motion since the technique passively moves the tibia into IR with each repetition. However, the weightbearing technique also passively moves the ankle into DF, therefore it was surprising to see no changes in DF mobility. It is possible the participants in this study had adequate DF mobility, creating a ceiling effect for further increases in DF ROM. A study among people with restricted DF mobility may have shown different results.
Reduced ankle DF ROM is a commonly found deficit within athletic and non-athletic populations and is commonly observed in patients following a lateral ankle sprain (Denegar et al., 2002; Hertel, 2002; Hubbard and Hertel, 2006; Tabrizi et al., 2000). However, reduced DF is also a risk factor for sustaining a lateral ankle sprain, therefore, numerous interventions for improving DF ROM have been studied (Terada et al., 2013). Traditionally, treatments for DF ROM deficits include the use of joint mobilizations for restoring the proper accessory motion, stretching of the triceps surae, modalities, or a combination of these therapies (Young et al., 2013). To our knowledge, no previous studies have examined...
the impact of T-IR ROM on DF mobility. Because previous studies have demonstrated the coupled motions of knee flexion, T-IR, and ankle DF ROM during functional tasks such as squatting or during gait (Bell-Jenje et al., 2015; McClay and Manal, 1997), we hypothesized that improving T-IR may also positively affect DF ROM. However, while the manual therapy intervention was effective at improving T-IR rotation in the short-term, it does not appear that this resulted in an increase in DF ROM.
Tibial IR ROM is not commonly quantified in the clinical environment, yet rotational motion at the tibia is essential for knee and ankle function and is often implicated as a compensatory strategy for various lower extremity conditions (Bell-Jenje et al., 2015; Bonci, 1999; Griffin et al., 2000; Matsumoto et al., 2000; Zhang et al., 1993). A previous reliability study using the same measurement technique showed average T-IR ROM to be approximately 13° with SEM ranging from 2.24–2.82 (Stanek et al., 2020). Because of the large standard deviations in the reliability study, the SEM was high. Using data from the current study and using the formula SEM = standard deviation x-√1-r, with r as the reliability of the measurement, the calculated SEM was 1.46. Collectively, participants in the current study started with approximately 8° of T-IR and participants in the intervention group reached values around 9.3°. Participants in the intervention group demonstrated over a 2° change in ROM with large effect sizes. These findings suggest clinically meaningful changes in T-IR ROM, however, additional research to support these findings is needed.
Methods and instrumentation for assessing T-IR ROM vary greatly throughout the literature. Therefore, it is important for clinicians to have the ability to quantify and address limitations when necessary. Our results suggest this technique could be a simple, yet effective method for increasing T-IR in the short term.
This study is not without limitations. First, we measured active, end-range T-IR and DF ROM. While previous authors have demonstrated these motions are coupled during functional tasks, it is possible T-IR occurs early within the functional task and maximum IR occurs prior to end-range DF ROM. Therefore, increasing the T-IR did not have a substantial effect on end-range DF ROM. Secondly, we used a healthy population with limited T-IR ROM, but normative values of T-IR vary considerably. Previously forthcoming work using similar methodology showed T-IR values between 12°–14° (Stanek et al., 2020). Our inclusion criteria required participants to have less than 12° of T-IR to potentially prevent a ceiling effect with the manual therapy MWM technique. Because of the wide variability within previously published normative values for T-IR (Lusin and Gajdosik, 1983; Makowski et al., 2005), less than 12° may not be a sufficiently restricted degree of mobility for T-IR. Furthermore, our population did not have a DF ROM deficit. It is possible our results for changes in DF ROM would have been different if we recruited a population with a known T-IR and DF deficit. Future research is needed to quantify consistent and accurate values for normal tibial rotation mobility. Furthermore, additional research should examine the effects of this manual therapy technique on functional tasks such as gait or squatting. Lastly, we compared a single treatment to a true control condition receiving no intervention. It is possible comparing to another intervention or a placebo intervention could have resulted in different findings.
In conclusion, a single manual therapy, MWM treatment is effective at increasing T-IR ROM in the short-term compared to no treatment. However, it did not affect closed-chain DF ROM. Clinicians are encouraged to examine tibial rotation mobility within their patients for potential deficits. Patients with deficits in T-IR mobility may benefit from using this manual therapy technique.
CONFLICT OF INTEREST
No potential conflict of interest relevant to this article was reported.
ACKNOWLEDGMENTS
The authors received no financial support for this article.
REFERENCES
Backman LJ, Danielson P. Low range of ankle dorsiflexion predisposes for patellar tendinopathy in junior elite basketball players: a 1-year prospective study. Am J Sports Med 2011;39:2626-2633.
Bell DR, Padua DA, Clark MA. Muscle strength and flexibility characteristics of people displaying excessive medial knee displacement. Arch Phys Med Rehabil 2008;89:1323-1328.
Bell-Jenje T, Oliver B, Wood W, Rogers S, Green A, McKinon W. The association between loss of ankle dorsiflexion range of motion, and hip adduction and internal rotation during a step down test. Man Ther 2015;21:256-261.
Bennell K, Talbot RC, Wajsweiner H, Techovanič W, Kelly DH, Hall AJ. Intra-rater and inter-rater reliability of a weight-bearing lunge measure of ankle dorsiflexion. Aust J Physiother 1998;44:175-180.
Bonci CM. Assessment and evaluation of predisposing factors to anterior cruciate ligament injury. J Athl Train 1999;34:155-164.
Chang A, Dunlop D, Song J, Hurwitz D, Cahue S, Sharma L. Hip abduc-
tion moment and protection against medial tibiofemoral osteoarthritis
progression. Arthritis Rheumatol 2015;52:3515-3519.
Collins N, Teys P, Vicenzino B. The initial effects of a Mulligan’s mobi-
lization with movement technique on dorsiflexion and pain in subacute
ankle sprains. Man Ther 2004;9:77.
Denegar C, Hertel J, Fonseca J. The effect of lateral ankle sprain on dor-
siflexion range of motion, posterior talar glide, and joint laxity. J Orthop
Sports Phys Ther 2012;42:166-173.
Denegar CR, Hertel J. Editorial: Clinical education reform and evidence-
based clinical practice guidelines. J Athl Train 2002;37:127-128.
Ferber R, Noehren B, Hamill J, Davis IS. Competitive female runners with
a history of iliotibial band syndrome demonstrate atypical hip and
knee kinematics. J Orthop Sports Phys Ther 2010;40:52-58.
Griffin LY, Agel J, Albolm MJ, Arendt EA, Dick RW, Garrett WE. Noncon-
tact anterior cruciate ligament injuries: risk factors and prevention
strategies. J Am Acad Orthop Surg 2000;8:141-150.
Hall EA, Docherty CL. Validity of clinical outcome measures to evaluate
ankle range of motion during the weight-bearing lunge test. J Sci Med
Sport 2017;20:618-621.
Hallen LG, Lindahl O. The “screw-home” movement in the knee joint.
Acta Orthop Scand 1966;37:97-106.
Hertel J. Functional anatomy, pathomechanics, and pathophysiology of
lateral ankle instability. J Athl Train 2002;37:264-375.
Hewett TE, Ford KR, Myer GD. Anterior cruciate ligament injuries in fe-
male athletes, part 2: a meta-analysis of neuromuscular interventions
aimed at injury prevention. Am J Sports Med 2006;34:490-498.
Hubbard TJ, Hertel J. Mechanical contributions to chronic lateral ankle
instability. Sports Med 2006;36:263-277.
Kiefer BN, Lemarr KE, Enriquez CC, Tivener KA, Daniel T. A pilot study:
perceptual effects of the voodoo floss band on glenohumeral flexibili-
ity. Int J Athl Ther Train 2012;22:29-33.
Lakens D. Calculating and reporting effect sizes to facilitate cumulative
science: a practical primer for t-tests and ANOVAs. Front Psychol
2013;4:863.
Leanderson J, Wykman A, Eriksson E. Ankle sprain and postural sway in
basketball players. Knee Surg Sports Traumatol Arthrosc 1993;1:203-
205.
Leavinger P, Gillardeux WL, Sprogis K. Frontal plane motion of the rearfoot
during a one-leg squat in individuals with patellofemoral pain syn-
drome. J Am Podiatr Med Assoc 2006;96:96-101.
Lusin GF, Gajdosik RL. Reliability of instrumentation and measurement
procedures for active internal and external tibial rotation. J Orthop
Sports Phys Ther 1983;4:154-157.
Makowski A, Birmingham T, Kramer J, Jogi P, Forwell L, Obright K. Test-
retest and Interrater reliability of goniometric tibial rotation range of
motion measurements. Physiother Can 2005;57:265-273.
Matsumoto H, Seedhom BB, Suda Y, Otani T, Fujikawa K. Axis location
of tibial rotation and its change with flexion angle. Clin Orthop Relat
Res 2000;371:178-182.
McClay I, Manal K. Coupling parameters in runners with normal and ex-
cessive pronation. J Appl Biomech 1997;13:109-124.
Milner C, Ferber R, Pollard C, Hamill J, Davis I. Biomechanical factors as-
soiated with tibial stress fracture in female runners. Med Sci Sports Exerc
2006;38:323-328.
Molgaard C, Rathleff MS, Simonsen O. Patellofemoral pain syndrome
and its association with hip, ankle, and foot function in 16- to 18-year-
old high school students: a single-blind case-control study. J Am Podi-
atri Med Assoc 2011;101:215-222.
Neely F. Biomechanical risk factors for exercise-related lower limb inju-
ries. Sports Med 1998;26:395-413.
Ness ME, Long J, Marks R, Harris G. Foot and ankle kinematics in pa-
tients with posterior tibial tendon dysfunction. Gait Posture 2008;27:
331-339.
Powden CJ, Hoch JM, Hoch MC. Reliability and minimal detectable change
of the weight-bearing lunge test: a systematic review. Man Ther 2015;
20:524-532.
Powers CM. The influence of abnormal hip mechanics on knee injury: a
biomechanical perspective. J Orthop Sports Phys Ther 2010;40:42-51.
Stanek J, Parish J, Rainville R, Williams J. Test-retest and intra-rater reli-
ability of assessing tibial rotation range of motion by two devices. Int J
Athl Ther Train 2020;25:263-269.
Stanek JM, Pieczynski AE. Effectiveness of clinician- and patient-applied
mobilisation with movement technique to increase ankle dorsiflexion
range of motion. Int J Ther Rehabil 2020;27:1-11.
Stanek JM, Sullivan T, Davis S. Comparison of compressive myofascial
release and the Graston Technique for improving ankle dorsiflexion
range of motion. J Athl Train 2018;53:160-167.
Tabrizi P, McIntyre WM, Quesnel MB, Howard AW. Limited dorsiflexion
predisposes to injuries of the ankle in children. J Bone Jt Surg Br 2000;
82:1103-1106.
Terada M, Pietrosimone BG, Gribble PA. Therapeutic interventions for in-
creasing ankle dorsiflexion after ankle sprain: a systematic review. J
Athl Train 2013;48:696-709.
Wang HK, Chen CH, Shiang TY, Jan MH, Lin KH. Risk-factor analysis of
high school basketball-player ankle injuries: a prospective controlled
cohort study evaluating postural sway, ankle strength, and flexibility.
Arch Phys Med Rehabil 2006;87:821-825.
Willems TM, Witvrouwen E, Delbaere K, Philippaerts R, Bourdoulouj H, De
Clercq D. Intrinsic risk factors for inversion ankle sprains in fe-
https://www.e-jer.org
190 https://doi.org/10.12965/jer.2142228.114
Stanek JM, et al. • Manual therapy for tibial rotation
males: a prospective study. Scand J Med Sci Sports 2005;15:336-345.
You JY, Lee HM, Luo HJ, Lee CC, Cheng PG, Wu SK. Gastrocnemius
tightness on joint angle and work of lower extremity during gait. Clin
Biomech. 2009;24:744-750.
Young R, Nix S, Wholohan A, Bradhurst R, Bradhurst L. Interventions for
increasing ankle joint dorsiflexion: a systematic review and meta-anal-
ysis. J Foot Ankle Res 2013;6:2-18.
Zhang LQ, Dobson S, Shiavi RG, Peterson S, Limbird TJ. Changes in knee
kinematics caused by ACL deficiency during fast walking. Gait Pos-
ture 1993;7:144-156. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3741,
1
],
[
3741,
9114,
2
],
[
9114,
13129,
3
],
[
13129,
16081,
4
],
[
16081,
18398,
5
],
[
18398,
23485,
6
],
[
23485,
28911,
7
],
[
28911,
29533,
8
]
]
} |
6b9c8483afb1fc09d9f0bc003dec3298a9a7f04a | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 5,
"total-fallback-pages": 0,
"total-input-tokens": 15321,
"total-output-tokens": 4991,
"fieldofstudy": [
"Medicine"
]
} | A study of efficacy of oral probiotics in management of cases with symptomatic white discharge per vagina in a tertiary care hospital
Pillai L¹, Sadhya², Narmadha N.S³, Reddy A.S.⁴
¹Dr Lekshmi Pillai, Junior Resident, ²Dr Sadhya, Junior Resident, ³Dr Narmadha N.S, Senior Resident, ⁴Dr Alla Satyanarayana Reddy, Professor and HOD; all authors are affiliated with Department of Obstetrics and Gynaecology, Vinayaka Mission's Medical College & Hospital, Karaikal, Puducherry.
Address for Correspondence: Dr Alla Satyanarayana Reddy, Professor and HOD, Department of Obstetrics and Gynaecology, Vinayaka Mission's Medical College, Karaikal, Puducherry
Abstract
Background: Urogenital infections are the most common gynecological condition constituting about 25% of outpatients. Because of higher recurrence rates and resistance to standard antimicrobials now a days the use of probiotics in augmenting normal bacterial populations is gradually achieving scientific acceptance. Objective: Determine the efficacy of probiotics in treating women with symptomatic white discharge per vagina (WDPV), role of oral probiotics in restoring the vaginal flora. Methods: 70 women aged between 18 to 45 yrs (mean age 35yrs) with symptomatic WDPV who are attending gynecology outpatient procedures, these patients underwent Grams stain, received antibiotics along with probiotics (L. rhamnosus GR-1 and L. fermentum RC-14) for a period of 1 week, again reviewed with repeat Grams stain. Results: Among post-treatment group 46 % of patients showed >30 organisms/100× objective. Fifty percent of patients showed counts between 5 and 30 among post-treatment, but the response in terms of symptomatic relief was about 74%. The improvement in the lactobacilli count was interpreted using Nugents scoring. Conclusion: The combination of probiotic (L. rhamnosus GR-1 and L. fermentum RC-14) is not only safe for daily use in healthy women, but it can reduce colonization of the vagina by potential pathogenic bacteria and yeast.
Keywords: Probiotics, Lactobacilli, Urogenital infections
Introduction
Urogenital infections afflict an estimated few billion women in a year, the size of this problem and the increased prevalence of multidrug resistant pathogens make it imperative for alternate treatment. The microorganisms that colonize the vagina play a major role in maintenance of resistance against infestations from pathogenic organisms. When this flora is dominated by lactobacilli or a commensal flora, the person is regarded as being healthy in terms of the urogenital tract, unless other specific disease traits are evident.
When the vault is colonized primarily or solely by pathogenic bacteria, such as Escherichia coli or Gardnerella vaginalis [1-3] the patient is generally regarded as having an abnormal flora. Antimicrobial therapy has been reasonably effective at curing bacterial infections of the bladder and vagina, but mounting drug resistance and failure of antibiotics to change host receptivity to pathogen recurrences, plus a negative impact on patient quality of life make it imperative that alternative therapeutics be found [4-7].
Probiotics are regarded as ‘Live microorganisms which when administered in adequate amounts confer a health benefit on the host’[8]. A recent Food and Agriculture Organization of the United Nations and the World Health Organization Working Group has developed guidelines for what constitutes a true ‘probiotic’, and very few so called health products currently meet these criteria because they have no published clinical studies showing a benefit of their strains on the host [9]. Probiotic Lactobacillus rhamnosus GR-1 and Lactobacillus fermentum RC-14 have been shown in open studies to colonize the vagina following oral intake [10,11].
Bacterial vaginosis (BV) is the most common cause of abnormal vaginal discharge in women of childbearing
age. The causative organisms for this condition are Gardnerella vaginalis, Mycoplasma hominis and anaerobic bacteria. It is thought that a shift to a symptomatic BV state may simply be due to a decline in the levels of ‘beneficial’ lactic acid and hydrogen peroxide-producing lactobacilli and/or an increase in the levels of Gram-negative anaerobes. A variety of events can contribute to the development of BV in which a mixture of the organisms listed above is usually present in concentrations 100 to 1,000 times greater than in the healthy vagina.
The standard scoring system termed the ‘Nugent score’ is an accepted technique using microscopic examination of a Gram-stained smear of vaginal discharge for determining BV. Due to the wide variety of Gram smear results from vaginal samples that can be considered normal, specific bacterial types need not be reported, but may be listed as ‘organisms resembling normal urogenital flora’, Yeast should always be reported with an added comment, such as ‘Candida species are normal flora in the genital area of 30 to 40% of women. The presence of yeast must be correlated with the clinical picture’. Smear results that score >7 in the Nugent scoring system should be reported as ‘consistent with bacterial vaginosis’. It is acceptable not to report cells, or bacteria, and only report presence or absence of yeast, and whether smear results are consistent with BV or not [12].
Available evidence now indicates that certain strains of lactobacilli when administered to patients can colonize the vagina and reduce the risk of BV. Studies have been carried out to assess the efficacy of single strain or combination of probiotics administered orally or Intravaginally in the treatment of BV. In addition, the effect of probiotics in conjunction with antimicrobial regimen has to be evaluated. So this study is aimed to determine the efficacy of probiotics in treating women with symptomatic WDPV.
Materials and Methods
Design of study: This is a prospective randomized clinical study done on women with symptomatic white discharge per vagina (WDPV).
Settings: Symptomatic white discharge per vagina (WDPV) patients attending gynecology outpatient of Vinayaka Mission's Medical College, Karaikal, Puducherry for a period of 2 years (2014-2016).
Study population: In the present study, 70 women with history of WDPV received probiotics along with antibiotics were selected.
Inclusion criteria
- Females patients aged between 18 to 45 yrs (mean age 35yrs) will be included in the study.
- Patients willing to give written informed consent.
- Clinical diagnosis was confirmed by Nugents score.
- Patients who have been newly diagnosed and/or recurrent vulvovaginitis not treated in the previous one month.
Exclusion criteria
- Pregnant or nursing women
- Patient Menstruating at the time of diagnosis
- Usage of antibacterial drugs either systemically or intravaginally within last two weeks
- Patients already on medications for vulvovaginitis.
- Patients taking immunosuppressive, or immunostimulating medications, systemic corticosteroids within 3 months prior to study.
- Patients involved in any other study in previous one month.
- Patients with comorbid conditions like diabetis mellitus and Sexually transmitted diseases (STDs) like Gonorrhea, Syphilis, Chlamydia, AIDS.
- Patients with history of allergy to metronidazole, clotrimazole, clindamycin,
Method of study: Women were examined at their first visit—after detailed history and clinical examination, including local examination to see the amount, character of discharge and for presence of cervical movement tenderness. Routine investigations to rule out presence of anemia, diabetes and urinary infection are done along with Gram stain of the vaginal discharge to study the type of organism and the load of lactobacilli, which is defined using Nugent scoring (table 1 and 2). These patients receive a combination of antibiotics (Ofloxacin + Ornidazole + fluconazole) along with probiotics containing 2,500 million spores of Lactobacilli rhamnosus GR-1 and L. fermentum RC-14, for a period of 1 week.
Table-1: Laboratory examination of vaginal smears and the determination of the Nugent score
| Lactobacilli | Score | Gardnerella, Bacteroides | Score | Curved Gram-negative bacilli | Score | Sum=*N score |
|-------------|-------|--------------------------|-------|-----------------------------|-------|--------------|
| 30 or > | 0 | 0 | 0 | 0 | 0 | 0 |
| 5-30 | 1 | <1 | 1 | <1 | 1 | 3 |
| 1-4 | 2 | 1-4 | 2 | 1-4 | 1 | 5 |
| <1 | 3 | 5-30 | 3 | 5-30 | 2 | 8 |
| 0 | 4 | 30 or > | 4 | 30 or > | 2 | 10 |
Note: Number of organisms seen/100× objective
Table-2: Showing the Interpretation of Nugent score
| N-score | Reports |
|---------|-----------------------|
| 0-3 | Clue cells not present Smear not consistent with BV |
| 4-6 | Clue cells are present Smear consistent with BV |
These patients are called back after 1 week and examined by the same gynecologist, asked regarding symptom relief, examination findings are compared and Grams stain is repeated to look for treatment response and also for the restoration of vaginal flora.
Statistical Analysis: Data was collected and tabulated as shown in results. Statistical analysis was done using Microsoft Excel. Frequency and percentage of each parameter was calculated and analyzed
Results
In the present study, 70 women with history of WDPV received probiotics along with antibiotics. Fifty two percent of patients were aged between 21 and 35 years indicating the increased incidence of RTI in reproductive age group. Forty-six percent had history of pain abdomen along with WDPV and the duration was between 15 days and 6 months in 74% of them.
Among them 48% had received treatment before coming here and were not relieved of the symptoms. On examination, there was copious discharge in 66, 58% had cervical and vaginal congestion, 48% had erosion on the cervix.
Forty eight percent had hemoglobin levels between 8 and 10 gm% (mean ± SD: 10.73 ± 1.21), this shows the correlation between anemia and vaginal infections. Four percent had random blood sugars >160 mg/dl (mean ± SD: 87.19 ± 13.48), 15% of them had associated urinary tract infection.
Pretreatment Gram’s stain is interpreted with respect to the lactobacilli score (Table 3) using one of the criteria’s in Nugent’s score.
Among patients in pretreatment group, 66% of them had <1 organism/100× objective, this showed the shift in vaginal flora, only 2% of them showed count between 5 and 30. Forty-two percent of patients showed >30 organisms/100× in the post-treatment Grams stain. Fifty percent of patients showed counts between 5 and 30 after post-treatment. Pap smear is done for all the patients, 66% of them showed inflammatory. Seventy four (74%) are relieved of symptoms, there was response even in terms of improved vaginal flora (Table 4).
Nine patients (18%) were not relieved of symptoms, even though there was improvement in vaginal flora in seven of these nonresponders, they were not relieved symptomatically. The cause among these patients were non infective, i.e, chronic cervicitis in three patients, diabetes mellitus in two patients, CIN-2 and three in two patients, one patient had Cu-T in situ which had caused recurrent PID, one patient had history of immunocompromised status which caused recurrent pelvic inflammatory disease.
Table-3: Lactobacilli score -pre- and post-treatment
| Lactobacilli score (number of organisms seen/100× objective) | Pretreatment (n = 70) | Post-treatment (n = 70) |
|-------------------------------------------------------------|---------------------|------------------------|
| 0 (30 or >) | Nil | 46% |
| 1 (5-30) | 2% | 50% |
| 2 (1-4) | 12% | 3% |
| 3 (<1) | 66% | 2% |
| 4 (0) | 20% | Nil |
Table-4: Response of treatment
| Response | Number of patients (n = 70) | % |
|----------|----------------------------|-----|
| Yes | 52 | 74.0|
Only 32% patients had side effects like nausea, vomiting in 26%, giddiness in 8% and pain abdomen in 2% of patients. But these side effects cannot be completely attributed to use of probiotics only, as in the study they receive additional antibiotics also.
Discussion
The therapy resulted in a significant improvement in the vaginal flora in terms of increased lactobacilli presence. The outcome was not designed to be mechanism-based, but the results indicate that intestinal passage of these probiotic strains led to a beneficial impact on the vaginal microflora.
This may have occurred due to the strains themselves ascending to the vagina from the rectal area. It is feasible that the therapy caused an alteration in the mucosal immunity of the host (via the gut and/or vagina) and that this played a part in reducing pathogen counts. This study was concurrent with the previous studies. Bohbot and Cardot (2012) found that positive impact of the oral administration of LCR35 on vaginal microbiota and also decrease in the Nugent score in healthy women and therefore the maintenance of the quality of their vaginal microbiota [13].
Wagner and Johnson (2012) showed that Lactobacillus rhamnosus GR-1 and Lactobacillus reuteri RC-14 strains used in commercial products inhibit infectivity of Candida albicans the major cause of VVC [14]. Larsson et. al showed that aggressive treatment of patients with BV with antibiotics combined with lactobacillus administration can provide a long lasting cure[15].
The loss of vaginal lactobacilli appears to be the major factor in the cascade of changes leading to bacterial vaginosis and relapses are associated with failure to establish a healthy lactobacilli dominated vaginal flora.
The mode of action has not been elucidated but might comprise:
- Increased ascension of probiotic and/or indigenous lactobacilli from the rectal skin to the vagina.
- Reduced ascension of pathogens from the rectal skin to the vagina.
- Enhancement of the intestinal mucosal immunity which affects vaginal immunity rendering the environment less receptive to bacterial vaginosis organisms.
In our present study, the lactobacilli score was improved with oral probiotics. Among patients in pretreatment group, 66% of them had <1 organism/100× objective, this showed the shift in vaginal flora, only 2% of them showed count between 5 and 30.
Among post-treatment group 46 % of patients showed >30 organisms/100×. Fifty percent of patients showed counts between 5 and 30 among post-treatment. This shows the improved vaginal flora following treatment with probiotics.
Nine patients (18%) were not relieved of symptoms, even though there was improvement in vaginal flora in 7 of these nonresponders, they were not relieved symptomatically. The cause among these patients were non infective, i.e. chronic cervicitis in 3 patients, diabetes mellitus in 2 patients, CIN-2 and 3 in 2 patients, one patient had Cu-T in situ which had caused recurrent PID, one patient had history of immuno-compromised status which caused recurrent pelvic inflammatory disease.
Therefore only the altered vaginal flora leading to bacterial vaginosis should not be blamed on, as other predisposing factors has to be treated simultaneously.
Although antimicrobial therapy is generally effective in eradicating urogenital infections, there is still a high incidence of recurrence. There is good clinical evidence to show that the intestinal and urogenital microbial flora have a central role in maintaining both the health and well-being of humans.
**Conclusion**
This study clearly showed that combination of probiotic (L. rhamnosus GR-1 and L. fermentum RC-14) is not only secure for daily use in healthy women, but it could decrease colonization of the vagina by potential pathogenic bacteria and yeast.
**Funding:** Nil, **Conflict of interest:** Nil
**Permission from IRB:** Yes
**References**
1. Wasiela M, Hanke W, Kalinka J. Association between abnormal microbiological flora of the lower genital tract in early pregnancy and socioeconomic, demographic and environmental risk factors Med Sci Monit 2001;7:1250-55.
2. Schwebke JR, Richey CM, Weiss2 HL. Correlation of behaviors with microbiological changes in vaginal flora. J Infect Dis. 1999 Nov;180(5):1632-6.
3. Bruce AW, Chadwick P, Seddon JM, Vancott GF. The significance of perineal pathogens in women. J Urol. 1974 Dec;112(6):808-10.
4. Sewankambo N, Gray RH, Wawer MJ, Paxton L, McNain D, Wabwire-Mangen F, Serwadda D, Li C, Kiwanuka N, Hillier SL, Rabe L, Gaydoss CA, Quinn TC, Konde-Lule J. HIV-1 infection associated with abnormal vaginal flora morphology and bacterial vaginosis. Lancet. 1997 Aug 23;350(9077):546-50.
5. Reid G, Bruce AW, Beheshti M. Effect of antibiotic treatment on receptivity of uroepithelial cells to uropathogens. Can J Microbiol. 1988 Mar;34(3):327-31.
6. Petrof EO, Schwartz DN, Quinn JP. Urinary tract infections and a multidrug-resistant Escherichia coli clonal group. N Engl J Med. 2002 Feb 14;346(7):535-6.
7. Ellis AK, Verma S. Quality of life in women with urinary tract infections: is benign disease a misnomer? J Am Board Fam Pract. 2000 Nov-Dec;13(6):392-7.
8. FAO/WHO. Evaluation of health and nutritional properties of powder milk and live lactic acid bacteria. Food and Agriculture Organization of the United Nations and World Health Organization Report 2001.
9. FAO/WHO. Guidelines for the evaluation of probiotics in food. Report of a joint FAO/WHO Working Group 2002.
10. Reid G, Bruce AW, Fraser N, Heinemann C, Owen J, Henning B. Oral probiotics can resolve urogenital infections. FEMS Immunol Med Microbiol. 2001 Feb;30(1):49-52.
11. Reid G, Beuerman D, Heinemann C, Bruce AW. Probiotic Lactobacillus dose required to restore and maintain a normal vaginal flora. FEMS Immunol Med Microbiol. 2001 Dec;32(1):37-41.
12. Bijeta, Shreshtha Singh. Incidence of bacterial vaginosis in patients with idiopathic preterm labour. Int J Reprod Contracept Obstet Gynecol. 2015; 4(3): 641-646.
13. Champagne CP, Ross RP, Saarela M, Hansen KF, Charalampopoulos D. Recommendations for the viability assessment of probiotics as concentrated cultures and in food matrices. Int J Food Microbiol. 2011 Oct 3;149(3):185-93. doi: 10.1016/j.ijfoodmicro.2011.07.005. Epub 2011 Jul 14.
14. Wagner RD, Johnson SJ. Probiotic lactobacillus and estrogen effects on vaginal epithelial gene expression responses to Candida albicans. J Biomed Sci. 2012 Jun 20;19:58. doi: 10.1186/1423-0127-19-58.
15. Larsson et al. Extended antimicrobial treatment of bacterial vaginosis combined with human lactobacilli to find the best treatment and minimize the risk of relapse. BMJ Infectious Diseases.2011;11:223. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3890,
1
],
[
3890,
8007,
2
],
[
8007,
11685,
3
],
[
11685,
15950,
4
],
[
15950,
19411,
5
]
]
} |
e3ff62403a8fa870eaa9b09fa066f1db7d7a1c6c | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 13,
"total-fallback-pages": 0,
"total-input-tokens": 38242,
"total-output-tokens": 14810,
"fieldofstudy": [
"Biology"
]
} | Coatamer and dimeric ADP ribosylation factor 1 promote distinct steps in membrane scission
Rainer Beck,1 Simone Prinz,2 Petra Diestelkötter-Bachert,1 Simone Röhling,1 Frank Adolf,1 Kathrin Hoehner,1 Sonja Welsch,2 Paolo Ronchi,3 Britta Brügger,1 John A.G. Briggs,2,3 and Felix Wieland1
1Heidelberg University Biochemistry Center, Heidelberg University, 69120 Heidelberg, Germany
2Structural and Computational Biology Unit and 3Cell Biology and Biophysics Unit, European Molecular Biology Laboratory, 69117 Heidelberg, Germany
Formation of coated vesicles requires two striking manipulations of the lipid bilayer. First, membrane curvature is induced to drive bud formation. Second, a scission reaction at the bud neck releases the vesicle. Using a reconstituted system for COPI vesicle formation from purified components, we find that a dimerization-deficient Arf1 mutant, which does not display the ability to modulate membrane curvature in vitro or to drive formation of coated vesicles, is able to recruit coatamer to allow formation of COPI-coated buds but does not support scission. Chemical cross-linking of this Arf1 mutant restores vesicle release. These experiments show that initial curvature of the bud is defined primarily by coatamer, whereas the membrane curvature modulating activity of dimeric Arf1 is required for membrane scission.
Introduction
Coated vesicle formation generally requires GTPases and coat protein complexes. In the secretory pathway, small GTPases are used to initiate coat recruitment: Sar1p for COPII-coated vesicles and Arf1 for COPI- and clathrin-coated vesicles. Next, the membrane is sculpted to form a bud, and finally, membrane separation takes place to complete vesicle formation. In endocytosis, the scission of clathrin-coated vesicles containing AP2 generation, Arf1-GTP and coatamer should act in concert to sculpt the membrane to form a bud and, subsequently, bring about membrane separation.
Here, we investigate the molecular mechanisms that underlie the formation of curvature and subsequent scission of a coated vesicle. Previously, we and others have reported that Arf1 has the ability to modulate the shape of liposomal bilayers (henceforth called membrane surface activity; Beck et al., 2008; Krauss et al., 2008; Lundmark et al., 2008). We now show that it is coatamer that sculpts the curvature of a membrane bud and
Supplemental material can be found at: http://doi.org/10.1083/jcb.201011027
Figure 1. Membrane surface activity of Arf1 and coatomer. (A) Membrane surface activity of Arf1 analyzed in GUVs. GUVs containing 0.5 mol% 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-lissamine rhodamine B sulfonyl were incubated with 3.5 µM Arf1-wt and 0.4 µM ARNO in the presence or absence of 1 mM GTP as indicated and recorded in a confocal laser-scanning microscope (LSM 510; Carl Zeiss) with a 63× objective lens and a pinhole.
that the membrane surface activity of Arf1 is not involved in bud formation but rather is required for scission. We further present a novel mechanistic model in which dimerization of a small GTPase plays a key role in vesicle scission.
Results
Arf1 is required for scission of COPI vesicles
Recently, Arf1 was shown to induce positive curvature on membranes (Beck et al., 2008; Krauss et al., 2008; Lundmark et al., 2008) by either monitoring tubulation of membrane sheets in light microscopy or EM of tubulated liposomes. Although we showed that this tubulation activity of Arf1 is ultimately required for vesicle biogenesis (Beck et al., 2008), it is unknown whether this activity is actually bending the membrane physically during COPI vesicle formation. Thus, we henceforth use the term “membrane surface activity” when we refer to Arf1-induced changes on liposomal bilayer morphology. This allows discriminating membrane surface activity of Arf1 and membrane curvature, which is ultimately induced on the Golgi membrane to form a vesicle bud during vesicle biogenesis.
As an alternative approach to the published data mentioned in the first paragraph, we monitored Arf1–GTP-induced membrane surface activity on giant unilamellar vesicles (GUVs) by confocal microscopy using either C-terminally fluorescently labeled Arf1, fluorescently labeled GTP (not depicted), or fluorescently labeled phospholipids (Fig. 1 A). GTP-dependent tubulation of GUVs occurred at Arf1 concentrations of 2–5 µM. When Arf1 concentrations of 0.5 µM and below were used, membrane deformation was not observed, in agreement with previous observations (Manneville et al., 2008).
As a next step, we asked whether the presence of a coat-omer would have a contribution to Arf1-mediated membrane surface activity by analyzing membrane sheets in a phase-contrast light microscopy assay (Roux et al., 2006; Beck et al., 2008; Krauss et al., 2008). After addition of Arf1, the guanine nucleotide exchange factor ADP ribosylation factor (Arf) nucleotide binding site opener (ARNO; Chardin et al., 1996), and GTP to a hydrated lipid surface in the absence of coatomer, planar lipid sheets (Fig. 1 B, left) were converted into tubules (Fig. 1 B, top right; in line with Beck et al., 2008). This effect presumably results from the insertion of Arf1’s amphipathic helix into the membrane (Antonny et al., 1997), possibly with its myristoyl residue perpendicular to the membrane lipid acyl chains (Liu et al., 2010). In experiments to control for a contribution to this membrane surface activity of Arf’s N-terminal myristoylated amphipathic helix, we used a His-tagged truncated protein lacking the amphipathic helix, ΔNΔ7-Arf1, on membrane sheets containing 5 mol percent (mol%) Ni++ lipids. This allows the truncated protein to be recruited via His-Ni++ interaction (Fig. S1). Arf1 lacking its N-terminal amphipathic helix exerted no membrane surface activity (Video 1). This is in line with a study on a similar function for Sar1p (Lee et al., 2005), demonstrating that for membrane surface activity of the small GTPase, the amphipathic helix is required. Next, we investigated the contribution of coatomer to membrane surface activity in this setup. Strikingly, simultaneous addition of coatomer and Arf1 leads to formation of morphologically distinct tubular membrane structures that are shorter than those generated by Arf1 in the absence of coatomer (Fig. 1 B, bottom right).
We next sequentially added first Arf1 and then coatomer to a hydrated lipid surface (Video 2 and Fig. 1 C). The fine tubules formed after Arf1 addition (Fig. 1 C, b, arrows) became shortened a few seconds after addition of coatomer (Fig. 1 C, c and d, arrows). At the same time, novel shorter tubular structures arose (Fig. 1 C, c–e, arrowheads) that became predominant ~8 s after coatomer addition (Fig. 1 C, f). The observations shown so far indicate that there are two distinct activities on the membrane surface, one by Arf1 alone and a second one after the addition of coatomer: coatomer is able to remodel Arf1-induced membrane tubules.
As published previously, Arf1–GTP can form a dimer on the membrane (Beck et al., 2008), and its membrane surface activity in vitro depends on dimerization. A dimerization-deficient mutant, Arf1-Y35A, cannot induce tubules under these conditions either in the absence or the presence of coatomer and does not support COPI vesicle formation. Expression of the mutant Arf1-Y35A cannot rescue Arf1/2 deletion in yeast. However, Arf1-Y35A is capable of recruiting coatomer to membranes in a GTP-dependent manner (Beck et al., 2008).
The structures, which result from the addition of Arf1 and coatomer to lipid surfaces (as observed in Video 2 and Fig. 1 C), cannot be resolved at the level of light microscopy, and therefore, to dissect the contributions of Arf1 and of coatomer to membrane deformation, we used cryo-EM. Liposomes were incubated either with Arf1–wild type (wt) or Arf1-Y35A in the presence of ARNO, coatomer, and guanine nucleotides (Fig. 2 A). With Arf1-wt, we observed coated liposomal structures of quite homogeneous size, reflecting reconstituted COPI vesicles as expected (Fig. 2 A, left). The diameter of the free vesicles was 59 ± 3 nm, consistent with previous observations (Spang et al., 1998; Bremser et al., 1999). We also saw vesicles in the process of budding, in which the bud membrane had remained continuous with the donor lipidome. The diameter of the buds was 61 ± 4 nm. No free
size equivalent to one Airy disk diameter. (B) Membrane surface activity of Arf1 and coatomer. Lipids containing the p23 lipopeptide were spotted on a glass surface and hydrated with buffer containing GTP and 50 nM of the exchange factor ARNO. The lipid surface was observed before (left) and after addition of 1 µM myristoylated Arf1–GDP (top right) or by coincubation of 1 µM Arf1 and 0.25 µM coatomer (cm; bottom right). (C) Dissecting membrane surface activities of Arf1 and coatomer. (a) Lipids containing the p23 lipopeptide were spotted on a glass surface and hydrated with buffer containing GTP and the exchange factor ARNO as described in this legend. The image was taken, and thereafter, Arf1 was added, and tubule formation was observed (Video 1). (b) 0.25 µM coatomer was added to the chamber, leading to an immediate and nonspecific loss of most tubular structures caused by capillary flow forces. One frame afterward (t = 0), remaining Arf1-generated tubules are depicted (arrows). (c–f) Images were taken at 2, 4, 6, and 8 s after the addition of coatomer. The rapid degradation of Arf1-generated tubules (arrows) was followed over time, whereas new tubular structures with a distinct morphology were generated in the presence of coatomer (arrowheads). Bars, 5 µm.
activity of Arf1-Y35A, formation of coated buds can still take place, implying a predominant role for coatomer in governing the shape of the vesicle. The shape could be governed directly by the geometry of polymerized coatomer and/or by coatomer positioning Arf1’s myristoylated N-terminal helix to provide bud curvature. In summary, the Arf1-mediated membrane surface activity observed in Fig. 1 is not required to sculpt the shape of a nascent vesicle bud.
Evaluation of 148 coated vesicles or buds counted in the Arf1-wt liposome samples revealed that 22% of the structures unequivocally represent free vesicles, whereas with Arf1-Y35A, vesicles or budding structures were observed in the absence of GTP. Strikingly, with dimerization-deficient mutant Arf1-Y35A, few distinct vesicles were found. Nevertheless, flower-like bud structures could be seen (Fig. 2 A, right), in which multiple budding events are taking place from individual liposomes. The bud membranes are still continuous with the liposomal membrane: scission has not taken place. The diameter of the buds is 63 ± 3 nm, the same as that for Arf1-wt. A similar result was obtained when Golgi-enriched membranes rather than liposomes were used (Fig. 2 B). These analyses show that despite the absence of membrane surface activity of Arf1-Y35A, formation of coated buds can still take place, implying a predominant role for coatomer in governing the shape of the vesicle. The shape could be governed directly by the geometry of polymerized coatomer and/or by coatomer positioning Arf1’s myristoylated N-terminal helix to provide bud curvature. In summary, the Arf1-mediated membrane surface activity observed in Fig. 1 is not required to sculpt the shape of a nascent vesicle bud.
only 2% were found separated from the liposomes (n = 120; Fig. 2 A). When Golgi membranes were used, increased background in the images caused by the membrane preparation makes it difficult to unambiguously quantify the number of vesicles that are released and that remain attached to donor membranes. We therefore quantitatively assessed vesicle release after isolation of COPI vesicles based on their buoyant density using Western blotting (Fig. 2 C). Free COPI vesicles were recovered in the presence of Arf1-wt in a GTP-dependent manner, as indicated by the presence of signals for transferrin receptor δ-COP and Arf1. In contrast, the monomeric mutant Arf1-Y35A did not support the reconstitution of free vesicles. These findings are consistent with our previous observations from in vitro Golgi budding assays, in which we could not reconstitute free COPI vesicles with the dimerization-deficient mutant Arf1-Y35A; only background amounts (<2%) of vesicles were recovered with Arf1-Y35A as compared with Arf1-wt (Beck et al., 2008). For further quantitative analysis of COPI reconstitutions and EM of isolated vesicles, see also Fig. 4 in this paper. Thus, although COPI buds are formed on Golgi membranes using either Arf1-wt or Arf1-Y35A, only Arf1-wt releases those buds to yield free vesicles (Fig. 2 C).
The dimerization-deficient Arf1-Y35A can exchange GDP with GTP and recruit coatomer to membranes, yet the mutant cannot exert membrane surface activity and, therefore, cannot drive formation of free vesicles. Now, we find that coatomer recruited by Arf1-Y35A forms coated buds, as shown by cryo-EM (Fig. 2, A and B), but that vesicle scission does not take place, as shown by biochemical experiments (Fig. 2 C). Together, these observations indicate that vesicle production requires a combination of curvature-forming activity by coatomer, which defines the shape of the bud, and membrane surface activity contributed by Arf1. Furthermore, they assign a clear function for the membrane surface activity of Arf1 during scission. What are the molecular mechanisms that underlie this function?
**Scission of a vesicle depends on dimerization of Arf1**
As Arf1-Y35A fails to dimerize, we hypothesized that the formation of an Arf1-GTP dimer may be required to destabilize the membrane at the bud neck and allow fission. To challenge this hypothesis, we tested whether a forced dimerization of the Arf1-Y35A mutant by chemical cross-linking would restore scission activity, as might be expected if dimerization was the only defect of this mutant. To this end, the single cysteine residue of both Arf1 and Arf1-Y35A was replaced with serine, and the C-terminal lysine was substituted with cysteine, yielding Arf1-C159S-K181C and Arf1-Y35A-C159S-K181C (from here on referred to as Cys-wt and Cys-Y35A, respectively). Published work has demonstrated that adding a Cys residue to the C terminus of the small GTPase is permissive for Arf1 function (Manneville et al., 2008).
These variants were then analyzed in a liposomal binding assay. Liposomes were isolated by centrifugation and analyzed for their content of Arf1 variants by Western blotting. Arf1-wt and Cys-wt were found to bind to membranes in a GTP-dependent manner and to a comparable extent (Fig. 3 A, compare lane 2 with 4 and lane 6 with 8). Note that the faster migrating band in the input lanes reflects myristoylated Arf1, and the top band reflects the nonmyristoylated form of Arf1, which fails to bind membranes and, therefore, does not show up in the liposomal fraction. Thus, exchange of Cys 159 to Ser and Lys 181 to Cys does not compromise Arf1’s specific binding to membranes. In the case of the mutant Cys-Y35A, no binding was observed (Fig. 3 A, lanes 10 and 12). This was expected, as it was shown previously that binding to liposomal membranes of the dimerization-deficient Arf1-Y35A variant required the presence of coatomer (Beck et al., 2008).
Next, the Cys variants were dimerized by reaction with a homobifunctional SH-reactive reagent, bismaleimidohexane (BMH), and the extent of cross-linking was analyzed by SDS gel electrophoresis. Both proteins were dimerized efficiently and to a similar extent, as shown by Coomassie staining in Fig. 3 B, in which the Arf1 dimers migrate with an apparent molecular mass of ~37 kD.
A well-established static light scattering assay (Bigay and Antonny, 2005) was used to monitor membrane dynamics of Arf1-wt, Arf1-Cys, cross-linked Arf1-Cys (cl-Arf1-Cys), and coatomer. As depicted in Fig. S2, nucleotide exchange of Arf1-wt and Cys-wt is comparable. Cl⁻ Cys-wt shows a faster rate of GTP loading, probably because of the increased membrane avidity of the dimer. Arf GTase-activating protein (ArfGAP)–mediated GTP hydrolysis is comparable for all three proteins; however, the dimeric construct leaves the membrane with slightly slower kinetics, likely caused by the need of hydrolyzing two nucleotides in one molecule (Fig. S2).
To study the membrane-binding properties of the dimerized proteins, chemically cross-linked Cys-wt was tested for membrane binding as before analyzed by floatation, as shown for the non–cross-linked Arf1 variants earlier in this paper. As depicted in Fig. 3 C, chemical cross-linking of Cys-wt results in efficient membrane binding comparable with that of Arf1-wt (Fig. 3 C, compare the ratio of lanes 3 and 4 with the ratio of lanes 7 and 8). The larger fraction of bound cl-Cys-wt likely reflects increased avidity resulting from dimerization. Membrane avidity was increased by dimerization to an extent that led to some binding even in the absence of GTP (Fig. 3 C, lane 6). Most remarkably, the dimerization-deficient Arf1 variant Cys-Y35A, upon dimerization by chemical cross-linking, gains capability to bind to membranes even in the absence of a coatomer, as shown in Fig. 3 C (lane 12). Again, some binding of chemically cross-linked Cys-Y35A is observed in the absence of GTP (Fig. 3 C, lane 10).
The experiments in Fig. 2 show a scission arrest for monomeric Arf1-Y35A when compared with Arf1-wt. We next analyzed whether chemically cross-linked Cys-Y35A dimers can support the scission reaction, i.e., form free COPI vesicles. Cys-wt and Cys-Y35A were chemically cross-linked and incubated with Golgi membranes and the coatomer in the presence or absence of GTP followed by isolation of COPI vesicles based on their buoyant density and analysis by Western
To control for possible effects of the Cys mutation and chemical cross-linking on Arf1 function, reconstituted COPI vesicles were probed by Western blotting for cargo and noncargo (excluded) markers (Fig. S4). We find uptake of \( \alpha \)-mannosidase II in all COPI vesicle fractions independent of the Arf1 used, indicating that this Golgi resident enzyme is taken up into the vesicles as expected. As an excluded protein, we analyzed G\( \alpha \)s, which was shown previously to localize to the Golgi but is excluded from COPI vesicles blotting (Fig. 4 A) and EM (Fig. 4 B; Weimer et al., 2008; Beck et al., 2009a). Arf1-wt served as a positive control (Fig. 4 A, lane 4). Like Arf1-Y35A (Fig. 2 C), the non–cross-linked variant Cys-Y35A failed to produce free vesicles (Fig. 4 B and Fig. S3). Strikingly, upon dimerization by chemical cross-linking, this mutant gives rise to efficient vesicle formation to an extent comparable with that of chemically cross-linked Cys-wt, as shown in Fig. 4 A (lanes 12 and 8).
Figure 3. Binding of Arf1 and Arf1 variants to synthetic liposomes. [A] Comparison of the binding ability of Arf1-wt, Cys-wt, and Cys-Y35A to synthetic liposomes in the absence and presence of GTP. Arf1 variants were mixed with liposomes to a final concentration of 1.5 \( \mu \)M protein and 0.5 mM lipid in the presence of ARNO in a total volume of 100 \( \mu \)l. After 15 min of incubation at 37\(^\circ\)C with or without 1 mM GTP, the samples were floated to an interface between 25 and 0% (wt/vol) sucrose. 10% of the collected liposomal fractions was compared with 5% of the input and analyzed for the presence of Arf1 and the Arf1 variants by SDS-PAGE and Western blotting, respectively. non-myrArf1, nonmyristoylated Arf1; myrArf1, myristoylated Arf1. [B] Cross-linking of the Cys variants using BMH. Purified Arf1 protein was mixed with BMH in a molar ratio of 2:1 and incubated for 1 h at RT. Thereafter, the cross-linking reaction was quenched by the addition of DTT and analyzed by SDS-PAGE and Coomassie staining. [C] Analysis of the binding ability of cross-linked Cys-wt (cl-Cys-wt) and Cys-Y35A (cl-Cys-Y35A) to synthetic liposomes in the absence and presence of GTP. The assay was performed as outlined in A. I, input; L, liposome-bound fraction.
How is this dimerization of the small GTPase linked to the scission reaction? To address this mechanism at a molecular level, we studied the interactions of Arf1 with a coatomer that shapes the membrane to form a bud.
Anchoring of Arf1 in its overlaying scaffold of coatomer
wt Arf1-GTP is stably anchored in the shell of the budding vesicle by specific interactions with various subunits of coatomer, as indicated by site-directed photolabeling experiments (Zhao et al., 1997, 1999; Sun et al., 2007). Therefore, we assessed whether Arf1-wt and Arf1-Y35A adopt the same conformation and interactions within the coat. To this end, Arf1 variants were generated containing a photoreactive benzophenone derivative of phenylalanine (p-benzoyl-l-phenylalanine [Bp]) at position I49 or Y167, previously shown to contact coatomer at different sites. Upon UV irradiation, covalent bonds will be formed between the
(Helms et al., 1998). As a result, with all Arf1 variants, we find efficient exclusion of Gαs. Thus, neither the Cys mutation nor its cross-linking had detectable influence on cargo uptake or exclusion.
Reconstituted vesicles were further analyzed by negative stain EM (Fig. 4 B), and the data were quantified (Fig. 4 C). Although in the non–cross-linked Cys-Y35A sample, there was a background amount of ~90 vesicles per 42 meshes (a number similar to that obtained in negative controls, in which no Arf1 was added and in which a few vesicles are formed because of residual Arf1 present in the Golgi preparations as shown in Fig. 4 C), after cross-linking, ~700 vesicles were counted in the same field size. This reflects an efficiency of vesicle formation of ~70% when compared with dimerized Cys-wt. These results show that the arrest in vesicle scission caused by the Y35A mutation can be rescued by chemical cross-linking–induced dimerization. Dimerization of Arf1 is therefore required for membrane scission during vesicle formation.
Arf1-Y35A (Dascher and Balch, 1994). As expected, microinjection of Arf1-wt or Arf1-Y35A was not lethal and did not show alterations in subcellular localization of Golgi markers (unpublished data). As a striking result, we observed cell lethality 4 h after injection of Arf1-Y35A-Q71L, however, not of Arf1-Q71L. We analyzed cells 2 h after microinjection. In immunofluorescence analyses with antibodies directed against attached and integral Golgi membrane markers, as well as against coatomer, we observed that Arf1-Y35A-Q71L (and not Arf1-Q71L) causes loss of cis-peripheral Golgi proteins (GM130; Fig. S5 A) and, to a lesser extent, GMAP-210 (not depicted). The integral Golgi protein giantin remains unaffected, whereas a reduced Golgi localization of 1,4 galactosyltransferase (GalT) is observed for both Arf1-Y35A-Q71L and Arf1-Q71L. With antibodies directed against coatomer 2 h after injection of Arf1-Y35A-Q71L, a more condensed Golgi-like pattern is seen compared with Arf1-Q71L. Analysis by EM of thin sections 2 h after injection is shown in Fig. S5 B. Injection of Arf1-Q71L gave rise to an accumulation of vesicular structures (Fig. S5 B, A–D) as expected (Tanigawa et al., 1993) and left the morphology of the stacked Golgi cisternae intact. In the case of Arf1-Y35A-Q71L, we were unable to observe any Golgi stacks within the injected cells (Fig. S5 B, E–H). Thus, the condensation observed with coatomer as a Golgi marker in immunofluorescence is reflected by a disappearance of stacked cisternae.
A photo–cross-link is observed between position 49 of both Arf1-wt-I49Bp and Arf1-Y35A-I49Bp and γ1- and γ2-COPs (Fig. 5 A) and between position 167 of both Arf1-wt-Y167Bp and Arf1-Y35A-Y167Bp and δ-COP (Fig. 5 B). The corresponding bands in both cases are of similar intensity. A cross-link, e.g., between α-COP with photolabile Arf1 variants, was not observed, in accordance with Zhao et al. (1999) and Sun et al. (2007). These results establish that the point mutation in Arf1-Y35A leaves intact the known interactions of coatomer with the small GTPase and indicate that it is missing the interface of Arf1-Y35A with its kin rather than its interfaces with coatomer, which impairs membrane fusion.
Effects of dimerization-deficient Arf1 in vivo
To analyze the effect of dimerization deficiency of Arf1 in a living cell, cells were microinjected with cDNAs encoding Arf1 variants. Because the effects of Arf1-Y35A can be rescued by endogenous Arf1-wt, we also used GTP-locked forms of Arf1-wt and Arf1-Y35A (Dascher and Balch, 1994). As expected, microinjection of Arf1-wt or Arf1-Y35A was not lethal and did not show alterations in subcellular localization of Golgi markers (unpublished data). As a striking result, we observed cell lethality 4 h after injection of Arf1-Y35A-Q71L, however, not of Arf1-Q71L. We analyzed cells 2 h after microinjection. In immunofluorescence analyses with antibodies directed against attached and integral Golgi membrane markers, as well as against coatomer, we observed that Arf1-Y35A-Q71L (and not Arf1-Q71L) causes loss of cis-peripheral Golgi proteins (GM130; Fig. S5 A) and, to a lesser extent, GMAP-210 (not depicted). The integral Golgi protein giantin remains unaffected, whereas a reduced Golgi localization of β1,4 galactosyltransferase (GaIT) is observed for both Arf1-Y35A-Q71L and Arf1-Q71L. With antibodies directed against coatomer 2 h after injection of Arf1-Y35A-Q71L, a more condensed Golgi-like pattern is seen compared with Arf1-Q71L.
Analysis by EM of thin sections 2 h after injection is shown in Fig. S5 B. Injection of Arf1-Q71L gave rise to an accumulation of vesicular structures (Fig. S5 B, A–D) as expected (Tanigawa et al., 1993) and left the morphology of the stacked Golgi cisternae intact. In the case of Arf1-Y35A-Q71L, we were unable to observe any Golgi stacks within the injected cells (Fig. S5 B, E–H). Thus, the condensation observed with coatomer as a Golgi marker in immunofluorescence is reflected by a disappearance of stacked cisternae.
**Figure 5.** Interactions of Arf1 with coatomer probed by site-directed photo–cross-linking. Arf1 variants with a photolabile amino acid residue in either position 49 or 167 were prepared as described in Materials and methods and used for coatomer recruitment to Golgi membranes. Membranes were separated by centrifugation and UV irradiated followed by SDS-PAGE and Western blotting. (A) Analysis of photo–cross-link products with the photolabile amino acid derivative in position 49. Lanes 1 and 2 show Cys-wt and Cys-Y35A, respectively, decorated with anti-Arf1 antibodies. Lanes 3 and 4 show samples as in lanes 1 and 2 decorated with anti-γ-COP and, as a control, with anti-α-COP antibodies. (B) Analysis of photo–cross-link products with the photolabile amino acid derivative in position 167. Lanes 1 and 2 are decorated with anti-Arf1 antibodies, and lanes 3 and 4 are decorated with anti-δ-COP and anti-α-COP antibodies. For details of preparation of site-directed photolabile Arf1 derivatives see Materials and methods. Molecular masses are given in kilodaltons.
Surface activity (McMahon and Gallop, 2005; Pucadyil and Schmid, 2009). To build the initial vesicular shell, Arf1 binds coatomer via several COPI subunits (Zhao et al., 1997, 1999; Sun et al., 2007), the membrane via its myristoylated \(\alpha\)-helix (Antonny et al., 1997), and another Arf1 monomer via the dimerization interface (Beck et al., 2008). Arf1 will therefore be linked tightly to both the coat above and the phospholipid bilayer below. In the region of a bud’s neck, membrane areas exist with positive and negative curvature (Drin and Antonny, 2005). Activated Arf1 will most stably be bound to regions where the membrane is positively curved (with less tightly packed outer leaflet lipids) perpendicular to the inserted amphipathic helix. Insertion of the helix in an orientation perpendicular to negative curvature (where lipids are more tightly packed) would create an energetically unfavorable state.
The binding of activated Arf1 to the membrane could contribute to scission in two conceptually different ways. In the first, Arf1 could be arranged to form a ring around the bud neck, with the helices oriented perpendicular to the neck. This model has been proposed for Sar1 (Drin and Antonny, 2005) and requires a specific arrangement of the small GTPase at the bud neck, different to that within the spherical bud coat. In a second model, depicted in Fig. 6, Arf1 is incorporated in an arrangement stable only in the spherical surface of the bud (Fig. 6, Arf1-wt in blue and Arf1-Y35A in red). During budding, Arf1 and coatomer are recruited at the edge of the growing coat, a region that has increasing negative curvature as the bud becomes more complete. Enforcement by multiple coatomer interactions of Arf1 dimers in these negatively curved regions would induce a membrane surface activity (McMahon and Gallop, 2005; Pucadyil and Schmid, 2009). To build the initial vesicular shell, Arf1 binds coatomer via several COPI subunits (Zhao et al., 1997, 1999; Sun et al., 2007), the membrane via its myristoylated \(\alpha\)-helix (Antonny et al., 1997), and another Arf1 monomer via the dimerization interface (Beck et al., 2008). Arf1 will therefore be linked tightly to both the coat above and the phospholipid bilayer below. In the region of a bud’s neck, membrane areas exist with positive and negative curvature (Drin and Antonny, 2005). Activated Arf1 will most stably be bound to regions where the membrane is positively curved (with less tightly packed outer leaflet lipids) perpendicular to the inserted amphipathic helix. Insertion of the helix in an orientation perpendicular to negative curvature (where lipids are more tightly packed) would create an energetically unfavorable state.
A model for membrane scission
The production of COPI-coated vesicles likely results from an interplay between a scaffold mechanism, in which coatomer drives bending of the membrane to form a COPI bud, and an independent mechanism, in which shallow insertion of the amphipathic helix of Arf1 into the membrane exerts a membrane
Together, these data are compatible with a requirement in vivo for dimeric Arf1. The dramatic phenotype in vivo is likely because Arf1 not only is involved in the formation of COPI vesicles but also of AP1, AP3, AP4, and GGA (Golgi localized, \(\gamma\)-adaptin ear containing, Arf binding) carriers.
Discussion
The results presented in this paper establish that the point mutation in Arf1-Y35A leaves Arf1’s known coatomer interactions intact and permits recruitment of coatomer to membranes and formation of a bud but leads to a block in scission. At the molecular level, we show that this fission arrest results from a loss of the propensity of the small GTPase to dimerize upon activation. By forcing dimerization through chemical cross-linking of Arf1-Y35A, the scission arrest of the mutant can be overcome. Dimerization of Arf1 is therefore required for separation of a COPI vesicle from its donor membrane.
We note that direct cryo-EM of the reconstituted reaction shows that coated buds are formed by both Arf1-wt and Arf1-Y35A (Fig. 2), suggesting that only the Arf1-wt can yield released vesicles. Biochemical separation by sucrose gradient purification confirms that only Arf1-wt and not Arf1-Y35A yields released vesicles. Because both Arf1-wt and the mutant are treated in the same manner, these observations argue strongly against mechanical manipulation or physical perturbation as the cause of vesicle release in our observations.
A model for membrane scission
The process of COPI budding and fission is depicted. Arf1 is recruited to the neck of a growing bud and stabilized in this location by coatomer (Arf1-Y35A in red; Arf1-wt in blue). As the growing bud becomes completed, the local membrane curvature creates an unfavorable situation for the insertion of the myristoylated amphipathic helix of Arf1. If Arf1 is enforced in this area by its multiple interactions with the covering network of polymerized coatomer, this will lead to local strain in the membrane (in red). The resulting metastable intermediate can then be relaxed in an irreversible manner by membrane separation. The resulting shell of polymerized coatomer is drawn with a gap because any possible contribution to membrane fission by closing this gap is not addressed here.
increasing strain in the membrane. This could be released by scission, providing a basic mechanism for membrane separation. Destabilization of the Arf1 dimerization interface through the Y35A mutation would reduce the stability with which Arf1 is anchored within the membrane. Although the interaction of monomeric Arf1-Y35A molecules with the covering scaffold of polymerized coatomer is intact, the binding energy between two Arf1 molecules is missing, and therefore, the force is correspondingly lower by which Arf1 is kept in energetically unfavorable zones of negative curvature. The resulting lack of membrane strain would lead to a block in scission. At this point, we cannot exclude the possibility that dimerization occurs selectively during the final constriction step at the vesicle neck.
The conclusions presented here are based on in vitro observations in a defined liposomal system and on Golgi membranes. Combined with the known inability of Arf1-Y35A to rescue Arf-deficient yeast (Beck et al., 2008), these results provide compelling evidence that dimerization of Arf1 represents a key mechanism for scission in the COPII system. Likewise, in the mammalian living cell, dimerization deficiency of Arf1 locked in its activated state is lethal and causes severe disruption of Golgi architecture (Fig. S5). Arf1 might have a similar role in scission during the formation of related adaptor-dependent vesicles. Indeed, direct interactions of Arf1 with corresponding subunits of clathrin adaptor complexes 1 (Stamnes and Rothman, 1993; Austin et al., 2000, 2002), 3 (Austin et al., 2002), and 4 (Boehm et al., 2001) and the GGA coat (Puertollano et al., 2001) have been previously described. In this context, it is of note that the dimerization-deficient mutant Arf1-Y35A was also able to recruit to membranes the adaptor protein complex I (Beck et al., 2008). Furthermore, the finding that Sar1p, like Arf1, exerts membrane surface activity, which is required for the release of COPII buds (Lee et al., 2005), suggests a general role of small GTPases in vesicle formation and release. It will be of interest in the future to analyze whether, in the COPII system, oligomerization of Sar1p (Long et al., 2010) provides the molecular mechanism that underlies the process of membrane separation. In vivo, additional factors, lipids, and proteins, such as ArfGAPs, brefeldin A ADP-ribosylated substrate, and others, were suggested to contribute to vesicle release (Beck et al., 2009b; Hsu et al., 2009).
In summary, we were able to dissect cooperating contributions to vesicle budding and fission of Arf1 and coatomer. On the one hand, coatomer recruited by Arf1 is needed to form the curvature of a COPII bud, and on the other hand, dimeric Arf1’s membrane surface activity in cooperation with coatomer drives membrane separation.
Materials and methods
Proteins
Reagents for expression of site-directed photolabile proteins in Escherichia coli were provided by P.G. Schultz (The Scripps Research Institute, La Jolla, CA). Antibodies directed against Gsa were provided by B. Nürnberg (Universitätsklinikum Tübingen, Tübingen, Germany). The cDNAs for the following Arf1 variants were generated by site directed mutagenesis: Arf1Y35A (Beck et al., 2008), Arf1C159SK181C (Cys-wt), Arf1-Y35A-C159SK181C (Cys-Y35A), Arf1-I49AmberC159SK181C (Cys-Y35A-I49Bp), Arf1-Y35A-I49BpC159SK181C (Cys-Y35A-I49Bp), Arf1-Y35A-Y167AmberC159SK181C (Cys-Y35A-Y167Bp), and Arf1-Y35A-Y167BpC159SK181C (Cys-Y35A-Y167Bp). Full-length myristoylated human Arf1-wt and the Cys variants were recombinantly expressed and purified as described previously (for photolabile proteins see Photo-cross-linking experiments; Franco et al., 1998). In short, human Arf1 and yeast N-myristoyltransferase were coexpressed in E. coli supplied with BSA-loaded myristate. Cell lysates were subjected to 35% ammonium sulfate, and the precipitate was enriched in myristoylated Arf1 was further purified by DEAE ion exchange. After cell lysis and ultracentrifugation, Arf1-Y35A was subjected to a 35% ammonium sulfate precipitation and centrifuged, and the supernatant was bound to a phenyl-Sepharose high performance column (Pharmacia Biotech) and developed with a descending ammonium sulfate in 20 mM Tris-HCl buffer, pH 8.0, and 1 mM MgCl₂ at RT. Eluted fractions were analyzed by immunoblotting with the anti-Arf1 antibody, pooled, concentrated in spin-column filters with a 104-kDa cutoff (Millipore), and subsequently, purified by gel filtration on a Superdex 75 (GE Healthcare). Fractions of interest were pooled and concentrated.
Coatomer was purified from rabbit liver (Nickel and Wieland, 2001). His-tagged ARNO was expressed in E. coli and purified by Ni-nitrilotriacetic acid chromatography (Chardin et al., 1996).
Chemical cross-linking of Arf1 proteins
A protein concentration of 100 µM or higher was used for chemically cross-linking GDP-loaded Cys-wt or Cys-Y35A in a molar ratio of 2:1 with the homobifunctional bismaleimide cross-linker BMH (Thermo Fisher Scientific) in 20 mM Hepes buffer at pH 7.0 according to the manufacturer’s protocol. GDP-loaded Arf1-wt is not cross-linked under these conditions. Subsequently, the cross-linking reaction was quenched with DTT at a final concentration of 100 mM.
Preparation of Golgi membranes and liposomes
Golgi membranes were purified from rat liver homogenates (Tabas and Karnfeld, 1979). Lipids were purchased from Avanti Polar Lipids, Inc., except for phosphatidic acid, which was obtained from Sigma-Aldrich. Lipids were derived from natural sources. Golgi-like liposomes were prepared containing 1 mol% phosphatidylinositol-4,5-bisphosphate (P(1,4,5)P₃) and 2 mol% p23 lipopeptide, which was synthesized according to Nickel and Wieland (2001). Size selection was performed by extrusion through 400-nm polycarbonate filter membranes (Avestin).
GUVs preparation and imaging
GUVs were generated by the electroswelling method with a Golgi-like lipid mix supplemented with 3 mol% p23 lipopeptide, 1 mol% P(1,4,5)P₃, 0.1 mol% 1,2-dioleyl-sn-glycero-3-phosphoethanolamine-N-biotinyl, and 0.5 mol% 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-lysissamine rhodamine B sulfonyl in 300 mM sucrose. Lab-Tek chambered cover slides were preincubated with 1 mg/ml BSA/BSA-biotin (100:1; mol/mol) for 30 min, rinsed three times with HKM buffer (50 mM Hepes-KOH, pH 7.4, 150 mM KCl, and 1 mM MgCl₂) and subsequently with 0.1 mg/ml avidin, and rinsed again three times with HKM buffer.
For visualizing of Arf1-induced tubules, 20 µl of the GUV preparation was transferred into a coated Lab-Tek chambered cover slide and incubated after sequentially adding 3.5 µM Arf1-wt, 0.4 µM ARNO, and 1 mM GTP in a total volume of 200 µl for 10 min at RT. Confocal images were acquired with a laser-scanning microscope (510 Meta; Carl Zeiss) equipped with a 543-nm HeNe laser and a 560 low pass filter.
Arf1-induced tubulation of membrane sheets
A system similar to that previously described in Roux et al. (2006) was used. A chamber of approximately 30 µl was built between two microscope slides with two layers of paraffin as a spacer. Golgi-like lipids containing 1 mol% P(1,4,5)P₃, and 2 mol% p23 lipopeptide (Bremser et al., 1999) were spotted on the glass surface, and the solvent (CHCl₃) was evaporated. The lipids were hydrated in the presence of nucleotide with 20 µl assay buffer (25 mM Hepes-KOH, pH 7.4, 150 mM KCl, 1 mM DTT, and 1 mM GTP or GDP). Then, protein samples were sequentially added to give final concentrations of 1 µM Arf1, 50 nM ARNO, and 250 nM coatomer, and membrane morphology was observed at RT in a phase-contrast light microscope (Axiomat 200M; Carl Zeiss) using a Plan Apochromat 100x objective (NA = 1.4). Images were captured with a camera (AxioCam MRm; Carl Zeiss). The imaging software used was Axiosvision (Carl Zeiss) and Imager (National Institutes of Health). Real-time recordings are appended to supporting information.
Cryo-EM
COPI reconstitution assays were performed with 20 µg liposomes in the presence of 10 µg Arf1-wt (or Arf1-Y35A), 3 µg ARNO, 250 µM GTPγS, 1 mM MgCl2, 20 µg coatomer, and 100 mM NaCl in 50 mM Hepes, pH 7.5. Alternatively, 20 µg Golgi-enriched membrane was used instead of synthetic liposomes. Reactions were incubated for 30 min at 37°C and transferred to 4°C during preparation for EM. Samples were vitrified by plunge-freezing on holey carbon grids. Grids were imaged using an electron microscope (Tecnai F30; FEI) equipped with a 4,000,000-pixel charge-coupled device camera (Eagle; FEI) and operated at 300 kV. Data were collected between 4 and 6-µm underfocus 39,000 magnification, resulting in a pixel size of 0.3 nm at the specimen level. Dose per image was 15–25 e Å-2.
Negative staining EM
A carbon-coated grid was put on top of a 5-µl droplet of purified COPI vesicles. After 10 min of adsorption at RT, proteins were fixed by putting the grid onto a 20-µl droplet of 1% glutaraldehyde in assay buffer (25 mM Hepes-KOH, pH 7.2, and 2.5 mM Mg-aceglate), washed, dehydrated in EM of thin sections of cells acetate in 1.8% methylcellulose for 10 min on ice. These steps were performed at RT. Afterward, the sample was washed four times with 20 µl of water. Then, staining was performed with 0.4% uranyl acetate in 1.8% methylcellulose for 10 min on ice.
EM of thin sections of cells
Hela cells were grown on gridded coverslips (CELLocate; Eppendorf) to ~30% confluence and microinjected with plasmids encoding either GFP-tagged Arf1-G77Q-Y35A double mutant or the Arf1-G77Q single mutant as a control (see Immunofluorescence imaging of Arf1 variants in Hela cells for details on microinjection). 2 h after injection, transfected cells were identified by fluorescent light microscopy, and their position on the gridded coverslip was recorded and mapped. Cells were chemically fixed for 30 min at RT with 2.5% glutaraldehyde in 1 M Na cacodylate buffer, postfixed on ice with 2% OsO4 in the same buffer, washed, dehydrated in a graded series of ethanol, and embedded in their in situ orientation in epoxy resin (Glycldether 100; Carl Roth).
70-µm-thick sections of mapped areas of interest were cut (from the bottom to the top of the cells) with a microtome (Ultratcut UCT; Leica) and a diamond knife, placed on copper grids (2 x 1-mm slot), and poststained with Reynold’s lead citrate. Profiles of injected cells were identified and examined with a transmission electron microscope (operated at 100 kV; Morgagni; FEI) equipped with a 1,000 x 1,000-pixel charge-coupled device camera.
Membrane-binding assay
Flotation experiments were performed in HKM buffer (Hepes-KOH, pH 7.4, 120 K-acetate, and 1 mM MgCl2) containing 100 mM DTT in a total volume of 100 µl using 1.5 µM Arf1, 0.05 µM guanine nucleotide exchange protein ARNO, and 0.5 mM liposomes in the presence or absence of 1 mM GTP. After incubation for 15 min at 37°C, sucrose was added to a final concentration of 30%. The samples were overlaid with 300 µl of 25% sucrose and 50 µl HKM buffer and centrifuged for 1 h at 250,000 g in a rotor (SW60Ti; Beckman Coulter). 10% of the top fraction was analyzed for bound proteins by SDS-PAGE and Western blotting.
Vesicle budding assay
To generate COPI-coated vesicles, 125 µg of salt-washed Golgi liposomes (Beck et al., 2009a) were mixed with 5 µg myristoylated Arf1, 40 µg coatomer, and 0.1 mM GTPγS (or 1 mM GTP) in assay buffer (25 mM Hepes-KOH, pH 7.2, 2.5 mM Mg-aceglate, and 100 mM DTT) in a total volume of 250 µl. After incubation for 10 min at 37°C, the salt concentration was raised to 250 mM KCl, and the sample was centrifuged at 12,000 g for 10 min. The supernatant containing COPI vesicles was loaded on top of two sucrose cushions (5 µl of 50% and 50 µl of 37% sucrose) and centrifuged for 50 min at 100,000 g in a rotor (SW60Ti). COPI-coated vesicles were concentrated at the interface between 50 and 37% sucrose, 2% of the input and 50% of the isolated vesicle fraction were analyzed by SDS-PAGE and Western blotting.
Photo-cross-linking experiments
For expression of photolabile Arf1 variants, the plasmids pBad-RNA-HArf1 mutant-TAG and pBB-PAFKS were cotransformed into DH10B E. coli strains (Wang et al., 2001). The cells were grown in 2xYT (yeast extract and tryptone) medium containing 30 µg/ml kanamycin and 25 µg/ml tetracycline until OD600 = 0.6. After a washing step with M9 medium, the cells were transferred in glycerol minimal medium and leuE medium containing the appropriate antibiotics, 1 mM myristic acid, and 1 mM 8p. Protein expression was induced by the addition of 0.5% arabinose. Cells were grown for 22 h at 27°C, harvested by centrifugation, and lysed in 25 mM Tris-HCl, pH 7.2, 50 mM KCl, 1 mM DTT, and protease inhibitor cocktail (Roche). Lysates were cleared by centrifugation for 30 min at 10,000 g, and the supernatants were centrifuged for 60 min at 100,000 g. The cell lysates containing Arf1 variants were stored at −80°C. 5 µg photolabile Arf1 variants and 25 µg Golgi membranes were incubated in assay buffer (25 mM Hepes-KOH, pH 7.2, 25 mM Mg-aceglate, 100 mM DTT, and 200 mM sucrose) in the presence or absence of 100 mM GTPγS for 5 min at 37°C. Coatomer was added, and the sample was incubated for additional 15 min at 37°C. Golgi membranes were recovered by loading the sample onto a 1.5% sucrose cushion followed by a 30 min centrifugation at 16,000 g. The pellet was resuspended in assay buffer and irradiated at 366 nm for 40 min. Samples were analyzed by SDS-PAGE and Western blotting.
Static light scattering
Nucleotide exchange and hydrolysis on chemically cross-linked Arf1 was measured as previously described (Bigay and Antonny, 2005). Golgi-like liposomes containing 1 mol% P(4,5)P2 and 2 mol% P23 lipopeptidase were microinjected over time in 25 mM Hepes-KOH, pH 7.4, 150 mM KCl, 1 mM MgCl2, and 1 mM MgCl2 by using a spectral photometer (FP-6500; Jasco). 1 µM Arf1-wt, 1 µM Arf1 Cys-wt, or 0.5 µM chemically cross-linked cCys-wt was added followed by 1 mM GTP and 0.2 µM coatomer. Nucleotide exchange was started by the addition of 2 mM EDTA (after 60 s) to chelate Mg++. After nucleotide exchange, the Mg++ concentration was raised to 5 mM, and 25 nM ArfGAP2 was injected (after 640 s).
Immunofluorescence imaging of Arf1 variants in HeLa cells
The bicistronic plasmid for the expression of EGFP (used as a marker to identify the injected cells) and coding for the different Arf1 variants were microinjected at the concentration of 500 ng/µl into the nucleus of Hela Kyoto cells using a microinjector (Transjector 5246 and Micromanipulator 5171; Eppendorf). The cells were fixed with 3% PFA 2 h thereafter. For immunostainings, we used standard procedures, diluting the antibodies in PBS containing 10% FCS and 0.1% saponin. Primary antibodies used were rabbit polyclonal giantin (Abcam), mouse monoclonal GM130 (BD), mouse monoclonal GaT (Cellmab), and rabbit polyclonal β Cop (raised in our laboratory with standard procedures). Secondary antibodies used were Alexa Fluor 568–conjugated anti–mouse and Alexa Fluor 568–conjugated anti–rabbit (Invitrogen). Confocal sections were acquired every 300 nm across the entire volume of the cells using a 53x Plan Apochromat oil immersion objective (NA 1.4) on a laser-scanning confocal microscope (SP5; Leica). Maximum projections of the image stacks were generated with the SP5 analysis software.
Online supplemental material
Fig. S1 shows membrane binding of His-tagged proteins to Ni-liposomes. Fig. S2 shows nucleotide exchange and hydrolysis by chemically cross-linked Arf1 variants. Fig. S3 shows COPI reconstitutions from Golgi membranes with Arf1-Cys variants to analyze cargo markers included in or excluded from the vesicles. Fig. S5 shows in vivo analysis of dominant-negative Arf1-G77Q or Arf1-Y35A-G77Q in HeLa cells by single-cell thin-section EM and immunofluorescence microscopy. Video 1 shows analysis of membrane surface activity of N17Arf1. Video 2 shows analysis of membrane surface activity upon addition of Arf1-wt and membrane remodeling by subsequent addition of coatomer. Online supplemental material is available at http://www.jcb.org/cgi/content/full/jcb.201011027/DC1.
We thank Michael Brunner for helpful discussions and suggestions, Ingrid Meissner, Inge Reckmann, and Andrea Hellwig for technical assistance, Marco Fanini for helpful discussions, and Dan Cassel for critically reading the manuscript. This study was technically supported by use of the European Molecular Biology Laboratory EM core facility. Negative staining EM experiments were carried out in the laboratory of Hilmar Bading. We also thank the European Molecular Biology Laboratory Advanced Light Microscopy Facility team for their help with light microscopy and Leica for support of the facility. Reagents for expression of sterediolatable photolabile proteins in E. coli were generously provided by Dr. Peter G. Schultz. We thank Bernd Nürnberg for kindly providing antibodies directed against GAβ.
Role of Arf1 dimerization in membrane scission • Beck et al. 775
Downloaded from jcb.rupress.org on August 18, 2017
Wang, L., A. Brock, B. Herberich, and P.G. Schultz. 2001. Expanding the genetic code of Escherichia coli. Science. 292:498–500. doi:10.1126/science.1060077
Weimer, C., R. Beck, P. Eckert, I. Reckmann, J. Moelleken, B. Brügger, and F. Wieland. 2008. Differential roles of ArfGAP1, ArfGAP2, and ArfGAP3 in COPI trafficking. J. Cell Biol. 183:725–735. doi:10.1083/jcb.200806140
Yang, J.S., S.Y. Lee, S. Spanò, H. Gad, L. Zhang, Z. Nie, M. Bonazzi, D. Corda, A. Luini, and V.W. Hsu. 2005. A role for BARS at the fission step of COPI vesicle formation from Golgi membrane. EMBO J. 24:4133–4143. doi:10.1038/sj.emboj.7600873
Zhao, L., J.B. Helms, B. Brügger, C. Harter, B. Martoglio, R. Graf, J. Brunner, and F.T. Wieland. 1997. Direct and GTP-dependent interaction of ADP ribosylation factor 1 with coatomer subunit beta. Proc. Natl. Acad. Sci. USA. 94:4418–4423. doi:10.1073/pnas.94.9.4418
Zhao, L., J.B. Helms, J. Brunner, and F.T. Wieland. 1999. GTP-dependent binding of ADP-ribosylation factor to coatomer in close proximity to the binding site for dilysine retrieval motifs and p23. J. Biol. Chem. 274:14198–14203. doi:10.1074/jbc.274.20.14198 | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2458,
1
],
[
2458,
2898,
2
],
[
2898,
9689,
3
],
[
9689,
11436,
4
],
[
11436,
17867,
5
],
[
17867,
20152,
6
],
[
20152,
22102,
7
],
[
22102,
27210,
8
],
[
27210,
32526,
9
],
[
32526,
40505,
10
],
[
40505,
49669,
11
],
[
49669,
49669,
12
],
[
49669,
50816,
13
]
]
} |
9df5f0da8df0539255cf3d73fe4b67e31fa80739 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 4,
"total-fallback-pages": 0,
"total-input-tokens": 10852,
"total-output-tokens": 3564,
"fieldofstudy": [
"Computer Science"
]
} | Software Defined Networking for Organizations Network Automation
Diaz-Martinez Jorge Luis1st, De-La-Hoz-Franco Emiro2nd, Johan David Mardini Bovea3rd, Shariq Aziz Butt4th, Tauseef Jamal5th
1st-3rd Department of Computer Science and Electronics, Universidad de la Costa, Barranquilla, Colombia.
4-5th PIEAS University CS Department, Islamabad, Pakistan
1st [email protected]
2nd [email protected]
3rd [email protected]
4th [email protected]
5th [email protected]
Abstract: When new applications are deployed, virtual servers or dynamic applications are moved, new instances are launched where the networks must be able to respond immediately and provide the right kind of connectivity. That's why in recent years, adoption of software-based networks (SDNs) and growing interest in defined data centers (SDDCs) have driven a switch from traditional hardware-based networks to networks Based on the software thus enabling organizations to implement this trend to improve network agility by incorporating network automation into cloud-based technology platforms. While many organizations are still in the process of change, the adoption of software-based networks is already occurring. Increasingly, the software-based model of networks is established as a key resource to achieve the adaptation and simplification of changes in network components. However, in order to achieve this migration, it is necessary for organizations to travel on a path that requires evolution.
KEYWORDS: SDN (Software Defined Networking), ONF (Open Networking Foundation), Cloud Computing, OpenFlow Protocol.
1. Introduction:
The systems (Internet) has a few changes and advancements to fulfill the developing need for applications and different user’s services by increasing services such as social network, Mobile services, virtualization services, Cloud Computing-based systems etc., thus there is a need to restructure traditional architectures of network to meet the crowd traffic of users [1]. Conventional system designs present impediments to these new necessities, for example, constrained capacity to adjust to new innovations, the versatility of systems and the un-proficient utilization of access control strategies regularly make security gaps vulnerable to assaults. This has incited a scan for a few options to replace traditional networks. One of these alternatives, from the Open Networking Foundation (ONF), raises the use of Software Defined Networks (SDN) to meet the current requirements of Internet users [1], [2]. The SDN’s according to [1] [2] and [3] constitute a network architecture whose fundamental objective is to un-couple the control plane from the data plane, which facilitates a greater control and level of management over the connectivity equipment, guaranteeing the network administrator a centralized control. The term centralized control of the network has clearly logical connotation and therefore, the administration of the network can be centered on one or more controllers that is a control distributed in a physical manner there may even be backup servers in case of a failure of a certain server As a consequence of a centralized and direct control it is possible to enhance the security strategies of a specific substance or organization respond rapidly to changes in the prerequisites of the system or to an adjustment of new innovations and accomplish exceedingly versatile systems.
2. Concept:
The term SDN (Software Define Network or software Define network) according to [1] [4] is Define as the network architecture that allows to separate the control plane from the data plane to achieve more programmable, scalable and automatable network thus allowing accelerate the implementation and distribution of applications, greatly reducing cost through the automation of workflow based on policies. Characterized in the enabling of architectures in the cloud (Cloud Computing) through the distribution and mobility of applications and services in an automated way increasing the benefits of virtualization of data centers, since they increase flexibility the use of resources for reducing expenses for infrastructure. According to [5] software Define networks (SDNs) allows organizations to accelerate applications deployment and deployment by drastically reducing IT costs by automation policy-based workflow. SDN technology enables cloud architectures through applications distribution and mobility in an automated, on-demand, and scale manner. SDNs increase the benefits of data center virtualization, as they increase flexibility and resources utilization and reduce overhead and infrastructure costs. To achieve these business objectives SDNs converge the administration of
network services and applications into centralized and scalable coordination stages that can robotize the provisioning and setup of the whole framework. Basic concentrated IT strategies bind together dissimilar gatherings and IT work process. The outcome is a cutting edge framework that can conveyed new applications and administrations in minutes, rather than days or weeks as before SDN systems concurring to [6] [7] substitute the control level of the network hardware for a software layer infrastructure based on virtualization techniques thus making the network more programmable. Characterized by providing access to hardware based on programming through protocols such as OpenFlow and in the creation of virtual networks above the hardware that direct traffic through physical networks.
3. Normalization of SDN:
The organization ONF (Open Network Foundation) [3], which leads the evolution and normalization of critical elements (architecture and protocol) of SDN and other organizations such as (ATIS, Broadband Forum, ETSI, OIF, ITU-T, etc.) especially the IETF, through the group the I2RS group (Interface to the Routing System), are also working on extending their specifications to support SDN principles. In addition to the standardization bodies, there are several open source initiatives, such as Open Stack, which are specifying several SDN tools. Entities such as ETSI [7] and ONF [3,8] have collaborated since the creation of NFC ISG in 2012 developing strong collaborations to promote the development of the NFV specifications, which accelerates the adoption of NFV as SDN for their coordinated development. The aforementioned organizations thus show their commitment to support the requirements of the operators and a complementary approach in the development of standards, methodologies and knowledge sharing. ETSI NFV ISG will promote concept tests that use both NFV and SDN to demonstrate the benefits of using both technologies together. The ONF organization has developed a technical report that clearly shows how IT operators are combining NFV and SDN [8] [9] to achieve common goals of both technologies to improve the agility of the network, in turn explains the challenges that operators have to overcome for the effective implementation of NFV and presents some cases that demonstrate SDN enabled by Open Flow can satisfy the needs of a more programmable and flexible network to support NFV.
4. SDN ARCHITECTURE:
The SDN architecture according to [1] is constituted by 3 (three) layers as shown in fig. 1 and is specified as follows:
4.1 Infrastructure layer:
Consisting of network nodes that perform packet routing and routing, providing programmable open access under API down (southbound), as in the case of Open Flow.
4.2 Control layer:
The SDN controller is a software entity that has exclusive control over an abstract set of control plane resources, that is the entity that controls and configures the network nodes to correctly direct the traffic flows. The SDN controller eliminates the intelligence of switching and routing of data of the nodes that perform this function, passing to the SDN controller, which makes those decisions and selects the best path for traffic. The architecture describes a series of functions internal to the SDN controller and to the network element, but only the behavior of those aspects that are necessary to ensure interoperability is specified. The architecture is agnostic to the protocols used between interfaces. The architecture allows an SDN controller to manage a wide range of data plane resources, which offers the potential to unify and simplify its configuration.
4.3 Application layer:
It is made up of the applications for end users, which use the SDN communication services through the APIs upwards (northbound) of the control layer, such as JSON, REST, among others, which allows the services and applications to simplify and automate the tasks of configuration, provisioning and managing new services in the network, thus generating new routes for revenue and innovation in infrastructure.
5. STANDARD OpenFlow:
As per [11], the most famous particular for making a product characterized system is an open standard called OpenFlow, which permits arrange overseers to control directing tables remotely, along these lines getting to be one of the principal correspondence interface measures characterized. between the control and sending layers in an SDN engineering. Also, it permits direct access and control of the sending layer of system gadgets, regardless of whether virtual or physical. This convention is actualized on the two sides of the interface, between the system foundation and the SDN control programming utilizing the stream idea to recognize arrange traffic dependent on the gathering of predefined rules, which can be static or dynamic, programmable through SDN control programming [11, 18, 19]. According to [10, 12, 17], it forms the basis of open networks defined by standards-based software with collaboration from the academic and business sectors, with the Stanford and California universities in Berkeley leading the reins in the first instance. Currently, the Open Networking Foundation (ONF) is responsible for defining the standard.
6. ADVANTAGES OF SDN IMPLEMENTATION:
The main objective according to [13,14], the networks defined by software is the reduction of expenses for equipment and network operation, in turn increasing the speed of innovation to boost an open system, accelerating the introduction of new services and above all allowing Agile form scalability creating new business opportunities with their customers by offering them access to information about the state of the network and the management of their traffic flows more efficiently and more intelligently.
To obtain the maximum performance, utilization and simplicity, telecommunications operators, cloud service providers and companies can use SDN technology in the entire network, from the data center to the desktop, separating the hardware infrastructure from the plan of control, and applications this will solve the complexities that exist today and improve the agility of the business.
To respond to the challenges generated by conventional networks, organizations need to be able to automate the network from end to end and SDN makes it possible to make the control plane of the physical infrastructure independent.
According to [14, 16, 19] SDN technology is a flexible and scalable architecture deploying in a platform of applications and services able to respond quickly to changes in the needs of customers of a business, market or end user, where applications can demand resources network in real time, as bandwidth and quality of service can be adapted to services applied to the future.
7. CONCLUSION:
Companies are faced daily with the challenges of reducing the risks of implementing services, accelerating implementation times, and reducing operating expenses while giving rise to management in a general IT team. Secondly, companies need to incorporate a solution that allows them to support changes in customer services, facilitate network administration and maximize the use of resources. Software-based networks are the answer to address these challenges.
Software-based networks can be programmed directly and allow administrators to adjust the traffic flow of the network to meet changing needs which makes them a spry model. Then again, it is described as a concentrated innovation that can be arranged and improve assets rapidly, through computerized projects that can be composed independent from anyone else, without depending on exclusive programming. These kinds of systems depend on open and unbiased gauges which disentangle organize tasks and plans, on the grounds that the guidelines are given by the system controllers, and not by various conventions and seller explicit gadgets. Taking everything into account, programming based systems are dynamic, sensible, financially savvy and versatile.
References:
[1] Ali-Ahmad, Hassan, et al. "An SDN-based network architecture for extremely dense wireless networks." Future Networks and Services (SDN4FNS), 2013 IEEE SDN for. IEEE, 2013.
[2] Jamal, Tauseef, Pedro Amaral, and Khurram Abbas. "Flow Table Congestion in Software Defined Networks." ICDS 2018(2018): 57.
[3] Jain, Raj, and Subharthi Paul. "Network virtualization and software-defined networking for cloud computing: a survey." IEEE Communications Magazine 51.11 (2013): 24-31.
[4] Chen, Tao, et al. "Software-defined mobile networks: concept, survey, and research directions." IEEE Communications Magazine 53.11 (2015): 126-133.
[5] Yi, Shane, Cheng Li, and Qun Li. "A survey of fog computing: concepts, applications and issues." Proceedings of the 2015 workshop on mobile big data. ACM, 2015.
[6] Porras, Philip, et al. "A security enforcement kernel for OpenFlow networks." Proceedings of the first workshop on Hot topics in software defined networks. ACM, 2012.
[7] Bakshi, Kapil. "Considerations for software-defined networking (SDN): Approaches and use cases." Aerospace Conference, 2013 IEEE. IEEE, 2013.
[8] Janz, Christopher, et al. "Emerging transport Sdn architecture and use cases." IEEE Communications Magazine 54.10 (2016): 116-121.
[9] Matias, Jon, et al. "Toward an SDN-enabled NFV architecture." IEEE Communications Magazine 53.4 (2015): 187-193.
[10] Haleplidis, Evangelos. "Overview of RFC7426: SDN Layers and Architecture Terminology." IEEE 2017.
[11] Ishimori, Airtorn, et al. "Control of multiple packet schedulers for improving QoS on OpenFlow/SDN networking." Software Defined Networks (EWSDN), 2013 Second European Workshop on. IEEE, 2013.
[12] Padma, V., and P. Yogesh. "Proactive failure recovery in OpenFlow based software-defined networks." Signal Processing, Communication, and Networking (ICSCN), 2015 3rd International Conference on. IEEE, 2015.
[13] Jarschel, Michael, et al. "Interfaces, attributes, and use cases: A compass for SDN." IEEE Communications Magazine 52.6 (2014): 210-217.
[14] De Oliveira, Rogério Leão Santos, et al. "Using mini net for emulation and prototyping software-defined networks." 2014 IEEE Colombian Conference on Communications and Computing (COLCOM). IEEE, 2014.
[15] Doverspike, Robert, et al. "Using SDN technology to enable cost-effective bandwidth-on-demand for cloud services." Journal of Optical Communications and Networking 7.2 (2015): A326-A334.
[16] Jamal, T., & Mendes, P. (2010, October). Relay selection approaches for wireless cooperative networks. In 2010 IEEE 6th International Conference on Wireless and Mobile Computing, Networking and Communications (pp. 661-668). IEEE.
[17] Jamal, T., Haider, Z., Butt, S. A., & Chohan, A. (2018). Denial of Service Attack in Cooperative Networks. arXiv preprint arXiv:1810.11070.
[18] Jamal, T., & Butt, S. A. (2017). Cooperative Cloudlet for Pervasive Networks. Proc. of Asia Pacific Journal of Multidisciplinary Research, 5(3), 42-26.
[19] Jamal, T., Amaral, P., Khan, A., Zameer, A., Ullah, K., & Butt, S. A. (2018). Denial of Service Attack in Wireless LAN. ICDS 2018, 51. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4739,
1
],
[
4739,
7497,
2
],
[
7497,
10929,
3
],
[
10929,
15875,
4
]
]
} |
09fca535337931dda05c0856c70decb7854f5d40 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 5,
"total-fallback-pages": 0,
"total-input-tokens": 23677,
"total-output-tokens": 5960,
"fieldofstudy": [
"Physics",
"Mathematics"
]
} | Synchronization of a Josephson junction array in terms of global variables
Vladimir Vlasov and Arkady Pikovsky
Department of Physics and Astronomy, Potsdam University, 14476 Potsdam, Germany
(Dated: May 11, 2014)
We consider an array of Josephson junctions with a common LCR-load. Application of the Watanabe-Strogatz approach [Physica D, v. 74, p. 197 (1994)] allows us to formulate the dynamics of the array via the global variables only. For identical junctions this is a finite set of equations, analysis of which reveals the regions of bistability of the synchronous and asynchronous states. For disordered arrays with distributed parameters of the junctions, the problem is formulated as an integro-differential equation for the global variables, here stability of the asynchronous states and the properties of the transition synchrony-asynchrony are established numerically.
PACS numbers: 05.45.Xt, 74.81.Fa
I. INTRODUCTION
Synchronization in populations of coupled oscillators is a general phenomenon observed in many physical systems, see recent experimental studies of optomechanical, micromechanical, electronic, mechanical, chemical oscillators [1]. Synchronization effects are also ubiquitous in biology and social sciences. One of the basic examples of oscillating physical systems that being coupled synchronize, are Josephson junctions [2]. In theoretical studies of the Josephson junction arrays one typically either performs direct numerical simulation of the microscopic equations (see, e.g., [3]) or reduces the problem to the standard Kuramoto-type model [4–6].
Quite remarkable in this respect is the paper [8], where a careful comparison of the microscopic modeling and the reduced Kuramoto-type model has been performed. The authors demonstrated that a hysteretic transition to synchrony in an array of Josephson junctions can be explained by a Kuramoto-type modeling (where usually the transition is not hysteretic), if in its derivation one self-consistently accounts for changes of the oscillator parameters.
Our aim in this paper is to shed light on the hysteretic transitions to synchrony in Josephson arrays by studying the equations for global variables. In this approach, that is based on the seminal papers by Watanabe and Strogatz (WS) [8, 9], it is possible to formulate exact low-dimensional equations for the array, without using approximate reduction to the Kuramoto model. The paper is organized as follows. First, we formulate the equations for the array of identical junctions via the global variables. Analysis of these equations shows regions of bistability asynchrony–synchrony, and the hysteretic transitions. Then we proceed to non-identical junctions, where the equations are of more complex form. Here we analyze stability of asynchronous states, and show numerically that the transition to synchrony is also hysteretic.
II. IDENTICAL JUNCTIONS
A. Formulation in terms of global variables
We start with formulating the system of equations for the Josephson junction series array with a LCR load. Our setup is the same as in refs. [4–6], the equations for the junction phases $\varphi_i$ and the load capacitor charge $Q$ read
$$\frac{\hbar}{2e} \frac{d\varphi_i}{dt} + I_c \sin \varphi_i = I - \frac{dQ}{dt},$$
$$L \frac{d^2Q}{dt^2} + R \frac{dQ}{dt} + \frac{Q}{C} = \frac{\hbar}{2e} \sum_{i=1}^{N} \frac{d\varphi_i}{dt}.$$ (1)
Here $N$ is the number of junctions, described by a resistive model with critical current $I_c$ and resistance $r$, while $L, C, R$ are parameters of the LCR-load. It is convenient to introduce dimensionless variables according to
$$\omega_c = \frac{2eI_c}{\hbar}, \quad t^* = \omega_c t, \quad Q^* = \omega_c L^* Q / I_c, \quad I^* = I / I_c,$$
$$R^* = \frac{R}{r N}, \quad L^* = \frac{\omega_c L}{r N}, \quad C^* = N \omega_c r C,$$ (2)
and to rewrite the system (1) in a dimensionless form (dropping asterixes for simplicity)
$$\dot{\varphi}_i = I - \epsilon \dot{Q} - \sin \varphi_i,$$
$$\ddot{Q} + \gamma \dot{Q} + \omega_0^2 Q = I - \frac{1}{N} \sum_{i=1}^{N} \sin \varphi_i,$$ (3)
where $\epsilon = 1 / L^*$, $\gamma = (R^* + 1) / L^*$, and $\omega_0 = 1 / \sqrt{L^* C^*}$.
The global coupling can be represented through the complex mean field (Kuramoto order parameter)
$$Z = r e^{i \theta} = \frac{1}{N} \sum_{i=1}^{N} (\cos \varphi_i + i \sin \varphi_i),$$
$$\text{Im}(Z) = \frac{1}{N} \sum_{i=1}^{N} \sin \varphi_i.$$ (4)
and the equations for the junction phases can be written as
$$\dot{\varphi}_i = I - \epsilon \dot{Q} + \text{Im}(e^{-i\psi_i}).$$
(5)
This form of the phase equation allows us to use the Watanabe-Strogatz ansatz [8, 9], applicable to general systems of phase equations driven by a common force and having form
$$\dot{\varphi}_i = f(t) + \text{Im}(G(t)e^{-i\psi_i}).$$
(6)
with arbitrary real $f(t)$ and complex $G(t)$ (in our case $f = I - \epsilon \dot{Q}$, $G = 1$). We use the formulation of the Watanabe-Strogatz theory presented in Ref. [10]. The ensemble is characterized by three global time-dependent WS variables $\rho, \Phi, \Psi$ and $N$ constants of motion $\psi_i$ (of which only $N - 3$ are independent) which are related to the phases $\varphi_i$ as
$$e^{i\varphi_i} = e^{i\Phi} \rho + \text{exp}(i(\psi_i - \Psi)) \rho \text{exp}(i(\psi_i - \Psi)) + 1$$
(7)
with additional conditions $\sum_i \cos \psi_i = \sum_i \sin \psi_i = \sum_i \cos 2\psi_i = 0$. The equations for the global WS variables read [8, 10]
$$\dot{\rho} = \frac{1 - \rho^2}{2} \text{Re}(e^{-i\Phi}),$$
$$\dot{\Phi} = \frac{1 - \rho^2}{2\rho} \text{Im}(e^{-i\Phi}),$$
$$\dot{\Psi} = 1 - \epsilon \dot{Q} + \frac{1 + \rho^2}{2\rho} \text{Im}(e^{-i\Phi}).$$
(8)
To close the system we need to add the equation for $Q$, where the imaginary part of the order parameter $Z$ enters, so $Z$ should be represented through the Watanabe-Strogatz variables. In general, the expression for $Z$ is rather complex (cf. [10, 11]) but in the case of a uniform distribution of the constants $\psi_i$, the order parameter is just $Z = pe^{i\Phi}$. This important case, where WS global variables $\rho, \Phi$ have a clear physical meaning as the components of the Kuramoto order parameter, will be treated below. Additionally, we notice that the variable $\Psi$ does not enter other equations, so we obtain a closed system of equations that describes the array
$$\dot{Z} = i(I - \epsilon \dot{Q})Z + \frac{1}{2} - \frac{Z^2}{2},$$
$$\ddot{Q} + \gamma \dot{Q} + \omega_0^2 Q = I - \text{Im}(Z).$$
(9)
B. Bistability and hysteretic transitions
Analysis of system (9) is our goal in the rest of this section. Before proceeding, some remarks are in order. First, in the derivation of (9) no approximation except for an assumption of a uniform distribution of constants $\psi_i$ has been made. The latter is a restriction on initial conditions, we discuss its relevance below. Second, the order parameter $Z$ does not vanish in the case of full asynchrony of junctions: for noncoupled junctions with $\epsilon = 0$ we get a steady state $Z_0 = i(I - \sqrt{T^2 - 1})$. This non-vanishing value appears because free junctions rotate non-uniformly and the “natural” distribution of the phases in the asynchronous state is not uniform.
We start the analysis of (9) with finding its steady states. Because at such a state $\dot{Q} = 0$, the coupling vanishes and the steady state describing the asynchronous regime with $Z_0 = i(I - \sqrt{T^2 - 1})$, $Q_0 = \omega_0^2 \sqrt{T^2 - 1}$ is the only stationary solution. Stability of this solution is determined by the fourth-order characteristic equation
$$\lambda^4 + \gamma \lambda^3 + (\omega_0^2 + I^2 - 1)\lambda^2 + +[(\gamma - \epsilon)(I^2 - 1) + \epsilon I \sqrt{T^2 - 1}]\lambda + \omega_0^2(I^2 - 1) = 0.$$
(10)
The stability border can be easily found by assuming $\lambda = i\omega$:
$$\omega_0^2 = (I^2 - 1) + \frac{\epsilon}{\gamma} \sqrt{T^2 - 1}(I - \sqrt{T^2 - 1}).$$
(11)
The fully synchronous solution of (9) corresponds to the case $|Z| = 1$, so that only the phase $\Phi$ changes, according to the system
$$\dot{Q} + \gamma \dot{Q} + \omega_0^2 Q = I - \sin \Phi,$$
$$\dot{\Phi} = I - \epsilon \dot{Q} - \sin \Phi.$$
(12)
We have found the limit cycle in Eq. (12) numerically and determined its stability by finding the largest multiplier. Together with expression (11) this allows us to find the domains of stability of the asynchronous and synchronous states, together with the region of bistability of these regimes, see Fig. [11]
In Fig. [12] we give another illustration of the bistability, presenting the dependence of $Z_0$ on parameter $I$, together with the value $|Z| = 1$ in the synchronous case. Here we also show what happens if our basic assumption at derivation of eqs. (9), namely of a uniform distribution of constants $\psi_i$, is not satisfied. We have simulated an ensemble of 100 junctions, preparing the initial conditions with a nonuniform distribution of constants $\psi_i$ as described in ref. [10], appendix C. Instead of leading to a stable state $Z_0$, the desynchronous population now shows an oscillating variable $Z(t)$, minima and maxima of which are marked with squares. In the synchronous regime, $|Z| = 1$ as before, and the information on the constants $\psi_i$ gets lost as synchrony establishes.
III. NONIDENTICAL JUNCTIONS
A. Formulation of the model
There are two parameters of individual junctions that can differ: the critical current $I_c$ and the resistance $r$.
FIG. 1. (Color online) Domains of stability of synchronous (above lower dashed line) and asynchronous (below upper solid line) states on the plane of parameters \((\omega_0^2, \Omega^2)\), where \(\Omega = \sqrt{I^2 - 1}\) is the natural frequency of the junctions. Here \(\epsilon = 0.5,\) and \(\gamma = 1.0\) (a), 1.7 (b), 2.7 (c).
FIG. 2. Dependence of the order parameter \(|Z|\) on the current \(I\) for 100 junctions. Line: uniform distribution of constants \(\psi_i\), squares: nonuniform distributions.
\[
\dot{\phi}_{ki} = (1 + \eta_k)(1 + \xi_k) \sin \phi_{ki}
\]
\[
\dot{Q} + \gamma \dot{Q} + \omega_0^2 Q = I - \frac{1}{N} \sum_{k=1}^{M} (1 + \eta_k)(1 + \xi_k) \sum_{i=1}^{P} \sin \phi_{ki}.
\]
To each group the Watanabe-Strogatz ansatz as described in the previous section can be applied, and as a result instead of the identical array equations (9) we obtain a system
\[
\ddot{Q} + \gamma \dot{Q} + \omega_0^2 Q = I - \left( \frac{1}{M} \sum_{k=1}^{M} (1 + \eta_k)(1 + \xi_k) \text{Im}(Z_k) \right),
\]
\[\dot{Z}_k = (1 + \eta_k) \left( i(I - \epsilon \dot{Q}) Z_k + (1 + \xi_k) \frac{1 - Z_k^2}{2} \right),\]
where average \(\langle \rangle\) is taken over all groups. Starting from (14) one can easily take a thermodynamic limit of an infinite number of groups \(M \to \infty\), in this limit \(Z_k \to Z(\eta, \xi)\). Then (14) reduces to an integro-differential equation that includes the distribution function \(W(\eta, \xi)\) of disorder parameters \(\xi, \eta\) (cf. [10]):
\[
\dot{Q} + \gamma \dot{Q} + \omega_0^2 Q = I - \int \int d\eta d\xi W(\eta, \xi) \langle (1 + \eta)(1 + \xi) \text{Im}(Z(\eta, \xi)) \rangle,
\]
\[\dot{Z}(\eta, \xi) = (1 + \eta) \left( i(I - \epsilon \dot{Q}) Z + (1 + \xi) \frac{1 - Z^2}{2} \right).\]
B. Asynchronous state and its stability
The asynchronous state is the steady state of the system (15):
\[ Z_0(\eta, \xi) = \frac{I - \sqrt{I^2 - (1 + \xi)^2}}{1 + \xi}, \]
\[ Q_0 = \omega_0^{-2} \int d\eta d\xi \ W(\eta, \xi) (1 + \eta) \sqrt{I^2 - (1 + \xi)^2}, \]
where we assume \( \langle \xi \rangle = \langle \eta \rangle = 0 \). Remarkably, the disorder in the junction resistances (parameter \( \eta \)) does not influence the value \( Z_0 \), only the disorder in critical currents (parameter \( \xi \)). However, the stability of this asynchronous state depends on distributions of \( \eta \) and \( \xi \). We consider two cases, with a disorder in one parameter only.
(i) Disorder in resistances. Here we assume that \( W(\eta, \xi) = \delta(\xi)W_{\eta}(\eta) \) where \( W_{\eta} \) is a uniform distribution in the interval \( (-\mu, \mu) \). To study the perturbations in the integral equation (15) at the steady solution (16), we discretized the integral using 500 nodes and found the eigenvalues of the resulting matrix. The results for the maximal eigenvalue are shown in Fig. 3a. One can see that, with increasing the external current \( I \), the asynchronous state loses stability almost at the same critical value as for identical junctions (expression (11)), but for large values of \( I \) the stability is restored. The region of instability decreases for larger disorder \( \mu \).
(ii) Disorder in critical currents. Here we assume that \( W(\eta, \xi) = \delta(\xi)W_{\xi}(\xi) \), where \( \xi \) is the width of the uniform distribution. With the same procedure as in case (i) we found the stability eigenvalues that are shown in Fig. 3b. Qualitatively, the pictures look similar: both disorders result in a finite (in terms of the external current \( I \)) region of instability of the asynchronous state.
Both calculations presented in Fig. 3 show, that the main effect of disorder in arrays is in the establishing of stability of the asynchronous state for large values of current \( I \), while only in some range (which decreases with disorder) the asynchrony is unstable. We illustrate the appearing synchrony patterns in disordered arrays in the next subsection.
C. Numerical simulations
Dynamics of the nonhomogeneous arrays of Josephson junctions is illustrated in Figs. 4. As above, we consider not a general situation where both the critical current and the resistance are spread, but cases where one of these parameters has a distribution. In numerical simulations we use the discrete representation. In order to...
avoid spurious non-smooth solutions, an additional very small viscous term $\sim (Z_{k+1} + Z_{k-1} - 2Z_k)$ was added to the equation for $Z_k$ that ensures numerical stabilization of the integro-differential equation.
To characterize synchrony we calculated the average over the array order parameter $z = M^{-1} \sum_k Z_k$ and plot it vs. parameter $I$ in Fig. 4. In the asynchronous state this parameter attains the fixed point (cf. Eq. (15)), while in the synchronous state it oscillates around some mean value (because of disorder the synchrony is not complete, so $|z| < 1$). Remarkably, also in the case of disorder, the transition to synchrony demonstrates hysteresis both for small and large values of $I$, as can be seen on panels (b),(c),(e), and (f) of Fig. 4.
IV. CONCLUSION
In this paper we applied the approach by Watanabe and Strogatz to the description of the synchronization transition in an array of Josephson junctions with an LCR load. For identical junctions a closed low-dimensional system of equations for global variables (the Watanabe-Strogatz variables for the junctions and two variables describing the load) demonstrates a region of bistability at the transition from asynchrony to full synchrony, so that this transition shows hysteresis. This confirms previous results based on the approximate self-consistent reduction to the Kuramoto model [7]. For nonidentical junction the method yields an integro-differential system, as each group of junctions having certain parameters is described by the WS variables. Here, with the growth of the variability of parameters, the region of synchronization shrinks. Transition to synchrony in this case is also hysteretic.
Validity of the WS approach to the Josephson junction array is based on the fact, that for standard junctions the dependence of the superconducting current on the phase is a simple sine function. Therefore, the theory is also valid for so-called $\pi$-junctions [12], where the current has an opposite direction but nevertheless is proportional to $\sin(\phi)$. However, for recently constructed so-called $\phi$-junctions [13], where the phase dependence of the current contains the second harmonics, the WS approach is not applicable, and synchronization of such junctions remains a challenging problem.
ACKNOWLEDGMENTS
V. V. thanks the IRTG 1740/TRP 2011/50151-0, funded by the DFG /FAPESP.
[1] G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, Phys. Rev. Lett. 107, 043603 (2011); M. Zhang, G. S. Wiederhecker, S. Manipatruni, A. Barnard, P. McEuen, and M. Lipson, ibid. 109, 233906 (2012); A. A. Temirbayev, Z. Z. Zhanabaev, S. B. Tarasov, V. I. Ponomarenko, and M. Rosenblum, Phys. Rev. E 85, 015204 (2012); E. A. Martens, S. Thutupalli, A. Fournier, and O. Hallatschek, “Chimera states in mechanical oscillator networks,” arXiv:1301.7608 [nlin.AO] (2012); M. R. Tinsley, S. Nkomo, and K. Showalter, Nature Physics 8, 662 (2012).
[2] A. K. Jain, K. K. Likharev, J. E. Lukens, and J. E. Sauvageau, Phys. Reports 109, 309 (1984); S. Benz and C. Burroughs, Appl. Phys. Lett. 58, 2102 (1991); C. B. Whan, A. B. Cawthorne, and C. J. Lob, Phys. Rev. B 53, 12340 (1996); A. B. Cawthorne, P. Barbara, S. V. Shitov, C. J. Lobb, K. Wiesenfeld, and A. Zangwill, ibid. 60, 7575 (1999).
[3] P. Hadley, M. R. Beasley, and K. Wiesenfeld, Phys. Rev. B 38, 8712 (1988); G. Filatrella, N. F. Pedersen, and K. Wiesenfeld, Phys. Rev. E 61, 2513 (2000).
[4] K. Wiesenfeld and J. W. Swift, Phys. Rev. E 51, 1020 (1995).
[5] K. Wiesenfeld, P. Colet, and S. H. Strogatz, Phys. Rev. Lett. 76, 404 (1996).
[6] K. Wiesenfeld, P. Colet, and S. Strogatz, Physical Review E 57, 1563 (1998).
[7] T. Heath and K. Wiesenfeld, Ann. Phys. (Leipzig) 9, 689 (2000).
[8] S. Watanabe and S. H. Strogatz, Phys. Rev. Lett. 70, 2391 (1993).
[9] S. Watanabe and S. H. Strogatz, Physica D 74, 197 (1994).
[10] A. Pikovsky and M. Rosenblum, Physica D 240, 872 (2011).
[11] A. Pikovsky and M. Rosenblum, Phys. Rev. Lett. 101, 264103 (2008).
[12] A. I. Buzdin, Rev. Mod. Phys. 77, 935 (2005).
[13] H. Sickinger, A. Lipman, M. Weides, R. G. Mints, H. Kohlstedt, D. Koelle, R. Kleiner, and E. Goldobin, Phys. Rev. Lett. 109, 107002 (2012). | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4435,
1
],
[
4435,
9501,
2
],
[
9501,
11263,
3
],
[
11263,
13831,
4
],
[
13831,
18041,
5
]
]
} |
95ad881d726cead19aafc5dd911e8d833bb7e897 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 8,
"total-fallback-pages": 0,
"total-input-tokens": 26134,
"total-output-tokens": 9828,
"fieldofstudy": [
"Medicine"
]
} | INTRODUCTION
The World Health Organization report on diabetes (WHO, 2016b) emphasizes the enormous size and burden of diabetes worldwide. Globally, approximately 422 million adults aged over 18 years are living with type 2 diabetes (WHO, 2016b). The majority of those diagnosed with type 2 diabetes do not achieve the recommended glycaemic control, as it requires considerable self-discipline and motivation concerning diet, exercise and blood glucose testing (WHO, 2016b). Inadequate blood glucose control may result in blindness, kidney failure, amputation and several other long-term consequences that can significantly affect people’s quality of life (IDF, 2017). Consequently, people with type 2 diabetes need support delivered by skilled nurses to promote diabetes management and healthy choices (WHO, 2016b).
Electronic health technologies (eHealth) have been endorsed as tools for dealing with the rising numbers of people with type 2 diabetes. Today, electronic communication (eCommunication), particularly electronic mail (e-mail) and text messages, has to some extent, supplemented face-to-face consultations among people with type 2 diabetes (Ye et al., 2010). However, technology itself will not transfer support and counselling of patients without healthcare professionals who have the knowledge and skills to effectively practise under this new digital paradigm of patient care. WHO (2016a) argues that the key for providing high-quality eHealth services is training and continuing professional development of healthcare professionals. However, research addressing electronic communication between patients and nurses is in its early stages (Koivunen & Saranto, 2017).
This study is extending on an earlier published study about how diabetes nurses in primary care experienced the process of learning to practise the intervention Guided Self-Determination in face-to-face consultations among people with type 2 diabetes (Oftedal, Kolltveit, Zoffmann, Hörnsten, & Graue, 2017). In this current study, we move from face-to-face consultation to Guided Self-Determination in an electronic format with the purpose of developing knowledge about what may be needed to support nurses in shifting health intervention communications into the electronic format.
2 | BACKGROUND
The advances in technology and the potential benefits for health care have resulted in a variety of eHealth interventions in clinical practice. Most of these interventions refer to medical and health support that is personalized, interactive and based on data obtained from patients, in contrast to information that patients may get from generalized websites on health and disease (Elbert et al., 2014). Many eHealth interventions are based on asynchronous communication (refers to communication in delayed time such as e-mail and blogs), to foster communication whenever it is convenient for the healthcare professionals or patients, thus freeing the patient from the necessity of travelling to the clinic at a precise time to receive counselling (Huxley, Atherton, Watkins, & Griffiths, 2015). A systematic review (Ye et al., 2010) shows that the use of e-mail in patient-provider communication has the potential to improve health communication between patients and providers, thus increasing satisfaction and the quality of care. Other studies reveal that electronic communication between healthcare professionals and patients can improve patient-centred care (Cornwall, Moore, & Plant, 2008), facilitate patient information (Kinnane, Milne, Kinnane, & Milne, 2010), prevent dropout and deterioration of patients’ health (Das, Faxvaag, & Svanaes, 2015). However, eHealth interventions for people with type 2 diabetes appear to vary widely in terms of follow-up, length and quality (Pal et al., 2013). Previous systematic review reveals the need for eHealth interventions based on a theoretical framework that would provide appropriate patient-tailored feedback from healthcare professionals (Pal et al., 2013). A recent study, using a theory-driven intervention, shows that diabetes nurses (DNs) experienced this Guided Self-Determination (GSD) intervention for type 2 diabetes as a constructive counselling method for stimulating patients’ reflections and motivation for diabetes management (Oftedal et al., 2017). Based on these findings, we, in this current study, adapted the GSD approach to an asynchronous eHealth intervention based on written communication. However, incorporating eHealth in clinical practice may represent a disruptive change in the health care and work settings (Koivunen, Niemi, & Hupli, 2015) and a review has identified these challenges; lack of knowledge about the eHealth technology, perception of usefulness, lack of time, training or limited access (Ye et al., 2010). It is argued that if healthcare professionals are dissatisfied with the eHealth intervention, it is unlikely that an intervention would be implemented (Li, Talaei-Khoei, Seale, Ray, & Macintyre, 2013). Therefore, an effort should be made to investigate what is actually taking place when eHealth intervention is implemented in clinical practice. More specifically, it is important to investigate the unintended consequences of eCommunication among nurses in clinical setting (Melby & Hellesø, 2014). A systematic review stated that eCommunication between patients and nurses has not really been studied from the nursing professionals’ point of view (Koivunen & Saranto, 2017). In addition, no studies have explored nurses’ perspectives on the use of GSD intervention in written eCommunication portals geared towards people with type 2 diabetes in primary care.
2.1 | Aim
The aim was to explore what can be learned about the written form for health communication from the experiences of diabetes nurses using an asynchronous electronic Guided Self-Determination intervention for people with type 2 diabetes in primary care. Towards this end, the study was guided by the following question: From a nursing perspective, what is gained and what is lost through written electronic communication?
2.2 | Design/Method
This small exploratory study has a qualitative design with an Interpretive Description (ID) methodology (Thorne, 2016), which is a qualitative research strategy developed for the purpose of advancing knowledge in the applied disciplines. As ID is particularly relevant to questions arising from daily clinical practice and for developing new knowledge and insight about clinically topic that may generate changes in health care, the methodology was ideally suited to this study. The data were collected in 2016 by means of individual interviews with four DNs in general practice, representing rural and urban municipalities in south-western Norway.
2.3 | Electronic Guided Self-Determination intervention
In this study, the eHealth intervention was based on GSD developed for people with type 2 diabetes (Karlsen et al., 2016). The GSD is a theory-driven counselling approach founded in the synthesis of grounded theories, self-determination theory, life skills theory and humanistic values theory (Zoffmann et al., 2016; Zoffmann, Harder, & Kirkevold, 2008). The purpose is to guide patients and health professionals through mutual reflection (Zoffmann & Lauritzen, 2006) using a six-stage interaction process: (a) establishment of a mutual person-nurse relationship with clear I-you-borders; (b) self-exploration; (c) self-understanding; (d) shared decision-making; (e) action; and (f) feedback from action. This process is facilitated by the use of several semistructured reflection sheets that are intended to empower the patient to become self-determined and to develop adequate life
A purposive sample of diabetes DNs was selected from general practitioners (GPs). However, potential recruits for this study were relatively few, as not many GPs in Norway employ Registered Nurses. Therefore, to obtain as many recruits as possible, the first author (BO) disseminated information about the study during a professional meeting for DNs and by telephone to GPs in south-western Norway, inviting them to participate. The inclusion criteria for nurses were as follows: Nurses must: (a) be Registered Nurses and employed in a general practice; (b) have more than 1 year of experience in diabetes care; (c) have completed a test about the GSD; and (d) be willing to use GSD in an electronic written format. The head of the practice approved the participation of the nurses in the study. Five Registered Nurses with particular diabetes expertise were invited to participate. One DN was reported sick. In total, four DNs consented to participate. All study participants were women, aged from 36 - 56 years. The median duration of their experience in diabetes care was 7 years (ranging from 4 - 22 years). Three of the four DNs had formal postgraduate education in diabetes care (60 ECTS) and all had been trained in the GSD method (Oftedal et al., 2017). However, none of the DNs had been trained in GSD on an eHealth platform.
### 2.5 Data collection
Individual interviews were performed with the DNs after they had used the electronic GSD platform for patients with type 2 diabetes (spring 2016). The research BCHK, who is also a registered diabetes nurse, conducted the interviews and each interview took place at the University and was limited to 1 hr. A thematic semistructured interview guide was developed by the authors (BO & BCHK), including follow-up questions designed to make it possible for the study participants to highlight perspectives relevant for the research topic. First, DNs were asked an initial question about their overall experience with the eGSD for patients with type 2 diabetes. This question was followed up by more specific questions concerning their experiences using written electronic communication with patients and how they experienced the patient relationship when counselling via Internet. The interviews were audiotaped and transcribed verbatim. The text was imported into QSR International’s NVivo 11™ software programme for analysis.
### 2.6 Data analysis
The analysis was guided by Interpretive Description (ID; Thorne, 2016). An important factor in ID is to begin with an open-minded reading of the transcribed text to obtain the sense of the whole. Three members of the research team (BO, BK and MG) read the text several times, without focusing too much on details at this early stage of the analysis, but roughly coding the sequences that were
| TABLE 1 eGSD intervention |
|-----------------------------|
| **The first session at the GPs office** | Preparing for subsequent consultations:
| | Invitation to work together
| | The HbA1c measurement
| **eConsultations and focus:** | Reflection sheets (RS)
| **(1) Your life with diabetes** | Important events and periods in your life
| | At present, what do you find difficult about living with diabetes?
| | Unfinished sentences—your needs, values, habits and opportunities
| | A picture, metaphor or expression of your life with diabetes
| **(2) Focus for change** | Room for diabetes in your life Your plans for changing your way of life
| **(3) Work with changes** | Clarification of challenge in your life with diabetes Previous problem-solving: thoughts, feelings, goals and actions Dynamic problem-solving
| **(4) Changes in daily life** | Blood glucose self-monitoring and your reasons for self-monitoring New strategies and long-term plan for change Dynamic judgement of current and future problem-solving
considered important for the analysis. Questions asked of the material during this initial reading and re-reading process were as follows: What is seen? What is going on and what does it mean? Following this first preliminary coding, a closer examination of the labelled statements was conducted and general questions such as what is the main message in the material and what new understanding can the data provide were asked of the data (Thorne, 2016). In this study, relevant analytic questions included: In what ways do the DNs describe and explain their experience with eGSD? What do they describe as lost through written electronic communication and why and what kinds of experiences have they gained through the written electronic communication and why? Through this analytic questioning process, the codes were initially grouped into tentative patterns. The research team discussed the patterns and the relationship between these patterns and sections in the material and concluded the analytic process by conceptualizing the findings in a form that illustrated the application of the GSD intervention based on written eCommunication from the perspective of these diabetes nurses.
### 2.7 | Ethics
The Norwegian Social Sciences Data Services approved the study (No. 39454). All respondents provided informed written consent before the individual interviews and were guaranteed confidentiality and the right to withdraw from the study at any time. The anonymity of participants was maintained by removing names from records and transcriptions.
### 2.8 | Findings
The main finding of this study was that nurses did find the written eCommunication to be a disruptive format in their capacity to deliver care. However, this disruption presented both advantages and disadvantages to the clinical context, which became apparent as they reflected on the gains and losses associated with this form of care delivery. Their interpretation of the nature of this disruption is presented here in the context of three major themes that emerged from their accounts, each of which reveals elements of the nuances of these changes. The following themes were identified: (a) Replacing basic and advanced communicative skills with written expressions; (b) Making process transparent; and (c) Creating space for reflection and insight. Quotations from the interviews are presented to illustrate how nurses expressed their experiences with the asynchronous GSD written eCommunication.
#### 2.9 | Replacing basic and advanced communicative skills with written expressions
The nurses said that eCommunication, as a result of its reliance on electronic, written function, changed their way of communicating with the patients and represented other aspects than in an oral dialogue. One aspect that emerged from the analysis was that nurses experienced the electronic, written communication with patients to be challenging because the various layers of communication that occur during face-to-face encounter were lost in an written eCommunication. For example, emotional cues from vocal intonation or body language were missing. In particular, nurses highlighted that body language such as eye contact, posture and gesture, and facial expressions and the general non-verbal expression was lacking. These expressions helped nurses identify the reactions, questions and needs of patients, which then facilitated nurses' understanding and informed their responses, often without words. They described the written eCommunication as “totally free of body language” due to the inability to read non-verbal expression. In the absence of such expressions and interaction with patients, nurses lost the opportunity to better align their messages with patients need. For example, one nurse expressed the following:
> I like eye contact and interpreting body language and moods. I cannot do that between the lines. When you speak to the patient, I can tell when they seem skeptical. This is not caught up online, because it is so filtered
(3).
When communicating face-to-face, nurses said that they could use more of their senses to assess the patient’s expressions or voice and thus evaluate their emotional or mental state of the patient. On the other hand, the absence of non-verbal communication was also perceived as an advantage. One nurse experienced face-to-face communication as noisy and as a barrier to the reflective responses to patient in face-to-face setting, stating, “You are affected by expression, sounds. All senses are fully operational” (3).
The use of advanced communication skills such as mirroring and active listening was reported as difficult under the scheme of eGSD counselling. Some nurses reported experimenting with different text expressions such as ellipses (....), question marks, cur- sive or boldfaced type and used of emojis when trying to mirror interactions with the patient. However, despite the use of creative writing, they found it difficult to use the advanced communicative skills they had learnt as part of the GSD training. One nurse reported the following: "I tried with value clarification responses to the degree it was possible to use these tools, but it wasn’t easy. I was aware that this was the GSD I would be able to offer" (4).
Another aspect that characterized the nurses’ experience of written eCommunication was how it changed their relationship with the patients. Nurses described the relationship with patients to be good and constructive, but also depicted is as being more distant. As a result, closeness to the patient was lost as expressed by one nurse:
> “The relationship was good, but it was distanced. I felt like they (the patients) were out in the world and I was here. I felt like I was missing something—a sense of closeness both parties needed” (3).
Similarly, the asynchronous environment reduced nurses’ feelings of “being there” with the patient, which could be potentially detrimental to building a therapeutic relationship. In this case, face-to-face contact offers richer stimuli, including auditory, visual, tactile and behavioural stimuli and smells and gestures, which were reported
as being lost in the electronic environment with patients. On the other hand, nurses also reflected that written eCommunication with patients could sometimes be perceived as personal as expressed by one nurse:
...I think that when it was in writing, it became personal. Here's someone who's at home and writing to me via e-mail or in my chart and responded with «Hi Peter», or whatever their name was. Kind regards, xx, turned into a friendly but not completely informal response, so I still think they felt considered (4).
### 2.10 | Making process transparent
This theme reflects on how using electronic written, instead of verbal communication, makes the counselling process transparent. The nurses reported that the written, electronic environment provided an easier means for following the patient’s progress during the GSD, as the written text could be read repeatedly by both patients and nurses. Thus, this transparency extended in both directions. Some nurses noted that it could increase their ability to provide appropriate counselling and support. However, the analysis also revealed that other nurses perceived this process to be challenging, as text is irrevocable and they therefore lost the possibilities to change the text. They described certain difficulties in writing and reported that they often wrote, deleted and rewrote messages while reflecting on how patients would perceive the message. One nurse said the following: “At many points I would reconsider the responses I gave, but when you're talking with someone across from you, you don’t spend nearly as much time considering what you should answer as you do when it is in writing” (2).
The nurses also stressed that written eCommunication is not a neutral tool and carries the risk of content being misinterpreted. They were aware that text could be perceived as much harsher or more powerful than verbal communication. As a consequence, the nurses spent a lot of time constructing sentences and formulating the answer to reduce the risk or avoid misunderstandings that potentially could harm a constructive relationship with patients. Some nurses reported performance anxiety in regard to written eCommunication because they were afraid that their written text was not good enough. One nurse reported the following:
I've found it difficult. It's a new way to do it. I spent a lot of time considering what and how I should write: How will she interpret this – and feeling a certain performance anxiety about what is written in black and white – is it good enough? (1)
However, some nurses reported that practicing communication in writing also led to awakening and better communication with the patients in face-to-face consultations.
### 2.11 | Creating space for reflection and insight
This theme highlights how the nurses perceived written eCommunication to be a tool for reflection, prompting them to take time in composing messages and reflecting on them before sending them to patients. Compared with face-to-face consultations, which require an immediate response to the patient, nurses found written eCommunication to result in messages that were well thought out and that was reflected on more deeply before responding to patients. For example, one nurse expressed the following: “It makes you more conscious about writing words to send. In that way I spent more time thinking about what I respond to the patient and what you should ask about and what you write” (2). In addition, some nurses appreciated that asynchronous eCommunication made it possible to read patients’ narratives when they were alone and not in face-to-face consultations with patients. This point of view was related to the fact that some patients’ narratives affected them strongly and, therefore, they appreciated having time alone to better understand these narratives. In this sense, nurses observed that some patients found it easier to share their challenges with diabetes in written form rather than during verbal consultation with the nurses. These written narratives from patients gave nurses a deeper insight into patients’ thoughts and experiences as expressed by the following quotation:
But at the same time, with the patient I’m working with now, she writes a lot. She has a lot of thoughts that haven’t been present in the yearly checkups. She writes a lot about herself and her own and her family’s background and why she feels this way. A lot of it has come out when she sat down to write (1).
The nurses reported that the eGSD approach had reoriented their support from giving diabetes advice and information to prompting patients’ responsibility for their own health. They also stated that they spent a lot of time to reflect on how to stimulate patients’ reflections, decision-making and choice in an electronic written format as expressed by one nurse: “I will constantly write what I think the patient should do”(2). Apparently, writing requires more attention, reflection and time than verbal expression. In this respect, all nurses reported that the written eCommunication was time-consuming. However, they also found time spent to be a constructive aspect. For instance, since eCommunication takes advantage of the delivery of asynchronous messages, nurses had time to obtain the information needed to respond to patients, including information they did have immediately at hand or in mind. Another aspect the nurses highlighted as an advantage was that asynchronous written eCommunication offers flexibility in regard to responding to patients. Nurses could thus respond to patients when they had time and without additional influencing factors. For example, one nurse reported the following:
The thing that was positive about it all was when I got the reflection sheets back from the patient. I could sit down in peace and quiet and read through without
being disturbed by patients or others. What does it say between the lines? What does it really say? From that I could offer feedback. In one way it was easier when it was in digital formats than face to face (3).
On the other hand, they were concerned about how to maintain their professional role in written eCommunication. That was particularly expressed when they reflected over how asynchronous written eCommunication allowed them to be available 24/7 and thus responding to patients whenever they had time. Consequently, they were worried that responding to patients outside working hours could influence the nurses’ professional role in a negative way.
## 3 | DISCUSSION
The aim of this study was to explore what can be learned about the written form for health communication from the experiences of diabetes nurses using an asynchronous electronic Guided Self-Determination intervention for people with type 2 diabetes in primary care. The findings of this study challenge us to reflect on the potential and limitations of written electronic communication and to add to our understanding of what might be needed to support healthcare professionals in shifting health intervention communications into an electronic format.
### 3.1 | Rethinking the essence of communication
The findings of the current study indicate that the asynchronous eGSD intervention requires new ways of communicating and a rethinking of the essence of communication between nurses and patients. Particularly, the findings show that a lack of non-verbal communication cues became a important challenge for the nurses. A similar observation was also reported in another study investigating non-verbal communication in text-based medical consultation among physicians (Björk, Hillborg, Augutis, & Umefjord, 2017). Thus, this finding is not surprising, as non-verbal communication is an inherent value for healthcare professionals to give comprehensive care to patients. Conversely, our study also indicates that the absence of non-verbal communication can increase nurses’ reflective responses, as their interpretation was not affected by patients’ non-verbal expression. Accordingly, in the light of our findings and assuming that use of digital written communication will continue to increase in clinical settings, it seems timely to question the degree to which the absence of non-verbal communication contributes to or detracts from clinical practice. Alternatively, and more specifically, it will be important to gain an understanding of situations in clinical practice where non-verbal communication becomes unnecessary to give patients adequate support. Is it possible that written communication in some situations could be more beneficial for both patients and nurses than face-to-face communication? Nurses and other healthcare professionals who are directly involved in the consequences of eHealth in clinical practice and the patients who are directly affected by these communications all have a key role to play in promoting the debate that will allow us to decide on best practices.
Another factor that was reported as lost when using asynchronous written eCommunication was the opportunity of using advanced communication skills like active listening or mirroring. Our study suggests that several creative writing strategies, such as the use of emoji, were developed by the nurses to compensate for advanced communication methods. Yet, the nurses reported they did not feel they succeeded with this strategy. This finding may indicate that written eCommunication is not necessarily a reduced form of face-to-face communication, but offers an entirely different vehicle for communication with its own unique advantages and limitations. Therefore, our findings support the findings of previous study reporting that there is a need to improve communication skills in written texts (Björk et al., 2017; van Houwelingen, Moerman, Ettema, Kort, & Cate, 2016) and that educational efforts to include written eCommunication in the nurse students curricula should be prioritized, as it is likely that text-based consultations will expand in the future (Booth, 2006). Healthcare professionals and clinical educators could be a key conduit for stimulating change and increasing the focus on eCommunication.
### 3.2 | Achieving a more transparent and reflective counselling
It is well known that electronic devices augment transparency and the findings of this current study support the position that written eCommunication may increase the opportunity of achieving a more transparent communication form in the counselling delivery process. Accordingly, the current findings become an important indicator that we will need to recognize and attend to electronic intervention as a factor contributing to a more transparent healthcare system. Indeed, the findings indicate that nurses support a culture that is open and transparent, as this makes it easier for them to follow patients during the counselling process. The WHO (2017) argues that the transparency of all communications is essential to building trust in health care. Silverman, Draper, and Kurtz (2016) also advocate that transparency promotes relationship building and reduces unnecessary patient uncertainty about their care. However, because transparency requires that a written text remains online, the findings indicate that this made the nurses in this study more cautious in formulating their feedback. To reduce the risk of misinterpretation, they spent much time preparing and formulating their texts to ensure that they were correct. They said that they were concerned that the patients would perceive the written texts as harsh and strict and they emphasized how difficult it was to lose the opportunity to change the texts and adjust them according to the patients’ immediate responses. Accordingly, in the light of our findings, when introducing eGSD to clinical practice, it is important to consider that asynchronous written eCommunication may be worrisome to some nurses who are concerned about the accuracy of written messages. It may
also be suggested that not all nurses are sufficiently comfortable with posting written communications and there may need to be definable skill sets to allow nurses to practise in this manner. Nevertheless, the nurses’ concerns about how the patients would perceive their written communication are relevant, considering that several studies have revealed that many people cannot understand nor use written health information properly (Bailey et al., 2014; Jacobs, Lou, Ownby, & Caballero, 2016). It may, therefore, be assumed that written eCommunication could act as a reminder to help nurses become more conscious about the words and concepts they employ when consulting with patients. This interpretation is supported by a previous study (Björk et al., 2017) and our current study, which reveal that practicing written eCommunication can also lead to better communication skills in face-to-face consultations. This interesting perspective should be further investigated.
Another important finding was that the asynchronous environment made it possible to support the reflective responses that are valuable in GSD counselling, as nurses could read and respond to patients’ narratives when they were alone and not having face-to-face consultations with patients. Consequently, the feedback to patients was well thought out and deeply reflected on. Therefore, it seems possible that asynchronous eHealth intervention could help surmount the disruptive factors that are often encountered in face-to-face counselling. These findings are supported by other studies, which reveal that text-based consultation gives healthcare professionals time to think, reflect and fine-tune their answers (Björk et al., 2017; Dunn, 2012), which is a unique opportunity that is rarely available in face-to-face interactions.
3.3 | Limitations
In this exploratory study, we acknowledge that the sample is small. Malterud, Siersma, and Guassora (2016) emphasize that a study with clear and focused dialogue between researcher and participants requires fewer participants to offer sufficient data material than a study with an unclear or vague communication. In our study, the researcher (BCHK) has interviewed the participants in an earlier study (Oftedal et al., 2017) and has thus, already established contact and trust in the dialogue. In addition, the researcher has knowledge of both the diabetic work at GP and the GSD intervention. We therefore consider the data material, consisting of rich and varied accounts, to be trustworthy. It permits a preliminary understanding that adds to our knowledge of what might be needed to support healthcare professionals while shifting health intervention communications into an electronic format. However, we could not preclude that a large number of participants might have thrown open different perspectives.
Another limitation is that the nurses in this study were born before 1980 and are, therefore, “digital immigrants” (Prensky, 2005). That means that although many aspects of the technology might be adopted, just like those who learn another language later in the life, they retain an “accent.” It is, therefore, possible that nurses born after 1980 might have identified other dimensions of asynchronous written communication. It is also unknown whether these findings related to eCommunication would have changed had the nurses used the written asynchronous communication over time.
4 | CONCLUSION
The findings indicate that asynchronous written eCommunication could disrupt nurses’ possibilities to use basic and advanced communication skills and that written expression may not currently be adequate for replacing the communication skills that are traditionally used in clinical practice. However, the findings also suggest that asynchronous written eCommunication can foster deep and thoughtful responses to patients and as nurses become more conscious of the words they employ when responding in writing, they may enhance their communication skills in subsequent face-to-face interactions. In addition, written eCommunication increases the possibilities for intensified transparency of the counselling delivery process. Although much remains to be learned with regard to reconfiguring health intervention communications into electronic formats, this study highlights the potential advantages and limitations of using asynchronous written eCommunication in primary care.
ACKNOWLEDGEMENT
We thank the diabetes nurses for their participation in this study.
CONFLICT OF INTERESTS
We declare no conflict of interests.
AUTHOR CONTRIBUTIONS
BO, MG, VZ and BK designed the study. BO and B-CHK were involved in data collection. BO, MG, MK, ST, B-CHK and BK analysed the data. BO has mainly drafted the manuscript, but all authors have contributed to the drafting of the manuscript, revised it critically for scientific content, read and approved the final version.
ETHICAL APPROVAL
The Norwegian Social Sciences Data Services approved the study (No. 39454). All respondents provided informed written consent before the individual interviews and were guaranteed confidentiality and the right to withdraw from the study at any time.
ORCID
Bjørg Oftedal http://orcid.org/0000-0002-6320-8509
Margareth Kristoffersen http://orcid.org/0000-0002-0800-1169
REFERENCES
Bailey, S. C., Brega, A. G., Crutchfield, T. M., Elasy, T., Herr, H., Kaphingst, K., ... Schilling, D. (2014). Update on health literacy and diabetes. *Diabetes Educator, 40*(5), 581–604. https://doi.org/10.1177/0145721714540220
Björk, A. B., Hillborg, H., Augutis, M., & Umefford, G. (2017). Evolving techniques in text-based medical consultation - Physicians' long-term experiences at an Ask the doctor service. *International Journal of Medical Informatics, 105*, 83–88. https://doi.org/10.1016/j.ijmend.2017.05.013
Booth, R. G. (2006). Educating the future eHealth professional nurse. *International Journal of Nursing Education Scholarship, 3*(1), 1–10. https://doi.org/10.2202/1548-923X.1187
Cornwall, A., Moore, S., & Plant, H. (2008). Embracing technology: patients', family members' and nurse specialists' experience of communicating using e-mail. *European Journal of Oncology Nursing, 12*(3), 198–208. https://doi.org/10.1016/j.ejon.2007.09.008
Das, A., Fyvaag, A., & Svanæs, D. (2015). The impact of an eHealth portal on health care professionals’ interaction with patients: Qualitative study. *Journal of Medical Internet Research, 17*(11), e267–e267. https://doi.org/10.2196/jmir.4950
Dunn, K. (2012). A qualitative investigation into the online counselling relationship: To meet or not to meet, that is the question. *Counselling and Psychotherapy Research, 12*(4), 316–326. https://doi.org/10.1080/14733314.2012.697772
Elbert, N. J., van Os-Medendorp, H., van Renselaar, W., Ekeland, A. G., Hakkaart-van Roijen, L., Raat, H., ... Pasmans, S. G. M. A. (2014). Effectiveness and cost-effectiveness of eHealth interventions in somatic diseases: a systematic review of systematic reviews and meta-analyses. *Journal of Medical Internet Research, 16*(4), e110–e110. https://doi.org/10.2196/jmir.2790
Huxley, C. J., Atherton, H., Watkins, J. A., & Griffiths, F. (2015). Digital communication between clinician and patient and the impact on marginalised groups: a realist review in general practice. *British Journal of General Practice, 65*(641), e813–e821. https://doi.org/10.3399/bjgp15X687853
IDF (2017). IDF diabetes atlas. In Eighth edition. Retrieved from: https://www.diabetesatlas.org/
Jacobs, R. J., Lou, J.Q, Owny, R. L., & Caballero, J. (2016). A systematic review of eHealth interventions to improve health literacy. *Health Informatics Journal, 22*(2), 81–98. https://doi.org/10.1177/1460458214534092
Karlsen, B., Oftedal, B., Stangeland Lie, S., Rokne, B., Peyrot, M., Zoffmann, V., & Graue, M. (2016). Assessment of a web-based Guided Self-Determination intervention for adults with type 2 diabetes in general practice: a study protocol. *British Medical Journal Open, 6*(12), e013026–e13026. https://doi.org/10.1136/bmjopen-2016-013026
Kinnane, N. A., Milne, D. J., Kinnane, N. A., & Milne, D. J. (2010). The role of the Internet in supporting and informing carers of people with cancer: a literature review. *Supportive Care in Cancer, 18*(9), 1123–1136. https://doi.org/10.1007/s00520-010-0863-4
Koivunen, M., Niemi, A., & Hupli, M. (2015). The use of electronic devices for communication with colleagues and other healthcare professionals – nursing professionals’ perspectives. *Journal of Advanced Nursing, 71*(3), 620–631. https://doi.org/10.1111/jan.12529
Koivunen, M., & Saranto, K. (2017). Nursing professionals’ experiences of the facilitators and barriers to the use of telehealth applications: a systematic review of qualitative studies. *Scandinavian Journal of Caring Sciences, 32*(1), 24–44. https://doi.org/10.1111/scs.12445
Li, J., Talaei-Khoei, A., Seale, H., Ray, P., & Macintyre, C. R. (2013). Health care provider adoption of eHealth: Systematic literature review. *Interactive Journal of Medical Research, 2*(1), e7. https://doi.org/10.2196/ijmr.2468.
Malterud, K., Siersma, V. D., & Guassora, A. D. (2016). Sample size in qualitative interview studies: Guided by information power. *Qualitative Health Research, 26*, 1753–1760.
Melby, L., & Hellesa, R. (2014). Introducing electronic messaging in Norwegian healthcare: unintended consequences for interprofessional collaboration. *International Journal of Medical Informatics, 83*(5), 343–353. https://doi.org/10.1016/j.jimend.2014.02.001
Oftedal, B., Kolltveit, B.-C.-H., Zoffmann, V., Hörnsten, Å., & Graue, M. (2017). Learning to practise the Guided Self-Determination approach in type 2 diabetes in primary care: A qualitative pilot study. *Nursing Open*, 4(3), 134–142. https://doi.org/10.1002/nop.276
Pal, K., Eastwood, S. V., Michie, S., Farmer, A. J., Barnard, M. L., Peacock, R., ... Murray, E. (2013). Computer-based diabetes self-management interventions for adults with type 2 diabetes mellitus. *Cochrane Database of Systematic Reviews, 3*, CD008776. https://doi.org/10.1002/14651858.CD008776.pub2
Prensky, M. (2005). Listen to the Natives. *Educational Leadership, 63*(4), 8–13.
Silverman, J., Draper, J., & Kurtz, S. (2016). Skills for communicating with patients (3rd ed.). London, UK: CRC Press.
Thorne, S. (2016). Interpretive Description: Qualitative research for applied practice (2nd ed.). London, UK: Routledge Taylor and Fracis group.
van Houwelingen, C. H., Moerman, A. H., Ettema, R. G. A., Kort, H. S. M., & ten Cate, O. (2016). Competencies required for nursing telehealth activities: A Delphi-study. *Nurse Education Today, 39*, 50–62. https://doi.org/10.1016/j.nedt.2015.12.025
WHO (2016a). Global diffusion of eHealth: Making universal health coverage achievable. In *World Health Organization: Retrieved from*: https://www.who.int/ehealth/
WHO (2016b). Global report on diabetes. Retrieved from https://www.who.int/diabetes/global-report/
WHO (2017). WHO Strategic communications framework for effective communication. In *World Health Organization: Retrieved from*: www.who.int/entity/communicating-for-health/en/
Ye, J., Rust, G., Fry-Johnson, Y., Strothers, H., Ye, J., Rust, G., ... Strothers, H. (2010). E-mail in patient-provider communication: a systematic review. *Patient Education and Counseling, 80*(2), 266–273. https://doi.org/10.1016/j.pec.2009.09.038
Zoffmann, V., Harder, I., & Kirkevold, M. (2008). A person-centered communication and reflection model: sharing decision-making in chronic care. *Qualitative Health Research, 18*(5), 670–685. 616p. https://doi.org/10.1177/1049732307311008
Zoffmann, V., Hörnsten, Å., Storbækken, S., Graue, M., Rasmussen, B., Wahl, A., & Kirkevold, M. (2016). Translating person-centered care into practice: A comparative analysis of motivational interviewing, illness-integration support and Guided Self-Determination. *Patient Education and Counseling, 99*(3), 400–407. https://doi.org/10.1016/j.pec.2015.10.015
Zoffmann, V., & Lauritzen, T. (2006). Guided Self-Determination improves life skills with Type 1 diabetes and A1C in randomized controlled trial. *Patient Education and Counseling, 64*(1–3), 78–86. https://doi.org/10.1016/j.pec.2005.11.017
How to cite this article: Oftedal B, Kolltveit B-CH, Graue M, et al. Reconfiguring clinical communication in the electronic counselling context: The nuances of disruption. *Nursing Open*. 2019;6:393–400. https://doi.org/10.1002/nop.2.218 | 2025-03-06T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
1686,
1
],
[
1686,
7695,
2
],
[
7695,
11517,
3
],
[
11517,
17667,
4
],
[
17667,
23518,
5
],
[
23518,
29617,
6
],
[
29617,
34911,
7
],
[
34911,
42122,
8
]
]
} |
7b0865678dca807af2d413a088ead04dec1325c8 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 6,
"total-fallback-pages": 0,
"total-input-tokens": 18933,
"total-output-tokens": 5274,
"fieldofstudy": [
"Medicine"
]
} | We retrospectively reviewed 2 male and 3 female patients who were between 15–38 years of age at the time of GKS. The characteristics of these patients are summarized in Table 1. Because 3 patients (case 1, 2, and 5) received GKS at another hospital and were referred for follow-up examinations, the precise rate of developing expanding hematomas remains unclear. These 3 patients underwent second GKS for remnant AVM at 38, 41, and 50 months after the first GKS, respectively. One patient (case 5) underwent a third GKS at 40 months after the second GKS. The initial presenting symptoms included seizure in 4 patients and intraventricular hemorrhage in 1 patient (case 3). Although there was some diversity, 4 AVMs were classified as Spetzler-Martin grade 3 and 1 AVM was classified as grade 4. Nidus volume at the time of the first GKS ranged between 4.2–34.5 mL. One patient (case 4) underwent partial embolization with Onyx prior to GKS. Fourteen to 35 Gy of radiation was delivered to the margin of the AVM, achieving an isodose level of 50%.
INTRODUCTION
Gamma knife radiosurgery (GKS) has become an effective and safe treatment for cerebral arteriovenous malformation (AVM). Here, we describe 5 patients with growing organized hematomas that developed from completely obliterated AVMs several years after GKS. The patients were 15, 16, 30, 36, and 38 years old at the time of GKS, respectively, and 3 patients were female. Four AVMs were located in the lobe of the brain, and the remaining AVM were in the thalamus. Between 2–12 years after GKS, patients developed progressive symptoms such as intractable headache or hemiparesis and enhancing mass lesions were identified. Follow-up visits revealed the slow expansion of the hematomas and surrounding edema. Steroids were ineffective, and thus surgery was performed. Histology revealed organized hematomas with a capsule, but there was no evidence of residual AVMs or vascular malformation. After surgery, the neurological symptoms of all patients improved and the surrounding edema resolved. However, the hematoma continued to expand and intraventricular hemorrhage developed in 1 patient whose hematoma was only partially removed. GKS for cerebral AVM can be complicated by growing, organized hematomas that develop after complete obliteration. Growing hematomas should be surgically evacuated if they are symptomatic. Radical resection of the hematoma capsule is also strongly recommended.
Key Words : Gamma knife radiosurgery · Intracranial arteriovenous malformation · Intracranial hemorrhage · Surgical procedure.
CASE REPORT
We retrospectively reviewed 2 male and 3 female patients who were between 15–38 years of age at the time of GKS. The characteristics of these patients are summarized in Table 1. Because 3 patients (case 1, 2, and 5) received GKS at another hospital and were referred for follow-up examinations, the precise rate of developing expanding hematomas remains unclear. These 3 patients underwent second GKS for remnant AVM at 38, 41, and 50 months after the first GKS, respectively. One patient (case 5) underwent a third GKS at 40 months after the second GKS. The initial presenting symptoms included seizure in 4 patients and intraventricular hemorrhage in 1 patient (case 3). Although there was some diversity, 4 AVMs were classified as Spetzler-Martin grade 3 and 1 AVM was classified as grade 4. Nidus volume at the time of the first GKS ranged between 4.2–34.5 mL. One patient (case 4) underwent partial embolization with Onyx prior to GKS. Fourteen to 35 Gy of radiation was delivered to the margin of the AVM, achieving an isodose level of 50%.
Other findings
Rt temporal
Cyst formation
IVH
2.8 y
None
8.6 y
6 mo
7 y
Pre-treatment
2.4 y
2 y
25 Gy, 50%
3 y
Rt weakness
2.5 y
Seizure
36/F
12.6 y
None
14 Gy, 50%
39 mo
Seizure
4.2
1
17 Gy, 50%
Rt f
Lt f
mRS
16/M
3.3 y
28 Gy, 50%
15 mo
20 Gy, 50%
7 y
8.1 y
Lt thalamus
5.6 y
9.6*
S2E1V1
14 Gy, 50%
S2E0V1
12 y
Lt weakness
1
Intractable headache
S1E1V1
Lt occipital
S-M grade
1
6 mo
4
AVM location
None
23 mo
34.5
50 mo
41 mo
Rt weakness
Interval between
Rt weakness
38/M
5.0 y
2.7 y
40 mo
0
None
30/F
Seizure
Seizure
35 Gy, 50%
38 mo
The GKS treatment results are summarized in Table 2. Cerebral angiography was performed between 29–67 months after the last GKS and confirmed the complete obliteration of the nidi. Serial magnetic resonance imaging (MRI) was used to evaluate all patients. In 4 patients (case 1, 2, 4, and 5), changed in radiation-induced imaging were observed 1–2 years after GKS; however, all patients were asymptomatic and mild changes in imaging did not indicate mass effects on the surrounding edema. Cyst formation was detected 6 years after GKS in the remaining patient (case 3); an Ommaya reservoir was subsequently placed in this patient.
New enhancing mass lesions were detected 2–12 years after the last GKS. These lesions were associated with the surrounding brain edema and were asymptomatic in all patients; 4 patients had progressive hemiparesis, and 1 patient had intractable headache (case 4). These symptoms did not improve when steroids were administered, and the enhancing lesions progressively increased in size on serial follow-up examinations. Our impression was that these lesions were radiation-induced necroses or cavernous malformations that developed after GKS.
All five study patients underwent a craniotomy, and the mass lesions were removed. Histological findings revealed that all lesions were organized hematomas with a capsule; there was no evidence of cavernous malformation. The neurological symptoms in 3 of 4 patients improved after surgical removal, and the surrounding brain edema was largely resolved. Modified Rankin scale (mRS) scores were 0 or 1. However, 1 patient, whose hematoma had only been partially removed (case 3), demonstrated transient neurological and radiological improvements that were then followed by symptom aggravation and recurrent bleeding. His final mRS score was 4 at 2 years after the onset of symptom aggravation.
**Illustrative cases**
**Case 2**
A 36-year-old female patient underwent GKS for right motor cortex AVM (13.4 mL volume) and received a marginal dose of 35 Gy in August 1998. Fifty months after the first GKS, she underwent a second GKS for the remaining AVM (3.3 mL volume) (Fig. 1A, B), in which a marginal dose of 26 Gy was administered. MRI performed 18 months after the second GKS revealed mild, asymptomatic, radiation-induced changes. Cerebral angiography was performed 29 months after the second GKS, which revealed the complete obliteration of the nidus (Fig. 1C). Seven years after the second GKS, the patient was transferred to our institution because of progressive left hemiparesis. Brain MRI revealed a gadolinium-enhanced hemorrhagic mass measuring 4×3.5×3 cm that was surrounded by extensive edema (Fig. 1D). However, cerebral angiography was performed around the same time, which showed the complete obliteration of the AVM. Brain MRI performed 7 months later revealed that the lesion had expanded, and the surrounding edema had become increasingly marked (Fig. 1E).
Symptoms did not improve following the administration of steroid. Therefore, microsurgery was performed on the expand-
Growing Organized Hematoma after GKS for AVM | JC Park, et al.
Case 2
A 57-year-old male patient underwent GKS because of an AVM located in the right frontal lobe (Fig. 1A). A marginal dose of 25 Gy was delivered. Cerebral angiography performed 6 months after GKS confirmed the complete obliteration of the AVM (Fig. 1B). A growing mass was observed at 97 months after the second GKS. This was identified as a hypovascular, yellowish, and rubbery mass with a tough capsule that contained multiple layers of organized hematoma. The entire mass and capsule were surgically removed. Brain edema and neurological symptoms and signs disappeared afterward. Postoperative MRI revealed significant improvement in mass effects (Fig. 1F).
Histological examination of the resected tissues revealed obliterated AVM vessels and an organizing hematoma (Fig. 2A). The hematoma contained organized, well-capsulated, multi-stage clots with hemosiderin deposits and thrombus (Fig. 2B, C). No indications of cavernous malformation were found.
Case 3
A 38-year-old male patient underwent GKS because of an AVM located in the left thalamus and posterior hippocampal gyrus (4.2 mL volume) (Fig. 3A, B), and a marginal dose of 25 Gy was administered. Cerebral angiography performed 60 months after GKS confirmed the complete obliteration of the AVM (Fig. 3C). A cyst at the previous AVM site developed 6 years after GKS (Fig. 3D), and the placement of an Ommaya reservoir was necessary. Follow-up images revealed that the cyst has not increased in size. However, an enhancing mass lesion associated with the cyst developed 12 years after GKS (Fig. 3E). The patient complained of left hemiparesis and severe headache.
Symptoms did not improve after administering steroids, and the patient underwent left parieto-occipital craniotomy. The operative field was limited due to the deep location of the lesion and the surrounding hypothalamus and midbrain. The lesion was hypovascular, gray, firm, and had a tough capsule. The mass and the capsule were removed along with the residual hematoma. Computed tomography (CT) was performed during the immediate postoperative period, which revealed the incomplete resection of the hematoma. Histological examination revealed an organized hematoma without any indications of cavernous malformation.
After surgery, the perilesional edema and neurological symptoms of the patient improved. However, 11 months after surgery, he developed a sudden loss of consciousness and right hemiplegia. Brain CT revealed intracerebral and intraventricular hemorrhage with hydrocephalus (Fig. 3F). The patient underwent external ventricular drainage and received conservative management thereafter. After 2 years of clinical follow-up examinations, the mRS score of the patient was 4, which indicates...
moderately severe disability.
**DISCUSSION**
We here describe an unusual type of hematoma that developed at the site of a completely obliterated AVM several years after GKS in 5 patients. While a chronic, organized, growing hematoma is a rare complication that develops after radiosurgery for AVM, there are several cases in the literature that describe this hematoma as growing from residual AVM or a totally obliterated AVM following radiosurgery. In our cases described here, chronic, organized, growing hematomas developed despite cerebral angiographic confirmation of total AVM obliteration and were further characterized by their late onset, slow growth, and relatively benign course.
expansion, and capsule formation. While previous histological examinations of expanding hematomas that developed after GKS report cavernous malformations (with or without radiation necrosis), the histological findings of our current series only revealed organized hematoma and a tough collagenous capsule; radiation necrosis and de novo cavernous malformation were not observed. Growing hematomas in association with cysts have also been reported, as noted in 1 patient (case 3) in our current series.
The initial source of a chronic encapsulated intracerebral hematoma is often a vascular anomaly. A number of possibilities have been proposed. Roda et al. proposed that chronic organized hematomas are probably caused by small vascular malformations that are destroyed or thrombosed during hemorrhagic episodes. Pozzati et al. suggested that such hematomas are due to occult, self-destructing vascular malformations, such as cavernous angioma or venous angioma. Hirsh et al. proposed that the hematoma capsule is composed of fibroblasts derived from the abnormal vessels of occult vascular malformations. However, how chronic organized hematomas develop from obliterated AVMS following GKS remains unclear. Lee et al. have suggested that the most likely initial cause is minor recurrent bleeding from fragile vessels within radionecrotic brain tissue. Moreover, like chronic subdural hematoma, the encapsulated wall of a chronic organized hematoma may promote the gradual growth of these hematomas, which occurs because of recurrent bleeding or exudation from the capillaries in the inner layer of the capsule. It is also possible that AVM degeneration after radiosurgery triggers the formation of organized hematomas. Moreover, Nakamizo et al. reported that the vascular endothelial growth factor (VEGF) pathway is activated after radiosurgery for AVM, which indicates increased angiogenesis; this could lead to chronic organizing hematoma. Only 1 of our current patients initially presented with hemorrhage and, during the latent period, no additional bleeding from the AVM was noted. However, in 3 of our present cases, mild radiation-induced changes in imaging were observed 1 or 2 years after GKS, although these changes were symptomless, and another patient developed cysts 6 years after GKS. Our histological examinations suggest that the hemorrhage was due to recurrent bleeding from the fragile vessels contained within the thick hematoma capsule, and there was no evidence of associated vascular anomalies. Although it cannot be excluded that the initial bleeding episode initiated the hematomas in our present cases, our observations suggest that continuous minor bleeding from necrotic brain tissue results in the expansion of hematomas.
Radiation-induced changes on MRI including perilesional edema are a significant clinical problem. In these situation, symptomatic patients are generally treated using corticosteroid therapy. Our experience suggests that chronic organized hematomas associated with GKS for AVM grow gradually and become symptomatic when there is severe edema in the surrounding brain structure. Surgical removal is necessary, if the hematoma and perilesional edema increase in size and become symptomatic, especially because steroid therapy does not effectively control the edema associated with the expanding hematoma and because this rare condition is progressive. After the expanding hematoma is removed, the peripheral brain edema will likely decrease and the neurological symptoms will probably immediately improve. However, the whole capsule should be removed; partial resection does not efficiently control this growing hematoma.
The risk factors for developing chronic organized hematoma remain unclear. When Takeuchi et al. summarized the clinicoradiological features of 7 patients with growing hematomas that developed after radiosurgery, they identified male sex, high frequency of basal ganglia involvement, long interval from radiosurgery to diagnosable hematoma, and high rate of residual nidus as associating factors. In contrast, in our 5 cases described here, all growing hematomas arose from completely obliterated AVMS (albeit after several years) and the AVMS were mainly located in superficial areas (4 AVM were located in the lobes, while 1 patient had an AVM in the thalamus). Some predisposing factors were identified in our current patients, although the actual rate and risk factors for growing hematoma after radiosurgery remain undetermined due to the low incidence of complications. We propose large volume AVM (longest diameter >3 cm in 4 cases), repeated radiosurgery, and large cumulative radiation dose as predisposing factors. Further studies are needed to ascertain the risk factors and mechanisms of growing hematomas that developed following GKS for AVM.
**CONCLUSION**
Chronic organized hematoma is a late complication that develops after GKS to treat AVM, even after complete obliteration. Although this is a rare complication, chronic organized hematomas seem to develop in patients with a high volume of AVMS who receive repeated radiosurgeries and high cumulative dose of radiation. To manage these symptoms, a chronic organized hematoma that surrounds the radiated AVM should be completely surgically resected. This will cause the surrounding brain edema to rapidly decrease and quickly resolve neurological symptoms.
**References**
1. Al Hinai Q, Tampieri D, Souhami L, Sadikot A, Sinclair D, Leblanc R : Cyst formation following radiosurgery for AVMs : report of 3 cases. Can J Neurol Sci 38 : 734-740, 2011
2. Clark AJ, Butowski NA, Chang SM, Prados MD, Clarke J, Polley MY, et al. : Impact of bevacizumab chemotherapy on craniotomy wound healing. J Neurosurg H14 : 1609-1616, 2011
3. Hirsh LF, Spector HB, Bogdanoff BM : Chronic encapsulated intracerebral hematoma. Neurosurgery 9 : 169-172, 1981
4. Izawa M, Chernov M, Hayashi M, Nakaya K, Kamikawa S, Kato K, et al. : Management and prognosis of cysts developed on long-term follow-up after Gamma Knife radiosurgery for intracranial arteriovenous malfor-
motions. Surg Neurol 68 : 400-406; discussion 406, 2007
5. Kaido T, Hoshida T, Uranishi R, Akita N, Kotani A, Nishi N, et al.: Radiosurgery-induced brain tumor. Case report. J Neurosurg 95 : 710-713, 2001
6. Kurita H, Sasaki T, Kawamoto S, Taniguchi M, Kitanaka C, Nakaguchi H, et al.: Chronic encapsulated expanding hematoma in association with gamma knife stereotactic radiosurgery for a cerebral arteriovenous malformation. Case report. J Neurosurg 84 : 874-878, 1996
7. Lee CC, Pan DH, Ho DM, Wu HM, Chung WY, Liu KD, et al.: Chronic encapsulated expanding hematoma after gamma knife stereotactic radiosurgery for cerebral arteriovenous malformation. Clin Neurol Neurosurg 113 : 668-671, 2011
8. Maruyama K, Shin M, Tago M, Kurita H, Kawahara N, Morita A, et al.: Management and outcome of hemorrhage after Gamma Knife surgery for arteriovenous malformations of the brain. J Neurosurg 105 Suppl : 52-57, 2006
9. Motegi H, Kuroda S, Ishii N, Aoyama H, Terae S, Shirato H, et al.: De novo formation of cavernoma after radiosurgery for adult cerebral arteriovenous malformation—case report. Neurol Med Chir (Tokyo) 48 : 397-400, 2008
10. Nakamizo A, Suzuki SO, Saito N, Shono T, Matsumoto K, Onaka S, et al.: Clinicopathological study on chronic encapsulated expanding hematoma associated with incompletely obliterated AVM after stereotactic radiosurgery. Acta Neurochir (Wien) 153 : 883-893, 2011
11. Pozzati E, Giuliani G, Gaist G, Piazza G, Vergoni G: Chronic expanding intracerebral hematoma. J Neurosurg 65 : 611-614, 1986
12. Roda JM, Carceller F, Pérez-Higueras A, Morales C: Encapsulated intracerebral hematomas: a defined entity. Case report. J Neurosurg 78 : 829-833, 1993
13. Shuto T, Matsunaga S, Suemaga J: Surgical treatment for late complications following gamma knife surgery for arteriovenous malformations. Stereotact Funct Neurosurg 89 : 96-102, 2011
14. Shuto T, Ohtake M, Matsunaga S: Proposed mechanism for cyst formation and enlargement following Gamma Knife Surgery for arteriovenous malformations. J Neurosurg 117 Suppl : 135-143, 2012
15. Takeuchi S, Takasato Y, Masaoka H: Chronic encapsulated intracerebral hematoma formation after radiosurgery for cerebral arteriovenous malformation. Neurol India 59 : 624-626, 2011
16. Takeuchi S, Takasato Y, Masaoka H, Hayakawa T, Otani N, Yoshino Y, et al.: Development of chronic encapsulated intracerebral hematoma after radiosurgery for a cerebral arteriovenous malformation. Acta Neurochir (Wien) 151 : 1513-1515, 2009
17. Wang X, Hui XH, Liu JP, Mao Q: Radiation-induced cavernous malformation at the site of arteriovenous malformation following gamma knife radiosurgery: case report. Clin Neurosurg 114 : 1287-1289, 2012
18. Williams BJ, Park DM, Sheehan JP: Bevacizumab used for the treatment of severe, refractory perilesional edema due to an arteriovenous malformation treated with stereotactic radiosurgery. J Neurosurg 116 : 972-977, 2012 | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3641,
1
],
[
3641,
7251,
2
],
[
7251,
10059,
3
],
[
10059,
10752,
4
],
[
10752,
16846,
5
],
[
16846,
19763,
6
]
]
} |
5a059180b6648b4916ad9bbce2e0a6cbcb9e20d3 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 4,
"total-fallback-pages": 0,
"total-input-tokens": 12342,
"total-output-tokens": 4264,
"fieldofstudy": [
"Psychology",
"Medicine"
]
} | COVID-19 related lockdown: a trigger from the pre-melancholic phase to catatonia and depression, a case report of a 59 year-old man
Giuseppe Sarli1*, Lorenzo Polidori1, David Lester2 and Maurizio Pompili3
Abstract
Background: The pre-melancholic model described by Tellenbach may provide a common model for understanding the psychological implications of the lockdown. In this case report, we describe a rare catatonic status as a psychological implication linked to the COVID-19 pandemic, a really unique global situation.
Case presentation: B is a 59 year-old man with mute psychiatric anamnesis whose mother suffered from a major depressive disorder. As the lockdown began, he started to develop concerns about his family’s economic condition. According to his wife, he could see no end to the epidemic and no future at all. Moving from this, he started to show a severe and rapidly progressive depression and to develop mood congruent delusions. In addition, he had increasing anhedonia, apathy, starvation and insomnia. This turned in the end into a catatonic-like state, along with a deep desire to die. Admitted to the psychiatry ward in a state of mutism, he was discharged after 15 days with a diagnosis of “Major depressive disorder, single severe episode with no psychotic behavior”. He was treated with Sertraline, Olanzapine and Lorazepam.
Conclusions: Our aim is to draw attention to the effect of the lockdown upon a Tellenbach-like personality structure. Identifying this type of pre-morbid personality structure could help clinicians understand and treat some cases of patients with severe major depressive disorders elicited by the COVID-19 pandemic.
Keywords: Lockdown, Typus Melancholicus, Catatonia, Major depressive disorder, Covid-19
Background
In December 2019, an unexpected epidemic broke out in in Wuhan, Hubei Province, China [1]. A novel coronavirus was identified and found to be responsible for a disease named by the World Health Organization as coronavirus disease 2019 (COVID-19). COVID-19 is an acute respiratory syndrome caused by the coronavirus 2 (SARS-CoV-2) [2]. So far, the virus has caused more than 400,000 deaths, affecting almost 8 million people in 229 countries [3]. Italy has been one of the most hard hit countries, with a peak in March 2020. On March the 11th, the Istituto Superiore di Sanità confirmed that Italy was second in the number of deaths due to COVID-2019 after China [4]. On the same day, the whole country was declared a red zone, and a lockdown began. The Italian Government introduced progressive mitigation measures that ended with the mandatory closing of almost all commercial and productive activities in order to drastically limit social interaction and prevent the spreading of the virus [5–7].
The pandemic brought, not only the risk of death because of the infectious disease, but also psychological suffering and discomfort as a result of the risk of being...
infected by the virus and the great socioeconomic changes linked to the quarantine (such as social distancing, financial problems and changes in routines) [8]. These stressors were experienced by patients with a pre-existing psychiatric disease, but also by those with no psychiatric history, thereby resulting in new psychiatric problems [9, 10].
Below, we describe the case of an adult with no prior psychiatric history, who developed catatonia and showed severe depressive symptoms after facing economic struggles and quarantine isolation during the COVID-19 pandemic.
**Case presentation**
B is a 59 year-old man living in Rome with his wife, with no prior psychiatric history but whose mother had been treated by a specialist for a major depressive disorder. The couple lives in a residential suburban area of the Italian capital, and they both come from middle-low income families. B does not have any brothers or sisters, and he inherited the house where the couple lives. They got married after many years in a relationship, and they do not have any children. The couple runs a Shiatsu center that is their only source of income. They have a professional staff working with them, and this, in addition to the bills and the rent, makes the management costs of their business high. Thus, they have to work long hours in order to preserve their economic stability. They are both shy, and they have few friends.
B is described by his wife as a meticulous person with a strong sense of duty, concerned with orderliness and very emotional. His concern with orderliness affects his interpersonal relationships, especially with his family members. He finds it very difficult to express disagreement with his parents and with his wife. His greatest concern is his wife’s satisfaction and happiness in order to maintain harmony in their relationship, and this manifests itself in his work. For him, there is peace and serenity when things occur as expected. When unpredicted events occur, he becomes anxious and tries to resume his life as planned.
His sense of duty is illustrated by his way of relating to other people. For him, it is crucial to do not anything wrong and always to be correct and not in debt to others. At work, his main goal is to keep his clients satisfied and avoid any quarrel with them. If any problem occurs, he feels guilty, and he focuses on solving the problem.
All these pre-morbid elements belong to the *Typus Melancholicus* described by the German psychiatrist Hubertus Tellenbach (1914–1994) as a type of personality related to unipolar depression [11, 12].
On March 11th, they were obliged to close their center as a consequence of the COVID-19 lockdown. B became very concerned about their economic situation and, as reported by his wife, he could see no end to this epidemic and no future opportunity to restart their business and overcome COVID-19 related economic issues. He began to show a severe and rapidly progressive depression and to develop mood-congruent delusions related to pauperization and ruin, as well as hopelessness, anhedonia, apathy, starvation and insomnia. In the 10 days preceding his hospitalization, he slept only a few minutes each day, and he did not eat at all. Furthermore, his wife reported that the patient seemed unable to perceive and reply to environmental stimuli. The only words he uttered were about his hopelessness, ruin and financial crisis, and he was unable to see himself in the future. He had undergone a narrowing of the field of consciousness, as described by Janet in 1909, in both sensory perception and behavior [13], in his case, focused on financial problems related to COVID-19.
In the 2–3 days prior to his admission, he was reported as lying on the bed all day in a catatonic-like state, without speaking or replying to his wife. The only thought he was able to verbalize was his desire to die. He begged his wife to end his life, which led her to call an ambulance.
After his admission to the emergency room, he remained in a state of mutism. He would shake his head to reply to the psychiatrist’s questions. When he was asked by the doctor, “Do you think I can help you?” he shook his head to indicate “No” and moved his eyes. As listed in the Diagnostic and Statistical Manual of Mental Disorders Fifth Edition, there were three or more symptoms in order to diagnose catatonia [14]; more specifically, B displayed stupor, mutism and waxy flexibility. He cooperated for the nasopharyngeal swab to tested for COVID-19. A brain CAT scan indicated no organic lesions. A 4 mg Lorazepam vial and a 5 mg Olanzapine tablet were administered. The patient was then moved to our psychiatry ward for further observation and treatment.
Once in our psychiatry ward, Mr. B was assessed with several psychometric scales. We used the Columbia – Suicide Severity Rating Scale (C-SSRS), the Physical and Psychological Pain Scale, the Orbach Mental Pain Scale (OMMP), the Psychache Scale (PAS) and the Beck Hopelessness Scale (BHS) in order to evaluate his suicide risk, ideation and intention. Moreover, we tested for the presence of anxious-depressive disorders using the Hamilton Rating Scale for Depression (HAM-D), the Beck Depressive Inventory (BDI-II) and the Hamilton Rating Scale for Anxiety (HAM-A). Furthermore, we administered the Brief Psychiatric Rating Scale (BPRS) for a global psychiatric evaluation of the patient, the Childood Trauma Questionnaire (CTQ) to assess any traumatic history, and the Insight Scale (IS) to measure his level of insight.
He was discharged after 15 days, during which he showed slow improvement. He was diagnosed with “Major depressive disorder, single severe episode with no psychotic behavior”, and the following therapy was prescribed: Sertraline 50 mg 2 tablets at 8.00; Olanzapine...
5 mg 1½ tablet at 22.00 and Lorazepam 2.5 mg 1 tablet at 20.00.
Discussion and conclusions
The depressive episode of B resembles the catamnestic picture of the *Typus Melancholicus* depicted by Hubertus Tellenbach. The COVID-19 lockdown (with no clues about when it would end) disrupted his orderly world, and he felt powerless, unable to put everything back in place, unable to provide for his family and unable to fulfill his financial duties (such as taxes, rent and pay for his staff).
Moving from Tellenbach description of the Typus Melancholicus, we can observe an ongoing evolution toward endogenous depression starting with a pre-melancholic phase. In this stage, three main elements can be described: includence, remanence, and despair.
The constellation of *includence* is a condition in which the attempt to maintain orderliness conflicts with the need to overcome it [15]. This creates stress in the personality structure of the patient who tries to go beyond his own limitations without changing his attitude toward orderliness and consciousness. During the lockdown, the loss of an organized daily routine and the lack of control over events puts the core stability of this personality structure at risk. B’s concerns were about his Shiatsu center and his customers. The changes imposed by the lockdown put the stability of the “immutable world” of the patient at serious risk, including his relationships and the affective bonds linked to his job. This new situation (the lockdown and the economic stress) undermined his psychological state that, hitherto, had been stable.
The constellation of *remanence* concerns the “danger of remaining behind regarding the subject’s own expectations” [15]. In such a condition, such as during a lockdown where time seems to be stuck, the Typus Melancholicus can not see a future. Everything is frozen in an empty present. During the lockdown, it was impossible for Mr. B to engage in his typical “nomothetetic hyperactivity” and “hypnomic consciousness”: Mr. B was a very active person, working 12 h a day and always looking for some new life goals to accomplish. The lockdown clearly made it impossible for him to accomplish his unrealistic expectations. His situation overwhelmed Mr. B so that he felt “guilty” and “inauthentic” since he was not providing for his family as he felt that he should.
After these two constellations start to manifest, the patient begins the transition from a pre-morbid personality to a melancholy state, and perhaps an endogenous depression, as a result of the despair that is generated, leaving the patient feeling hopeless and helpless.
Another contribution to the role of pre-morbid personality on the development of psychiatric disorders was given by Ernst Kretschmer (1888–1964). The German psychiatrist focused on the existing correlation between biography and personality traits of patients later diagnosed as delusional with the introduction of the “sensitve delusion of reference” (sensitiver Beziehungswahn). He postulated that vulnerable and anancastic personality traits associated with real and repeated insults will first lead to a dysphoric and suspicious attitude, then to delusion-like ideas and, finally, to proper delusions. Kretschmer’s main purpose was to identify particular patterns that could eventually lead to delusional states. Kretschmer can be recognized as a pioneer, introducing the concept of “multidimensional psychiatry”, taking into account biological and biographical factors [16].
The pre-melancholic model described by Tellenbach might be a good model for understanding the psychological implications of the pandemic lockdown. The pandemic has elicited many psychiatric symptoms, especially for those with a pre-morbid personality structure which was in a fragile state before the pandemic began. The lockdown presents an opportunity to analyze the effects of socio-economic factors on the mental health of people with differing pre-morbid conditions during the “second wave” of affective disorders attendant upon the pandemic.
Abbreviations
COVID-19: Coronavirus disease 2019; SARS-CoV-2: Acute respiratory syndrome caused by the coronavirus 2; CAT: Computerized axial tomography
Acknowledgements
We would like to thank the patient for his cooperation.
Authors’ contributions
GS collected patient’s information and data, reviewed the literature and drafted the case report. LP mostly dealt with psychopathological features and drafted the paper. DL edited and reviewed the report for the submission. MP critically reviewed the case report and the diagnostic results and coordinated the preparation and revision of the manuscript. All authors read and approved the final manuscript.
Funding
Not applicable.
Availability of data and materials
This is a single-patient case report. Data sharing is not applicable to this article as no dataset were generated or analyzed in the present study.
Ethics approval and consent to participate
Not applicable.
Consent for publication
Written informed consent was obtained from the patient for the publication of this case report.
Competing interests
The authors declare that they have no competing interests.
Author details
1Psychiatry Residency Training Program, Faculty of Medicine and Psychology, Sapienza University of Rome, Rome, Italy. 2Department of Psychology, Stockton University, Galloway, NJ, USA. 3Department of Neuroscience, Mental Health and Sensory Organs, Faculty of Medicine and Psychology, Suicide Prevention Centre, Sant’Andrea Hospital, Sapienza University of Rome, Rome, Italy.
References
1. Chen N, Zhou M, Dong X, Qu J, Gong F, Han Y, et al. Epidemiological and clinical characteristics of 99 cases of 2019 novel coronavirus pneumonia in Wuhan, China: a descriptive study. Lancet. 2020;395(10223):507–13.
2. World Health Organization. Naming the coronavirus disease (COVID-19) and the virus that causes it. 2020. https://www.who.int/emergencies/diseases/novel-coronavirus-2019/technical-guidance/naming-the-coronavirus-disease-(covid-19)-and-the-virus-that-causes-it. Accessed 16 June 2020.
3. World Health Organization. WHO Coronavirus Disease (COVID-19) Dashboard. 2020. https://covid19.who.int/. Accessed 16 June 2020.
4. Remuzzi A, Remuzzi G. COVID-19 and Italy: what next? Lancet. 2020;395(10231):1225–8.
5. Saglietto A, D’Ascenzo F, Zoccai GB, De Ferrari GM. COVID-19 in Europe: the Italian lesson. Lancet. 2020;395(10230):1110–1.
6. Conte G. Decreto del Presidente del Consiglio dei Ministri 11 marzo 2020: Gazzetta Ufficiale; 2020. https://www.gazzettaufficiale.it/eli/id/2020/03/11/20A01605/sg. Accessed 16 June 2020.
7. Conte G. Decreto del Presidente del Consiglio dei Ministri 9 marzo 2020: Gazzetta Ufficiale; 2020. https://www.gazzettaufficiale.it/eli/id/2020/03/09/20A01558/sg. Accessed 16 June 2020.
8. Brooks SK, Webster RK, Smith LE, Woodland L, Wessely S, Greenberg N, et al. The psychological impact of quarantine and how to reduce it: rapid review of the evidence. Lancet. 2020;395(10227):912–20.
9. Yahya AS, Khawaja S, Chukwuma J. The impact of COVID-19 in psychiatry. Prim Care Companion CNS Disord. 2020;22:2.
10. Goldberg JF. Psychiatry’s niche role in the COVID-19 pandemic. J Clin Psychiatry. 2020;81(3):20.
11. Stanghellini G, Bentelli M. Assessing the social behavior of unipolar depressives: the criteria for typus melancholicus. Psychopathology. 2006;39(6):179–86.
12. Englebert J, Stanghellini G. Typus melancholicus and melancholia: theoretical synthesis using a clinical case. Encephale. 2016;42(1):105–11.
13. van der Hart O, Horst R. The dissociation theory of Pierre Janet. J Trauma Stress. 1989;2(4):397–412.
14. American Psychiatric Association, editor. Diagnostic and Statistical Manual of Mental Disorders. 5th ed. Arlington: American Psychiatric Association; 2013. p. 119–21. Catatonia.
15. Ambrosini A, Stanghellini G, Langer AL. Typus melancholicus from Tellenbach up to the present day. Actas Esp Psiquiatr. 2011;39(5):302–11.
16. Chaudhury S, Khan C. Understanding delusions. Ind Psychiatry J. 2009;18(1):3–18.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. | 2025-03-06T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2944,
1
],
[
2944,
8759,
2
],
[
8759,
14338,
3
],
[
14338,
16973,
4
]
]
} |
69d2d5029f23cc68098c13966796d75901fbb24f | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 5,
"total-fallback-pages": 0,
"total-input-tokens": 23049,
"total-output-tokens": 3518,
"fieldofstudy": [
"Medicine"
]
} | ORIGINAL ARTICLE
ENDOSCOPIC TYMPANOPLASTY TEMPORALIS FASCIA VERSUS CARTILAGE: COMPARATIVE STUDY
Naveen Kumar A. G1, Ravikeerthi G2
HOW TO CITE THIS ARTICLE:
Naveen Kumar A. G, Ravikeerthi G. “Endoscopic Tympanoplasty Temporalis Fascia versus Cartilage: Comparative Study”. Journal of Evolution of Medical and Dental Sciences 2015; Vol. 4, Issue 67, August 20; Page: 11648-11652, DOI: 10.14260/jemds/2015/1680
ABSTRACT: OBJECTIVE: To compare the graft acceptance rates and auditory outcomes of endoscopic cartilage tympanoplasty operations with those of endoscopic primary tympanoplasty using temporalis fascia in a homogenous group of patients. MATERIAL AND METHODS: This prospective study was conducted on 64 patients between the ages of 15 to 50 years. All patients had a central tympanic membrane perforation without infection in middle ear or upper respiratory tract. RESULTS: Anatomical results in terms of graft uptake and intact tympanic membrane over a period of 2 years showed good results both in 26(92.85%) cases in cartilage group and in 33(91.66%) cases in temporalis fascia group. The average post-operative Air bone gap in endoscopic fascia tympanoplasty group was 14.61db and 15.65db in endoscopic cartilage tympanoplasty group. CONCLUSION: Endoscopic tympanoplasty is a minimally invasive, sutureless procedure with better patient compliance. Tympanoplasty with cartilage graft has a high degree of graft take up. Tympanoplasty with cartilage provides better results in terms of integrity and intactness of the graft and less percentage of postoperative discharge from the operated ear. KEYWORDS: Cartilage, Temporalis fascia, Endoscopic tympanoplasty.
INTRODUCTION: Tympanoplasty is a procedure used to eradicate disease in the middle ear and to reconstruct the hearing mechanism.1 although tympanoplasty is a highly successful procedure in 90–95% of well ventilated middle ears, the prognosis is poorer in cases with eustachian tube dysfunction, infection, adhesive tympanic membrane, and total perforation in tympanic membrane. Since the introduction of tympanoplasty by Wullstein in 1952,2 and Zoellner in 1955,3 different types of grafts have been used to reconstruct tympanic membrane. These include temporalis fascia, periostia, perichondria, cartilage, vein, and fat.4
Cartilage was first used by Utech in 1959 but it was in 1963, when Salen,5 and Jansen,6 first reported the use of composite graft for tympanic membrane reconstruction.
Temporalis fascia remains the most commonly used material for tympanic membrane reconstruction, with a success rate of 93% to 97% in primary tympanoplasties.7 However, during the last decade, there has been a renewal of interest in the use of cartilage as an alternative to more traditionally used temporalis fascia graft.
The major advantage of cartilage is its stiffness and bradytrophic metabolism, which make it particularly suitable for difficult conditions, such as subtotal perforations, adhesive otitis, and revision cases,8 although there have been concerns that these may affect adversely acoustic transfer and the hearing.
There has been an increase in the use of cartilage in tympanoplasty with surgeons reporting improved outcomes when compared with temporalis fascia used alone.9
ORIGINAL ARTICLE
But recent studies fails to show any statiscal difference in post-operative hearing outcome when cartilage is compared to fascia or perichondrium as grafting material in tympanoplasty. The purpose of this study was to compare the graft acceptance rates and auditory outcomes of endoscopic cartilage tympanoplasty operations with those of endoscopic primary tympanoplasty using temporalis fascia in a homogenous group of patients.
METHODS: The present study is conducted at the department of otorhinolaryngology, Sapthagiri institute of medical science & research Centre, Bangalore. There were total of 64 patients in the 15-50 year age group suffering from chronic suppurative otitis media. The inclusion criteria included were a dry and non-discharging ear at least for three weeks, a conductive hearing loss with good cochlear reserve and intact ossicular chain. The exclusion criteria were squamosal variety of chronic otitis media, sensorineural hearing loss and patients less than 15yrs.
The cases were randomly selected using a periodic random number to avoid a bias in selection of cases. All patients were operated endoscopically. Pre and post-operative PTA was performed. The air bone gap of each patient was calculated at 500 Hz, 1000 Hz, 2000 Hz both pre and postoperatively and compared Anesthesia- Local Infiltration with (2% lignocaine with 1:100000 adrenaline).
The temporalis fascia was harvested through a separate incision 2cm above the superior attachment of pinna in 36 no. of cases. Cartilage was harvested from the tragus in 16 cases and from conchal cartilage in 12 cases. The tympanomeatal flap is raised using circular knife and the margin of the perforation is freshened. The continuity and the mobility of ossicles are visualized subsequently.
After taking care of the ossicular continuity the graft/tragal or conchal cartilage [Fig 1] harvested is placed over the intact ossicles and the tympanomeatal flap is placed over the graft. The meatus is packed with gel foam soaked in antibiotic solution. All the steps were performed under endoscopic vision.
RESULTS: The patients were in the age group of 15-50 years with mean of 31 years of age. The total no. of patients were 64 of which 24 were male and 40 females. Of the total patients 36 underwent endoscopic fascia tympanoplasty and rest 28 underwent endoscopic cartilage tympanoplasty. All cases had intact ossicular chain intraoperatively. The preoperative average ABG was 31 and 29db for fascia and cartilage groups respectively.
Anatomical results in terms of graft uptake and intact TM over a period of 2 years showed good results both in 26(92.85%) cases in cartilage group [Fig. 2] and in 33(91.66%) cases in temporalis fascia group. Two residual perforation were seen in cartilage group with no retraction. In fascia group, there were 3 failures [Fig. 3] which included one retraction and two perforations. The average post-operative ABG in endoscopic fascia tympanoplasty group was 14.61db and 15.65db in endoscopic cartilage tympanoplasty group.
**Figure 2:** Endoscopic picture of good graft uptake [03 months post cartilage tympanoplasty]
**Figure 3:** Residual perforation post tympanoplasty with temporalis fascia graft.
**DISCUSSION:** Chronic suppurative otitis media is a very common condition in the practice of otolaryngology both in developed as well as developing countries & Tympanoplasty is one of the most common forms of surgery in otology. The cartilage is experiencing a renaissance in ear surgery because it appears to offer an extremely reliable method for reconstructing of the tympanic membrane.10
The results are generally quantifies in terms of take up of the grafts and post-operative hearing improvement, which is assessed subjectively and objectively using pure tone audiometry & speech reception threshold.
Gerber, et al.\textsuperscript{1} studied the hearing results in patients who had cartilage tympanoplasty. The results were comparable to temporalis fascia. They advocated that a cartilage graft is useful to prevent recurrence or progression of postoperative retraction pockets.
Dornhoffer,\textsuperscript{2} found the same results after comparing cartilage with fascia. Duckert,\textsuperscript{3} found excellent hearing results with cartilage with closure of the ABG to within 10db was achieved in 87% of the tympanoplasty. Milewski,\textsuperscript{4} reported a post-operative average ABG of <30db in 92.4% and <10db in 43.6% of 197 tympanoplasty using cartilage. Lin, et al., also observed good results and advocated that this technique be used in older patients and in patients with co-morbidities.\textsuperscript{5}
In our series, the hearing improvement in audiometric parameters was comparable in both groups. On the other hand closure of the perforation with cartilage compares favourably with temporalis fascia techniques with take up rates varying from 91-96%. Cartilage tympanoplasty has many advantages in situations such as recurrent, residual, total perforations, chronic mucosal dysfunction or severely atelectatic tympanic membranes, whereas fascia and perichondrium undergo atrophy and subsequent failure.\textsuperscript{6} The cartilage tympanoplasty offers an otologist another reliable material in his armamentarium for tympanic membrane reconstruction.
In our study 7% reperforation seen in cartilage group & 8.3% reperforation in facia group. In our present study no retraction or lateralization was observed in average follow up of 2years.
**SUMMARY AND CONCLUSION:** Endoscopic tympanoplasty has following advantage it’s sutureless, minimally invasive & reduced operative time. The cartilage tympanoplasty offers an otologist another reliable material in his armamentarium for tympanic membrane reconstruction.
Cartilage is a reliable graft material for reconstruction of the tympanic membrane in COM with adhesive tympanic membrane, perforations especially in total and anterior perforations.
Cartilage is also recommended in recurrent perforations, older patients and in patients with co-morbidities.
**REFERENCES:**
1. Aina JG, Lloyd BM, Dennis P. Committee on conservation of hearing, American Academy of Ophthalmology and Otalaryngology: Standard classification for surgery of chronic ear disease. Arch Otalaryngol 1965; 81:204.
2. Wullstein HL. Functional operations in the middle ear with split thickness skin graft. Arch Otorhinolaryngol 1953; 161:422Y35.
3. Zoellner F. The principles of plastic surgery of the sound conducting apparatus. J Laryngol Otol 1955; 69:567.
4. Heermann H. Tympanic membrane plastic with temporal fascia. Hals-Naser-Ohren 1960; 9:136.
5. Salen B. Myringoplasty using septum cartilage Acta Otalaryngol 1963 Suppl 188:82-91.
6. Jansen C.Cartilage-tympanoplasty.laryngoscope.1963; 73:1288-1302.
7. Sheehy JI, Anderson RG. Myringoplasty -A review of 472 cases. Ann Otol Rhinol Laryngol 1980; 89:331.
8. Neumann A, Kevenhoerster K, Gostian AO. Long-term results of palisade cartilage tympanoplasty. Otol Neurotol.2010; 3:1:936-9.
9. Onal K, et al. Perichondrium/cartilage island flap and temporalis muscle fascia in Type I tympanoplasty. J Otolaryngol Head Neck Surg 2011; 40:295.
10. Adkins WY. Composite autograft of tympanoplasty and tympanomastoid surgery. Laryngoscope 1990; 100:244-247.
11. Gerber MJ, Mason JC, Lambert PR. Haring results after primary cartilage tympanoplasty. Laryngoscope 2002; 110:1994-1999.
12. Dornhofer JO. Hearing results with cartilage tympanoplasty. Laryngoscope. 1997; 107:1094-1099.
13. Duckert LG, Muller J, Makielski KH, Helms JO. Composite autograft 'sheild' reconstruction of remnant tympanic membranes AmJ Oto.1995; 116:21-26.
14. Milewski C. Composite graft tympanoplasty in the treatment of ears with advanced middle ear pathology. Laryngoscope. 1993; 103:1352-1356.
15. Lin YC, Wang WH, Weng HH, Lin YC. Predictors of surgical and hearing long-term results for inlay cartilage tympanoplasty. Arch Otolaryngol Head Neck Surg. 2011 Mar; 137(3):215-9.
16. Chen XW, Yang H, Gao RZ, Yu R, Gao ZQ. Perichondrium/cartilage composite graft for repairing large tympanic membrane perforations and hearing improvement. Chin Med J (Engl). 2010 Feb 5; 123(3):301-4.
AUTHORS:
1. Naveen Kumar A. G.
2. Ravikeerthi G.
PARTICULARS OF CONTRIBUTORS:
1. Assistant Professor, Department of ENT, Sapthagiri Institute of Medical Sciences and Research Centre, Bangalore.
2. Assistant Professor, Department of ENT, Sapthagiri Institute of Medical Sciences and Research Centre, Bangalore.
FINANCIAL OR OTHER COMPETING INTERESTS: None
NAME ADDRESS EMAIL ID OF THE CORRESPONDING AUTHOR:
Dr. Naveen Kumar A. G,
Assistant Professor,
Department of ENT,
Sapthagiri Institute of Medical Sciences and Research Centre, Bangalore-90.
E-mail: [email protected]
Date of Submission: 06/08/2015.
Date of Peer Review: 07/08/2015.
Date of Acceptance: 17/08/2015.
Date of Publishing: 18/08/2015. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3264,
1
],
[
3264,
5800,
2
],
[
5800,
6937,
3
],
[
6937,
10351,
4
],
[
10351,
12223,
5
]
]
} |
071b449c159b4c5150a6e2e885363ad9b97da853 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 6,
"total-fallback-pages": 0,
"total-input-tokens": 18187,
"total-output-tokens": 6114,
"fieldofstudy": [
"Medicine"
]
} | A study on the relationship between mouth breathing and facial morphological pattern
Ana Paula Bianchini¹, Zelita Caldeira Ferreira Guedes², Marilena Manno Vieira³
Summary
Breathing is responsible for facial and cranial morphology development. **Aim**: investigate in order to see if there is any relationship between oral breathing and facial type. **Material and Methods**: 119 male and female teenagers, with ages ranging between 15 and 18 years. The sample was separated in two groups: A-50 teenage oral breathers, 28 males and 22 females; and group B- 69 teenage nasal breathers, 37 males and 32 females. The sample was collected at the Centro de Atendimento e Apoio ao Adolescente do Departamento de Pediatria da UNIFESP/EPM. We evaluated breathing and facial measures. **Results**: by means of anthropometric indexes we classified facial types and associated them with the person's breathing type, Hypereuriprosopic (Total=0; oral breathers 0%; nasal breathers 0%); Euriprosopic (Total=14; oral breathers 2.52%; nasal breathers 9.24%); Mesoprosope (Total=20; oral breathers 19.32%; nasal breathers 21.01%); Leptoprosopic (Total=37; oral breathers 14.29%; nasal breathers 16.81%; Hyperleptoprosopic (Total=48; oral breathers 5.89% nasal breathers 10.92%). The mesoprosopic facial type was found in 48 teenagers (40.33%) of whom 25 (21.01%) were oral breathers and 23 (19.32%) were nasal breathers. **Conclusion**: it was not possible to prove the existence of an association between oral breathing and facial type.
Key words: mouth breathing, face, anthropometry.
¹ Master's degree, speech therapist.
² Doctoral degree, assistant professor of Human Communication Disorders, Speech Therapy Department, Sao Paulo Federal University.
³ Doctoral degree, assistant professor of Human Communication Disorders, Speech Therapy Department, Sao Paulo Federal University.
Address for correspondence: Ana Paula Bianchini - Rua Brasílio Machado 330 Santo André SP.
Tel. (0xx11) 9356-6853.
Paper submitted to the ABORL-CCF SGP (Management Publications System) on March 3rd, 2006 and accepted for publication on March 31th, 2006. cod. 1757.
INTRODUCTION
Normal breathing is nasal, making it possible for inhaled air to be purified, filtered, warmed and humidified before reaching the lungs. Nose breathing protects the upper airways and is responsible for adequate craniofacial development.
Mouth breathing may result from upper airway obstruction or from habit wherein air flows through the mouth. According to the literature, this form of breathing may change the growth pattern of the face and lead to morphological and functional alterations in the whole organism.
Certain authors, such as Moccellin & Ciuff (1997), Marchesan (1998), Lusvarghi (1999) and Di Francesco (1999), have defined mouth breathers as those persons with half-open, dry and cracked lips, an anteriorized tongue, weak mandibular elevator muscles, a deep and narrow palate, dental alterations and predominantly vertical face growth.
Altered facial growth in mouth breathers has been studied by various health care professionals, including medical doctors, speech therapists and orthodontists.
Anthropometry is that part of anthropology that investigates the body measurements. Cephalometrics is that part of anthropometry that studies the linear measurements and angles of the head.
Indices are used in anthropology to describe sizes regardless of absolute values. The facial morphological index is the centesimal ratio between the morphological height and width. This index classifies faces as leptoprosopic - long and narrow face; euryprosopic - wide and short face; and mesoprosopic - balanced facial width and height. (Avila, 1958).
The aim of this study was to verify a possible relation between mouth breathing and the facial type, to ascertain the validity of statements in the literature describing mouth breathers as having a long face.
MATERIAL AND METHOD
We assessed 119 male and female adolescents aged between 15 and 18 years. The sample was divided into two groups: group A - 50 mouth-breathing adolescents, 28 male and 22 female, and group B - 69 nose-breathing adolescents, 37 male and 32 female. The sample was obtained from the Adolescent Clinic and Support Center of the Pediatrics Department, UNIFESP/ EPM.
Adolescents that had genetic syndromes, malformation of the mouth and face, mental disability, cranial trauma, mutilation and dental anomalies of number and or size were excluded from the study.
The type of dental occlusion was not taken into account.
The mouth-breathing group contained adolescents that had mixed or mouth breathing.
Subjects underwent phonoaudiological assessments that consisted of the following steps:
1) a clinical history
2) a clinical phonoaudiological test.
1) Clinical history:
The clinical history was taken from the participant and/or the caretaker to obtain identification data (name, age, sex, race) and information about respiratory conditions such as rhinitis, sinusitis, asthma, bronchitis, frequent colds, tonsillitis, daytime and/or nighttime mouth breathing and nighttime snoring.
2) Clinical phonoaudiological test:
The clinical test was composed of the following steps:
A - Assessment of breathing.
Based on direct observation of the resting position and on tests.
A1 - Lip position of rest, classified as open or closed. Open was when the patient’s lips did not touch and when muscular effort was required for contact between the upper and lower lip, a position that was not maintained for long.
A2 - Breathing was also assessed by filling the mouth with water; if the patient was unable to keep the mouth closed for at least three minutes, he or she would be considered a mouth breather. This test was supplemented by observation made during other clinical tests and by information obtained directly from the patients. (Vieira, 1986).
A3 - An Altman’s nasal breath mirror (in millimeters), placed below the nostrils, was used to assess the presence and symmetry of nasal airflow. Patients were instructed to breathe normally for a few seconds, after blowing their noses.
B) Assessment of the face
The facial index, the relation between facial height and width, was calculated to find the facial type. Measurements were taken directly from the face of each adolescent.
Subjects were seated with their hips, knees and ankles at 90° for the clinical test. Feet were flat on the ground, the spine was erect and touching the back of the chair. The head was oriented according to Frankfurt’s plane, parallel to the horizontal plane and with its median sagittal plane perpendicular to the horizontal plane.
The facial height, or the length of the anatomical face, was measured as a straight line from the nasion to the gnathion. The nasion is the cephalometric point on the midline of the face that is located on the nasofrontal suture. The gnathion is the most anterior and inferior point on the suture of the mentum along the midline of the face; it may be palpated in living persons.
The facial width, the distance between the most
laterally projecting points of the zygomatic arch, was measured between the right and left zygions. It may be established in living persons.
Facial height and width were measured in millimeters using a Mitutoyo model 500143 B digital pachymeter to which a 9 cm and 10 cm metal piece was attached on the external tips to make it possible for the rods to measure the facial height and width (zygions).
The facial proportion was obtained from the facial index or morphological facial index, which was based on these measurements. The facial index or morphological facial index is the centesimal relation between the height and width of the face, as follows:
\[
\text{Facial Morphological Index} = \frac{\text{Facial height}}{\text{Bizygomatic diameter}} \times 100
\]
This index is used to classify the facial types, as follows: hypereryprousopic - X-78.9; euryprosopic - 79.0-83.9; mesoprosopic - 84.0-87.9; leptoprosopic - 88.0-92.9; hyperleptoprosopic - 93.0-X. (Avila, 19585).
The UNIFEST/EPM Research Ethics Committee approved this study (protocol number 0738/03) and subjects signed a free informed consent form.
**RESULTS**
The hypereuryprosopic facial type was not found in our facial frequency study of male and female mouth and nose breathing groups. The most frequent facial type in males was the hyperleptoprosopic face, found in 33 adolescents (27.73%). In females, the most frequent facial type was the leptoprosopic face, found in 16 adolescents (13.45%). This difference is statistically significant, at \( p=0.008 \) (\( p<0.05 \)) (Table 1).
A comparative analysis between mouth and nose breathing groups based on Dunnett’s test found no predominance of one facial type over any other (Table 5).
| Gender | Female | Male | Total |
|--------|--------|------|-------|
| Nº | % | Nº | % |
| Hypereuryprosopic | 0 | 0 | 0 | 0 |
| Euryprosopic | 11 | 9.24 | 3 | 2.52 | 15 | 1.76 |
| Mesoprosopic | 12 | 10.08 | 8 | 6.73 | 20 | 16.80 |
| Leptoprosopic | 16 | 13.45 | 21 | 17.65 | 37 | 31.10 |
| Hyperleptoprosopic | 15 | 12.61 | 33 | 27.73 | 48 | 40.34 |
| Total | 54 | 45.38 | 65 | 54.62 | 119 | 100 |
| Breathing | Nasal | Oral | Total |
|-----------|-------|------|-------|
| Nº | % | Nº | % | Nº | % |
| Hypereuryprosopic | 0 | 0 | 0 | 0 | 0 |
| Euryprosopic | 11 | 9.24 | 3 | 2.52 | 14 | 11.76 |
| Mesoprosopic | 25 | 21.01 | 23 | 19.32 | 48 | 40.33 |
| Leptoprosopic | 20 | 16.81 | 17 | 14.29 | 37 | 31.10 |
| Hyperleptoprosopic | 13 | 10.92 | 7 | 5.89 | 20 | 16.81 |
| Total | 69 | 57.98 | 50 | 42.02 | 119 | 100 |
| Breathing | Nasal | Oral | Total |
|-----------|-------|------|-------|
| Nº | % | Nº | % | Nº | % |
| Hypereuryprosopic | 0 | 0 | 0 | 0 | 0 |
| Euryprosopic | 8 | 14.81 | 3 | 5.55 | 11 | 20.37 |
| Mesoprosopic | 8 | 14.81 | 4 | 7.4 | 12 | 22.23 |
| Leptoprosopic | 10 | 18.52 | 6 | 11.11 | 16 | 29.62 |
| Hyperleptoprosopic | 6 | 11.12 | 9 | 16.66 | 15 | 27.78 |
| Total | 32 | 59.26 | 22 | 40.74 | 54 | 100 |
| Breathing | Nasal | Oral | Total |
|-----------|-------|------|-------|
| Nº | % | Nº | % | Nº | % |
| Hypereuryprosopic | 0 | 0 | 0 | 0 | 0 |
| Euryprosopic | 3 | 4.61 | 0 | 0 | 3 | 4.61 |
| Mesoprosopic | 5 | 7.70 | 3 | 4.61 | 8 | 12.31 |
| Leptoprosopic | 10 | 15.39 | 11 | 16.93 | 21 | 32.31 |
| Hyperleptoprosopic | 19 | 29.23 | 14 | 21.53 | 33 | 50.77 |
| Total | 37 | 56.93 | 28 | 43.07 | 65 | 100 |
COMMENTS
The investigation of facial types in mouth and nose breathing males and females showed that there were 33 male hyperleptoprosopic adolescents (27.73%) and 16 female leptoprosopic adolescents (13.45%). The X² test revealed that there was a statistically significant difference between sexes (Table 1).
Our results are similar to those published by Gross, Kellum Hale et al. (1989). In their comparison between females and males they found the long face in 38.5% of their male subjects and in 30.9% of their females subjects out of a sample containing 133 subjects.
The study of facial types in mouth breathers showed that the mesoprosopic face was the most frequent facial type in 23 adolescents (19.32%) (Table 2). These findings are similar to those of Ferreira (1999), who also found that a higher proportion of his mouth-breathing subjects had the mesoprosopic face (5 patients - 44%). Our findings are also similar to those of Sabatosk & Maruo (2002) and Aidar, who “found 18 mesoprosopic facial types in a study of mouth breathers (40.90%)” (personal communication).
Our results disagree with those of Mattar (2002) who found a correlation between facial morphology and the type of breathing; in this study, mouth breathers (84.68% subjects) were predominantly dolichocephalic and nose breathers were mostly mesofacial (88.07 subjects).
Our results also disagree with those of Harterink & Vig (1989). Fields, Mocellin & Giuff (1997), and Manganello (2002), who state that the mouth-breathing habit could change the face and muscle balance, resulting in a higher rate of the long face (“Aidar L, Mota J, Marins C. 2004, personal communication”).
Investigation of the face type in nose breathers revealed that there were 25 mesoprosopic adolescents (21.01%), 20 leptoprosopic adolescents (16.81%), 13 hyperleptoprosopic adolescents (10.92%) and 11 euryprosopic adolescents (9.24%) (Table 2).
These results are similar to those of Jabur (1997), who found a balance in the distribution of patients with vertical growth (9 subjects - 39.13%) and patients with a harmonic pattern (10 subjects - 43.47%). Our results also agree with those of Vig, Sarver, Hall and Warren (1981), who found normal facial proportions and labial competence in 10 subjects (35.71%).
A higher frequency of the mesoprosopic facial type in mouth breathers was not expected; in the literature many authors, such as Tourne (1990) and Mocellin & Giuff (1997), have stated that there is a relation between the long face and mouth breathing. According to these authors, mouth breathers keep their mouths constantly open and the tongue in a lowered position, without exerting pressure on the palate, resulting in external compression of the maxilla by the external muscles of the mouth. The hard palate tends to deepen, forming an ogival palate. The palate puts upward and forward pressure on the cartilaginous septum, causing its deviation and the elongated and narrowed face.
Investigation of the face type frequency in female nose and mouth breathers revealed that there were 10 leptoprosopic adolescents (18.52%) and 9 hyperleptoprosopic adolescents (16.66%) (Table 3).
In males, the hyperleptoprosopic face was the most frequent facial type in both nose breathers (19 adolescents - 29.23%) and mouth breathers (14 adolescents - 21.53%) (Table 4).
We were unable to compare these results with the literature, as we found no published papers describing the frequency of facial types in adolescents for each sex.
A comparative analysis between the nose-breathing group and the mouth-breathing group, based on the
analysis of variance and Levene’s test at p<0.001, revealed different means. We therefore applied Dunnett’s test, enabling us to compare the mean facial indices; we found no frequency differences between facial types (Table 5).
Our results agree with those of Linder Aronson (1970),18 who found a low frequency of adenoid patients with an increased facial height (25.9%). These findings are different from those published by authors that used different methods, such as Mocellin & Ciuff (1997) and Hartgerink, Vig (1989).12 Their results suggested that mouth breathing influenced facial form in 58.4% of their patients that were labially incompetent, and 56.2% of their patients that were labially competent. Manganello, Silva and Aguiar (2002) found that 40% of mouth breathers had an increased facial height. Principato (1986) concluded that 67% of his orthodontic patients had an abnormal growth of the lower facial height and increased nasal resistance to the passage of air.
Our findings are also different from those of Jabur et al. (1997),15 who found an increased frequency of patients with a vertical growth pattern and mouth breathing (9 subjects - (39.13%) and 10 patients (43.47%) with a harmonic pattern.
FINAL COMMENTS
Based on our findings we were unable to demonstrate a relation between mouth breathing and increased facial height. We thus agree with Bhat & Enlow (1995) and Kluemper (1995) who in their papers showed that there is individual, genetic and regional variation.
There is much controversy about whether mouth breathing leads to the long face syndrome. Many clinicians believe that delayed growth of the dentofacial complex is the result of environmental and genetic forces. Recent findings suggest that mouth breathing by itself is not necessarily harmful for growth. Some hereditary patterns may favor mouth breathing compared to others. Mouth breathing in a subject with a vertical growth pattern and mouth breathing (9 subjects - (39.13%) and 10 patients (43.47%) with a harmonic pattern.
CONCLUSION
- We found no relation between mouth breathing and facial type.
- We found no statistically significant difference in the frequency of facial types in nose and mouth breathers.
- The mesoprosopic type was the most frequent facial type found in the current study; it was present in 25 adolescents (21.01%) of the mouth-breathing group, and in 23 adolescents (19.32%) of the nose-breathing group.
REFERENCES
1. Mocellin L, Ciuff, CV. Alteração oclusal em respiradores bucais. J Bras Ortod Ortop Maxilar 1999;2:47.
2. Marchesan IQ. Aspectos clínicos da motricidade oral. In: Fundamentos em fonoaudiologia. Rio de Janeiro: Guanabara Koogan;1998. p.23-36.
3. Lusvarghi L. Identificando o respirador bucal. Rev APCD 1999;53(4):14-19.
4. Di Francesco RC. Respirador bucal: a visão do otorrinolaringologista. J Bras Fonoaudiol 1999;1:56-60.
5. De Avila JB. Antropologia racial In: Antropologia física: Introdução. Rio de Janeiro: Agir; 1958. p.147-60.
6. Vieira MM. Da influência da deglutição atípica sobre os resultados do tratamento ortodontico da mal-oclusão dental [tese de mestrado]. São Paulo: Escola Paulista de Medicina; 1986.
7. Rosner B. Fundamentals of biostatistics. 2o ed. Boston: Duxbury Press; 1986.
8. Gross AM, Kellun MGD, Hale EMCD et al. Myofunctional and dentofacial Relationships in second grade children. Angle Orthod 1989;60(4):247-53.
9. Ferreira ML. A incidência de respiradores bucais em indivíduos com oclusão Classe II. J Bras Ortod Ortop Facial 1999;21:223-40.
10. Sabatoski CV, Maruo H, Camargo ES, Oliveira JHG. Estudo comparativo de dimensões craniofaciais verticais e horizontais entre crianças respiradoras bucais e nasais. J Bras Ortod Ortop Facial 2002;7(39):246-57.
11. Mattar SEM. Padrão esquelético e caracteristicas oclusais de crianças respiradoras bucais e nasais [tese de mestrado]. Ribeirão Preto: Universidade de São Paulo; 2002.
12. Hartgerink DV, Vig PS. Lower anterior facial height and lip incompetence: do not predict nasal airway obstruction. Angle Orthod 1989;59(1):17-22.
13. Fields HW, Warren DW et al. Relationship between vertical dentofacial morphology and respiration in adolescents. Am J Orthod Dentofacial Orthop 1991;99(2):147-54.
14. Manganello LC, Silva AAF, Aguiar, MB. Respiração bucal e alterações Dentofaciais. Rev Assoc Paul Cirur Dent 2002;56(6):419-22.
15. Jabur LB, Macedo AM, Craveiro LH, Nunes MM. Estudo clínico da correlação entre padrão respiratório e alterações ortodonticas e miofuncionais. Rev Odontol UNICID 1997;9(2):105-17.
16. Vig PS, Sarver DM, Hall DJ, Warren DW. Quantitative evaluation of nasal airflow in relation to facial morphology. Am J Orthod 1981;79(3):263-72.
17. Tourne PML. The long face syndrome and impairment of the nasopharyngeal airway. Angle Orthod 1990;60(3):167-76.
18. Linder-Aronson S. Adenoids: their effect on mode of breathing and nasal airflow and their relationship to characteristics of the facial skeleton and the dentition. Acta Otolaryngol Suppl. 1970;265:5-132.
19. Principato JJ, Kerrigan JP, Wolf P. Pediatric nasal resistance and lower anterior vertical face height. Otolaryngol Head Neck Surg 1986;95 (2):226-9.
20. Bhat M, Enlow DH. Facial variations related to headform type. Angle Orthod 1985;55(1):269-80.
21. Kluemper GT, Vig PS, Vig KWL. Nasorespiratory characteristics and craniofacial morphology. Eur J Orthod 1995;17(1):491-5. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2141,
1
],
[
2141,
7097,
2
],
[
7097,
10862,
3
],
[
10862,
14466,
4
],
[
14466,
19272,
5
],
[
19272,
19860,
6
]
]
} |
ffd5547b96f2f1b2c37350241176ab3ca91bb2e0 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 4,
"total-fallback-pages": 0,
"total-input-tokens": 15113,
"total-output-tokens": 4573,
"fieldofstudy": [
"Computer Science"
]
} | 1 Introduction
Our approach to multilingual named entity (NE) recognition in the context of the CoNLL Shared Task consists of the following ingredients:
Feature engineering A human expert (though not necessarily a language expert) determines relevant features to be used to determine whether or not a word is part of a named entity.
Extraction In a first phase a conditional Markov model extracts candidate NE phrases, but does not classify them yet into LOC, ORG, etc.
Classification In the second phase a classifier looks at candidate phrases proposed by the extractor in their sentential context and labels them as LOC, ORG, etc.
2 Feature engineering
Languages differ widely in the conventions they use to signal named entities. Spanish, French, and English use the case distinction of the modern Roman alphabet to indicate proper names, and upper case is a fairly good indicator of a proper name. The situation is quite different in German, where upper case is a poor cue. In traditional Chinese scholarly works, certain proper names are indicated by underlining, and without that form of annotation locating a proper name would seem quite challenging. In light of the diversity found across languages and orthographic conventions, it is unclear whether any effective multilingual named entity extraction system will ever be built that does not rely on human expertise for customizing it to a particular language and domain.
Since we started by building a Spanish system without knowing what other language it would have to be applied to, the features we ended up using are all rather simple and generic in nature. No language experts were consulted. In the extraction component, we look at the orthographic string of a word with accents removed (since there are some inconsistencies regarding the presence or absence of accents), and we determine whether it starts with an upper case character. For the classification component we look at entire candidate phrases, and determine the length of the phrase, its position in a sentence, the immediately surrounding words, and what words occur within the phrase. For a word inside the phrase we determine whether it starts with and upper or lower case character (or neither), whether it contains any upper case or lower case characters (or neither), and we also use the entire orthographic string with accents removed.
Fortunately, these features carry over fairly well to Dutch, the second language of the Shared Task, and may also have been sufficient for French or English, but would probably fall short for German. Needless to say, radically different orthographic systems may require entirely different approaches, so the multilingual scope of our proposal is fairly limited.
3 Extraction
The extraction component discards the specific labels LOC, ORG, etc. (from now on we refer to these as sort labels) and only predicts whether a token is at the beginning of (B), inside (I), or outside (O) a phrase (we will call these bare labels phrase tags). While this move is not unproblematic, we determined empirically that overall performance was higher using only bare phrase tags without sort labels, compared with a single-phase approach that tries to predict phrase tags and sort labels together using a single (conditional or joint) Markov model. The underlying rationale was to enable the extractor to concentrate on any morpho-syntactic regularities across different sorts of phrases without having to determine the sort label yet, which may require
more context: for example, Spanish named entities can contain *de*, and this is the case across all sorts; or certain names like *Holanda* are ambiguous between **LOC** and **ORG** depending on whether they refer to countries on the one hand, or their governments or national soccer teams on the other. In light of this it makes sense to delay the assignment of sort labels and concentrate on extracting candidate phrases first.
Our extraction approach uses conditional Markov models, and we shall illustrate it using a first order model. Generalizations to higher order models are straightforwardly possible. The problem we are trying to solve is this: we want to find a sequence of phrase tags $\mathbf{t}$ given a sequence of words $\mathbf{w}$. We find the optimal $\mathbf{t}^*$ as
$$
\mathbf{t}^* = \arg \max \limits_{\mathbf{t}} P(\mathbf{t}|\mathbf{w}) = \arg \max \limits_{\mathbf{t}} \frac{G(\mathbf{w}, \mathbf{t})}{W(\mathbf{w})},
$$
where the conditional model $P$ is expressed in terms of a joint generative model $G$ of tags and words, and a language model $W$.
Since $\mathbf{t}$ and $\mathbf{w}$ have the same length $n$, we regard the training data as a sequence of pairs, rather than a pair of sequences (the two representations are isomorphic via a zipper operation familiar to Python or Haskell programmers), and decompose the generative model $G$ using a first order Markov assumption:
$$G(\mathbf{w}, \mathbf{t}) = S(w_1, t_1) \prod_{i=2}^{n} G_1(w_i, t_i|w_{i-1}, t_{i-1}).$$
Doing the same for $W$ and using a designated start event $(w_0, t_0)$ instead of the start distribution $S$ we obtain:
$$P(\mathbf{t}|\mathbf{w}) = \prod_{i=1}^{n} \frac{G_1(w_i, t_i|w_{i-1}, t_{i-1})}{W_1(w_i|w_{i-1}).}$$
We further decompose the conditional distribution $G_1$ as follows:
$$G_1(w_i, t_i|w_{i-1}, t_{i-1}) = T(t_i|w_i, w_{i-1}, t_{i-1}) U(w_i|w_{i-1}, t_{i-1}).$$
In addition to the first order assumption above, the only other assumption we make is that $U(w_i|w_{i-1}, t_{i-1}) = U(w_i|w_{i-1})$, which allows us to conclude that $U = W_1$, and so our conditional sequence model simplifies to
$$P(\mathbf{t}|\mathbf{w}) = \prod_{i=1}^{n} T(t_i|w_i, w_{i-1}, t_{i-1}).$$
This is starting to look familiar: $T$ is a conditional distribution over a finite set of phrase tags, so in principle any probabilistic classifier that uses (features derived from) the variables that $T$ is conditioned on could be substituted in its place. Approaches like this have apparently been used informally in practice for some time, perhaps with a classifier instead of $T$ that does not necessarily return a proper probability distribution over tags. Probability models that predict the next tag conditional on the current tag and an observed word have been criticized for a weakness known as the Label Bias Problem (Lafferty et al., 2001); on the other hand, the practical effectiveness of approaches like the one proposed here for a very similar task was demonstrated by Punyakanok and Roth (2001).
Finding the optimal tag sequence for a given sequence of words can be done in the usual fashion using Viterbi decoding. Training is fully supervised, since we have labeled training data, but could in principle be extended to the (partly) unsupervised case. We only implemented supervised training, which is mostly trivial. When using a simple conditional next-tag model it is especially important to have good estimates of $T(t_i|w_i, w_{i-1}, t_{i-1})$. We use a strategy of backing off to less and less informative contexts. In the worst case, $T(t_i|w_{i-1})$ can be estimated very reliably from the training data (in fact, good estimates for much longer tag histories can be found). When conditioning on words, the situation is rather different. For example, we see relatively few events of the form $(w_i, w_{i-1}, t_{i-1})$ in the training data (out of the space of all possible events of that form), and so we may back off to $(w_i, u_{i-1}, t_{i-1})$, where $u_{i-1}$ is binary valued and indicates whether the preceding word started with an upper case letter. We have not determined an optimal back-off strategy, and for now we use an intuitively plausible strategy that tries to use as much conditioning information as possible and backs off to strictly less informative histories. In all cases it is important to always condition on the preceding tag $t_{i-1}$, or else we would be left with no information about likely tag sequences.
We used first and second order models of this form and manually searched for good parameter settings on a held-out portion of the training data. It turns out that the second order model performs about the same as the first order model, but is at a disadvantage because of data sparseness. Therefore we only consider first order models.
in the rest of this paper. The performance of the first order model on the development data sets is summarized in Table 1. Note that these figures can be obtained for any system by first piping its output through `sed` using the command `s/-\(LOC\|MISC\|ORG\|PER\)/-FOO/g`. As will become clearer below, within each language it so happens that the extraction component performs better than the classification component, i.e. for now the performance bottleneck is the classification component.
| Language | Precision | Recall | $F_{\beta=1}$ |
|----------|-----------|--------|---------------|
| Spanish dev. | 87.60% | 86.86% | 87.23 |
| Dutch devel. | 85.84% | 84.55% | 85.19 |
Table 1: Extraction results obtained for the development data sets for the two languages used in this shared task.
### 4 Classification
The candidate phrases proposed by the extraction component are subsequently annotated with sort labels. The main advantage of dividing up the task this way is that we can take a lot more context into account for classifying phrases. For example, features that may be relevant now include: the length of the phrase, the first/last $k$ words in the phrase, the position of the phrase in the sentence, whether the words *fútbol* or *liga* were mentioned in the same sentence, etc. Such features would be awkward to incorporate into a single-phase approach using a Markov model to predict phrase tags at the same time as sort labels.
We chose a fairly standard independent feature (a.k.a. “naive Bayes”) model, mostly as a matter of convenience. Obviously any other classifier framework could have been used instead. For both languages we use as features the length of the phrase, its distance from the start of the sentence, the identity of the words inside the phrase viewing it as a set of words (i.e., discarding positional information), the identity and other properties (including whether a word starts with an upper/lower case letter) of the first $k$ and last $k'$ words in the phrase, and the identity and other properties of the word(s) preceding and following the phrase. The optimal parameter settings differ for Spanish and Dutch. For example, in Spanish the identities of the first $k = 6$ words is very important for classification performance, whereas long preceding or trailing contexts do not help much, if at all. For Dutch, the identities of words inside the phrase is less helpful ($k = 3$ is optimal), and more preceding and trailing context has to be used. In addition, knowing whether a sentence (or, ideally, a news article) is about soccer was helpful for Spanish. A feature that tests for the presence of *fútbol* and a few semantically related words is the only aspect of the classification component that is particular to one language. Other language specific information, e.g. names of Spanish provinces, did not turn out to be useful.
Table 2 shows performance figures for the classification component on the raw development data. Equivalently one can think of these results as if we had applied our classifiers to the output of a perfect extraction component that does not make any mistakes. We can already see for Spanish that performance is lowest for the sort *MISC*, which does not seem very homogeneous, and may perhaps best be chosen by default if no other class applies. Trying to predict *MISC* directly seems to be a misguided effort. This will become even clearer below when we look at the overall performance of our approach.
| Language | Precision | Recall | $F_{\beta=1}$ |
|----------|-----------|--------|---------------|
| Spanish dev. | 71.37% | 87.82% | 78.74 |
| MISC | 70.80% | 79.55% | 74.92 |
| ORG | 87.95% | 78.18% | 82.78 |
| PER | 91.05% | 84.12% | 87.45 |
| overall | 82.17% | 82.17% | 82.17 |
| Dutch devel. | 75.57% | 70.17% | 72.77 |
| MISC | 79.68% | 79.55% | 74.92 |
| ORG | 82.30% | 66.42% | 73.51 |
| PER | 70.21% | 85.88% | 77.26 |
| overall | 76.39% | 76.39% | 76.39 |
Table 2: Classification results obtained for the development data sets for the two languages used in this shared task.
### 5 Putting it all together
A theoretical problem with our task decomposition is how to train the classifiers used in the second phase. What they will eventually see as input is the output of the extraction component, which may
contain mistakes, e.g., cases where the beginning or end of a phrase was mispredicted. Since we want to build and refine the classification component independently of the extraction component, we have to train the classifiers on the phrases in the labeled training data. It is not clear a priori that this kind of independent development comes without a performance penalty, since we may have forgotten to show the second-phase classifiers examples of truncated or badly mangled phrases that were produced because of imperfections of the extraction component which makes up the first phase of our approach. Based on the independence assumption behind the task decomposition we would expect the overall performance on the Spanish development data set to be
$$0.8723 \times 0.8217 \approx 0.7168.$$
As we can see from the actual results in Table 3, this is not very far from the observed performance. We conclude that independent development of the two components did not impact overall performance.
### 6 Conclusion
We presented a simple, knowledge-poor named entity recognizer using standard components. Our decomposition into extraction and classification phases was motivated by the common syntactic regularities and the ambiguous status of some named entities. We have shown that the conditional next-tag model used for extraction is not unprincipled (a criticism brought forward by McCallum et al. 2000) against next-tag classifiers that do not output probabilities, but arises naturally from a conditional sequence model and plausible independence assumptions. This extraction model achieves fairly high accuracy (and just as observed by Punyakanok and Roth 2001) it outperforms a joint generative Markov model. A separate classification step makes it easy to use sentence-level features and large amounts of contexts. Such features would be difficult to integrated into standard models, the major exception being conditional random fields (Lafferty et al., 2001), compared to which the approach proposed here is much simpler.
### References
John Lafferty, Andrew McCallum, and Fernando Pereira. 2001. Conditional random fields: Probabilistic models for segmenting and labeling sequence data. In *ICML-01*, pages 282–289.
Andrew McCallum, Dayne Freitag, and Fernando Pereira. 2000. Maximum entropy Markov models for information extraction and segmentation. In *ICML 2000*, pages 591–598.
Vasin Punyakanok and Dan Roth. 2001. The use of classifiers in sequential inference. In *NIPS-13*, pages 995–1001.
| | precision | recall | $F_{\beta=1}$ |
|--------|-----------|--------|---------------|
| LOC | 65.76% | 74.65% | 70.70 |
| MISC | 45.56% | 54.16% | 49.49 |
| ORG | 77.40% | 70.12% | 73.58 |
| PER | 85.01% | 76.60% | 80.59 |
| overall| 72.35% | 71.74% | 72.04 |
| | precision | recall | $F_{\beta=1}$ |
|--------|-----------|--------|---------------|
| LOC | 77.18% | 73.34% | 75.21 |
| MISC | 44.47% | 50.88% | 47.46 |
| ORG | 76.75% | 77.57% | 77.16 |
| PER | 80.20% | 77.69% | 78.92 |
| overall| 74.03% | 73.76% | 73.89 |
| | precision | recall | $F_{\beta=1}$ |
|--------|-----------|--------|---------------|
| LOC | 69.87% | 67.23% | 68.52 |
| MISC | 64.69% | 62.87% | 63.77 |
| ORG | 69.65% | 56.11% | 62.15 |
| PER | 63.93% | 75.85% | 69.38 |
| overall| 66.42% | 65.43% | 65.92 |
| | precision | recall | $F_{\beta=1}$ |
|--------|-----------|--------|---------------|
| LOC | 79.04% | 76.78% | 77.89 |
| MISC | 69.60% | 59.98% | 64.43 |
| ORG | 64.27% | 63.17% | 63.71 |
| PER | 69.21% | 78.80% | 73.70 |
| overall| 70.11% | 69.26% | 69.68 |
Table 3: Results obtained for the development and the test data sets for the two languages used in this shared task. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3518,
1
],
[
3518,
8317,
2
],
[
8317,
12624,
3
],
[
12624,
16606,
4
]
]
} |
0eadf15ea8fb3cbafec35817f6aab05c76970cc0 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 8,
"total-fallback-pages": 0,
"total-input-tokens": 25141,
"total-output-tokens": 6966,
"fieldofstudy": [
"Biology",
"Medicine"
]
} | INTRODUCTION
Free-living Acanthamoeba spp. are distributed worldwide, especially in soil, fresh water, water tank of cooling tower, and contact lens container [1]. Acanthamoeba castellanii can cause clonic granulomatous amoebic encephalitis (GAE) while A. castellanii and A. polyphaga can induce acanthamoebic keratitis (AK) [2-5]. A. castellanii generally causes AK through oxygen deficiency, weak stratum basal tears, and excessive corneal stimulation in contact lens wear. When A. castellanii is inoculated into eye via contact lens, it can infect corneal epithelial cell and induce inflammation (keratitis) [6].
The first case of AK was reported in 1973. Since then, about 5,000 cases of AK have been recorded in USA [7]. In South Korea, about 43 cases of AK were reported in 2008. In 154 cases of Austrian AK, 89% persons were contact lens wearers and 19% had corneal transplantation [8]. Some commercial contact lens container solution has less effective amoebicidal activity, because cell wall of acanthamoebic cyst has resistance to disinfection solution commonly used in the house [9,10]. Due to increasing demand for contact lens, the problem of AK is becoming a social issue while contentable prevention or treatment drugs have not been developed yet [11,12].
Acanthamoeba sp. can mainly proliferate on contact lens surface after contact lens storage solution is contaminated, resulting in eye infection [6]. Although wearing contact lens is a major cause of AK, most cases of AK in experimental animals are induced by the presence of corneal damage before the exposure of pruritic amoeba [13,14]. Nevertheless, intraocular infections do not easily occur in animal experiments due to strong neutrophil reaction and increased resistance to nutritional and delayed infections, although A. castellanii trophozoites can penetrate corneal endothelium [12].
On the other hand, it has been reported that AK is easily induced by caustic amoebic cysts because of their strong resistance to disinfectant chemicals, the expression of cysteine proteinase, and so on [9,10]. However, the development mechanism of AK differs depending on the infection type of amoeba.
in trophozoic or cystic form because there are not enough studies on AK development. In this study, we investigated the in vitro cytotoxicity of *A. castellanii* trophozoites or cysts to target corneal cells and cytokine secretion in target cells by cultivating in order to elucidate the mechanism of AK development.
It is possible to hypothesize that there is a difference in the development mechanism of AK according to infectious type of amoeba, trophozoite or cyst. Therefore, immunological studies on cytopathological and inflammatory reaction of host cells co-cultured with amoeba trophozoites or cysts are necessary. In this study, we investigated morphologic cytopathic effects and in vitro cytotoxicity by culturing *A. castellanii* trophozoites or cysts with corneal epithelial cells as target cells. Secretion patterns of pro-inflammatory cytokines were then observed.
**MATERIALS AND METHODS**
**Culture and encystation of *A. castellanii***
*A. castellanii* trophozoites were axenically cultured with PYG medium (2% proteose peptone, 0.2% yeast extract, 0.1 M glucose, 4 mM MgSO$_4$·7H$_2$O, 0.4 mM CaCl$_2$, 3.4 mM sodium citrate 2H$_2$O, 50 µM Fe(NH$_4$)$_2$(SO$_4$)$_2$·6H$_2$O, 2.5 mM KH$_2$PO$_4$, 2.5 mM Na$_2$HPO$_4$, pH 6.5) at 25°C [15]. Cyst formation was done according to previous method [16]. Briefly, *A. castellanii* trophozoites were washed with PBS (pH 7.4) twice, centrifuged at 1,500 rpm for 5 min, and placed into 12-well plates (5 × 10$^5$ cells/ml) with encystment medium (95 mM NaCl, 5 mM KCl, 8 mM MgSO$_4$, 0.4 mM CaCl$_2$, 1 mM NaHCO$_3$, 20 mM Tris-HCl, pH 9.0). After induction of cyst formation, all remaining trophozoites were removed by treatment with 0.05% N-lauroylsarcosine sodium salt solution (Sarcosyl; Sigma Chemical Co., St Louis, Missouri, USA) at room temperature for 20 min [17,18].
**Cultivation of human corneal epithelial cells**
Human corneal epithelial cells (HCECs) were cultured with keratinocyte basal medium (KB; Lonza, Walkersville, Maryland, USA) at 37°C in a 5% CO$_2$ incubator. HCECs were cultured in 75-cm$^2$ flasks (Nunc, Naperville, Illinois, USA) until they became monolayer. Then 5 ml of trypsin-EDTA (1X) solution was added. Cells were harvested, washed with PBS (pH 7.4) 3 times, and placed into 6-well plates at density of 5 × 10$^5$ cells/ml. After incubation at 37°C for 3 hr, monolayer-cultured HCECs were used for experiments.
Cytopathic changes of HCECs co-cultured with *A. castellanii*
HCECs cultured in 6-well plates (5 × 10$^5$ cells/ml) were co-cultured with *A. castellanii* trophozoites only (5 × 10$^5$ cells/ml), cysts only (5 × 10$^5$ cells/ml), or both trophozoites and cysts (each 2.5 × 10$^5$ cells/ml) at 37°C in a 5% CO$_2$ incubator for 3, 6, 9, 12, and 24 hr. After culturing, to observe cytopathic effects in target cells cultured with trophozoites or cysts of amoeba, numerical and morphological changes were determined by phase contrast microscopy (Olympus, Shinjuku, Tokyo, Japan). To determine in vitro cytotoxicity of amoeba against target cells, the amount of lactate dehydrogenase (LDH) released from cultured HCECs was measured using Cytotox 96 non-radioactive cytotoxicity assay (Promega, Madison, Wisconsin, USA) as described previously [19].
**Cytokines expression from HCECs co-cultured with *A. castellanii***
To determine expression levels of cytokine genes from target cells in the above culture system, RT-PCR was carried out for interleukin 1 alpha (IL-1$\alpha$), interleukin 6 (IL-6), and interleukin 8 (IL-8) genes. Briefly, total RNA was isolated from cultured HCECs with RNeasy mini kit (QIAGEN, Valencia, California, USA). The cDNA was subjected to RT-PCR with gene-specific primers (Table 1) targeting human IL-1$\alpha$, IL-6, IL-8 using a Quantstudio 3 real-time RT-PCR instrument (Thermo Fisher Scientific, Singapore). PCR condition was as follows: 40 cycles of denaturing at 95°C for 5 sec, annealing at 60°C for 34 sec, and extension at 72°C for 30 sec.
**Levels of cytokines released from HCECs co-cultured with *A. castellanii***
To determine levels of cytokines (IL-1$\alpha$, IL-6, and IL-8) secreted from target cell, LISA kits (R&D Systems, Minneapolis, Minnesota, USA) were used following the manufacturer’s instructions. Briefly, each 100 µl of supernatant from HCECs co-cultured with amoebic trophozoites or cysts was placed into a 96-well polystyrene microplate containing 100 µl of assay di-
**Table 1. Primers used for real time RT-PCR**
| Gene | Forward primer (5’ to 3’) | Reverse primer (5’ to 3’) |
|--------|--------------------------|---------------------------|
| Actin | TGGCACCCAGCACAATGAAA | CTAAGCTATATGGCGCTTAG |
| IL-1$\alpha$ | GAAATCTGACTTCAAAATGCCTGAT | TATCTTGGGGCCAGTGCTCAGCTACA |
| IL-6 | AAGCCAGAGGAGCCACAAAGT | TGTCCTGCGCCACATTGTTC |
| IL-8 | GCAGTTTCCGCCAAGGAGGCGTC | TTCTCGTTGTGGCGCGATGTCG |
lent RD1W and reacted at room temperature for 2 hr. After washing with wash buffer four times, 200 µl of human IL-6 conjugate was added to the well on and reacted at room temperature for 24 hr. After washing, 50 µl of substrate solution was added and the reaction absorbance was measured at wavelength of 450 nm on an ELISA reader.
Statistical analysis
This experiment was repeated three times or more. Difference between experimental and control groups was analyzed using Student’s t-test. Statistical significance was accepted at P < 0.05.
RESULTS
Encystation of *A. castellanii*
Results of cyst formation of *A. castellanii* trophozoites cultured in encystment media revealed round precysts consisting of a single cell wall were at 24 hr. From 48 hr after induction of cyst formation, complete cysts with double-walled polygons were formed. After inducing cyst formation for 72 hr, complete cysts of polygonal double wall were observed (Fig. 1). They were used for subsequent experiments.
Cytopathic changes of HCECs induced by *A. castellanii*
Results of cytopathic changes of HCECs co-cultured with *A. castellanii* trophozoites and/or cysts revealed that the number of HCECs was decreased over time in all experimental groups (cultured with trophozoites only, cysts only, or both trophozoites and cysts) compared to that of control panned dendritic HCECs. In addition, round or dissolving cell wall shapes were observed in all experimental groups (Fig. 2). Particularly, after 6 hr of culture with amoebic trophozoites, *A. castellanii* tro-
phozoites were attached to HCECs for phagocytosis. After 12 and 24 hr of culture, more attachments were observed. Additionally, the number of target cells was decreased significantly after 24 hr of incubation (Fig. 2). For HCECs cultured with amoeba cysts, they transformed into long and rounded form after 12 hr of culture. After 24 hr of culture, HCECs were not adhered to the bottom of the plate any more, which were floating and dissolved or dead (Fig. 2).
In vitro cytotoxicity of *A. castellanii* to HCECs
Results of in vitro cytotoxicity of *A. castellanii* to HCECs based on LDH release assay revealed that amounts of LDH released from HCECs were increased over time in all experimental groups in comparison with those in control HCECs (Fig. 3). When trophozoites were cultured with HCECs, in vitro cytotoxicities of *A. castellanii* to HCECs after 3, 6, 9, 12, and 24 hr of incubation were 2.2, 6.7, 22.6, 28.2, and 67.6% respectively (Fig. 3). When both trophozoites and cysts were cultured with HCECs, in vitro cytotoxicities of *A. castellanii* to HCECs were 3.0, 9.0, 28.0, 34.2, and 74.0% after 3, 6, 9, 12, and 24 hr of incubation, respectively (Fig. 3). When cysts only were cultured with HCECs, in vitro cytotoxicities of *A. castellanii* to HCECs were 3.6, 11.3, 33.0, 42.6, and 86.8% after 3, 6, 9, 12, and 24 hr of incubation, respectively (Fig. 3). When only cysts were cultured with HCECs, the amoebic in vitro cytotoxicity was the highest.
mRNA expression levels of cytokines in HCECs induced by *A. castellanii*
To determine what kind of cytokines were secreted in corneal epithelial cells, lysates of HCECs co-cultured with *A. castellanii* trophozoites or cysts were subjected to real time RT-PCR for Fig. 4. Expression of cytokines in HCECs co-cultured with *A. castellanii* trophozoites or cysts. *P < 0.005.
detection of IL-1α, IL-6, IL-8, and CXCL1 genes. Results showed that mRNA levels of IL-1α, IL-6, IL-8, and CXCL1 in HCECs cultured with trophozoites were significantly increased after 3 hr, reaching the highest level after 6 hr. They were then decreased over time (Fig. 4). When HCECs were co-cultured with only ameba cysts, mRNA levels of IL-6, IL-8, and CXCL1 were significantly increased after 3 hr, reaching the highest expression levels after 6 hr of incubation (Fig. 4).
Cytokines secreted from HCECs induced by A. castellanii
Since IL-6 and IL-8 mRNA expression levels in HCECs co-cultured with A. castellanii were increased, ELISA was performed to observe secretion levels of cytokines IL-6 and IL-8 induced by and A. castellanii. When HCECs were cultured with amoeba trophozoites, amounts of IL-6 secreted into cultured medium after 1, 3, 6, 12, and 24 hr of incubation were 91.25, 893.58, 1042.58, 620.25, and 133.25 pg/ml, respectively. Amounts of secretion started to increase at 3 hr after culture, reaching the highest level at 6 hr after culture. They were then gradually decreased (Fig. 5A). Amounts of IL-6 secreted from HCECs cultured with amoeba cysts after 1, 3, 6, 12, and 24 hr were 80.25, 457.25, 484.92, 438.58, and 403.25 pg/ml, respectively. IL-6 was highly secreted at 3 hr after incubation. It was secreted the most at 6 hr after incubation followed by gradual decrease (Fig. 5A). Amounts of IL-8 secreted to the culture medium from HCECs co-cultured with only amoeba trophozoites were 6.3, 25.97, 218.97, 292.97, and 380.97 pg/ml after 1, 3, 6, 12, and 24 hr of incubation, showing a continuous increasing trend with increasing incubation time (Fig. 5B). When HCECs were cultured with amoeba cysts, amounts of IL-8 secreted into the culture medium were 16.3, 23.3, 128.97, 160.3, and 303.63 pg/ml after 1, 3, 6, 12, and 24 hr of incubation, respectively, as showing an increasing trend with incubation time (Fig. 5B).
**DISCUSSION**
The incidence of AK is increasing with increasing number of contact lens wearers. Its initial diagnosis is difficult, and a variety of pathophysiological studies are needed to develop a contact storage solution effective to kill amoeba. In addition, definite therapeutic agents for AK are limited [20-23].
In the results of cytopathic effect and cytotoxicity of A. castellanii trophozoites on HCECs, the number of target cells was decreased with increasing incubation time. Such decrease in the total number of target cells is mainly due to amoebic phagocytosis. In the case of cystic type treatment, HCECs changed into a round and elongated shape over time with many dead cells, thereafter, showing a slightly different phenomenon from the case of trophozoites treatment.
The cytotoxicity of amoeba cysts to HCECs was higher than that of amoeba trophozoites. Their cytotoxicities were the strongest at 24 hr after incubation (trophozoites, 67.6%; cysts, 86.8%). Cytotoxic changes and death of target cells are probably due to cytolytic factors such as serine protease, metalloproteinase, and cysteine protease secreted from A. castellanii [24-27]. The cytotoxicity was somewhat higher in the amoebic cyst co-culture, and then a further research is needed on the elucidation of these related materials. Like other mucosal epithelial cells, corneal epithelial cells can detect pathogenic microorganisms and engage in innate immune response that involves macrophages and neutrophils. It is known that macrophages and neutrophils play an essential role in the elimination of pathogens, resulting in an inflammatory reaction [28].
phils of Chinese hamster corneal epithelial cells can kill amoeba trophozoites. When AK-induced hamster was treated with anti-MIP2 antibody, an inhibitor of macrophage inflammatory protein-2 (MIP-2), symptoms of AK were worse [22]. The production of IL-6 and IL-8 may cause barrier destruction of the corneal epithelium and inflammation of the ocular surface [29]. In this study, mRNA expression levels of IL-1α, IL-6, and IL-8 in HCECs cultured with A. castellanii cysts and trophozoites for 3 and 6 hr were significantly higher than those in the control group. Especially, expression levels of IL-6 were decreased at 12 and 24 hr post incubation with trophozoites. This might be due to a decrease in target cells caused by amoebic phagocytosis.
In the results of HCECs co-culture with amoeba cysts for 6 hr, IL-6 secretion levels were 484.92 pg/ml, whereas 1,042.58 pg/ml in culture with trophozoites. And then, they were rapidly increased with incubation time, showing difference between infectious (co-cultured) types of amoeba, as which trophozoites induce higher secretion than cysts. It is thought that some substances secreted from cysts have different cytopathic mechanisms, while amoebic trophozoites show cytopathic effects by phagocytosis as well as secretion of some cytolytic or immune materials. In addition, it is believed that there are different mechanisms between the cytopathic effect and the inflammatory reaction resulted of the immune response. The difference between A. castellanii cysts and trophozoites co-culture needs to be determined in further studies such as molecular cloning and characterization of some substances secreted differently between cysts and trophozoites.
In conclusion, these results suggest that cytopathic changes and pro-inflammatory cytokines release of HCECs in response to A. castellanii, in considering especially amoebic cysts contamination/infection, are an important mechanism for AK development.
ACKNOWLEDGMENT
This research was supported by a grant (2018R1D1A1B0-7047302) of the Basic Science Research Program through the National Research Foundation (NRF) funded by the Ministry of Science and ICT, Republic of Korea.
CONFLICT OF INTEREST
The authors declare no conflict of interest related to this study.
REFERENCES
1. Schuster FL, Visvesvara GS. Free-living amoebae as opportunistic and non-opportunistic pathogens of humans and animals. Int J Parasitol 2004; 34: 1001-1027.
2. Marciano-Cabral F, Cabral G. Acanthamoeba spp. as agents of disease in humans. Clin Microbiol Rev 2003; 16: 273-307.
3. Im K, Kim DS. Acanthamoebiasis in Korea: two new cases with clinical cases review. Yonsei Med J 1998; 39: 478-484.
4. van Klink F, Alizadeh H, Stewart GL, Pidherney MS, Silvany RE, He Y, McCulley JP, Niederkorn Y. Characterization and pathogenic potential of a soil isolate and an ocular isolate of Acanthamoeba castellanii in relation to Acanthamoeba keratitis. Curr Eye Res 1992; 11: 1207-1220.
5. Visvesvara GS, Stehr-Green JK. Epidemiology of free-living amoeba infections. J Protozool 1990; 37 (suppl): 25-33.
6. Auran JD, Starr MB, Jakobiec FA. Acanthamoeba keratitis. A review of the literature. Cornea 1987; 6: 2-26.
7. Visvesvara GS. Amebic meningoencephalitides and keratitis: challenges in diagnosis and treatment. Curr Opin Infect Dis 2010; 23: 590-594.
8. Walochnik J, Scheikl U, Haller-Schober EM. Twenty years of Acanthamoeba diagnostics in Austria. J Eukaryot Microbiol 2015; 62: 3-11.
9. Hiti K, Walochnik J, Haller-Schober EM, Fasching C, Aspock H. Viability of Acanthamoeba after exposure to a multipurpose disinfecting contact lens solution and two hydrogen peroxide systems. Br J Ophthalmol 2002; 86: 144-146.
10. Zanetti S, Fiori PL, Pinna A, Usai S, Carta F, Fadda G. Susceptibility of Acanthamoeba castellanii to contact lens disinfecting solutions. Antimicrob Agents Chemother 1995; 39: 1596-1598.
11. Seal DV. Acanthamoeba keratitis update- incidence, molecular epidemiology and new drugs for treatment. Eye (Lond) 2003; 17: 893-905.
12. Hurt M, Niederkorn J, Alizadeh H. Effects of mannose on Acanthamoeba castellanii proliferation and cytolytic ability to corneal epithelial cells. Invest Ophthalmol Vis Sci 2003; 44: 3424-3431.
13. Hurt M, Apte S, Leher H, Howard K, Niederkorn J, Alizadeh H. Exacerbation of Acanthamoeba keratitis in animals treated with anti-macrophage inflammatory protein 2 or antineutrophil antibodies. Infect Immun 2001; 69: 2988-2995.
14. van Klink F, Alizadeh H, He Y, Mellon IA, Silvany RE, McCulley JP, Niederkorn Y. The role of contact lenses, trauma, and Langherans cells in a Chinese hamster model of Acanthamoeba keratitis. Invest Ophthalmol Vis Sci 1993; 34: 1937-1944.
15. Visvesvara GS, Balamuth W. Comparative studies on related free-living and pathogenic amebae with special reference to Acanthamoeba. J Protozool 1975; 22: 245-256.
16. Sohn HJ, Kang H, Seo GE, Kim JH, Jung SY, Shin HJ. Efficient Liquid Media for Encystation of Pathogenic Free-Living Amoebeae. Korean J Parasitol 2017; 55: 233-238.
17. Moon EK, Xuan VH, Chung DI, Hong Y, Kong HH. Microarray analysis of differentially expressed genes between cysts and tro-
phozoites of *Acanthamoeba castellanii*. Korean J Parasitol 2011; 49: 341-347.
18. Moon EK, Hong Y, Lee HA, Quan FS, Kong HH. DNA methylation of gene expression in *Acanthamoeba castellanii* encystation. Korean J Parasitol 2017; 55: 115-120.
19. Kim JH, Kim D, Shin HJ. Contact-independent cell death of human microglial cells due to pathogenic *Naegleria fowleri* trophozoites. Korean J Parasitol 2008; 46: 217-221.
20. Brown TJ, Cursons RT, Keys EA. Amoebae from antarctic soil and water. Appl Environ Microbiol 1982; 44: 491-493.
21. Cerva L, Serbus C, Skocil V. Isolation of limax amoebae from the nasal mucosa of man. Folia Parasitol (Praha) 1973; 20: 97-103.
22. Lyons TB, Kapur R. Limax amoebae in public swimming pools of albany, schenectady, and rensselaer counties, new york: their concentration, correlations, and significance. Appl Environ Microbiol 1977; 33: 551-555.
23. Paszko-Kolva C, Yamamoto H, Shahamat M, Sawyer TK, Morris G, Colwell RR. Isolation of amoebae and *Pseudomonas* and *Legionella* spp. from eyewash stations. Appl Environ Microbiol 1991; 57: 163-167.
24. Niederkorn JY, Alizadeh H, Leher H, McCulley JP. The pathogenesis of *Acanthamoeba* keratitis. Microbes Infect 1999; 1: 437-443.
25. Claerhout I, Kestelyn P. *Acanthamoeba* keratitis: a review. Bull Soc Belge Ophtalmol 1999; 274: 71-82.
26. Alizadeh H, Pidherney MS, McCulley JP, Niederkorn JY. Apoptosis as a mechanism of cytolysis of tumor cells by a pathogenic free-living amoeba. Infect Immun 1994; 62: 1298-1303.
27. Shin HJ, Cho MS, Kim HI, Lee M, Park S, Sohn S, Im KI. Apoptosis of primary-culture rat microglial cells induced by pathogenic *Acanthamoeba* spp. Clin Diagn Lab Immunol 2000; 7: 510-514.
28. Kurpakus-Wheater M, Kernacki KA, Hazlett LD. Maintaining corneal integrity how the “window” stays clear. Prog Histochem Cytochem 2001; 36: 185-259.
29. Kernacki KA, Barrett RP, Hobden JA, Hazlett LD. Macrophage inflammatory protein-2 is a mediator of polymorphonuclear neutrophil influx in ocular bacterial infection. J Immunol 2000; 164: 1037-1045.
| 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2169,
1
],
[
2169,
7060,
2
],
[
7060,
8612,
3
],
[
8612,
10453,
4
],
[
10453,
14048,
5
],
[
14048,
19207,
6
],
[
19207,
21271,
7
],
[
21271,
21271,
8
]
]
} |
a299b5d500c9e226538b8d87d15e0ec1a2684573 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 12,
"total-fallback-pages": 0,
"total-input-tokens": 39828,
"total-output-tokens": 17581,
"fieldofstudy": [
"Psychology"
]
} | The role of a nature-based program in fostering multiple connections to nature
Julia Baird1,2 · Gillian Dale1 · Jennifer M. Holzer1 · Garrett Hutson1,3 · Christopher D. Ives4 · Ryan Plummer1
Received: 26 August 2021 / Accepted: 13 February 2022 / Published online: 29 April 2022
© The Author(s) 2022
Abstract
Reconnecting to nature is imperative for the sustainability of humans on Earth, offering a leverage point for system change. Connections to nature have been conceptualized as a typology of five types as follows: material; experiential; cognitive; emotional; and, philosophical, ranging from relatively shallow to deeper connections, respectively. Educational programs that immerse individuals in nature have been designed to build an appreciation for places travelled, awareness of environmental issues and to promote pro-environmental behaviours. Using quantitative and qualitative data from 295 individuals who participated in National Outdoor Leadership School (NOLS) programs ranging from 14 to 90 days, we tested hypotheses to understand whether and to what extent NOLS influenced the five types of connections to nature. We further investigated whether deeper connection types were associated with greater intentions for pro-environmental behaviours. Findings showed that individuals generally reported greater connections to nature after the NOLS program, with emotional and material connections increasing the most. While intentions for pro-environmental behaviour increased from pre- to post-program, deeper connections to nature did not correspond to greater intention for pro-environmental behaviour. The strongest predictor of intention for pro-environmental behaviour was a cognitive connection, though an emotional connection was also a significant predictor. Ultimately, we found that the NOLS program fosters multiple connections to nature and increases intentions for pro-environmental behaviour. We call for more research to understand the relationships among connection to nature types and how those interactions may influence intentions for pro-environmental behaviour—in nature-based educational programs and in other contexts.
Keywords Connections to nature · NOLS · Pro-environmental behaviour
Introduction
(Re)connecting to the biosphere and becoming active stewards is a prerequisite for sustainability of the Earth System (Folke et al. 2011). Disconnections between humans and nature have fostered perspectives in which human actions are perceived as external interventions, separate from ecosystem functioning (Folke et al. 2011). These disconnects have occurred for a variety of reasons, including physical lack of access, technology, and reliance on imported goods (Turner et al. 2004; Soga and Gaston 2016; Doringer et al. 2017). A lack of connection between humans and nature has been linked to ‘living in overshoot’ of a safe operating space within the planet’s boundaries (Lade et al., 2020; Fischer and Riechers 2019).
Connecting, or reconnecting, to nature is critical for acknowledging the interconnected reality of social systems and ecological systems (i.e., social-ecological system (SES))
(Berkes and Folke 1998; Folke et al. 2016). In parallel to earth system science, which recognises the need for human societies to function within ecological limits, other bodies of scholarship have emphasised the importance of people’s lived experiences and perceptions of nature. According to Mackay and Schmitt (2009), nature connection “refers to a subjective sense of ‘oneness’ with nature that arises from incorporating nature into one’s self-definition”. The theoretical basis of the connection to nature concept can be traced from the biophilia hypothesis (Wilson 1984; Kahn and Kellett 2002), ecopsychology, and the psychology of interpersonal relationships (Whitburn et al. 2020). While related concepts such as sense of place (Eaton et al. 2019), “extinction of experience” (Pyle 1993; Soga and Gaston 2016), and “nature deficit disorder” (Louv 2005) have been developed in other fields, the connection to nature concept has been extensively conceptualized and operationalised within psychology (Restall and Conrad 2015; Ives et al. 2017). Psychological researcher Schultz (2002, p. 67), for example, views a connection to nature as “the extent to which an individual includes nature within [their] cognitive representation of self”. Mayer and Franz (2004) emphasize the affective and experiential aspects of connection. Perrin and Benassi (2009) focus on individuals’ beliefs and attitudes regarding their connection (Geng et al. 2015).
There are at least 17 different scales used to measure connection to nature (Whitburn et al. 2020; Restall and Conrad 2015; Tam 2013), most of which focus on feelings toward nature (affect), cognition (knowledge and beliefs about nature), and behaviour (actions and experiences). Some scales assess connection to nature as a single measure often defined as emotional attachment (Whitburn et al. 2020). Additionally, other research has emphasised multiple pathways to strengthening nature connection, including direct contact with nature, emotional engagement, meaning formation, and appreciation of beauty and compassion (Lumber et al. 2017). Ives et al. (2018) contend that the term ‘connection’ has been used to represent a spectrum of concepts and experiences of nature, and that there is a need to define and operationalise a more expansive concept that can encompass understandings from earth system science, sociology, psychology and grounded analytical approaches. As a result, they sought to capture this range by conceptualizing five categories of nature connections along a spectrum from external to internal experience. These categories recognize different scales of social aggregation (from the individual to society), and include the following: (1) material (consumption of nature’s materials and goods), (2) experiential (direct interaction with the natural environment), (3) cognitive (knowledge or awareness of the environment and attitudes/values toward nature), (4) emotional (feelings of attachment or empathy), and (5) philosophical (worldview on nature: what it is, why it matters, and our relationship to it) (Ives et al. 2018).
Reconnecting to nature encompasses shifts in worldviews and understanding of the function of systems (Abson et al. 2017). Thus, reconnecting to nature, at both the individual and the societal level, may offer a potential leverage point for broader system change (cf Meadows 1999; Abson et al. 2017; Richardson et al. 2020; Riechers et al. 2021). One of the mechanisms by which reconnection to nature effects change is by “shap[ing] the values and paradigms that underpin human action” (Abson et al. 2017: 34). Nature connections span a spectrum from deep to shallow (Ives et al. 2018), yet they may be especially important for influencing deeply rooted paradigms and beliefs, with Richardson et al. (2020) suggesting that nature-based interventions can be powerful as deep leverage points that shape meanings and emotions associated with nature.
Pro-environmental behaviours are human actions taken for the environment, which may be underpinned by connections to nature. Many efforts have been made to understand the relationship between connectedness to nature and pro-environmental behaviour (PEB) (i.e., behaviours that consciously attempt to minimize negative environmental impacts; Kollmuss and Agyeman 2002). A recent meta-analysis of 37 studies on connections to nature and PEB identified a positive association between the two (Whitburn et al. 2020). However, the nature of this relationship is not always straightforward. Multiple factors influence PEB, including childhood experiences, personality, knowledge, education, norms and habits, attitudes, values, worldviews, place attachment, and demographic factors, among others (Gifford 2014). When focusing specifically on the relationship of connections to nature and PEB, not all connections to nature have equal relationships to behaviour. Scales measuring different types of connections to nature vary with respect to their correlation with pro-environmental behaviour, with the strongest correlation for ‘commitment to the environment’ and the weakest for ‘inclusion of nature in self’ (Whitburn et al. 2020:187).
The ‘extinction of experience’ is a particularly important cause of a widespread societal experiential disconnection to nature (Pyle 1993; Soga and Gaston 2016). People—particularly those in urban areas—are less and less likely to engage directly with nature, which in turn has negative consequences for how we perceive nature as well as our tendency towards PEB (Soga and Gaston 2016). Nature experiences or physical contact/engagement with nature, particularly outdoor programs, may enhance connectedness to nature (Lumber et al. 2017; Meltzer et al. 2018).
Outdoor program participants do not universally have positive experiences with their surroundings and the programs do not necessarily increase responsible environmental behaviour (Haluza-DeLay 1999). However, other studies of outdoor programs and experiences have shown promise in improving pro-environmental attitudes and related concepts (Ewert and McAvoy 2000). Examples include developing new meanings
connected to nature (Palmberg and Kuru 2010), increased knowledge of natural areas (Gillett et al. 1991), and delineating how appreciative outdoor experiences early in life may influence views toward the environment later (Ewert et al. 2005). One longitudinal research study demonstrated that an appreciation of nature is part of a suite of long-term outcomes for those who participated in a NOLS (formerly the National Outdoor Leadership School: https://www.nols.edu/en/) outdoor program, which is the program we focus on for this study (Sibthorp et al. 2008). Other studies on NOLS have also shown short-term positive results on outcomes related to human–nature connection including improving attitudes toward wilderness areas and supporting the development of an environmental ethic and a sense of place (Gress and Hall 2017; Hutson et al. 2019; Waage et al. 2012). Yet, the potential pathways for how future PEBs may or may not link to these human–nature concepts remains unclear. We build specifically on the exploratory work of Baird et al. (2020) to understand connections to nature described from NOLS and expressed intentions for PEB.
For the current study, we used Ives et al.’s (2017; 2018) conceptualization and typology of connections to nature to examine how a range of connections to nature, from shallow to deep, may be related to participation in a NOLS course. The objectives of this study were as follows: (1) to test the potential for an outdoor experience to enhance connections to nature; and, (2) to examine the relationship between connection type and intention for future pro-environmental behaviour. We hypothesized that an experiential ‘intervention’ (in the form of an intensive outdoor program) would result in increased connections to nature. We further hypothesized that deeper connections to nature (e.g., emotional connection) would have a stronger relationship with intention for future PEB than shallow connections to nature (e.g., material). There are three ways in which this study makes a contribution to research on human–nature connection and sustainability as follows: (1) NOLS represents a holistic, immersive, sustained nature connection ‘intervention’ which is different from other studies focused on testing the effects of a nature experience; (2) we study nature connection in a multi-dimensional way; and, (3) we investigate relationships between the multi-dimensional nature connections and intentions to change behaviour.
Materials and methods
Participants
A total of 295 (137 females, 153 males, 4 non-binary, 1 transgender) individuals who had recently completed a NOLS course between June 2019 and January 2020 participated in this study. Participants ranged in age from 16 to 63 with a mean age of 23 years (SD = 8.1). The majority of participants lived in the United States (N = 276; 93.6%) and participated in one of the Summer NOLS courses (N = 253; 85.8%). Approximately 38% of respondents (N = 111) reported that they had previously participated in a NOLS excursion. Of the 295 participants, 21 did not complete all of the questionnaire items as instructed, and thus the number of participants varied for each analysis. Participation in the study took approximately 20 min and was voluntary (unpaid). All participants provided informed, written consent prior to participating. This study was approved by the Human Research Ethics Board at Brock University and conducted in accordance with Tri-Council ethical guidelines.
NOLS program
NOLS is a leading source and teacher of wilderness skills and leadership that serves people and the environment. NOLS facilitates extended wilderness expeditions across the world for participants of many ages who wish to learn expeditionary and leadership skills. The NOLS expedition curriculum centers on leadership, environmental studies, outdoor skills, and risk management. The NOLS curriculum is delivered through backpacking, mountaineering, rock climbing, sea kayaking, and many other outdoor activity types (NOLS 2016). NOLS programs teach students experientially through facilitating the knowledge and skill development required to lead others competently in a variety of wilderness and community environments (NOLS 2016). The teaching of environmental studies at NOLS begins with building a scientific foundation of ecological concepts and processes. Activities and classes with themes related to ecology, appreciation of places traveled, and minimum impact practices parallel classes on land management and environmental issues within areas visited. These activities and classes are framed to help students to make curricular connections and promote pro-environmentalism in everyday life (O’Donnell 2014).
Materials and procedure
A questionnaire was created to collect data about participant demographics (age, gender, place of residence) and their experiences with, and connections to, nature using a mix of quantitative and qualitative questions (see Appendix 1 for questions analysed for this study). The questionnaire was administered using Qualtrics, an online survey.
1 Note that many of qualitative questions included in the questionnaire are part of a separate study, and thus were not included in this paper.
software. It was shared as a link in an email sent to all participants from the NOLS program, directly after completing NOLS courses. Courses ranged in length from 14 to over 90 days and took place at 13 different NOLS locations including wilderness areas in the United States, Canada, Mexico, Chile, Scandinavia, New Zealand, and India.
The questionnaire was designed to capture pre- and post-course responses using a single-assessment retrospective pretest–posttest design (Little et al. 2020) as a result of program constraints (Hill 2020). That is, the questionnaire was administered only after the course was complete, but asked about both pre- and post-course connections to nature. This approach, querying respondents’ pre-course responses along with their post-course responses after the completion of the course, has benefits (e.g., less onerous for participants; may reduce response-shift bias where the respondents’ understanding of the constructs changes over time) and challenges including the potential for several biases (e.g., acquiescence, social desirability, effort justification) (Geldhof et al. 2018; Hill 2020; Little et al. 2020; Thomas et al. 2019). In this case, the design was used out of necessity due to program constraints. However, this approach reflects a broader interest in retrospective pretest–posttest design as a mechanism to alleviate a common concern about response shift bias in traditional pre- and posttest designs (e.g., Moore and Tananis 2009). The exception to collecting both (retrospective) pre- and post-course data was the demographic information (which would not have changed pre- to post-course) and some questions that focused on post-course outcomes (e.g., changes in behavioural intentions) which were of interest only at that time period. Further, philosophical connection to nature was only assessed using quantitative measures post-course due to a questionnaire design issue.
Connection to nature questionnaire
Four of the five connection to nature types from Ives et al.’s (2018) typology were operationalized adhering as closely as possible to the definitions set out in their work. We recognize that, in parallel to our work to operationalize this typology, other efforts to do so were developed (Riechers et al. 2020; Meis-Harris et al. 2021). Some of our measures overlap with those of Meis-Harris et al. (2021); however, those developed by Riechers et al. (2020) are qualitative and thus distinct. Future work to define a standard set of scales to measuring the connections to nature would be useful to advance this framework.
Philosophical connection to nature was derived from De Groot and van den Born (2003) and Van den Born (2008). Participants were presented with four statements (e.g., “People are entrusted with nature; we are stewards of it. We have a responsibility to manage it responsibly”), and were asked to select the one that most closely aligned with their perspective. Individuals received a score of 4 if they selected the statement that represented the most ecocentric perspective (i.e., strongest philosophical connection to nature), a score of 3 if they selected the statement that represented the second most ecocentric perspective, and so on.
Emotional connection was assessed using Kals et al.‘s (1999) emotional affinity toward nature scale. Participants received 10 statements (e.g., “When I spend time in nature, I feel carefree.”), and used a 5-point Likert scale (1 = strongly disagree; 5 = strongly agree) to rate how well each statement described their own feelings. Scores were averaged (correcting for reverse-keyed items) for a total mean emotional connection score out of 5, with higher scores indicating greater emotional connection.
Cognitive connection was divided into two factors based on the description in Ives et al. (2018). The first factor was environmental awareness using the revised new ecological paradigm (NEP) scale (Dunlap et al. 2000) based on the prior use of the scale for this purpose by Schultz et al. (2002). The second factor was environmental attitude, using statements from Bradley et al. (1999). The awareness and the attitude subscales consisted of 15 statements each (e.g., “Humans are severely abusing the environment” for the awareness scale, and “Laws regarding water quality should be stricter” for the attitude scale). Participants were asked to rate their level of agreement with each statement using a 5-point Likert scale (1 = strongly disagree; 5 = strongly agree). An “awareness” score was derived by averaging (correcting for reverse-keyed items) scores across the items from the awareness subscale, for a total score out of 5. Similarly, an “attitude” score was calculated by averaging the scores across the items in the attitude subscale, for a maximum total score out of 5. Higher scores indicated a greater cognitive connection.
Two questions were included to assess experiential connection to nature. Participants were asked to indicate whether they had previously completed a NOLS-like course (yes/no), as well as the frequency with which they visited parks and wilderness areas. These responses were then used to examine whether previous experiences mediated the relationship between participating in a NOLS course and connection to nature (see “results” below).
Material connection was measured using two items that directly related to material consumption from Karp (1996). Participants used a 5-point Likert scale (1 = never; 5 = very often) to rate how often they would likely engage in two behaviours (“Buy organic foods” and “Purchase environmentally friendly and/or energy efficient products”). Scores were averaged for a total mean material connection score out of 5, with higher scores indicating a higher material connection.
Finally, we reviewed responses to the survey question, “Please elaborate on how your connection to nature did
or did not change as a result of participating in a NOLS course.” This question was included to understand how respondents perceived their own connection to nature. Only those responses that reported a change in level of connection to nature were analysed (n=35). Responses were coded using the Ives et al. (2018) typology and a second round of coding identified emergent themes outside of the typology. Frequencies were calculated for each code.
### Pro-environmental behaviour
Since the questionnaire was designed to capture changes immediately after the experiential intervention (NOLS course), pro-environmental behaviour was not feasible to collect (i.e., there was no time to engage in PEB after the course and before the questionnaire was administered). Accordingly, future intentions for PEB were measured instead. This represents a different, but related, construct. Intent and behaviour are moderately correlated (Grimmer and Miles 2017), and there is evidence that this relationship is mediated by the formulation of a plan, and moderated by factors including the extent to which the individual has behavioural control, the shopping context, and environmental involvement (e.g., support for environmental groups) (Carrington et al. 2010; Grimmer and Miles 2017). Future intentions for PEB were measured pre- and post-course using items adapted from Karp (1996), Halpenny (2010), and Cooper et al. (2015). Participants received a list of 17 PEBs (e.g., “Talk to others about environmental issues”), and were asked to indicate how often they would likely engage in these behaviours (1 = never; 5 = very often). An overall PEB score was calculated by averaging across the 17 items for a total mean score out of 5, with higher scores indicating a greater pro-environmental intent. There is a relationship between PEB and material connections to nature, and we separate the two by strictly scopeing material connections as directly related to material consumption, while PEB are not, and are more broadly defined.
### Data analysis
The quantitative data were analysed using a variety of techniques (see below) including paired-samples t-tests, correlations, and multiple regression in IBM® SPSS Statistics. Qualitative data were analysed using a deductive coding approach, using Ives et al.’s (2018) connections to nature as a primary source for codebook development. Responses were assigned one or more connection types and frequencies were calculated. Further, themes among responses to common connection types were identified using an inductive approach. For any analysis based on gender, only those who identified as female or male were included, as the number of respondents identifying otherwise was very small (n=5).
### Results
#### NOLS and connection to nature
First, a series of paired-samples t-tests with Bonferroni corrections were conducted to examine whether connectedness to nature (emotional connection, material connection, attitude and awareness (attitude and awareness together constituted the cognitive connection but were treated separately for the analysis)) changed as a result of participation in a NOLS course. Quantitative measures of philosophical connections were not included in this analysis because only post-course data were collected, and experiential connections were not included because the course was considered a consistent experiential connection across all respondents. All four connectedness to nature measures used in this analysis significantly increased from retrospective pre-test to posttest (see Fig. 1a), all p’s < 0.001; all d’s > 0.588, indicating that participation in a NOLS course was associated with an increase in connectedness to nature.
In addition, a qualitative analysis of responses to the following survey question was undertaken in an effort to understand how respondents articulated their own nature connections: “Please elaborate on how your connection to nature did or did not change as a result of participating in a NOLS course.” Respondents were more likely to identify emotional (15) or experiential connections (11) than cognitive (3) or philosophical connections (6). No material connections were described in response to the question. Responses categorized as cognitive connections generally mentioned appreciation of beauty, appreciation of complexity, awe of nature, and understanding of nature’s importance. Emotional connections were classified as such because emotional language was present, rather than reasons or explanations. Examples included the following:
Whenever I look around me at vast mountain ranges or a sparkling lake, I just feel joy of the memories of this course and I know I will carry that and grow from that for the rest of my life. I have fallen in love with nature and wildlife.
Rarely were statements categorized as experiential connections simply statements of experience; rather, they were statements of experience paired with language that characterized another type of connection. For example:
I have never been in such a remote area for such an extended period of time [experiential]. It was very humbling [philosophical].
I gained a greater respect for the joy and pain it can bring by simply existing [philosophical]. Some days hiking were terribly hard, yet at night it soothes you once you get to camp [experiential].
Philosophical connections generally mentioned something that impressed the respondent and directly prompted reflection on their personal role in nature. For example:
My perspective on the importance and scale of nature has increased and I have a greater respect for it than I previously did. I also realized how fragile each ecosystem is and the importance of protecting them.
Next, we examined whether the magnitude of increase in connectedness to nature differed amongst the four connection types measured (emotional, material, attitude, and awareness). For each of the connection types, we created a normalized pre/post difference score ([post–pre]/pre) and then conducted a repeated-measures ANOVA with a Bonferroni-corrected post-hoc test. There was a significant effect of type of nature connection, $F(3,804) = 39.04$, $p < 0.001$, $\eta^2 = 0.14$, such that the increase in both emotional and material connection scores, $F(2,280) = 9.72$, $p < 0.001$, $\eta^2 = 0.07$, awareness, $F(2,280) = 4.27$, $p = 0.03$, $\eta^2 = 0.03$, and attitude, $F(2,284) = 19.38$, $p < 0.001$, $\eta^2 = 0.14$, such that older individuals had higher baseline connectedness scores than younger individuals. However, age was unrelated to baseline material connection scores, $F(2,280) = 2.51$, $p = 0.26$, $\eta^2 = 0.01$. Age was also associated with pre/post-course changes in emotional connection, $F(2,281) = 3.06$, $p = 0.049$, $\eta^2 = 0.02$, awareness, $F(2,279) = 3.55$, $p = 0.03$, $\eta^2 = 0.03$, and material connection, $F(2,279) = 3.59$, $p = 0.03$, $\eta^2 = 0.03$, indicating older individuals showed smaller changes in connectedness to nature as a result of participating in NOLS.
Gender was also associated with pre-NOLS scores for all four measures of connectedness to nature (all $r’s > 2.8$; all $p’s < 0.005$; all $d’s > 0.34$), indicating females had higher connectedness to nature scores than did males; however, gender was not associated with changes in any of the four connectedness measures (all $F’s < 1.7$; all $p’s > 0.20$). Due to a low number of non-binary ($n = 4$) and transgender ($n = 1$) respondents, they were not included in this statistical analysis.
Previous experience with a NOLS course was associated with baseline (pre-NOLS) scores on all four connectedness to nature variables (all $r’s > 2.4$; all $p’s < 0.02$; all $d’s > 0.29$), such that individuals with previous experience had higher connectedness scores. Previous experience was negatively associated with changes in emotional connection, $F(1,279) = 9.62$, $p = 0.002$, $\eta^2 = 0.04$, awareness, $F(1,278) = 11.85$, $p = 0.001$, $\eta^2 = 0.04$, and material connection, $F(1,279) = 4.16$, $p = 0.04$, $\eta^2 = 0.01$, indicating individuals who had previously participated in NOLS showed smaller increases in connectedness from pre to post as compared to first-time participants. Change in attitude, however, was not associated with previous NOLS experience, $F(1,281) = 0.68$, $p = 0.41$, $\eta^2 = 0.002$.
Understanding changes in connectedness to nature
We then conducted a series of one-way ANOVAs with Scheffe post-hoc to examine whether demographics (i.e., age, gender, previous NOLS experience) and responses to the post-NOLS experience questions (i.e., “Has participating in a NOLS course changed how you will live in everyday life?” and “Has your connection to nature changed as a result of participating in a NOLS course?”), both of which were “yes/no” questions) were associated with variations in both baseline connectedness to nature scores (i.e., pre-NOLS scores) and normalized pre/post differences for the four connectedness variables.
For the demographic variables, age was significantly associated with pre-NOLS scores for emotional connection, $F(2,282) = 9.72$, $p < 0.001$, $\eta^2 = 0.07$, awareness, $F(2,280) = 4.27$, $p = 0.03$, $\eta^2 = 0.03$, and attitude, $F(2,284) = 19.38$, $p < 0.001$, $\eta^2 = 0.14$, such that older individuals had higher baseline connectedness scores than younger individuals. However, age was unrelated to baseline material connection scores, $F(2,280) = 2.51$, $p = 0.26$, $\eta^2 = 0.01$. Age was also associated with pre/post-course changes in emotional connection, $F(2,281) = 3.06$, $p = 0.049$, $\eta^2 = 0.02$, awareness, $F(2,279) = 3.55$, $p = 0.03$, $\eta^2 = 0.03$, and material connection, $F(2,279) = 3.59$, $p = 0.03$, $\eta^2 = 0.03$, indicating older individuals showed smaller changes in connectedness to nature as a result of participating in NOLS.
Gender was also associated with pre-NOLS scores for all four measures of connectedness to nature (all $r’s > 2.8$; all $p’s < 0.005$; all $d’s > 0.34$), indicating females had higher connectedness to nature scores than did males; however, gender was not associated with changes in any of the four connectedness measures (all $F’s < 1.7$; all $p’s > 0.20$). Due to a low number of non-binary ($n = 4$) and transgender ($n = 1$) respondents, they were not included in this statistical analysis.
Previous experience with a NOLS course was associated with baseline (pre-NOLS) scores on all four connectedness to nature variables (all $r’s > 2.4$; all $p’s < 0.02$; all $d’s > 0.29$), such that individuals with previous experience had higher connectedness scores. Previous experience was negatively associated with changes in emotional connection, $F(1,279) = 9.62$, $p = 0.002$, $\eta^2 = 0.04$, awareness, $F(1,278) = 11.85$, $p = 0.001$, $\eta^2 = 0.04$, and material connection, $F(1,279) = 4.16$, $p = 0.04$, $\eta^2 = 0.01$, indicating individuals who had previously participated in NOLS showed smaller increases in connectedness from pre to post as compared to first-time participants. Change in attitude, however, was not associated with previous NOLS experience, $F(1,281) = 0.68$, $p = 0.41$, $\eta^2 = 0.002$.
Next, perceived change in overall connectedness to nature was positively associated with changes in emotional connection, $F(1,275) = 11.38$, $p = 0.001$, $\eta^2 = 0.04$, awareness, $F(1,272) = 8.08$, $p = 0.005$, $\eta^2 = 0.03$, and attitude, $F(1,276) = 5.85$, $p = 0.02$, $\eta^2 = 0.02$, indicating individuals who believed that they had increased their connection to nature showed a concomitant pre/post change for these connection types. Change in material connection, however, was not associated with perceived changes in nature connectedness $F(1,276) = 1.65$, $p = 0.20$, $\eta^2 = 0.01$.
Finally, the belief that NOLS would change how individuals lived their lives going forward was positively associated with changes in emotional connection, $F(1,277) = 4.31$, $p = 0.04$, $\eta^2 = 0.02$, awareness, $F(1,275) = 4.77$, $p = 0.02$, $\eta^2 = 0.02$, and material connection, $F(1,278) = 6.85$, $p = 0.01$, $\eta^2 = 0.03$, such that participants who indicated that NOLS was life-changing showed larger pre/post differences in connectedness.
**Predicting changes in intentions for pro-environmental behaviour**
Intentions for pro-environmental behaviour (PEB) scores significantly increased from pre-test to post-test, $t(284) = -21.17$, $p < 0.001$, $d = 0.76$ (see Fig. 1b). We conducted a correlational analysis to examine whether changes in our four connectedness variables were associated with pre/post changes in intentions for PEB ([post–pre]/pre; see Fig. 2b). Change in material connection had the strongest relationship with PEB ($r = 0.574$), followed by awareness ($r = 0.492$), attitude ($r = 0.412$), and emotional connection ($r = 0.391$; all $p$’s < 0.001). The high correlations prompted us to conduct a series of confirmatory factor analyses to determine whether these constructs were distinct. In all cases, with the exception of material connection which was virtually assessing the same underlying construct as PEB, these distinctions were confirmed (see electronic supplementary material for PCA results). Accordingly, material connections were not included in any further analyses.
To further explore these relationships between emotional and cognitive connections to nature (awareness and attitude) and future intentions for PEB, we ran a multiple regression with change in intentions for PEB as the criterion and change in emotional connection, awareness, and attitude as the predictors. Overall, the model explained a significant 31.9% of the variance in PEB change, $R = 0.565$; $F(3,272) = 42.51$, $p < 0.001$. Change in emotional connection ($r^2 = 0.04$), awareness ($r^2 = 0.08$), and attitude ($r^2 = 0.02$) each emerged as significant unique predictors of intentions for PEB change.
Age, previous experience, perceived change in connectedness, and belief that how individuals live their lives will change (i.e., intended future PEB) following NOLS, were all associated with changes in two of three connectedness variables. As such, we ran a hierarchical multiple regression to examine whether the three predictors identified here (emotional connection, awareness, and attitude) still explained unique variance in intentions for PEB once these other factors had been statistically controlled. Age and the three post-NOLS experience questions were entered as predictors in Step 1, followed by the three connectedness variables in Step 2 (see Table 1). Ultimately, change in emotional connection, awareness, and attitude remained as unique predictors of intentions for PEB change, with no other predictors reaching significance, suggesting that their relationship with intended PEB is unrelated to demographic factors, previous experience, or beliefs about how the experience affected the participant.
| Predictor | $r^2$ | Beta | $t$ | $p$ |
|---------------|-------|-------|-------|------|
| Age | 0.024 | -0.155 | -2.64 | 0.009*|
| Experience | 0.023 | -0.156 | -2.62 | 0.009*|
| Connectedness | 0.016 | 0.129 | 2.18 | 0.030*|
| Life change | 0.025 | 0.159 | 2.69 | 0.008*|
| Age | 0.004 | -0.065 | -1.27 | 0.204|
| Experience | 0.004 | -0.064 | -1.21 | 0.228|
| Connectedness | 0.001 | 0.032 | 0.63 | 0.532|
| Life change | 0.008 | 0.089 | 1.74 | 0.083|
| Emotional | 0.025 | 0.180 | 3.18 | 0.002*|
| Awareness | 0.063 | 0.302 | 5.01 | <0.001**|
| Attitude | 0.025 | 0.189 | 3.15 | 0.002*|
*p < 0.05
**p < 0.001
Discussion
(Re)connecting to nature is relevant to deeper structures and paradigms that underpin behaviours as an emergent system property and offer a promising pathway to system level sustainability. However, individuals connect to nature in different ways and not all connection types hold the same potential as levers for broader system change (Ives et al. 2018). In this study, we examined the changes in connectedness to nature before and after an intensive outdoor program, hypothesizing that connectedness to nature would increase as a result of participation in this program. We further hypothesized that deeper connections to nature would correlate more strongly with greater future intention for PEB than would shallower connections. Here, we interpret the results using these two hypotheses to organize the discussion.
H1: Connectedness to nature will increase with an intensive outdoor program experience
All types of connections to nature showed a significant increase after participating in a NOLS program. Emotional and material connections showed the greatest numerical increase among the four types measured quantitatively. This finding provides evidence that an experience in nature (and in particular, NOLS courses which included an educational component) has a positive effect on multiple connection to nature types, providing a ‘pathway to nature connectedness’ (Lumber et al. 2017; Richardson et al. 2020).
It is important to note that pre-NOLS scores were already high (the average across all connection types was ~4 on a scale of 5). Despite this initial high connectedness, connections to nature still increased after participating in a NOLS program. Those who had participated in previous experiences of this type showed higher pre-NOLS connectedness to nature and their connections increased less than others’. This indicates that connectedness to nature may be long-lasting and our results show a ceiling effect consistent with other NOLS research on wilderness attitudes (Gress and Hall 2017). Despite less additive advantage for building connections to nature, there may be other important benefits to participating in multiple outdoor programs. Stern et al. (2008) found that the length of environmental education programs had a positive effect on multiple variables including connectedness to nature, though they faded over time. The authors concluded that longer programs might enhance long-term outcomes, which is consistent with our results. Similarly, Schultz and Tabanico (2007) found a significant correlation between frequency of visits to natural places and implicit association test scores (which they determined measures implicit connections with nature) across a series of studies. Our study contributes the perspective of a longer, sustained educational program in nature that is different from other studies. It highlights the potential for longer programs and longer periods in nature to influence multiple connections to nature. This is consistent with work by Høyem (2020) who emphasized a distinction between time in nature and reflection on the relationship between people and nature in supporting environmentally responsible behaviour. Only the latter was related to behaviour in their study. Høyem’s (2020) research provides an important perspective that not only were participants spending time in nature, but that they were actively engaged in an educational program. The relative importance, or interactions, of these two aspects of NOLS were not individually examined in this study. The disentangling of time in nature with educational programming would be a useful next step to understand the effect of each.
Further, we examined qualitative responses to an open question of how the respondents’ connection to nature had changed and coded these responses using Ives et al.’s (2018) typology. Here, respondents mentioned emotional and experiential connections more often than any other type, and material connections were not identified. This signals that the concept of connecting to nature, when left to the interpretation of respondents, did not include material connections, even though material connections were identified as the type that increased the most when specifically measured. Rather, respondents largely focused on the emotional and experiential types of connection when responding to the open-ended question. This finding lends further support for using a multi-dimensional typology of connections to nature and using specific tools to query each. Further work to develop methods for assessing material connections (e.g., through tracking resource flows) would be worthwhile along with exploring in more detail how different forms of material connection and consumption relate to physical environmental impacts. Related, but from a different perspective, the overlap between material connectedness and future intentions for PEB opens questions about whether others perceive material connections as a connection to nature at all, or rather as separate actions. Further research to interrogate this question would be valuable.
H2: Deeper connections to nature will be related to a greater intention for future pro-environmental behaviour
Independent of demographic factors, previous experiences, and respondents’ beliefs about how the experience affected them, changes in connections to nature—specifically, emotional and cognitive (both awareness and attitude)—were unique, positive predictors of change in intentions for PEB. However, we were unable to definitively identify whether...
changes in deeper connections to nature were consistently related to a stronger future intention for PEB. The lack of quantitative data related to the philosophical connection pre-NOLS, as well as the strong correlation between material connection and PEB, resulted in a focus on two connections to nature as follows: emotional and cognitive. Material connections and PEB may indeed be a single construct; however, there is value in considering direct consumption (as a subset of the broad range of PEB) as a connection to nature in its own right, following Ives et al. (2018). We found that changes in awareness (part of the cognitive connection) was the strongest predictor of changes in future intention for PEB. This is consistent with previous studies and literature reviews focused on determinants of PEB (e.g., Kollmuss and Agyeman 2002; Blankenberg and Alhusen 2018). For example, in the context of action related to climate change, Masud et al. (2015) found that awareness was directly and indirectly (through attitudes) related to PEB. Müller et al. (2009) found that awareness of risks to nature contributed significantly to willingness for PEB in adolescents. A review of factors that influence PEB by Gifford and Nilsson (2014) identified problem awareness as a significant, indirect influence on PEB intentions. In line with the literature on determinants and factors related to PEB, we acknowledge that the relationship between connection to nature types and intentions for PEB may not be direct in all cases (e.g., between awareness or attitude and PEB) (Kollmuss and Agyeman 2002; and elaborated on in the limitations below); thus further research to assess the potential for mediation and/or moderation among connection types would be beneficial. Furthermore, it is possible that philosophical connections did not require as substantial a shift in order to support and facilitate behaviour change among participants, yet this may be different for alternative cohorts.
Changes in connection(s) to nature which most strongly predicted shifts in future intention for PEB have important implications. While the NOLS program most substantially increased emotional connection, this was not the connection type most strongly related to behaviour—cognitive and material connections were. Thus, the programs may be building deeper connections, but those emotional connections may not be connecting to actions and are thus potentially less effective in facilitating positive environmental change. However, emotional connections may be a slower variable; one that is less directly connected to action but more influential as an indirect factor leading to system change (a deeper leverage point). It may also be plausible that the emotional connection to nature served as scaffolding for other connection types to interact and grow. As other research indicates (Halpenny 2010; Schwass, et al. 2021), there are potential pro-environmental gains to be achieved from additional research on how people transfer an emotional connection from one area in nature to the environment as a whole. Additionally, there is a need for future research to distinguish more carefully between types of PEB. Our findings contribute, and lend additional nuance, to discussions about connections to nature in relation to the goal of broader system changes. Future studies could compare actual behaviours that promote local, small-scale environmental benefits (e.g., litter picking) vs. those that target system-wide change (e.g., political campaigning). Klaniecki et al. (2018) suggest that both can be associated with connection to nature at different scales: from local places to globally significant ecosystems. It would be worthwhile for future research to consider how this concept of scale intersects with different forms of nature connection proposed by Ives et al. (2018).
Our results are consistent with past outdoor program literature showing a positive change in human–nature concepts resulting from participation in an immersive, educational nature-based program (Gress and Hall 2017; Mittelstaedt et al. 1999; Sibthorp et al. 2008; Waage et al. 2012). Outdoor programs outside of NOLS can capitalize on our results by finding ways to unravel how emotional, cognitive, and material connections to nature exist within curricular structures to maximize the potential development of nature connection and future PEB. Paisley et al. (2008) showed that NOLS outdoor program participants generally learn through the following five domains: structure-oriented mechanisms (built into courses by curriculum planners), instructor-oriented mechanisms (the ways in which instructors teach and direct the flow of educational content), student-oriented mechanisms (independent participant learning), student-and-instructor-oriented mechanisms (learning resulting from student and instructor actions), and qualities of the environment (learning through engagement with both natural and social environments). These learning mechanism domains can be applied in future research to different outdoor program processes and learning activities to better understand how participants learn nature connection and develop intentions for PEB. Our results suggest identified learning mechanisms that relate most to emotional, cognitive, and material connections to nature should be carefully considered in curricula planning to best support connections to nature and future PEB.
Further, past research on learning mechanisms, and environmental education outcomes from participation in an outdoor education program demonstrate that opportunities for transformational learning depended on separation from normal life activities, the learning community, experiencing challenges, and time in nature (D’Amato and Krasy 2011). Each of these factors should be examined in terms of their effects on connections to nature and PEB development. More recent work on NOLS and transformational learning highlights the importance of participants needing to experience a challenge to their usual frame of reference to achieve perspective transformation (i.e., a permanent shift of
an individual’s frame of reference or understanding of how the world works) (Meert-Brandsma et al. 2020). Frames of reference share common characteristics with philosophical connectedness to nature. Additional research parsing out connections to nature and PEB and how they interact with a frame of reference challenge will be helpful in understanding short and potential long-term NOLS program learning outcomes, and the extent to which they can be situated within a connectedness to nature lens.
These findings also have potential to inform interventions to connect people to nature outside formal, immersive outdoor programmes. We suggest that landscape practitioners who design and curate natural spaces for people (such as national parks, reserves, and urban open spaces) should consider the potential of these spaces to enhance multiple forms of connections to nature. For example, providing space for appreciation of beauty and allowing places to evoke awe and wonder (enhancing emotional connections), as well as intentionally providing information that can educate and challenge (stimulating attitudinal connections). Doing so may result in a more holistic connection experience and effect and sustain behaviour change.
There are some limitations to our study. We queried pre- and post-NOLS connections to nature and intentions for PEB in a single instrument administered post-NOLS. While there are arguments for and against using this approach (e.g., Little et al. 2020; Moore and Tananis 2009), this decision was practical and we acknowledge that biases may exist in the dataset as a result (Geldhof et al. 2018; Hill 2020; Little et al. 2020; Thomas et al. 2019). Further, the lack of pre- and post-NOLS data for philosophical connections to nature limited our ability to assess the full suite of types of connections in our analyses. Nevertheless, while other studies have used Ives et al.’s (2018) typology in a quantitative approach (Meis-Harris et al. 2021), this was a first effort to quantitatively measure connections to nature in a longitudinal design. Finally, Gifford and Nilsson (2014) caution that self-reported intentions, and even self-reported behaviours, do not fully match actual behaviours. Although many researchers have documented a moderate-to-large statistical relationship between intended and actual behaviours (e.g., Albarracin et al. 2001; Armitage and Connor 2001; Azjen 1991; Oreg and Katz-Gerro 2006; Schwenk and Möser 2009; Webb and Sheeran 2006), there are significant interindividual variations in the strength of this relationship and a number of confounding variables that mediate the link between intentions and actions (e.g., Schwenk and Möser 2009; Webb and Sheeran 2006). Thus, we acknowledge that the future intentions for PEB expressed by respondents here may not necessarily reflect how actual behaviours have unfolded. Regardless, this study contributes to this body of scholarship and demonstrates the potential value of enhancing nature connection to bring about positive impacts for sustainability.
Conclusion
Respondents who participated in a NOLS outdoor program enhanced their connections to nature and increased their intentions for PEB. Using Ives et al.’s (2018) typology as a foundation for measuring changes in connections to nature, we identified changes in the following four connection types: material, experiential, cognitive (separated into awareness and attitude), and emotional. The greatest increase occurred in the emotional connection to nature; however, the connection type that best predicted changes in intentions for PEB was awareness (part of the cognitive connection type). We conclude that the NOLS program fostered multiple connections to nature and intentions for PEB. Thus, the NOLS program may act as an intervention, or lever, to build connections to nature which may ultimately bring about larger system change through PEB.
This research makes several contributions. First, the case study context is different than other studies focused on testing the effects of a nature experience. The NOLS context is unique because it represents a holistic, immersive, sustained nature connection ‘intervention’. Second, we study nature connection in a multi-dimensional way that is just emerging as a focus in the literature (e.g., Meis-Harris et al. 2021). Finally, we use this multi-dimensional approach to investigate relationships between connection types and intentions to change behaviour, connecting these concepts with the notion of system change (e.g., leverage points) (Ives et al. 2018; Abson et al. 2017). Further empirical research is needed to confirm the theoretical positioning of the five types of connections to nature in terms of shallow to deep system leverage points (Ives et al. 2018), and their interactions and positioning as direct or indirect drivers of action that supports broader system change for sustainability.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s11625-022-01119-w.
Acknowledgements We gratefully acknowledge the support of the NOLS program and Shannon Rochelle in particular, as well as the NOLS participants in this study. Julia Baird’s participation in this research was funded, in part, by the Canada Research Chairs program.
Author contributions Conceptualization: JB, GH, CDI, RP; methodology: JB, GD, GH, CDI, RP; formal analysis and investigation: JB, GD, JMH; writing: JB, GD, JMH, GH, CDI, RP; funding acquisition: JB; resources: GH; supervision: JB.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are
included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
References
Abson DJ, Fischer J, Leventon J, Newig J, Schomerus T, Vilsmaier U, Von Wehrden H, Abernethy P, Ives CD, Jager NW, Lang DJ (2017) Leverage points for sustainability transformation. Ambio 46(1):30–39
Ajzen I (1991) The theory of planned behavior. Organ Behav Hum Decis Process 50(2):179–211. https://doi.org/10.1016/0749-5978(91)90020-T
Albarracin D, Johnson BT, Fishbein M, Muellerleile PA (2001) Theories of reasoned action and planned behavior as models of condom use: a meta-analysis. Psychol Bull 127(1):142
Armitage CJ, Conner M (2001) Efficacy of the theory of planned behavior: a meta-analytic review. Br J Soc Psychol 40(4):471–499
Baird J, Hutson G, Plummer R (2020) Examining the potential of connections to nature as an outcome of NOLS. J Outdoor Recreat Educ Leader 12(4):367–379
Berkes F, Folke C (1998) Linking social and ecological systems for resilience and sustainability. In: Linking social and ecological systems: management practices and social mechanisms for building resilience, vol 1, no 4, p 4
Blankenberg AK, Alhusen H (2018) On the determinants of pro-environmental behavior—a guide for further investigations. SSRN J. https://doi.org/10.2139/ssrn.3186089
Bradley JC, Waliczek TM, Zajicek JM (1999) Relationship between environmental knowledge and environmental attitude of high school students. J Environ Educ 30(3):17–21
Carrington M, Neville B, Whitwell G (2010) Why ethical consumers don’t walk their talk: towards a framework for understanding the gap between the ethical purchase intentions and actual buying behaviour of ethically minded consumers. J Bus Ethics 97:139–158
Cooper C, Larson L, Dayer A, Stedman R, Decker D (2015) Are wildlife recreationists conservationists? Linking hunting, birdwatching, and pro-environmental behavior. J Wildl Manag 79(3):446–457
D’Amato LG, Crasyne MF (2011) Outdoor adventure education: applying transformative learning theory to understanding instrumental learning and personal growth in environmental education. J Environ Educ 42(4):237–254. https://doi.org/10.1080/00958964.2011.581313
De Groot WT, van den Born RJ (2003) Visions of nature and landscape type preferences: an exploration in The Netherlands. Landscape Urban Plann 63(3):127–138
Dorninger C, Abson DJ, Fischer J, von Wehrden H (2017) Assessing sustainable biophysical human–nature connectedness at regional scales. Environ Res Lett 12(5):055001
Dunlap R, Liere KV, Mertig A, Jones RE (2000) Measuring endorsement of the new ecological paradigm: a revised NEP scale. J Soc Issues 56(3):425–442
Eaton WM, Eanes FR, Ulrich-Schad JD, Burnham M, Church SP, Arbuckle JG, Cross JE (2019) Trouble with sense of place in working landscapes. Soc Nat Resour 32(7):827–840
Ewert A, Place G, Sibthorpe J (2005) Early life outdoor experiences and an individual’s environmental attitude. Leis Sci 27:229–235. https://doi.org/10.1080/10149040050930853
Ewert A, McAvoy LH (2000) The effects of wilderness settings on organized groups: a state-of-knowledge paper. In: Stephen McCool F, David Cole N, William Borrie T, O’Loughlin J, (Eds.) Wilderness science in a time of change conference—Volume 3: Wilderness as a place for scientific inquiry (p 13–26). Proceedings RMRS-P-15-VOL-3, Ogden, UT, May 23–27, 1999. Missoula, MT, U.S.: Department of Agriculture, Forest Service, Rocky Mountain Research Station
Fischer J, Reichers M (2019) A leverage points perspective on sustainability. People Nature 1(1):115–120
Folke C, Jansson Å, Rockström J, Olsson P, Carpenter SR, Chapin FS, Crépin AS, Daily G, Danell K, Ebbesson J, Elmqvist T (2011) Reconnecting to the biosphere. Ambio 40(7):719–738
Folke C, Biggs R, Norström AV, Reyers B, Rockström J (2016) Social-ecological resilience and biosphere-based sustainability science. Ecol Soc. https://doi.org/10.5751/ES-08748-210341
Geldhof GJ, Warner DA, Finders JK, Thogmartin AA, Clark A, Longway KA (2018) Revisiting the utility of retrospective pre-post designs: the need for mixed-method pilot data. Eval Program Plann 70:83–89
Geng L, Xu J, Ye L, Zhou W, Zhou K (2015) Connections with nature and environmental behaviors. PLoS One 10(5):e0127247
Gifford R, Nilsson A (2014) Personal and social factors that influence pro-environmental concern and behaviour: a review. Int J Psychol 49(3):141–157
Gilllette D, Thomas P, Skok R, McLaughlin T (1991) The effects of wilderness camping and hiking on the self-concept and the environmental attitudes and knowledge of twelfth graders. J Environ Educ 22(3):34–44. https://doi.org/10.1080/00958964.1991.10801966
Gress S, Hall T (2017) Diversity in the outdoors: national outdoor leadership school student’s attitudes about wilderness. J Exp Educ 80:114–134. https://doi.org/10.1177/1053825916698267
Grimmer M, Miles MP (2017) With the best of intentions: a large sample test of the intention-behaviour gap in pro-environmental consumer behaviour. Int J Consum Stud 41(1):2–10
Halpenny EA (2010) Pro-environmental behaviours and park visitors: the effect of place attachment. J Environ Psychol 30(4):409–421. https://doi.org/10.1016/j.jenvp.2010.04.006
Haluza-DeLay R (1999) The culture that constrains: experience of “nature” as part of a wilderness adventure program. J Exp Educ 22:129–137. https://doi.org/10.1177/10538259902200305
Hill LG (2020) Back to the future: considerations in use and reporting of the retrospective pretest. Int J Behav Dev 44(2):184–191
Höyem J (2020) Outdoor recreation and environmentally responsible behavior. J Outdoor Recreat’ Tour. https://doi.org/10.1016/j.jort.2020.100317
Hutson G, Peredun E, Rochelle S (2019) The impact of NOLS rocky mountain on the development of a sense of place. J Exp Educ 42(4):382–397
Ives CD, Giusti M, Fischer J, Abson DJ, Klaniecki K, Dorninger C, Laudan J, Barthel S, Abernethy P, Martín-López B, Raymond CM (2017) Human–nature connection: a multidisciplinary review. Curr Opin Environ Sustain 26:106–113
Ives CD, Abson DJ, von Wehrden H, Dorninger C, Klaniecki K, Fischer J (2018) Reconnecting with nature for sustainability. Sustain Sci 13(5):1389–1397
Kahn PH Jr, Kellert SR (eds) (2002) Children and nature: psychological, sociocultural, and evolutionary investigations. MIT press
Kollmuss A, Agyeman J (2002) Mind the gap: why do people act don’t walk their talk: towards a framework for understanding the case for spatial considerations. Sustain Sci 13(5):1375–1388
Kollmuss A, Agyeman J (2002) Mind the gap: why do people act don’t walk their talk: towards a framework for understanding the case for spatial considerations. Sustain Sci 13(5):1375–1388
Kollmuss A, Agyeman J (2002) Mind the gap: why do people act don’t walk their talk: towards a framework for understanding the case for spatial considerations. Sustain Sci 13(5):1375–1388
Kollmuss A, Agyeman J (2002) Mind the gap: why do people act don’t walk their talk: towards a framework for understanding the case for spatial considerations. Sustain Sci 13(5):1375–1388
Lade SJ, Steffen W, De Vries W, Carpenter SR, Donges JF, Gerten D, Hoff H, Newbold T, Richardson K, Rockström J (2020) Human impacts on planetary boundaries amplified by Earth system interactions. Nat Sustain 3(2):119–128
Little TD, Chang R, Gorrall BK, Waggenspack L, Fukuda E, Allen PJ, Noam GG (2020) The retrospective pretest–posttest design redux: on its validity as an alternative to traditional pretest–posttest measurement. Int J Behav Dev 44(2):175–183
Louv R (2005) Nature deficit. Orion 70–71
Lumber R, Richardson M, Sheffield D (2017) Beyond knowing nature: contact, emotion, compassion, meaning, and beauty are pathways to nature connection. PLoS ONE. https://doi.org/10.1371/journal.pone.0177186May
Mackay CM, Schmitt MT (2019) Do people who feel connected to nature do more to protect it? A meta-analysis. J Environ Psychol 65:101323
Masud MM, Akhtar R, Afroz R, Al-Amin AQ, Kari FB (2015) Pro-environmental behavior and public understanding of climate change. Mitig Adapt Strat Glob Change 20(4):591–600
Mayer FS, Frantz CM (2004) The connectedness to nature scale: a measure of individuals’ feeling in community with nature. J Environ Psychol 24:503–515
Meadows D (1999) Leverage points: places to intervene in a system. The Sustainability Institute, Hartland, USA
Meerts-Brandsma L, Sibthorp J, Rochelle S (2020) Using transformative learning theory to understand outdoor adventure education. J Adventure Educ Outdoor Learn 20(4):381–394. https://doi.org/10.1080/14729679.2019.1686040
Meis-Harris J, Borg K, Jorgensen BS (2021) The construct validity of the multidimensional AIMES connection to nature scale: measuring human relationships with nature. J Environ Manag 280:111695
Meltzer NW, Bobilya A, Faircloth WB, Mitten D, Chandler RM (2018) The effect of an outdoor orientation program on participants’ biophilic expressions. J Outdoor Environ Educ 21(2):187–205. https://doi.org/10.1080/242322-018-0013-x
Mittelstaedt R, Sanker L, VanderVeer B (1999) Impact of a week-long experiential education program on environmental attitude and awareness. J Exp Educ 22:138–148
Moore D, Tananis CA (2009) Measuring change in a short-term educational program using a retrospective pretest design. Am J Eval 30(2):189–202
Müller MM, Kals E, Pansa R (2009) Adolescents’ emotional affinity toward nature: a cross-sectorial study. J Dev Process 4(1):59–69
O’Donnell J (2014N) National Outdoor Leadership School environmental educator notebook. National Outdoor Leadership School, Lander, WY
Oreg S, Katz-Gerro T (2006) Predicting proenvironmental behavior cross-nationally: values, the theory of planned behavior, and value-belief-norm theory. Environ Behav 38(4):462–483. https://doi.org/10.1177/001401871560286012
Paisley K, Furman N, Sibthorp J, Gookin J (2008) Student learning in outdoor education: a case study from the National Outdoor Leadership School. J Exp Educ 30:201–222. https://doi.org/10.1177/10538550703000302
Palmberg I, Kuru J (2010) Outdoor activities as a basis for environmental responsibility. J Environ Educ 31(4):32–36. https://doi.org/10.1080/00958966009598649
Perrin JL, Benassi VA (2009) The connectedness to nature scale: a measure of emotional connection to nature? J Environ Psychol 29:434–440
Pyle R (1993) The thunder tree: lessons from an urban wildland. Houghton Mifflin, Boston, Massachusetts
Restall B, Conrad E (2015) A literature review of connectedness to nature and its potential for environmental management. J Environ Manag 159:264–278
Richardson M, Dobson J, Abson DJ, Lumber R, Hunt A, Young R (2020) Applying the pathways to nature connectedness at a societal scale: a leverage points perspective. Ecosyst People 16(1):387–401. https://doi.org/10.1080/26395916.2020.1844296
Riechers M, Balázi S, Abson DJ, Fischer J (2020) The influence of landscape change on multiple dimensions of human–nature connectedness. Ecol Soc 25(3):3. https://doi.org/10.5751/ES-11651-250303
Riechers M, Balázi A, García-Llorente M, Loos J (2021) Human-nature connectedness as leverage point. Ecosyst People 17(1):215–221
National Outdoor Leadership School. (2016). Learning goals and objectives for NOLS expeditions. Lander, WY. Retrieved from https://www.nols.edu/media/filer_public/c4/65/c465a321-a419-4766-8efa-811b3f955630/nols_learning_goalsandobjectives.pdf
Schultz PW (2002) Inclusion with nature: understanding the psychology of human-nature interactions. In: Schmuck P, Schultz PW (eds) The psychology of sustainable development. Kluwer, New York, pp 61–78
Schultz PW, Tabanico J (2007) Self, identity, and the natural environment: exploring implicit connections with nature. J Appl Soc Psychol 37(6):1219–1247
Schwass NR, Potter SE, O’Connell TS, Potter TG (2021) Outdoor journeys as a catalyst for enhanced place connectedness and environmental stewardship. J Outdoor Environ Educ 24:215–231. https://doi.org/10.1007/s42322-021-00079-6
Schwenk G, Möser G (2009) Intention and behavior: a Bayesian meta-analysis with focus on the Ajzen-Fishbein Model in the field of environmental behavior. Qual Quant 43(5):743–755
Sibthorp J, Furman N, Paisley K, Gookin J (2008) Long-term impacts attributed to participation in wilderness education: preliminary findings from NOLS. Res Outdoor Educ 9:86–103
Soga M, Gaston KJ (2016) Extinction of experience: the loss of human–nature interactions. Front Ecol Environ 14(2):94–101
Tam KP (2013) Dispositional empathy with nature. J Environ Psychol 35:92–104
Thomas EV, Wells R, Baumann SD, Graybill E, Roach A, Truscott SD, Crenshaw M, Crimmins D (2019) Comparing traditional versus retrospective pre-/post-assessment in an interdisciplinary leadership training program. Matern Child Health J 23(2):191–200
Turner WR, Nakamura T, Dinetti M (2004) Global urbanization and the separation of humans from nature. Bioscience 54:585–590
Van den Born RJ (2008) Human-nature connectedness at a societal scale: a leverage points perspective. Ecosyst People 16(1):215–221
Waage T, Paisley K, Gookin J (2012) Understanding the contribution of wilderness-based experiences to the creation of an environmental ethic in youth. Res Outdoor Educ 11:18–27
Webb TL, Sheeran P (2006) Does changing behavioral intentions engender behavior change? A meta-analysis of the experimental evidence. Psychol Bull 132(2):249
Whitburn J, Linklater W, Abrahamse W (2020) Meta-analysis of human connection to nature and proenvironmental behavior. Conserv Biol 34(1):180–193. https://doi.org/10.1111/cobi.13381
Wilson EO (1984) Biophilia. Biophilia. Harvard University Press
Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3146,
1
],
[
3146,
9294,
2
],
[
9294,
14524,
3
],
[
14524,
20425,
4
],
[
20425,
24980,
5
],
[
24980,
31616,
6
],
[
31616,
36046,
7
],
[
36046,
41612,
8
],
[
41612,
47749,
9
],
[
47749,
53730,
10
],
[
53730,
61118,
11
],
[
61118,
67811,
12
]
]
} |
9d499de25a9c168c5b4229e1958670d8ca363bc1 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 8,
"total-fallback-pages": 0,
"total-input-tokens": 29200,
"total-output-tokens": 12640,
"fieldofstudy": [
"Biology",
"Medicine"
]
} | Association of SELE genotypes/haplotypes with sE-selectin levels in Taiwanese individuals: interactive effect of MMP9 level
Semon Wu1,2†, Lung-An Hsu3,4†, Ming-Sheng Teng2, Jeng-Feng Lin5, Hsien-Hsun Chang2, Yu-Chen Sun6, Hsuan-Pu Chen7 and Yu-Lin Ko5,8*
Abstract
Background: E-selectin is implicated in various inflammatory processes and related disorders. We aimed to investigate the role of SELE-gene genotypes/haplotypes on plasma levels of MMP9 and sE-selectin in Taiwanese individuals.
Methods: Five hundred twenty individuals were enrolled. Seven tagging SELE single nucleotide polymorphisms were analyzed.
Results: SELE genotypes were found associated with MMP9 and sE-selectin levels. Multivariate analysis identified that the most significant genetic polymorphism (rs5368 genotype) was independently associated with MMP9 levels (P < 0.001). One haplotype (GGAGAGT) was marginally associated with MMP9 levels (P = 0.0490). One SELE SNP, (rs3917406, P = 0.031) was associated with sE-selectin levels after adjusting for MMP9 and sICAM1 levels. Subgroup and interaction analysis revealed association of SELE SNP rs10800469 with sE-selectin levels only in the highest quartile of MMP9 level (P = 0.002, interaction P = 0.023). Haplotype analysis showed one haplotype (AAAAAGC) borderline associated with sE-selectin level (P = 0.0511).
Conclusion: SELE genotypes/haplotypes are independently associated with MMP9 and E-selectin levels in Taiwanese individuals. The associations of SELE genotypes/haplotypes with sE-selectin levels are affected by MMP9 levels.
Keywords: E-selectin, Genetic association study, Polymorphism, Matrix metalloproteinase 9, Haplotype, Interaction
Background
Chronic inflammation plays an import role in a variety of pathological disorders, including chronic pulmonary disease, chronic renal disease, and cardiovascular disease [1-3]. Chronic inflammation is also associated with abdominal obesity, smoking, and physical inactivity. The process of inflammation involves the interplay of many pro-inflammatory markers including C-reactive protein, fibrinogen, cytokines, adhesive molecules, and proteases [1,4]. E-selectin, an endothelial adhesive molecule, is a glycoprotein expressed exclusively on endothelial cells in response to inflammatory cytokines. It mediates the interaction of circulating leukocytes in various physiological and pathological settings [5]. E-selectin is also involved in activation of intracellular signaling pathways involved in the trans-endothelial migration of leukocytes [6]. Leukocyte and endothelial interactions contribute to a variety of vascular disease processes, such as acute and chronic inflammation and atherosclerosis. Soluble E-selectin (sE-selectin), thought to be shed from activated endothelial cells, has also been associated with atherosclerosis [7].
Single nucleotide polymorphisms (SNPs) of the SELE gene, encoding the E-selectin protein, have been linked to various disease states. The Ser128Arg gene variant, the most commonly reported SELE-gene polymorphism,
is associated with a wide variety of disorders, including coronary artery disease, venous thrombosis, ischemic cerebral vascular disease, postoperative myocardial infarction, prognosis of colorectal cancer, restenosis after successful coronary angioplasty, severity of atherosclerotic arterial disease, peripheral arterial occlusive disease, and coronary calcification [8-12]. Common variants of the \textit{SELE} gene have also been found associated with the susceptibility to either Graves’ disease or hypertension [13-15]. However, the association between \textit{SELE} SNPs and E-selectin levels has been controversial [15-17], and the association between \textit{SELE} SNPs and other inflammatory marker levels has not been reported. This investigation aimed to elucidate the association between \textit{SELE} SNPs and the plasma levels of sE-selectin and MMP9, in Taiwanese individuals.
\section*{Methods}
\subsection*{Study population}
A total of 520 study participants were enrolled for study (mean ± SD): 264 men, age = 43.9 ± 9.4 years; 256 women, age = 45.8 ± 9.4 years. They responded to a questionnaire on their medical history and lifestyle characteristics, and were recruited during routine health examinations between October 2003 and September 2005 at the Chang Gung Memorial Hospital. All participants provided written informed consent. Exclusion criteria included cancer, current renal or liver disease, and a history of myocardial infarction, stroke, or transient ischemic attacks. In addition, individuals with a history of regular use of medication for diabetes mellitus, hypertension and/or lipid-lowering drugs were excluded from the analysis, because previous reports revealed that these agents affect the expression or concentrations of inflammatory markers [18-20]. The clinical and biometric features of the study group are summarized in Table 1. Hypertension was defined as a systolic blood pressure (BP) ≥ 140 mmHg and/or diastolic BP ≥ 90 mmHg, or regular use of antihypertensive medication. Obesity was defined as a body mass index (BMI) ≥ 25 kg/m², according to the Asian criteria [21]. Current smokers were defined as individuals who smoked at least one cigarette per day at the time of the survey. The study was approved by the Ethics Committee of the Tzu-Chi Memorial Hospital.
\subsection*{Laboratory examination}
Before starting the study, all participants underwent an initial screening assessment that included medical history, vital signs, a 12-lead electrocardiogram, and measurement of lipid variables and novel risk factors. A total of 15 mL of venous blood was collected in the morning
\begin{table}[h]
\centering
\caption{Baseline characteristics of the study subjects}
\begin{tabular}{lcccc}
\hline
& Total & Men & Women & \textit{P} value \\
\hline
Number & 520 & 264 & 256 & \\
Age (years) & 44.8 ± 9.4 & 43.9 ± 9.4 & 45.8 ± 9.4 & 0.023 \\
Systolic BP (mm Hg) & 112.8 ± 16.1 & 113.8 ± 14.3 & 111.8 ± 17.8 & 0.172 \\
Diastolic BP (mm Hg) & 75.0 ± 10.0 & 77.0 ± 9.8 & 73.0 ± 9.9 & < 0.001 \\
Total cholesterol (mg/dL) & 199.4 ± 36.2 & 202.7 ± 36.2 & 196.1 ± 36.0 & 0.036 \\
HDL-cholesterol (mg/dL) & 55.8 ± 14.5 & 49.9 ± 12.1 & 62.0 ± 14.1 & < 0.001 \\
LDL-cholesterol (mg/dL) & 116.7 ± 33.1 & 120.5 ± 34.3 & 112.8 ± 31.5 & 0.008 \\
Triglycerides (mg/dL) & 139.0 ± 111.4 & 170.1 ± 137.6 & 107.0 ± 60.7 & < 0.001 \\
Body mass index (kg/m²) & 24.1 ± 3.4 & 24.8 ± 3.1 & 23.4 ± 3.6 & < 0.001 \\
Waist circumference (cm) & 84.5 ± 9.5 & 87.5 ± 7.6 & 81.4 ± 10.3 & < 0.001 \\
Current smokers (%) & 19.8 & 35.2 & 3.9 & < 0.001 \\
Diabetes mellitus (%) & 2.5 & 2.7 & 2.4 & 0.526 \\
Glucose (AC) (mg/dL) & 95.5 ± 22.3 & 97.9 ± 25.6 & 93.1 ± 17.9 & 0.014 \\
HOMA-IR index & 2.2 ± 1.4 & 2.3 ± 1.6 & 2.0 ± 1.1 & 0.002 \\
CRP (mg/L) & 1.0 ± 1.4 & 1.1 ± 1.4 & 1.0 ± 1.3 & 0.060 \\
Fibrinogen (mg/dL) & 260.2 ± 66.7 & 257.7 ± 68.6 & 262.8 ± 64.7 & 0.381 \\
sE-selectin (ng/mL) & 52.5 ± 25.7 & 59.8 ± 27.0 & 45.0 ± 22.0 & < 0.001 \\
sICAM1 (ng/mL) & 239.8 ± 113.2 & 243.8 ± 109.6 & 235.8 ± 116.8 & 0.281 \\
MMP9 (ng/mL) & 141.9 ± 111.8 & 154.1 ± 112.8 & 129.4 ± 109.6 & < 0.001 \\
\hline
\end{tabular}
\end{table}
\textit{BP}, blood pressure; \textit{HDL}, high-density lipoprotein; \textit{LDL}, low-density lipoprotein; \textit{CRP}, C-reactive protein; \textit{sICAM1}, soluble intercellular adhesive molecule 1; \textit{sE-selectin}, soluble E-selectin; \textit{MMP9}, matrix metalloproteinase 9; Continuous variables are presented as mean ± SD. CRP, sICAM1, sE-selectin and MMP9 values were transformed logarithmically before statistical testing to meet the assumption of normal distributions; however, the untransformed data are shown.
after an overnight (8–12 hours) fast. Venous blood samples were collected from an antecubital vein using a 21-gauge needle. Serum, EDTA, sodium fluoride, and sodium citrate plasma were obtained by centrifugation at 3000 × g for 15 minutes at 4°C. Immediately thereafter, serum/plasma samples were frozen and stored at –80°C prior to analysis. All measurements were performed in a central laboratory. The homeostasis model assessment of insulin resistance (HOMA-IR) index was calculated using the formula: HOMA-IR = fasting serum insulin (μU/mL) × fasting plasma glucose (mmol/L)/22.5.
Assays
Most markers, including C-reactive protein (CRP), sE-selectin, sICAM-1, and MMP9 were measured using a sandwich enzyme-linked immunosorbent assay (ELISA) developed in-house. All in-house kits were compared with commercially available ELISA kits and showed good to excellent correlation [22-24]. Serum insulin levels were measured using an immunoradiometric assay (Bio-source, Nivelles, Belgium). Glucose was determined enzymatically using the hexokinase method. Total cholesterol and triglyceride concentrations were measured by automatic enzymatic colorimetry. High density lipoprotein (HDL) cholesterol levels were measured enzymatically after phosphotungsten/magnesium precipitation. Low density lipoprotein (LDL) cholesterol was either calculated from the Friedewald formula or, in patients with triglycerides > 400 mg/dL, detected with commercially available ELISA kits and showed good to excellent correlation [22-24]. Serum fibrinogen levels were determined using the Clauss method adapted with phosphotungsten/magnesium precipitation. Low density lipoprotein (LDL) cholesterol was either calculated from the Friedewald formula or, in patients with triglycerides > 400 mg/dL, detected with commercial reagents by standard protocol. Plasma fibrinogen levels were determined using the Clauss method adapted with phosphotungsten/magnesium precipitation. Low density lipoprotein (LDL) cholesterol was either calculated from the Friedewald formula or, in patients with triglycerides > 400 mg/dL, detected with commercial reagents by standard protocol. Plasma fibrinogen levels were determined using the Clauss method adapted with phosphotungsten/magnesium precipitation. Low density lipoprotein (LDL) cholesterol was either calculated from the Friedewald formula or, in patients with triglycerides > 400 mg/dL, detected with commercial reagents by standard protocol. Plasma fibrinogen levels were determined using the Clauss method adapted with phosphotungsten/magnesium precipitation.
Genomic DNA extraction and genotyping
Genomic DNA was extracted as reported previously [25,26]. From the published sequence of the SELE gene, oligonucleotide primers were generated to amplify fragments of genomic DNA containing the genetic polymorphisms reported on the websites of GenePipe (http://genepipe.ncgc.sinica.edu.tw/visualsnp) and the NCBI SNP database (http://www.ncbi.nlm.nih.gov/SNP). Seven SNPs within SELE were chosen in this study (Additional file 1: Table S1). Six tagSNPs were chosen according to a previous study reported by Chen et al. [15], who selected tagSNPs by running the tagger program implemented in Haplovew software. The SNP rs5361 (Ser128Arg) was selected because it was located in an exon, resulted in an amino acid substitution and has been linked to a wide variety of disorders [8-12]. Genotyping for the SNPs rs5368, rs3917412, and rs5361 was performed using polymerase chain reaction and restriction enzyme digestion. Genotyping for the SNPs rs10800469, rs3917406, rs2179172, and rs3917419 were performed using TaqMan SNP Genotyping Assays obtained from Applied Biosystems (ABI, Foster City, CA, USA).
Statistical analysis
To determine the association between gender and other clinical data, we used chi-square test and two-sided t-test for categorical variables and continuous variables, respectively. The clinical characteristics that were continuous variables are expressed as means ± SDs and were tested using a two-sided t-test or analysis of variance (ANOVA). Furthermore, a general linear model was applied to capture the major effect of each polymorphism on clinical phenotype variables, with BMI, age, gender and smoking status as confounding covariates. We used recessive models for numeric association test after recoding our SNPs from categorical variables to continuous variables, such as 0, 1 of a particular allele. CRP, sICAM1, sE-selectin, sP-selectin, and MMP9 values were transformed logarithmically before analysis to adhere to an assumption of normality. The result was adjusted by false discovery rate (FDR) for multiple test correction and the regression coefficient with FDR P value <0.05 was considered as significant. Besides, stepwise linear regression analysis was used to determine independent predictors of MMP9 levels. Interactions between each SNP, the level of sE-selectin, and MMP9 levels were tested with two-way ANOVA. When interaction terms were found to be significant, stratified analyses of the genetic variants of the genotypes (e.g., target genotypes affected by MMP9 levels) and sE-selectin level were performed to further investigate interactive effects while controlling for other variables including age, gender, BMI, and smoking. All calculations were performed with standard statistical SPSS software. For the assessment of association between haplotypes and clinical variables, Golden Helix SVS Win32 7.3.1 software were applied and the haplotype with FDR P value <0.05 was reported. We used SNPStats software (available at http://bioinfo.iconcologia.net/SNPstats) [27] to calculate the linkage disequilibrium between SNPs and the deviation from Hardy-Weinberg equilibrium. Values of P < 0.05 using a two-sided test were considered statistically significant.
Results
Clinical and biochemical characteristics
A summary of demographic features, clinical and lipid profiles, and inflammatory biomarkers for the study participants stratified by gender is provided in Table 1. No significant deviations from the Hardy-Weinberg equilibrium were detected for the studied polymorphisms (P = 0.73, 0.71, 0.17, 0.21, 0.88, 0.92, and 0.80 for SNPs rs10800469, rs3917406, rs3917412, rs5361, rs3917412, rs2179172,
rs3917419, and rs5368, respectively). All these SNPs were in strong pairwise linkage disequilibrium, except for rs5361, for which the calculation was not possible due to the identification of only two of this genotype among the study participants (Additional file 1: Table S2).
**Associations of the SELE gene polymorphisms with serum levels of MMP9 levels**
Table 2 presents a comparison of the distributions of the serum MMP9 concentrations according to SELE genotype status. With the recessive model, the minor alleles of rs3917419 and rs5368 were found to be associated with higher MMP9 levels ($P = 0.002$ and $P = 1.4 \times 10^{-4}$, respectively) after adjusting for age, gender, smoking status, and BMI (Table 2). These associations remained statistically significant after multiple comparisons adjustment (FDR $P = 0.005$ and $P = 6.9 \times 10^{-4}$, respectively).
**SELE haplotypes and MMP9 levels**
Because the single SNP regression demonstrated that multiple sites within the SELE gene significantly affect MMP9 level, haplotypes were inferred to capture possible allelic associations. In the present investigation, seven common haplotypes (≥ 1% frequency) were derived from seven SNPs, accounting for 99.6% of all inferred haplotypes (Table 3). In haplotype analysis, two haplotypes inferred from seven SNPs (AAAAAGC and GGAGAGT) were found to be associated with either decreased or increased MMP9 levels ($P = 0.0234$ and $P = 0.007$, respectively). However, only the observed association between haplotype GGAGAGT and MMP9 levels remained marginally significant after multiple comparisons adjustment (FDR $P = 0.0490$).
**Stepwise regression analysis of MMP9 levels using a general linear model in the study population**
In addition to five previously reported independent variables—age, current smoker, fibrinogen levels, fasting plasma glucose level, and an MMP9 SNP rs2274756 [28]—the E-selectin gene variants were used for further multivariate analysis. In a stepwise regression analysis, the most significant genetic polymorphism rs5368 genotypes with recessive model, age, gender, smoking status, and fibrinogen levels were all independently associated with MMP9 levels ($P < 0.001$) (Table 4).
**Associations of the SELE genotypes/haplotypes with sE-selectin levels: focus on interactive effects**
In contrast to the highly significant association with MMP9 levels, after the adjustment for age, gender, smoking status, and BMI, there was a marginally significant association of the SELE gene rs3917406 polymorphism with sE-selectin level ($P = 0.023$) (Table 2). Because of the significant association of sE-selectin levels with sICAM1, and MMP9 levels ($r = 0.306$, $P < 0.001$ for sICAM1 and $r = 0.177$, $P < 0.001$ for MMP9), associations between SELE genotypes/haplotypes and sE-selectin were explored again in a novel study population.
| rs Number and Genotypes | MMP9 (mg/L) | $P$ value* | Adjusted $P$ value | sE-selectin (mg/L) | $P$ value* | Adjusted $P$ value |
|-------------------------|-------------|------------|--------------------|-------------------|------------|--------------------|
| rs10800469 AA (n = 113) | 143.0 ± 107.4 | 0.929 | 1 | 55.0 ± 30.2 | 0.162 | 0.060 |
| AG + GG (n = 388) | 141.9 ± 113.9 | 0.477** | - | 51.9 ± 24.3 | 0.023 | 0.005 |
| rs3917406 GG (n = 122) | 159.4 ± 138.9 | 0.066 | 0.031 | 49.0 ± 27.6 | 0.943** | 0.865** |
| AA + AG (n = 378) | 136.6 ± 102.0 | 0.477** | - | 53.7 ± 25.1 | 0.023 | 0.005 |
| rs5361 AA (n = 487) | 142.9 ± 113.4 | 0.477** | - | 52.6 ± 25.7 | 0.943** | 0.865** |
| AC (n = 12) | 118.1 ± 62.7 | 0.964 | 0.031 | 56.3 ± 31.3 | 0.023 | 0.005 |
| CC (n = 0) | - | - | - | - | - | - |
| rs3917412 AA (n = 40) | 139.4 ± 84.5 | 0.964 | 0.031 | 49.5 ± 19.7 | 0.624 | 0.024 |
| AG + GG (n = 459) | 142.6 ± 114.7 | 0.477** | - | 52.9 ± 26.3 | 0.943** | 0.865** |
| rs2179172 CC (n = 21) | 137.8 ± 100.5 | 0.872 | 0.031 | 50.1 ± 24.9 | 0.772 | 0.492 |
| AA + AC (n = 476) | 143.0 ± 113.1 | 0.477** | - | 52.9 ± 25.9 | 0.943** | 0.865** |
| rs3917419 AA (n = 15) | 209.5 ± 119.3 | 0.002 | 0.336 | 61.1 ± 47.2 | 0.326 | 0.224 |
| AG + GG (n = 485) | 139.4 ± 110.9 | 0.002 | 0.336 | 53.4 ± 24.8 | 0.326 | 0.224 |
| rs5368 TT (n = 25) | 234.0 ± 209.9 | 1.1 × 10^{-4} | 0.336 | 45.6 ± 14.4 | 0.354 | 0.181 |
| CC + CT (n = 476) | 137.0 ± 102.5 | 1.1 × 10^{-4} | 0.336 | 52.6 ± 25.1 | 0.354 | 0.181 |
Continuous variables are presented as mean ± SD. MMP9 and sE-selectin values were logarithmically transformed before statistical testing to meet the assumption of normal distributions; however, the untransformed data are shown. *Multiple linear regression, adjusted for age, gender, smoking and BMI. **Multiple linear regression, adjusted for age, gender, smoking, BMI, sICAM1 and MMP9 levels. Adjusted $P$ values were computed by the false discovery rate method. **Comparison between AA and AC genotypes.
MMP9, respectively), we further elucidated possible interactive effects of sICAM1 and MMP9 levels on the association between the SELE gene polymorphisms and sE-selectin level. By multivariate analysis with sICAM1 and MMP9 levels included for analysis, significant associations of rs3917406 was found with sE-selectin level \( (P = 0.005) \) (Table 2). The association also remained statistically significant after multiple comparisons adjustment (FDR \( P = 0.031 \)) (Table 2). Subgroup analysis revealed association of SELE SNP rs10800469 with sE-selectin only in the highest quartile of MMP9 levels \( (66.0 \pm 38.7 \text{ vs. } 48.0 \pm 18.4 \text{ mg/dL, AA + AG vs. GG genotypes, } P = 0.002) \). Interaction analysis revealed interaction of SELE genotypes and MMP9 levels on sE-selectin levels (interaction \( P = 0.023 \)) (Figure 1). Haplotype analysis showed two haplotypes, AAAAAGC and GGAGCGC, were associated with sE-selectin levels \( (P = 0.0425, \text{ respectively}) \) (Table 5). However, after multiple comparisons adjustment, the association of GGAGCGC became insignificant; whereas the apparent association between haplotype AAAAAGC and sE-selectin levels became borderline significant (FDR \( P = 0.0511) \).
**Discussion**
The present investigation analyzed the association of genetic variants of the SELE gene with serum inflammatory marker levels. The results showed that, in addition to previously reported MMP9 genotypes, the SELE gene is the second locus that is significantly associated with MMP9 level in Taiwanese individuals. The association of SELE genotypes/haplotypes with MMP9 level is significant after the adjustment of other independent factors including age, gender, smoking status, fibrinogen levels, and MMP9 genotypes. To the best of our knowledge, this is the first investigation revealing that the genetic determinants of MMP9 levels may include a cellular adhesive molecule locus. Further, SELE genotypes/haplotypes are independently associated with sE-selectin levels, especially after the adjustment of sICAM1 and MMP9 levels. Interaction analysis also revealed an interactive effect of MMP9 level on the association of SELE genotypes with sE-selectin level. These results provide further evidence of the close relationship between cellular adhesive molecules and matrix metalloproteinases.
The association between cellular adhesive molecules and matrix metalloproteinases has been reported previously. Aoudjit et al. [29] demonstrated that firm adhesion of T lymphoma cells to endothelial cells participates in the production of MMP9 in both cell types through bi-directional signaling pathways, and identified ICAM-1/LFA-1 as a key interaction in the up-regulation of MMP9 in T lymphoma cells. MMP9 also cleaved membrane ICAM1 in an in vitro model, which may result in increased sICAM1 [30]. Although direct evidence linking E-selectin and MMP9 molecules is absent, there are several possibilities for the involvement of the SELE gene in the signaling pathways affecting gene expression and the serum level of MMP9. First, both E-selectin and MMP9 have been shown to be involved in the process of trans-endothelial migration (TEM) of leukocytes and cancer cells. Endothelial E-selectin is quickly and transiently expressed following a challenge by proinflammatory stimuli and plays a pivotal role in mediating cell-cell interactions between breast cancer cells, colon carcinoma cells, leukocytes,
and endothelial cells [31-34]. Historical literature reporting on MMP9 function in vitro also provided a compelling story implicating MMP9 as a rate-limiting extra-cellular protease involved in cell migration across basement membranes, a process that has been found to be orchestrated by an ever-increasing number of molecules, including selectins, integrins, and their ligands on the endothelium that mediate rolling, firm adhesion, and diapedesis [35-37]. Second, studies on endothelial signaling by adhesive molecules and the concomitant analysis of associated adapter proteins have been most successful for E-selectin and ICAM-1. There is ample evidence for the signal capacity of E-selectin, both towards the actin cytoskeleton as well as to p42 MAPK/ERK activation and the induction of c-fos [38-40]. MMP9, an inducible enzyme, can be expressed in a number of cells under the action of TNF-α, IL-1β, PDGF, and some other growth factors. This expression has been shown to be mediated via ERK1/2, p38 MAPK, and/or JNK signal transduction pathways [41-43]. Third, both E-selectin and MMP9 have been shown to be involved in cancer-cell invasion and metastasis. For a long time, the proteolytic remodeling of extracellular matrix by MMPs, serine proteases, and cathepsins was considered to be a critical determinant of tumor cell invasiveness [44]. Thus, further studies involving direct analysis of the interaction between E-selectin and MMP9 molecules using in vitro models may help us to elucidate the role of E-selectin on MMP9 expression.
Previous studies on the association between SELE SNPs and sE-selectin levels have been controversial. Chen et al. [15] revealed significant association of SELE haplotypes with sE-selectin level in a Chinese population. In a genome-wide association study, Paterson et al. [17] found no evidence (probability value < 0.01) of association between SNPs in or near the SELE gene and sE-selectin levels. After analyzing 628 individuals from different ethnic populations, Miller et al. [16] found no evidence of association between the SELE S128R polymorphism and circulating sE-selectin levels. Our data
**Figure 1** Interactive effect of MMP9 levels on the association between rs10800469 and sE-selectin levels. After adjusting for clinical covariates, minor allele of rs10800469 of the SELE gene was found to be associated with decreased sE-selectin levels, predominantly in highest quartile of MMP9 levels subjects (P = 0.002). Interaction analysis revealed an interaction of MMP9 levels with the rs10800469 genotype (interaction P = 0.023, after the adjustment of age, gender, BMI, smoking, sICAM1 and MMP9).
| SNP 1 | SNP 2 | SNP 3 | SNP 4 | SNP 5 | SNP 6 | SNP 7 | Frequency | Coef | SE | P value | Adjusted P value |
|-------|-------|-------|-------|-------|-------|-------|-----------|------|----|---------|-----------------|
| H1 | A | A | A | A | A | G | C | 0.2542| 0.0421| 0.0157 | 0.0073 | 0.0511 |
| H2 | G | G | A | G | A | G | T | 0.2266| -0.0167| 0.0133 | 0.2072 | 0.3626 |
| H3 | G | G | A | A | G | C | G | 0.2080| -0.0281| 0.0139 | 0.0425 | 0.1487 |
| H4 | A | A | A | G | A | A | C | 0.1384| 0.0255 | 0.0152 | 0.0935 | 0.2182 |
| H5 | G | A | A | G | A | G | C | 0.0651| -0.0175| 0.0213 | 0.4124 | 0.5774 |
| H6 | A | A | A | G | A | G | C | 0.0592| 0.0070 | 0.0242 | 0.7725 | 0.9012 |
| H7 | G | G | A | A | G | A | C | 0.0484| -0.0066| 0.0256 | 0.7968 | 0.7968 |
**Table 5** Association of SELE locus haplotypes with sE-selectin level (adjusted for age, gender, BMI, smoking, sICAM1 and MMP9).
SNP1: rs10800469, SNP2: rs3917406, SNP3: rs5361, SNP4: rs3917412, SNP5: rs2179172, SNP6: rs3917419, SNP7: rs5368. Multiple linear regression, adjusted for age, gender, smoking, BMI, sICAM1 and MMP9 levels. Adjusted P values were computed by the false discovery rate method.
revealed an association between SELE genotypes and sE-selectin levels only in the highest quartile of MMP9 levels. Proteolytic cleavage of cellular adhesive molecules on the cell membrane by proteases has been reported before, however, it is unknown if the membrane E-selectin molecule can be cleaved by MMP9. Significant associations between sE-selectin and MMP9 levels were noted in our study, suggesting a possible interaction between these two molecules. Further study is necessary to elucidate the role of MMP9 on sE-selectin level.
Some limitations of our study deserve consideration. One limitation of the study is the relatively low number of subjects genotyped; replication in a second cohort would improve the strength of the study. Furthermore, only seven of the SELE SNPs were analyzed, and the incomplete genotyping may not represent all of the haplotypes in the SELE gene. Another limitation of this study is its cross-sectional design, which could only draw limited inferences with regard to the relationships between exposure and outcome. After the use of FDR for multiple testing corrections, only few SELE genetic variances remained significantly associated with MMP9 or sE-selectin level and the association between haplotypes on MMP9 or sE-selectin levels became marginal. Therefore, cautious and conservative interpretation of the data is needed. Independent association studies with larger sample sizes and more complete genotyping, especially using a prospective design, are needed to confirm these results before any definitive conclusions can be drawn.
Conclusions
In conclusion, our data revealed for the first time that SELE SNPs are independently associated with MMP9 levels, in addition, SELE gene variants interacted with MMP9 levels for the association with sE-selectin levels in Taiwanese individuals. The findings have implications for the prediction of inflammation-related disorders. Further studies of the interrelationship between cellular adhesive molecules and matrix metalloproteinases are needed to confirm MMP9 levels as a possible link between SELE genotypes/haplotypes and inflammation-related disorders.
Additional file 1: Table S1. Primer sequences and restriction enzyme (RE) used in SELE gene polymorphisms. S2. Linkage disequilibrium between SELE genetic polymorphisms.
Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
S W and L-A H participated in genotyping, performed statistical analysis and drafted the manuscript. M-S T and H-H C prepared the DNA samples and participated in genotyping. J-F L participated in sample collection and prepared the DNA samples. Y-C S participated in ELISA assay. H-P C performed and corrected statistical analysis. Y-L H supervised the study and revised the manuscript. All authors read and approved the final manuscript.
Acknowledgements
This study was supported by a grant from the National Science Council, Taiwan (NSC100-2314-B-303-010), a grant from Tzu Chi University (TCRP 99001-04Y1-02) and grants from the Buddhist Tzu Chi General Hospital (TCRD-110-01-01 and TCRD-TPE-97-13) to Y-L. Ko, and a grant from the National Science Council, Taiwan (NSC 98-2314-B-182A-086) to L-A. Hsu.
Author details
1Department of Life Science, Chinese Culture University, Taipei, Taiwan.
2Department of Medical Research, Buddhist Tzu Chi General Hospital, Taipei Branch, Taipei, Taiwan. 3The First Cardiovascular Division, Department of Internal Medicine, Chang Gung Memorial Hospital, Taipei, Taiwan. 4Chang Gung University College of Medicine, Taipei, Taiwan. 5Division of Cardiology, Department of Internal Medicine, Buddhist Tzu Chi General Hospital, Taipei branch, 289 Jianguo Road, Xindian City, Taipei 231, Taiwan. 6Department of Laboratory Medicine, Chang Gung Memorial Hospital, Taipei, Taiwan.
7Department of Neurology, University of California, San Francisco, USA.
8School of Medicine, Tzu Chi University, Hualien, Taiwan.
Received: 30 June 2012 Accepted: 20 November 2012
Published: 29 November 2012
References
1. Hansson GK: Immune mechanisms in atherosclerosis. Arterioscler Thromb Vasc Biol 2001, 21:1876–1890.
2. Snoeck-Stroband JB, Postma DS, Lapperre TS, Gosman MM, Thiadens HA, Kaufman HF, Sont JK, Jansen DF, Steerk PZ: Airway inflammation contributes to health status in COPD: a cross-sectional study. Respir Res 2006, 7:146.
3. Keller CR, Odden MC, Fried LF, Newman AB, Angliman S, Green CA, Cummings SR, Harris TB, Shlipak MG: Kidney function and markers of inflammation in elderly persons without chronic kidney disease: the health, aging, and body composition study. Kidney Int 2007, 71:239–244.
4. Lind L: Circulating markers of inflammation and atherosclerosis. Atherosclerosis 2003, 169:205–214.
5. Krabbe KS, Pedersen M, Bruunsgaard H: Inflammatory mediators in the elderly. Exp Gerontol 2004, 39(suppl 1):67–89.
6. van Buul JD, Gordijk PL: Endothelial adapter proteins in leukocyte transmigration. Thromb Haemost 2009, 101:649–655.
7. Roldán V, Marín F, Lip GY, Bann AD: Soluble E-selectin in cardiovascular disease and its risk factors. A review of the literature. Thromb Haemost 2003, 90:1007–1020.
8. Ellsworth DL, Bielak LF, Turner ST, Sheedy PF 2nd, Boenwinkle E, Peyser PA: Gender- and age-dependent relationships between the E-selectin S128R polymorphism and coronary artery calcification. J Mol Med 2001, 79:390–398.
9. Andreotti F, Porto I, Cesà F, Maseri A: Inflammatory gene polymorphisms and ischaemic heart disease: review of population association studies. Heart 2002, 87:107–112.
10. Flex A, Gaetani E, Papaleo P, Strazza G, Proia AS, Pecorini G, Tondi P, Pola P, Pola R: Proinflammatory genetic profiles in subjects with history of ischemic stroke. Stroke 2004, 35:2270–2275.
11. Jilma B, Kyrle PA: Proinflammatory cytokines in the pathogenesis of Smurf1 and Smurf2 gene polymorphisms. Circulation 2010, 122:1276–1281.
12. Podgoreanu MV, White WD, Morris RW, Mathew JP, Stafford-Smith M, Welsby IJ, Gloccott HP, Milano CA, Newman MF, Schwinn DA, Perioperative Genetics and Safety Outcomes Study (PEGASUS) Investigative Team.
Inflammatory gene polymorphisms and risk of postoperative myocardial infarction after cardiac surgery. Circulation 2006, 114:274–281.
13. Takei T, Iida A, Nitta K, Tanaka T, Ohnishi Y, Yamada R, Maeda S, Tsunoda T, Takeoka S, Ito K, Honda K, Uchida K, Tsuichiyi K, Suzuki Y, Fujikota T, Uijie T, Nagane Y, Miyano S, Narita I, Geojy F, Nihei H, Nakamura Y: Association between single-nucleotide polymorphisms in select gene and immunoglobulin A nephropathy. Am J Hum Genet 2002, 70:781–786.
14. Chang YP, Liu X, Kim JD, Ikeda MA, Layton MR, Weder AB, Cooper RS, Kardia SL, Rao DC, Hunt SC, Luke A, Boerwinkle E, Chakravarti A: Multiple genotypes for essential hypertension susceptibility on chromosome 1q. Am J Hum Genet 2007, 80:253–264.
15. Chen H, Cui B, Wang S, Zhao Z, Sun H, Gu X, Zhao Y, Li X, Ning G: The common variants of E-selectin gene in Graves’ disease. Genes Immun 2008, 9:182–186.
16. Miller MA, Kery SM, Dong Y, Sagnella GA, Cook DG, Cappuccio FP: Circulating soluble E-selectin levels and the Ser 128Arg polymorphism in individuals from different ethnic groups. Nutr Metab Cardiovasc Dis 2005, 15:655–70.
17. Paterson AD, Lopes-Virella MF, Waggott D, Boright AP, Hosseini SM, Carter SL, Rao DC, Hunt SC, Luke A, Boerwinkle E, Chakravarti A: Multiple genotypes for essential hypertension susceptibility on chromosome 1q. Am J Hum Genet 2007, 80:253–264.
18. Bellosta S, Via D, Canavesi M, Pfister P, Fumagalli R, Paoletti R, Bernini F: HMG-CoA reductase inhibitors reduce MMP-9 secretion by macrophages. Arteroscler Thromb Vasc Biol 2009, 29:1658–1667.
19. Bellotta S, Via D, Caravelli M, Pfister P, Fumagalli R, Paoletti R, Bernini F: HMG-CoA reductase inhibitors reduce MMP-9 secretion by macrophages. Arteroscler Thromb Vasc Biol 2009, 29:1658–1667.
20. Haffner SM, Greenberg AS, Weston WM, Lee YS: A Cholesterol-independent membrane microdomain serves as a functional counter-receptor for E-selectin at the Colo205 cell surface and initiates signalling on E-selectin binding. J Biochem 2007, 142:55–64.
21. Tan CE, Ma S, Wai D, Chew SK, Tai ES: Can we apply the National Cholesterol Education Program Adult Treatment Panel definition of the metabolic syndrome to Asians? Diabetes Care 2004, 27:1162–1168.
22. Wu TL, Tsao KC, Chang CP, Li CN, Sun CF, Wu JT: Development of ELISA on microplate for serum C-reactive protein and establishment of age-dependent normal reference range. Clin Chim Acta 2002, 322:163–168.
23. Chan EC, Chang CP, Wu TL, Wu JT: Enzymatic Assay of Homocysteine on Microtiter Plate or a TECAN Analyzer Using Crude Lysate Containing Recombinant Methionine-Lysase. Ann Clin Lab Sci 2002, 35:153–160.
24. Wu TL, Chen TS, Tsao KC, Sun CF, Wu LL, Wu JT: Establishment of an in-house ELISA and the reference range for serum amyloid A (SAA). Complementarity between SAA and C-reactive protein as markers of inflammation. Clinica Chimica Acta 2007, 376:72–76.
25. Hsu LA, Ko YL, Hsu KH, Ko YH, Lee YS: Genetic variations in the cholesteryl ester transfer protein gene and establishment of high-density lipoprotein cholesterol levels in Taiwanese Chinese. Hum Genet 2002, 110:57–63.
26. Ko YL, Hsu LA, Hsu KH, Ko YH, Lee YS: The interactive effects of hepatic lipase promoter polymorphisms with gender and obesity on high-density-lipoprotein cholesterol levels in Taiwanese-Chinese. Atherosclerosis 2004, 172:135–142.
27. Sole S, Guino E, Valls J, Mirsa R, Moreno V: SNPsStats: a web tool for the analysis of association studies. Bioinformatics 2006, 22:1928–1929.
28. Wu S, Hsu LA, Teng MS, Lin JF, Chang HH, Chang PY, Hu CF, Ko YL: Association of matrix metalloproteinase 9 genotypes and cardiovascular disease risk factors with serum matrix metalloproteinase 9 concentrations in Taiwanese individuals. Clin Chem Lab Med 2010, 48:543–549.
29. Azudajj F, Potworowski EF, St-Pierre Y: Bi-directional induction of matrix metalloproteinase-9 and tissue inhibitor of matrix metalloproteinase-1 during T lymphoma/endothelial cell contact: implication of ICAM-1. J Immunol 1998, 160:2967–2973.
30. Fiore F, Fusco C, Romero P, Stamenkovic I: Matrix metalloproteinase 9 (MMP-9/gelatinase B) proteolytically cleaves ICAM-1 and participates in tumor cell resistance to natural killer cell-mediated cytotoxicity. Oncogene 2002, 21:5213–5223.
31. Lafayrie J, Joule F, Taher MM, Valerie K, Huet J: Transendothelial migration of colon carcinoma cells requires expression of E-selectin by endothelial cells and activation of stress-activated protein kinase-2 (SAPK/JNK) in the tumor cells. J Biol Chem 2001, 276:33762–33772.
32. Ayache T, Miller K, Sagis-Assell O, Levy-Nissenbaum O, Israeli-Amit M, Paskaran-Chop M, Jacob-Hirsch J, Amargalo N, Rechavi G, Witz IP: E-selectin regulates gene expression in metastatic colorectal carcinoma cells and enhances HMGB1 release. Int J Cancer 2008, 123:1741–1750.
33. Tremblay PL, Huet J, Auger FA: Mechanisms by which E-selectin regulates diapedesis of colon cancer cells under flow conditions. Cancer Res 2008, 68:5167–5176.
34. Zen K, Liu DQ, Guo YL, Wang C, Shan J, Fang M, Zhang CY, Liu Y: CD44v4 is a major E-selectin ligand that mediates breast cancer cell transendothelial migration. PLoS One 2008, 3:e1826.
35. Cernuda-Morollón E, Ridley AJ: Rho GTPases and leukocyte adhesion receptor expression and function in endothelial cells. Circ Res 2006, 98:757–767.
36. Hordijk PL: Endothelial signalling events during leukocyte transmigration. FEBS J, 2006, 273:4048–4413.
37. van Buul JD, Kanters E, Hordijk PL: Endothelial signalling by Ig-like cell adhesion molecules. Arterioscler Thromb Vasc Biol 2007, 22:1870–1876.
38. Tremblay PL, Auger FA, Huet J: Regulation of transendothelial migration of colon cancer cells by E-selectin-mediated activation of p38 and ERK MAP kinases. Oncogene 2006, 25:6563–6573.
39. Suzuki C, Kajima N: A Cholesterol-independent membrane microdomain serves as a functional counter-receptor for E-selectin at the Colo205 cell surface and initiates signalling on E-selectin binding. J Biochem 2007, 142:55–64.
40. Bräbek J, Mierek CT, Rösel D, Westey P, Fabry B: The role of the tissue microenvironment in the regulation of cancer cell motility and invasion. Cell Commun Signal 2010, 8:22.
41. Krishnamurtthy P, Rajsingh J, Lambers E, Qin G, Losordo DW, Kishore R: IL-10 inhibits inflammation and attenuates left ventricular remodeling after myocardial infarction via activation of STAT3 and suppression of HIF. Circ Res 2009, 104:e9–e18.
42. Mendes Sdos S, Candi A, Vansteenbrugge M, Pignon MR, Bult H, Boudjeltia KZ, Munaut C, Raes M: GABA-A receptor ameliorates homocysteine-induced MMP-9 activation by ERK pathway. J Cell Physiol 2009, 223:260–266.
43. Tyagi N, Gillespie W, Vacek JC, Sen U, Tyagi SC, Lominadze D: Activation of GABA-A receptor ameliorates homocysteine-induced MMP-9 activation by ERK pathway. J Cell Physiol 2009, 223:260–266.
44. van Kempen LC, Cousmans LM: MMP9 potentiates pulmonary metastasis formation. Cancer Cell 2002, 2:251–252. | 2025-03-06T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3055,
1
],
[
3055,
7735,
2
],
[
7735,
14006,
3
],
[
14006,
19104,
4
],
[
19104,
22555,
5
],
[
22555,
26893,
6
],
[
26893,
33005,
7
],
[
33005,
39987,
8
]
]
} |
a0c1f909650f7a76c260b1a19317a85cd0f671c4 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 10,
"total-fallback-pages": 0,
"total-input-tokens": 27130,
"total-output-tokens": 8796,
"fieldofstudy": [
"Medicine"
]
} | Optimising Medicines Administration for Patients with Dysphagia in Hospital: Medical or Nursing Responsibility?
David J. Wright 1,*, David G. Smithard 2,3, and Richard Griffith 4
1 Professor of Pharmacy Practice, School of Pharmacy, University of East Anglia, Norwich NR4 7TJ, UK
2 University of Greenwich, London SE9 2UG, UK; [email protected]
3 Consultant Physician, Queen Elizabeth Hospital, Woolwich, London SE18 4QH, UK
4 Senior Lecturer in Law, College of Human and Health Sciences, Swansea University, Swansea SA2 8PP, UK; [email protected]
* Correspondence: [email protected]
Received: 20 September 2019; Accepted: 5 February 2020; Published: 19 February 2020
Abstract: Dysphagia is common—not only associated with stroke, dementia, Parkinson’s but also in many non-neurological medical problems—and is increasingly prevalent in ageing patients, where malnutrition is common and pneumonia is frequently the main cause of death. To improve the care of people with dysphagia (PWD) and minimise risk of aspiration and choking, the textures of food and drinks are frequently modified. Whilst medicines are usually concurrently prescribed for PWD, their texture is frequently not considered and therefore any minimisation of risk with respect to food and drink may be being negated when such medicines are administered. Furthermore, evidence is starting to emerge that mixing thickeners with medicines can, in certain circumstances, significantly affect drug bioavailability and therefore amending the texture of a medicine may not be straightforward. Research across a number of hospital trusts demonstrated that PWD are three times more likely to experience medication administration errors than those without dysphagia located on the same ward. Errors more commonly seen in PWD were missed doses, wrong formulation and wrong preparation through medicines alteration. Researchers also found that the same patient with dysphagia would be given their medicines in entirely different ways depending on the person administering the medicine. The alteration of medicines prior to administration has potential for patient harm, particularly if the medicine has been designed to release medicines at a pre-defined rate or within a pre-defined location. Alteration of medicines can have significant legal implications and these are frequently overlooked. Dispersing, crushing or mixing medicines can be part of, or misconstrued as, covert administration, thus introducing a further raft of legislation. Guidance within the UK recommends that following identification of dysphagia, the ongoing need for the medicine should be considered, as should the most appropriate route and formulation, with medicines alteration used as a last resort. The patient should be at the centre of any decision making. Evidence suggests that in the UK this guidance is not being followed. This article considers the clinical and legal issues surrounding administration of medicines to PWD from a UK perspective and debates whether medicines optimisation should be the primary responsibility of the prescriber when initiating therapy on the ward or the nurse who administers the medicine.
Keywords: dysphagia; medicines administration; formulation alteration
1. Introduction
Swallowing problems can be difficult to manage, particularly in the acute medical setting. Staff are more aware of the issues around the provision of food and liquids. Consideration of medicine
administration is often forgotten, yet the administration of medicines to PWD in the hospital setting is fraught with day to day difficulties. Medication errors are a major concern in PWD and are the responsibility of the prescriber, and dispenser and the person administering the medication. This paper discusses the clinical and legal issues in reference to practice in the United Kingdom.
2. Swallowing Problems
Swallowing problems (Oro pharyngeal Dysphagia) are common in older people [1,2], and are defined as difficulty in food or liquid passing from the mouth, through the pharynx to the oesophagus and onwards to the stomach. Studies have reported a prevalence of approximately 15% of community dwelling older adults [3–6]. Dysphagia is now recognized as a geriatric syndrome as it has a multitude of aetiologies and contributes to a general decline in functional ability [1,2]. The occurrence of dysphagia in older people where no underlying medical issue has been identified is often referred to as presbyphagia, and in the presence of frailty, sarcopenic dysphagia is frequently referred to [7]. The commonest medical problems contributing to dysphagia prevalence are neurological [8–10] (stroke, dementia, motor neuron disease and multiple sclerosis); other less recognized causes are rheumatological, cardiorespiratory and infections (Table 1).
| Neurological | Non Neurological |
|----------------------------------|--------------------------------------------|
| Stroke | Cardiac Disease |
| Dementias | Respiratory disease |
| Multiple Sclerosis | Rheumatoid Arthritis |
| Motor Neuron Disease | Osteo Arthritis |
| Parkinson’s disease | Ankylosing Spondylisis |
| Head Injury | Scleroderma |
| Brain tumour | Sjogren’s Disease |
| | Intubation |
| | Frailty decompensation |
| | Malignancy |
| | Dry Mouth/ Xerostomia |
| | Poor mouth care |
| | Oral thrush |
| | Periodontal infection |
| | Psychological |
| | Loss of teeth |
| | Medication |
To swallow safely, several physiological processes need to occur in sequence. The bolus needs to be prepared and presented to the pharynx; whilst this is occurring, the larynx elevates and rotates forward to the base of the tongue (which has come backwards), the soft palate descends and the posterior wall of the pharynx moves forward. As the larynx elevates, the true and false vocal cords approximate and close the pharynx off and breathing ceases momentarily. The bolus passes through the pharynx and through an open upper oesophageal sphincter. Once the bolus has passed, the system relaxes and returns to the resting state.
Dysphagia is important because of its association with poor functional status in many cases [4] and increased morbidity and mortality [11]. Malnutrition and dehydration are common in people with dysphagia due to poor access to food and fluids or poor intake secondary to modified diets and fluids [12]. It is considered likely that many older people admitted to hospital with pneumonia will have an underlying problem with dysphagia [13,14]. Despite this acknowledgement that 44%-55% of people admitted with pneumonia may well have dysphagia, and that dysphagia is a common sequelae of frailty decompensation or other comorbidities, its presence is not routinely screened for [15] and frequently poorly managed.
Before a management plan can be formulated, whether the patient can swallow safely or not needs to be identified. In the clinical situation, this may be done informally by members of the multidisciplinary team observing a person eat or drink (Table 2). A more formal approach may be used such as the bedside swallow assessments e.g., (TOR-BSST or GUSS [16,17] routinely used in stroke care. TOR-BSST has been validated in older patients [18]. A rapid screening questionnaire [19,20] must have reasonable specificity and sensitivity to trigger a referral to the speech and language therapy (pathology) department.
Table 2. Members of the multidisciplinary Team.
| Multidisciplinary Team |
|----------------------------------------|
| Patient |
| Family |
| Paid Carer |
| Speech and Language Therapist |
| Nursing staff |
| Dietitian |
| Chef |
| Physiotherapist |
| Pharmacist |
| Doctor |
The management of dysphagia is complex and involves a multidisciplinary team (Table 2). Following assessment by a speech and language therapist (or other trained professional), a management plan will be devised which may include further instrumental assessment. Once the nature of the dysphagia has been ascertained, the most appropriate method and route of providing nutrition (food and liquid) will be advised [1,11]. If it has been established that the oral route is still appropriate then it is necessary to determine whether liquid and foods require texture modification to prevent aspiration and choking [21]. To standardise this process, an international standard has been developed [21]. Following acute stroke, many people will recover their ability to swallow safely spontaneously [12], and following frailty decompensation this may occur also. For others, a period of rehabilitation may be appropriate [22]. There is no uniform approach to swallowing rehabilitation and the approach will need to be tailored to the individual and their particular problem (Table 3).
Table 3. Rehabilitation techniques and management options.
| Rehabilitation | Management |
|--------------------------------|-----------------------------|
| Tongue strength exercises (e.g., IOPI) | Modified diet |
| IQORO™ | Thickened Fluids |
| Vital Stim | Postural Manoeuvres |
| AMP Care | Parenteral Nutrition |
| Pharyngeal Stimulation | |
| Chin Tuck Against Resistance | |
| Shaker manoeuvre | |
| Laryngeal Resistance | |
| McNeil Programme | |
| EMG Feedback | |
| Transcranial Magnetic Stimulation | |
| Mirror Neurons | |
3. Medicine Administration
Medication is an important component of medical care, particularly in older and in particular frail older people who may have been prescribed multiple medications for their complex health needs. It is not uncommon, in a hospital environment, for food and medication to be stopped if there is any hint of dysphagia whilst awaiting assessment by a speech and language therapist. When a person has significant dysphagia, modified diets (food and liquids) may be recommended [21] and prescribed by the speech and language therapist; many clinical staff give no thought as to the effect that this may have on the bioavailability and pharmacokinetics of orally taken medication. Where medications are to be continued, there is often no structured medication review undertaken with a pharmacist [23]. The lack of consideration regarding how medicines are to be given to people with dysphagia by the prescriber (usually a doctor) creates significant difficulties for those who are expected to administer them (usually nursing staff). UK guidelines for management of medicines in patients with dysphagia recommend that, at the point of diagnosis, the presence of dysphagia should be assessed for, and medicines should be reviewed for ongoing suitability for the oral route and for those which are still required the formulation should be considered [24].
The medication review will need to include and begin with the simple question “is this medication needed?” And if it is, does the formulation need to change, or can it be taken with thickened fluids, or thickened itself if in a liquid formulation?
Where a suitable licensed formulation is not available, unlicensed options such as tablet crushing or dispersing can be undertaken [24]. However, the risks associated with this practice require careful consideration at the point of prescribing. The guidelines are written to ensure that administering nurses and carers are not faced with having to make complex decisions regarding administration at the bedside as this should have already been carried out by the prescriber to ensure that the process was simplified, legal and safe.
There is a range of approaches possible (selecting an alternative formulation, crushing or dispersing the medicine or omitting the medicine altogether) and depending on the nurse’s experience and training the final decision will differ. All options have clinical risks and potentially negative consequences. Whilst swapping formulation may seem to be the easiest option, administration via a different route or formulation can change the drug’s bioavailability and this has to be taken into account for medicines which are at either end of the dose range or those with small therapeutic windows. Crushing or dispersing tablets with no modification to their release profile can in itself create difficulties due to taste and stability. Furthermore, tablets and capsules are relatively inexpensive with respect to acquisition costs and switching to other formulations frequently results in an increase in cost. If the formulation is unlicensed, this can result in a very significant cost increase [25–27].
Switching to a liquid medicine may seem to be the most appropriate; however, its texture is an important factor and most are not provided with instructions on how to safely thicken or dilute them. Consequently, whilst they may be easier for the patient to swallow they may increase risk of aspiration and subsequent problems which can arise from this. With evidence appearing which suggests that thickeners can negate the effect of a medicine [25–27], the decision to thicken a liquid will often not be evidence based and will require careful monitoring of the patient to ensure that the treatment is still effective. Obviously omitting doses is never ideal unless the patient requests it or it is necessary to protect them. Interestingly, the omissions seen in the observational research were sometimes unintentional [28]. With nurses choosing to disperse tablets or capsule contents which are not designed to be dispersed and can take a significant amount of time, the dispersion was frequently left to happen and then nurses, who became engrossed in other activities, failed to return. This left the medicines in a slurry form next to the patient’s bed and not administered.
The act of crushing or dispersing medicines can be a safe alternative providing the medicine is not formulated such that drug release is modified. Slow release medicines frequently contain more than one ‘usual’ dose of the drug and consequently releasing this all at once can result in overdose and
has resulted in reformulation of modified release products such as Oxycodone to reduce overdose associated deaths [29]. Similarly, if a medicine has a coating to either protect it from the stomach’s acidic environment, protect the gastrointestinal tract from the medicine itself or to deliver the medicine further down the gastro-intestinal tract, then any disruption of this can potentially harm the patient.
4. Medication Errors
A large-scale observational study undertaken in one region of England across four different hospitals found that patients with dysphagia were three times more likely to experience medication administration errors than those without dysphagia [28]. Patients with dysphagia were more likely to experience errors in drug preparation, less likely to receive their medication at all and more likely to receive their medicine in the wrong formulation. Where tablets and capsules were modified prior to administration, and thereby rendered unlicensed, there was no evidence that this practice had been authorised by a prescriber and consequently the practice was, strictly speaking, in contravention of the Human Medicines Regulations [30]. Similar results were found when care home staff were observed administering medicines to residents with and without dysphagia [31].
Medication errors in people with dysphagia were believed to be largely due to the additional complexity of having to administer a medicine to a patient with dysphagia [28]. This was because the prescribed formulations were not designed for patients with dysphagia, for administration via an enteral tube or because the nurse did not have the information at hand to make an informed choice as to what the best option would be. These beliefs were reinforced when the same patient was observed receiving the same medicines by two different nurses and received them entirely differently [32]. One recommendation resulting from the large number of errors seen at the point of medicines administration to patients with dysphagia was that nurses should be regularly observed to identify and address any learning needs [33]. Consequently, the responsibility for the medication errors seen within patients with dysphagia was being placed with the administering nurse.
5. Legal Aspects of Medication Administration
The Human Medicines Regulations 2012, regulation 46 [30], generally requires that medicinal products for human use are supplied and administered in accordance with a marketing authorisation. This defines the medicine’s terms of use in a summary of product characteristics which outlines the indications, recommended doses, contraindications and route of the medicine. The marketing authorisation also reassures health professionals of the medicine’s efficacy, safety, and quality.
The Medicines and Healthcare Products Regulatory Agency (MHRA) recognises that there will be situations where there is a need to use a medicine outside the terms of use set out in the statement of product characteristics [34]. The MHRA defines this as ‘off-label’ use and accepts it might be necessary to the clinical need of a patient. ‘Off label’ use includes the use of the medicine to treat a condition not specified in the marketing authorisation, using the medicine with a patient group not covered by the marketing authorisation or administering the medicine via a route not specified in the statement of product characteristics. Altering the formulation of a medicine by crushing or dispersing is considered to be ‘assembly’ and consequently the final product is unlicensed.
Whilst off label use is not recommended by the MHRA, they acknowledge that it is not unlawful if responsibility is assumed by the prescriber and is to be preferred to the use of an unlicensed medicine that has not been assessed for quality, safety and efficacy [34].
There are increased risks to the patient as a result of using a medicine off-label or unlicensed and both the MHRA [34] and the General Medical Council [35] caution that a health professional who causes harm to a patient as a result of off-label or unlicensed use would be in breach of their duty of care and liable in negligence. To discharge that duty of care, health professionals must ensure that the decision to use a medicine off label or unlicensed is based on reliable evidence. The patient must be provided with sufficient information about the medicine to allow them to make an informed decision [36]. Consequently, a prescriber choosing to authorise the use of a medicine, either off-label...
or unlicensed, should seek advice before doing so, if they are at all unsure about the safety of this prescription. The obvious source of advice is either local medicines information or the ward pharmacist. Both will be used to information requests of this nature and will be able to provide advice regarding options available and safety in a timely manner. A non-prescribing nurse choosing to ‘unlicense’ a medicine without authorisation from a prescriber should also seek advice at this stage so that the prescriber request can be appropriately informed.
Interestingly, the act of dispersion or crushing could be seen as ‘covert administration’ as a third party such as a relative watching medicines be crushed or dispersed and then mixed in with food or even just water could interpret this as hiding the medicine prior to administration. ‘Covert administration of medicines’ occurs when the drug is given in a concealed form [37]. The result is that the person is unknowingly taking medication. If the medicine is being given to an individual without capacity, this could be construed as being concealed; therefore, the law and regulatory guidance regarding covert administration should be considered.
The Care Quality Commission (CQC) (2015), the statutory regulator of health and adult care services in England have raised concerns that ‘what should be a last resort’ [Covert administration] is often regarded as ‘normal practice’ carried out for the convenience of staff rather than the best interests of patients. The CQC warns that to covertly administer medicines without first exploring other options is unlawful and fined a care provider some £4000 for unsafe management of medicines including the unsafe use of covert administration [38].
The Nursing and Midwifery Council (NMC) also considers covert administration to be a measure of last resort. As a general principle, by disguising medication, the patient is being led to believe they are not receiving medication, when in fact they are. The NMC Code at standard 16.5 does not consider this to be good practice [39]. The Nursing and Midwifery Council removed a nurse from the professional register after she was found to have routinely hidden medicine in jelly babies, jam sandwiches and custard without consent or other authority [40].
The National Institute for Health and Care Excellence (NICE) [41] argue that, unless there is an immediate need, covert administration should only occur when a management plan is in place following a formal best interest meeting. The purpose of this meeting is to agree whether administering medicines covertly is a necessary last resort measure in the patient’s best interests and it should be attended by nursing staff, the prescriber and pharmacist and a person who can communicate the views and interests of the patient such as a family member, friend or independent mental capacity advocate.
The Court of Protection holds that the use of covert administration of medicines with adults who lack decision making capacity is a serious interference with a person’s right to liberty and a private life under articles 5 and 8 of the European Convention of Human Rights [42]. The use of medication covertly, whether for physical health or for mental health, always calls for close scrutiny that, for vulnerable, incapable patients in hospital, can be achieved by obtaining a deprivation of liberty safeguard standard authorisation under the Mental Capacity Act 2005, schedule A1 [43].
6. Legal Guidance from the Court of Protection
The Court issued the following guidance to assist in cases of covert administration of medicine and deprivation of liberty;
- Where there is a covert medication policy in place to decide on the use of covert administration it must include full consultation between healthcare professionals and family.
- Administering medication covertly must be clearly identified within the care plan, assessment of deprivation of liberty and authorisation of a deprivation of liberty.
- If the standard authorisation is for longer than six months there should be clear provision for regular, monthly, reviews of the care plan.
- There should also be regular reviews involving the family, RPR and healthcare professionals.
• Any change of medication or treatment regime should trigger a review where the medication is covertly administered.
• Supervisory bodies and best interests’ assessors should consider placing appropriate conditions to the standard authorisation that ensure these guidelines are complied with.
If tablet crushing or dispersing is carried out in patients without capacity, then the covert administration law requires careful consideration to ensure that practitioners are not believed to be in contravention. The patient’s doctor would usually be the most appropriate healthcare professional to oversee and support this process.
7. Conclusions
It can be seen that dysphagia increases the likelihood of medication errors and if it is not considered at the point of prescription initiation by the prescriber on the older persons ward it can create significant problems for nurses administering their medicines. If nurses choose to crush or disperse tablets to make them easier to swallow this can be illegal, unsafe and misconstrued as covert administration in those without capacity.
Whilst dysphagia is not routinely screened for in older people’s wards and assessed in a timely manner along with concurrent medication review, the patient is going to be at increased risk, as is the nurse who administers the medicines. Nurses are healthcare professionals who are expected to make autonomous decisions; however, it would be better if they were not routinely placed in this situation when faced with administering medicines to patients with dysphagia.
Although the paper is written from a UK perspective, the clinical facts remain wherever the problem is identified and it is perhaps legislation which differs. UK legislation is based on that from the European Union and therefore many of the legal considerations translate across Europe. Most countries have licensing laws and again changing medicines or using them outside of the license will usually transfer responsibility to the individual who chooses that course of action. The main differences may be surrounding laws regarding covert administration and assessment of patient capacity; however, it would be deemed unethical in most countries to administer medicines to a patient without their express consent. Consequently, alternative approaches to obtaining consent are required when individuals are unable to make decisions for themselves.
Considering the complexity of managing medicines in PWD, we therefore believe that ultimately it is the responsibility of the prescriber to routinely identify dysphagia in older persons, request that its nature is assessed by a speech and language therapist and then prescribe in such a manner that it minimises risk for all concerned. In order to achieve this, the ward pharmacist or local medicines information service should be used to identify the options available and the final decision made in discussion with the patient to identify their preferences. Where the patient does not have capacity, then appropriate members of the family should be included within this to ensure that it is not misconstrued as covert administration.
If the nurse is faced with administering medicines to a patient with dysphagia whereby the medicines have not been reviewed and options discussed with the patient or relative, then they should contact the pharmacist or local medicines information. Armed with evidence and options available, they should then speak to the patient and prescriber to decide how best to prescribe and administer the medicines.
In summary, therefore, dysphagia is everyone’s problem and is best managed by the multi-disciplinary ward team with the patient at the centre of all decision making.
Author Contributions: Conceptualization, D.J.W., and R.G. D.J.W. wrote the original draft preparation, D.G.S. & R.G.; writing—review and editing. All authors have read and agreed to the published version of the manuscript.
Funding: The authors received no external funding for preparing this paper. The payment for open access was made through an unrestricted grant from Rosemont Pharmaceuticals.
Conflicts of Interest: David Wright has previously undertaken consultancy work for Rosemont Pharmaceuticals, manufacturers of generic liquid medicines.
References
1. Baijens, L.W.; Calve, P.; Cras, P.; Ekberg, O.; Forster, A.; Kolb, G.F.; Leners, J.C.; Masiero, S.; Mateos-Nozal, J.; Ortega, O.; et al. European Society for Swallowing Disorders-European Geriatric Medicine Society white paper: Oropharyngeal dysphagia as a geriatric syndrome. *Clin. Interv. Aging* **2016**, *11*, 1403–1428. [CrossRef] [PubMed]
2. Smithard, D.G. Dysphagia: A Geriatr. giant? *Med. Clin. Rev.* **2016**, *2*, 1–7. [CrossRef]
3. Bloem, B.R.; Lagaay, A.M.; van Beck, W.; Haan, J.; Roos, R.A.; Wintzen, A.R. Prevalence of subjective dysphagia in community residents aged over 87. *Br. Med. J.* **1990**, *300*, 721–722. [CrossRef] [PubMed]
4. Kertscher, B.; Speyer, R.; Fong, E.; Georgiou, A.M.; Smith, M. Prevalence of oropharyngeal dysphagia in the Netherlands: A telephone survey. *Dysphagia* **2014**, *30*, 114–120. [CrossRef]
5. Madhavan, A.; LaGorio, L.A.; Crary, M.A.; Dahl, W.J.; Carnaby, G.D. Prevalence of and Risk Factors for Dysphagia in the Community Dwelling Elderly: A Systematic Review. *J. Nutr. Health Aging* **2016**, *20*, 806–815. [CrossRef] [PubMed]
6. Wilkins, T.; Gilles, R.A.; Thomas, A.M.; Wagner, P.J. The prevalence of dysphagia in primary care patients: A HamesNet Research Network study. *J. Am. Board Fam. Med.* **2007**, *20*, 144–150. [CrossRef]
7. Wakabayashi, H. Presbyphagia and sarcopenic dysphagia: Association between aging, sarcopenia and deglutition disorders. *J. Frailty Aging* **2014**, *3*, 97–103.
8. Takizawa, C.; Gemmell, E.; Kenworthy, J.; Speyer, R. A Systematic Review of the Prevalence of Oropharyngeal Dysphagia in Stroke, Parkinson’s Disease, Alzheimer’s Disease, Head Injury, and Pneumonia. *Dysphagia* **2016**, *31*, 434–441. [CrossRef]
9. Roden, D.F.; Altman, K.W. Causes of dysphagia among different age groups: A systematic review of the literature. *Otalaryngologic Clin. N. Am.* **2013**, *46*, 965–987. [CrossRef]
10. Smith, H.A.; Kindell, J.; Baldwin, R.C.; Waterman, D.; Makin, A.J. Swallowing problems and dementia in acute hospital settings: Practical guidance for the management of dysphagia. *Clin. Med.* **2009**, *9*, 544–548. [CrossRef]
11. Wirth, R.; Dziewas, R.; Beck, A.M.; Clave, P.; Hamdy, S.; Heppner, H.J.; Langmore, S.; Leischker, A.H.; Martino, R.; Pluschinski, P.; et al. Oropharyngeal dysphagia in older persons- from pathophysiology to adequate intervention: A review and summary of an international meeting. *Clin. Inerv. Aging* **2016**, *11*, 189–208. [CrossRef] [PubMed]
12. Smithard, D.G. Swallowing and stroke. *Neur. Sffects Recovery. Cerebrovas Dis.* **2002**, *14*, 1–8. [CrossRef]
13. Carrion, S.; Roca, M.; Costa, A.; Arreola, V.; Ortega, O.; Palomera, E.; Serra-Pratt, M.; Cabre, M.; Clave, P. Nutritional status of older people with oropharyngeal dysphagia in a chronic vs acute clinical situation. *Clin. Nutr.* **2017**, *36*, 1110–1116. [CrossRef] [PubMed]
14. Ortega, O.; Martin, A.; Clave, P. Diagnosis and management of oropharyngeal dysphagia among older adults, state of the art. *J. Am Med. Dir. Assoc.* **2017**, *18*, 576–582. [CrossRef] [PubMed]
15. Smithard, D.; Westmark, S.; Melgaard, D. Evaluation of the prevalence of screening for dysphagia among older people admitted to medical services-an international survey. *OBM Geriatrics* **2019**, *3*. [CrossRef]
16. Martino, R.; Silver, F.; Teassell, R.; Bayley, M.; Nicholson, G.; Streiner, D.L.; Diament, N. The Toronto Bedside Swallowing Assessment Screening Test (TOR-BSST). *E. Stroke* **2009**, *40*, 555–561. [CrossRef]
17. Trapl, M.; Enderle, P.; Nowtony, M.; Teuschl, Y.; Matz, K.; Dachenhausen, M. Dysphagia Bedside Screening for acute stroke patients. *Stroke* **2007**, *38*, 2948–2952. [CrossRef]
18. Park, Y.-H.; Bang, H.L.; Han, H.-R.; Chang, H.K. Dysphagia screening measures for use in nursing homes: A systematic review. *J. Korean Acad. Nurs.* **2015**, *45*, 1–13. [CrossRef]
19. Uhm, K.E.; Kim, M.; Lee, Y.M.; Kim, B.R.; Kim, Y.S.; Choi, J.; Han, S.H.; Kim, H.J.; Yoo, K.H.; Lee, J. The easy dysphagia symptom questionnaire for older adults. *T ELIGM* **2019**, *10*, 47–52.
20. Tsang, K.; Lau, E.S.; Shazra, M.; Eyres, R.; Hansjee, D.; Smithard, D.G. A new simple bedside screening tool-4QT, Can it identify those with swallowing problems® A pilot study. 2020; Submitted for publication.
21. Cichero, J.A.; Lam, P.; Steele, C.M.; Hanson, B.; Chen, J.; Dantas, R.O.; Duivestein, J.; Kayashita, J.; Lecko, C.; Murray, J.; et al. Development of International Terminology and Definitions for Texture-Modified Foods and Thickened Fluids Used in Dysphagia Management: The IDDSI Framework. *Dysphagia* 2017, 32, 293–314. [CrossRef] [PubMed]
22. Momosaki, R.; Yasunaga, H.; Matsui, H.; Horiguchi, H.; Fushimi, K.; Abo, M. Effect of dysphagia rehabilitation on orla intake in elderly patients with aspiration pneumonia. *Geriatr. Gerontol. Int.* 2014. [CrossRef]
23. Kelly, J.; D’Cruz, G.; Wright, D. Patients with dysphagia: Experiences of taking medication. *J. Adv. Nurs.* 2010, 66, 82–91. [CrossRef] [PubMed]
24. Wright, D.; Begent, D.; Crawford, H. Medication management of adults with swallowing difficulties. In *Consensus Guideline on the Medication Management of Adults with Swallowing Difficulties*; Mebendium Group Publishing Ltd.: Buckinghamshire, UK, 2017.
25. Griffith, R. Unlicensed medicines: The right to prescribe ‘specials’ and the problem of overcharging. *Brit. J. Comm. Nurs.* 2013, 18, 380–382. [CrossRef]
26. Tomita, T.; Goto, H.; Sumiya, K.; Yoshida, T.; Tanaka, K.; Kudo, K.; Kohda, Y. Effect of Food Thickener on the Inhibitory Effect of Mitiglinide Tablets on Post-prandial Elevation of Blood Glucose Levels. *Dysphagia* 2017, 32, 449–453. [CrossRef]
27. Mabuchi, S.; Ouchi, S.; Suzuki, R.; Sasaki, M.; Nakamura, M.; Izumimoto, N.; Hakamada, T.; Toyoshima, K.; Abe, Y.; Kaneko, E.; et al. Case report of an undisintegrated magnesium oxide tablet in the stool in an elderly patient taking food thickener. *Geriatr. Gerontol. Int.* 2017, 17, 2615–2616. [CrossRef]
28. Kelly, J.; Wright, D.; Wood, J. Medicine administration errors in patients with dysphagia in secondary care: A multi-centre observational study. *J. Adv. Nurs.* 2011, 67, 2615–2627. [CrossRef]
29. Sessler, N.E.; Downing, J.M.; Kale, H.; Chilcoat, H.D.; Baumgartner, T.F.; Coplan, P.M. Reductions in reported deaths following the introduction of extended-release oxycodone (OxyContin) with an abuse-deterrent formulation. *Pharmacoepidemiol Drug Safety* 2014, 23, 1238–1246. [CrossRef]
30. Human Medicines Regulations 2012, Vol. SI 2012/1916. Available online: http://www.legislation.gov.uk/uksi/2012/1916/contents/made (accessed on 16 February 2020).
31. Serrano Santos, J.M.; Poland, F.; Wright, D.; Longmore, T. Medicines administration for residents with dysphagia in care homes: A small scale observational study to improve practice. *Int. J. Pharmaceutics* 2020, 589, 120898. [CrossRef] [PubMed]
32. Montgomery v Lanarkshire Health Board. Available online: https://chrismallonlawtutor.com/medical-law/montgomery-v-lanarkshire-health-board/ (accessed on 16 February 2020).
33. Care Quality Commission. CQC Fines Darlington Care Home £4,000 for Failure to Meet Medication Regulations; CQC: London, UK, 2012.
34. Mental Welfare Commission for Scotland. Covert Medication. *Legal and Practical Guidance*; Mental Welfare Commission for Scotland: Edinburgh, Scotland, 2006.
35. National Institute for Health and Care. Excellence Medicines Management in Care Homes. Available online: https://www.nice.org.uk/guidance/cs85/chapter/quality-statement-6-covert-medicines-administration (accessed on 16 February 2020).
42. Council of Europe. *European Convention on Fundamental Human Rights and Freedoms*; Council of Europe: Rome, Italy, 1950.
43. Council of Europe, European Convention on Fundamental Human Rights and Freedoms. Council of Europe: Rome, AG v BMBC & SNH. In EWCOP 37, 2016. Available online: https://www.ripfa.org.uk/resources/case-law-summaries/case-law-nov2016/case-6-ag-v-bmbc-and-snh-2016-ewcop-37/ (accessed on 16 February 2020).
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3474,
1
],
[
3474,
7738,
2
],
[
7738,
10999,
3
],
[
10999,
15640,
4
],
[
15640,
20185,
5
],
[
20185,
24435,
6
],
[
24435,
28549,
7
],
[
28549,
33001,
8
],
[
33001,
36324,
9
],
[
36324,
36996,
10
]
]
} |
40a276d8adf5dba22393058fb666a471657e31a7 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 26301,
"total-output-tokens": 10456,
"fieldofstudy": [
"Psychology",
"Biology"
]
} | On the One Hand or on the Other: Trade-Off in Timing Precision in Bimanual Musical Scale Playing
Floris Tijmen van Vugt1,2 and Eckart Altenmüller3
1 Department of Psychology, McGill University, Montreal, Quebec, Canada
2 Haskins Laboratories Inc., New Haven, Connecticut, United States
3 Hannover University of Music Drama and Media, Institute of Music Physiology, Hannover, Niedersachsen, Germany
ABSTRACT
Music performance requires simultaneously producing challenging movement sequences with the left and right hand. A key question in bimanual motor control research is whether bimanual movements are produced by combining unimanual controllers or through a dedicated bimanual controller. Here, 34 expert pianists performed musical scale playing movements with the left or right hand alone and with both hands simultaneously. We found that for the left hand, scale playing was more variable when playing with both hands simultaneously rather than with one hand at a time, but for the right hand, performance was identical. This indicates that when task constraints are high, musicians prioritize timing accuracy in the right hand at the cost of detriment of performance in the left hand. We also found that individual differences in timing substantially overlap between the unimanual and bimanual condition, suggesting control policies are similar but not identical when playing with two hands or one. In the bimanual condition, the left-hand keystrokes tended to occur before right-hand ones, and more so when the hands were further apart. Performance of the two hands was furthermore coupled so that they tended to be early and late together, especially in the beginning and end of each scale. This suggests that experts are able to achieve tightly coupled timing of scale playing movements between the hands. Taken together, these findings show evidence for partially overlapping and partially separate controllers for bimanual and unimanual movements in piano playing.
KEYWORDS
music performance
motor control
bimanual control
expertise
INTRODUCTION
Human motor performance often requires the use of left and right limbs simultaneously, such as controlling the legs to walk or using the hands to tie shoelaces (MacKenzie & Marteniuk, 1985; Oliveira & Ivry, 2008). In such cases, the movements produced by the limbs must be tightly coupled in order for the movement to be effective, and even small misalignment of the movements in time can have disastrous consequences. Music, and in particular piano playing, compound this challenge because they involve producing a great deal of keystrokes in a short amount of time (Globerson & Nelken, 2013; Münte, Altenmüller, & Jäncke, 2002). The timing of notes is critical in music because notes that occur early or late convey important expressive cues contributing to the emotional effect of music (Bhatara, Tirovolas, Duan, Levy, & Levitin, 2011). During bimanual piano playing, the two hands are often required to produce simultaneous sounds, which is challenging because work in auditory perception has shown that millisecond differences in note timing can be detected by the ear (Exner, 1875). A great deal of research investigates musicians’ control of timing (Jabusch, Alpers, Kopiez, Vauth, & Altenmüller, 2009; MacKenzie & Van Eerd, 1990; van Vugt, Furuya, Vauth, Jabusch, & Altenmüller, 2014; van Vugt, Jabusch, & Altenmüller, 2012, 2013; Wagner, 1971) but less is known about bimanual control.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Research on bimanual motor control has focused on how the two hands can achieve independence. It is famously difficult to pat your head and rub your stomach at the same time (Oliveira & Ivry, 2008). This is presumably because of cross talk between the control signals sent to the two hands. Instead of controlling the bimanual movement as a combination of two unimanual motor programs, it may therefore be more beneficial for the brain to consider the bimanual movement as a separate movement pattern. This idea is the basis of ongoing debate about whether bimanual movements are separate, atomic motor entities or combinations of unimanual control strategies (Marteniuk, MacKenzie, & Baba, 1984; Schmidt, 1975; Yokoi, Bai, & Diedrichsen, 2017). Previous work showed that force field dynamics learned in a unimanual reaching condition transferred partially to a bimanual condition (Nozaki, Kurtzer, & Scott, 2006), indicating that the control processes for bimanual reaching movements are partially overlapping and partially separate from those for the unimanual condition. Expert pianists have amassed many thousands of hours at their instrument and, therefore, it remains unclear whether at that stage the unimanual and bimanual representations are integrated or not.
Here, we monitored expert pianists performing the demanding task of playing musical scales at a fast rate, either with one hand at a time or with both hands separately. We approached the question whether unimanual and bimanual controllers are separated or integrated in three ways. First, if bimanual playing relies on a dedicated, separate controller, this should enable independent modulation of the precision of the two hands, that is, timing accuracy in one hand could be prioritized over another. We hypothesized that if one hand is prioritized, that hand may show the same variability during bimanual and unimanual playing, at the expense of an increase in variability during bimanual playing in the other hand. The second way to approach integration or separation of controllers was to investigate individual differences in scale playing timing. Previous work showed the existence of robust interindividual differences in scale playing timing between players (van Vugt et al., 2013) and here, we hypothesized that if bimanual control relies on a combination of unimanual controllers, the individual timing differences should be maintained between unimanual and bimanual control. The third way to approach the question of overlap or separation of uni- versus bimanual control was to assess the amount of temporal coupling between the hands. We hypothesized that if bimanual playing is achieved by executing two unimanual controllers in parallel the timing deviations of corresponding keystrokes of the two hands should be independent, but if bimanual control relies on an integrated
FIGURE 1.
Panel A: Participants played C-major scale with two hands simultaneously (bimanual) or one hand at the time (unimanual), alternatingly outward and inward playing directions. Panel B: In each block, inward and outward scales were recorded alternatingly (see example right hand unimanual block) and participants performed three blocks (left hand unimanual, right hand unimanual, and bimanual) in counterbalanced order.
controller, the hands may be early or late together. In order to assess this coupling, we investigated the correlation between timing deviation of corresponding keystrokes of the left and right hand.
**METHODS**
**Participants**
Thirty-four right-handed piano players participated in the experiment (18 female, 16 male). They were enrolled in the prestigious piano programme at the Hannover Music School (HMTMH), Germany. Participants’ were 24.71 (SD = 4.40) years of age at the time of the experiment, and they had accumulated 13.82 (SD = 9.0) × 10^3 hours of training at the instrument over the course of 17.7 (SD = 4.02) years.
**Procedure**
Participants were seated at the Kawai MP9000 digital piano (Kawai, Krefeld, Germany) and were instructed to play C major scales using one hand at a time (unimanual) or both hands simultaneously (bimanual; see Figure 1, Panel A). Participants played the scales over two octaves in the inward or outward directions alternatingly with a short break in between each run. Playing was paced using a metronome producing clicks at 120 beats per minute and the instruction was to play four notes per metronome click. Participants were asked to use the conventional fingering (see Figure 1, Panel A) and play mezzo-forte in a smooth legato-style. The task was to play as evenly as possible, keeping in time with the metronome. In each block, approximately 30 cycles of the inward and outward scale were recorded without interruption in one condition (unimanual or bimanual, see Figure 1, Panel B) and all subjects performed three blocks: left hand unimanual, right hand unimanual, and bimanual scales. The order of these three blocks was counterbalanced (e.g., a possible ordering was left hand unimanual, bimanual, right hand unimanual). The keystrokes were captured through the MIDI interface and recorded on a PC through a custom-made C program for offline analysis.
**Data Analysis**
Scale runs with incorrect notes or omissions were discarded from further analysis. In each correct scale run, the intervals between the onset of subsequent keystrokes were calculated (inter-onset-interval, IOI, in milliseconds). In order to assess the timing accuracy, we computed the SD of the IOI, which is referred to as unevenness. The larger this value, the more variable the intervals are and hence, more irregular the timing of the keystrokes. We performed a repeated-measures analysis of variance (ANOVA) and report generalised η² effect sizes (Bakeman, 2005). In order to quantify the unique individual timing pattern of each pianist, we computed a timing fingerprint by averaging the IOIs for each pair of adjacent keystrokes in the scale, yielding a vector of 14 elements (corresponding to the 15 keystrokes in the two-octave scale).
**RESULTS**
Timing was more variable in bimanual playing relative to unimanual playing, but only in the left hand (see Figure 2). A repeated-measures ANOVA with factors condition (unimanual, bimanual), hand (left, right), and playing direction (inward, outward) revealed
a significant main effect of hand, $F(1, 33) = 55.36, p < .0001$ indicating that the left hand is more variable overall, as previously found. A two-way interaction between hand and direction was also found, $F(1, 33) = 6.11, p = .02, \eta^2 = .007$. Because of the interaction, we analysed the two hands separately. For the left hand, we found that bimanual playing was more variable than unimanual playing, $F(1, 33) = 21.39, p < .0001, \eta^2 = .05$, and outward scales were more variable than inward scales, $F(1,33) = 11.50, p = .002, \eta^2 = .03$. There was no interaction between direction and bi-/unimanual condition. In the right hand, there was no significant difference between unimanual or bimanual playing, $F(1, 33) = .89, p = .35$, there was also no effect of direction or interaction between those two, $F(1, 33) = .01, p = .91$.
In order to assess whether unimanual and bimanual control is governed by the same or different motor control processes, we assessed the pattern of individual differences for each pianist and investigated whether this was maintained from unimanual to bimanual playing.
Does the individual timing pattern in the unimanual condition predict the bimanual timing pattern? For each participant, the average timing pattern was computed as the vector of the average IOI for each keystroke (the timing "fingerprint", a vector of 14 elements corresponding to the intervals between 15 keystrokes, see Figure 3, Panel A for an example). We then computed the Euclidean distance between the bimanual and unimanual timing vector ("within;" one value) for each pianist and the average distance between the pianists’ bimanual timing vector and the unimanual timing vectors of all other pianists ("between;" one averaged value). We found that distances between the timing vectors were smaller within the same pianist than across pianists (see Figure 3, Panel B). A repeated-measures ANOVA with distance as the dependent variable and factors of hand (left, right), direction (inward, outward), and comparison (within, across) revealed an interaction between hand and comparison, $F(1, 33) = 6.98, p = .02, \eta^2 = .09$. For the two hands separately, the distances were smaller within than across pianists, $F(1, 33) > 197.88, p < .0001, \eta^2 > .17$ in both cases. Auxiliary findings were that distances were generally larger in the left hand, $F(1, 33) = 69.54, p < .001, \eta^2 = .11$, presumably because the left hand shows more variability between trials. This analysis revealed that at least a portion of individual timing deviations was preserved between the unimanual and bimanual condition.
A second analysis was performed where we extracted the scale runs within each individual pianist. Within each individual pianist, the timing of all possible pairs of individual scale runs (both unimanual and bimanual) was compared using the Euclidean distance measure. Then, these distances were grouped according to the kind of runs that were compared: unimanual versus unimanual, bimanual versus unimanual, or unimanual versus bimanual (see Figure 3, Panel C). The idea was that if unimanual and bimanual playing rely on separate motor representations, the distances between pairs of unimanual or pairs of bimanual scales should be smaller than between unimanual and bimanual scales. We ran an ANOVA with the factors of hand, playing direction, and comparison (three levels: unimanual vs. unimanual, bimanual vs. bimanual, unimanual vs. bimanual). It was found that the distance between the fingerprints of the left hand were greater overall than those of the right hand,
---
**FIGURE 3.** Individual timing patterns in the unimanual conditions predict the bimanual timing pattern. Panel A: Timing patterns between the unimanual and bimanual condition are similar within pianists but more different between different pianists. Black: example timing vector (fingerprint) of one pianist in the bimanual (dashed line) and unimanual (solid line) condition, and the timing vector of another pianist (orange). Panel B: Group data for the Euclidean distance (presented here as an average absolute distance for each keystroke interval), indicating that timing patterns are more similar between the unimanual and bimanual condition within pianists than across different pianists. Panel C: The timing patterns of individual scale runs were compared for each pianist within or across the unimanual and bimanual conditions. When comparing pairs of unimanual or pairs of bimanual scale runs, the timing patterns were more similar than when comparing a unimanual to a bimanual scale run and this was true for both hands and playing directions.
Although the left keystrokes preceded the right, the timing of the two hands was tightly coupled, especially in the beginning and end of the movement and when the hands were close together in space. Panel A: Left hand keystrokes occurred before the corresponding right hand keystrokes (left hand leads, right hand lags) when the hands were further apart. For outward scales, the left-right timing offset was close to 0 initially, when the hands were close together, and increased in the course of the scale run; the opposite pattern was found for the inward scales where hands were far apart initially and became closer together. Panel B: Left and right hand scales are coupled in time: The interval played by one hand correlates with the interval simultaneously played by the other hand. Panel C: The slope of the relationship between the lateness of the left and right hand is close to 1, implying that the hands are early or late together by the same amount. Panel D: The timing of the left and right hand is correlated across the entire scale, but more strongly in the beginning and end of the scale.
\[ F(1, 33) = 72.722, p < .0001, \] in line with greater timing variability in the left hand reported above. There was also an interaction between hand and comparison, \( F(2, 66) = 8.86, p < .001 \). Crucially, planned contrasts revealed that the cross-condition comparison (unimanual vs. bimanual) was significantly greater than the within-condition comparisons (unimanual vs. unimanual or bimanual vs. bimanual) for both hands and playing directions, \( F(1, 33) > 27.21, p < .0001, \eta^2 > .11 \) for all comparisons. This analysis thus reveals that there are differences in individual timing patterns of scales between the bimanual and unimanual conditions. Taken together with the earlier analysis (between pianists), this reveals a nuanced picture where some, but not all individual variation is retained between the unimanual and bimanual condition.
During bimanual playing, subjects were instructed to play corresponding keystrokes of the left and right hand exactly simultaneously. In reality, we observed small timing differences between the onset of the keystrokes of the two hands in the order of a dozen milliseconds. In general, left hand keystrokes occurred earlier in time than the corresponding keystrokes of right hand (see Figure 4, Panel A). Interestingly, when the hands were closer together in space, the keystrokes also occurred more close together in time and the timing offset between the hands increased as the hands moved further apart in space. For outward scales, the timing offset increased, \( F(1, 33) = 30.53, p < .0001, \) and for inward scales it decreased, \( F(1, 33) = 39.10, p < .0001 \) (Figure 4, Panel A).
The timing of the two hands was tightly coupled on a trial-by-trial basis. There was a correlation between the length of the interval played by the left hand in a particular trial and the interval played simultaneously by the right hand (see Figure 4, Panel B). In other words, when the left hand played a longer interval than the target interval (125 ms), the right hand also played a longer interval on average, \( F(1, 33) = 30.53, p < .0001, \eta^2=.48 \) for outward scales and \( F(1, 33) = 39.10, p < .0001, \eta^2=.54 \) for inward scales. The slope of this relationship between the intervals of the two hands was close to 1, indicating that the left and right hand tended to be early and late by the same amount of time (see Figure 4, Panel C). The correlation between the timing of the left and right hand was present across the entire scale, but more pronounced at the beginning and end of the scale (see Figure 4, Panel D). To test whether this was statistically significant, we performed an analysis of covariance (ANCOVA) with the individual correlation estimate (Pearson’s \( r \)) as the dependent variable and distance from the center of the scale (covariate, values from 0 to 7) and playing direction (inward, outward, which was not significant, \( F(1, 33) = .34, p = .56 \)) as factors. The distance from the center of the scale was significant, \( F(1, 33) = 7.14, p = .01, \eta^2=.07 \), which shows that the correlation between the hands was higher at the beginning and end of the scale run.
DISCUSSION
The present study investigated timing control of bimanual scale playing in expert musicians. A great deal of research in bimanual motor control has investigated the difficulty experienced in decoupling the movements of the two hands when the task requires it. Here, pianists played mirrored scale playing movements which, on the contrary, required tight coupling in time between the movements of the two hands in order to achieve simultaneity of the resulting sounds.
Key findings are that the left, but not the right hand is more variable during bimanual control than unimanual control. Individual timing patterns are partially, but not completely maintained between unimanual and bimanual conditions. The left-hand keystrokes tended to precede those of the right hand, especially when the hands were further separated in space, and both hands tended to be early and late together, especially in the beginning and end of each scale run. These findings suggest a great deal of integration between the hands and a priority given to temporal precision in the right hand.
The Right Hand is Prioritized During Bimanual Playing
The present data show that the left, but not the right hand is more variable during bimanual as opposed to unimanual playing. This suggests that the right hand is prioritized during bimanual control. In relation to the main question of this study, this suggests that bimanual control relies on a distinct controller in which timing precision can be different from that of the individual unimanual controllers. The present study only tested right-handed participants. As a result, it is possible, at least in principle, that the deterioration in timing accuracy in the left hand is because this is the nondominant hand. However, previous work suggested that timing asymmetries are related to musical practice, not handedness. Indeed, it was found that the left hand is generally less precise during musical scale playing (van Vugt et al., 2014), and this is true for both left- and right-handed pianists (Kopiez et al., 2011) and asymmetries in tapping performance between the hands are reduced with musical training (Jäncke, Schlaug, & Steinmetz, 1997). Kopiez et al. also provide an intriguing argument why the left-right asymmetry in unimanual playing may occur: They show that Western classical music tends to put higher demands on the right hand, as shown by a greater number of notes played by the right hand in typical repertoire. The current work extends the previous unimanual findings by showing that not only is the right hand more precise overall, its superior tempo-spatial precision is maintained during bimanual playing, at the expense of further deterioration in the left hand. Possibly the prioritization of the right hand observed in the present study is similarly driven by the fact that this hand tends to play more notes.
Two Equals One Plus One?
Does the brain treat bimanual control as a combination of the two unimanual control processes or is the bimanual controller a unit of its own, more or less independent of the two unimanual processes? The generalized motor program theory proposes the latter idea of a separate bimanual control process (Schmidt, 1975). In support of this theory, a recent sequence learning study found that there was no transfer from unimanual learning to bimanual performance (Yokoi et al., 2017). On a neural level, work on rhesus monkeys indicates that most cells in primary motor cortex show activity specific to bimanual movements (Donchin, Gribova, Steinberg, Bergman, & Vaadia, 1998). Furthermore, a study with macaque monkeys shows that transcortical connections reduce the correlation between the representations of the two unimanual movements, providing evidence for a separate bimanual representation (Rokni, Steinberg, Vaadia, & Sompolinsky, 2003). Alternatively, the brain may create bimanual control by simultaneously activating the two unimanual control processes (Marteniuk et al., 1984). If bimanual control builds on the unimanual controllers, learning in the unimanual condition should transfer to bimanual control. Indeed, previous studies have observed partial transfer between effectors in force field learning (Nozaki et al., 2006).
Early Together, Late Together
Timing of the two hands showed a great deal of coupling. When one hand's keystroke came early, there was a tendency for the other hand to also make an early keystroke. This correlation between the two hands occurred within individuals and for each of the various keystrokes separately, indicating that the coupling occurred on a trial-by-trial basis. This coupling between the keystrokes of the two hands supports the idea that bimanual playing is controlled using a distinct bimanual controller. If instead there were two independent unimanual controllers, it would be expected that timing deviations would be independent between the two hands. The finding is similar to observations in bimanual reaching movements, where short movements became longer when the other hand made a simultaneous long movement and vice versa (Marteniuk et al., 1984). These effects are generally thought to be due to cross-talk in the control signals sent to the two limbs (Oliveira & Ivy, 2008). The present data extend the previous work by showing that this phenomenon is still present in a selective sample of pianists from a world-class piano program (Hannover Music University), suggesting that even massed practice fails to achieve independence in the control between the two hands.
The present study found that timing in the two hands during bimanual control was tightly coupled. In the present study, the two hands produced mirror movements, leading to activation of homologous muscles. Because of the crossing between the hands, bimanual control tends to favour symmetric movements. For example, bimanual movements are more synchronous and less variable when they are produced by homologous muscles (Cohen, 1971). In a similar way, when humans produce cyclic antisymmetric movement patterns at high speeds, often they shift to the symmetric pattern in which homologous muscles are activated simultaneously (Haken, Kelso, & Bunz, 1985; Kelso, 1981; Ryu & Buchanan, 2004), again suggesting a preference for symmetric (in-phase) movement patterns. On a neural level, during unimanual movements, there is a tendency to activate homologous muscles of the two limbs. For example, during unimanual movements, excitability is modulated for the motor pathways for the unused hand.
during unimanual playing. Individual timing patterns were partially, timing precision of the two hands can be modulated differently than hand, which maintained its high level of timing accuracy. This provides control, but only in the left hand, indicating a priority given to the right was found that bimanual control was more variable than unimanual er bimanual and unimanual controllers are integrated or separate. It was investigated in bimanual coordination (Gooijers & Swinnen, 2014) and, therefore, these music-induced changes are thought to underlie the improved capacity for pianists to perform separate movements with the two hands. At first glance, the present data may seem to contradict previous work showing greater segregation of control of the two hands in musicians. However, note that in the present case, coupling between the two hands was adaptive to the task because it would increase synchrony of the keystrokes which is what participants were asked to do. Future research could build on the present study by investigating movements that are not mirrored, for example, by asking pianists to simultaneously produce an inward scale with one hand and an outward scale with the other hand, in which case achieving coupling between the hands is more challenging. The present data also showed that the left-hand keystrokes tended to occur earlier in time than the corresponding keystroke of the right hand, especially when the hands are further apart. This “left-lead” effect has been observed before and appears to occur especially when lower notes are played by another hand than the higher notes (Hartmann, 1932; Repp, 1996; Vernon, 1937), as is the case here. The left-lead phenomenon, by which lower notes played with the left hand appear early, is thought to reflect individual aesthetic choice (Repp, 1996) and, therefore, it is surprising that it occurs in the present study as well, where the participants were instructed to aim for regularity and synchrony rather than aesthetic playing. Other studies have reported an opposite pattern, known as the melody-lead effect, by which the keystrokes playing the melody may occur several dozens of milliseconds earlier than those playing the lower accompaniment notes (Palmer, 1989). However, the melody-lead effect has been shown to occur as an artifact of greater keystroke velocities for melody notes (Goelè, 2001).
The current work investigated timing control of challenging bimanual sequences in expert pianists and explored the question whether bimanual and unimanual controllers are integrated or separate. It was found that bimanual control was more variable than unimanual control, but only in the left hand, indicating a priority given to the right hand, which maintained its high level of timing accuracy. This provides support to the idea of a dedicated bimanual controller, in which the timing precision of the two hands can be modulated differently than during unimanual playing. Individual timing patterns were partially, but not completely maintained between bimanual and unimanual control, suggesting overlap between the motor representations guiding playing with two hands or with one. During bimanual control, the two hands were tightly coupled, tending to be early or late together, suggesting that the two hands are not driven by separate (unimanual) controllers, but rather using a single bimanual controller. In sum, the present study found evidence for partial but not complete overlap between unimanual and bimanual controllers.
The present data show, for the first time, that individual differences in the form of a timing fingerprint are partially, but not completely, preserved across unimanual and bimanual conditions. Individual differences were previously shown in deviations away from regularity in the order of milliseconds and these were consistent within pianists, enabling a machine learning algorithm to identify the players (van Vugt et al., 2013). The (partial) preservation of these timing patterns provides evidence for overlap between the unimanual and bimanual controllers, and the lack of complete preservation provides evidence that there is also a level on which these controllers are separate. Thus, rather than either complete separation or complete integration of the bimanual and unimanual controllers, the present study suggests that there may be partial overlap, which is in line with previous mixed results from the literature, where some studies find evidence for integration and others for separation of the bimanual and unimanual controllers (Marteniuk et al., 1984; Nozaki et al., 2006; Yokoi et al., 2017).
ACKNOWLEDGEMENTS We are indebted to Karl Hartmann for assistance in collecting the data.
REFERENCES Bakeman, R. (2005). Recommended effect size statistics for repeated measures designs. Behavior Research Methods, 37, 379–384. doi: 10.3758/BF03192707 Bhata, A., Tirovolas, A. K., Duan, L. M., Levy, B., & Levitin, D. J. (2011). Perception of emotional expression in musical performance. Journal of Experimental Psychology: Human Perception and Performance, 37, 921–934. doi: 10.1037/a0021922 Carson, R. G., Welsh, T. N., & Pamblanco-Valero, M.-A. (2005). Visual feedback alters the variations in corticospinal excitability that arise from rhythmic movements of the opposite limb. Experimental Brain Research, 161, 325–334. doi: 10.1007/s00221-004-2076-x Cohen, L. (1971). Synchronous bimanual movements performed by homologous and non-homologous muscles. Perceptual and Motor Skills, 32, 639–644. doi: 10.2466/pms.1971.32.2.639 Donchin, O., Gribova, A., Steinberg, O., Bergman, H., & Vaadia, E. (1998). Primary motor cortex is involved in bimanual coordination. Nature, 395, 274–278. doi: 10.1038/26220 Exner, S. (1875). Experimentelle Untersuchung der einfachsten psychischen Prozesse. III [Experimental investigation of the simplest psychological processes. III]. Pflügers Archiv Fur Die Gesamte Physiologie Des Menschen Und Thiere, 11, 402–412.
Globerson, E., & Nelken, I. (2013). The neuro-pianist. *Frontiers in Systems Neuroscience, 7.* doi: 10.3389/fnsys.2013.00035
Goebel, W. (2001). Melody lead in piano performance: Expressive device or artifact? *The Journal of the Acoustical Society of America, 110, 563–572.* doi: 10.1121/1.1376133
Gooijers, J., & Swinnen, S. P. (2014). Interactions between brain structure and behavior: The corpus callosum and bimanual coordination. *Neuroscience & Biobehavioral Reviews, 43,* 1–19. doi: 10.1016/j.neubiorev.2014.03.008
Haken, H., Kelso, J. A. S., & Bunz, H. (1985). A theoretical model of phase transitions in human hand movements. *Biological Cybernetics, 51,* 347–356. doi: 10.1007/BF00336922
Hartmann, A. (1932). Untersuchungen über das metrische Verhalten in musikalischen Interpretationsvarianten [Investigation about the metric relationships in musical interpretation variants]. *Archiv Für Die Gesamte Psychologie, 84,* 103–192.
Haslinger, B., Erhard, P., Altenmüller, E., Hennenlotter, A., Schwaiger, M., Gräfin von Einsiedel, H., … Ceballos-Baumann, A. O. (2004). Reduced recruitment of motor association areas during bimanual coordination in concert pianists. *Human Brain Mapping, 22,* 206–215. doi: 10.1002/hbm.20028
Jabusch, H.-C., Alpers, H., Kopiez, R., Vauth, H., & Altenmüller, E. (2009). The influence of practice on the development of motor skills in pianists: A longitudinal study in a selected motor task. *Human Movement Science, 28,* 74–84. doi: 10.1016/j.humov.2008.08.001
Jäncke, L., Schlaug, G., & Steinmetz, H. (1997). Hand skill asymmetry in professional musicians. *Brain and Cognition, 34,* 424–432. doi: 10.1006/brcg.1997.0922
Kelso, J. A. S. (1981). On the oscillatory basis of movement. *Bulletin of the Psychonomic Society, 18,* 63–63.
Kopiez, R., Jabusch, H.-C., Galley, N., Homann, J.-C., Lehmann, A. C., & Altenmüller, E. (2011). No disadvantage for left-handed musicians: The relationship between handedness, perceived constraints and performance-related skills in string players and pianists. *Psychology of Music, 40,* 357–384. doi: 10.1177/0305735610394708
MacKenzie, C. L., & Marteniuk, R. G. (1985). Bimanual coordination. *Advances in Psychology, 23,* 345–358. doi: 10.1016/S0166-4115(08)61147-4
MacKenzie, C. L., & Van Eerd, D. L. (1990). Rhythmic precision in the performance of piano scales: Motor psychophysics and motor programming. In M. Jannerod (Ed.), *Attention and Performance 13: Motor representation and control* (375–408). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
Marteniuk, R. G., MacKenzie, C. L., & Baba, D. M. (1984). Bimanual movement control: Information processing and interaction effects. *The Quarterly Journal of Experimental Psychology Section A, 36,* 335–365. doi: 10.1080/1460478408402163
Munte, T. F., Altenmüller, E., & Jäncke, L. (2002). The musician’s brain as a model of neuroplasticity. *Nature Reviews Neuroscience, 3,* 473–478. doi: 10.1038/nrn843
Nozaki, D., Kurtzer, I., & Scott, S. H. (2006). Limited transfer of learning between unimanual and bimanual skills within the same limb. *Nature Neuroscience, 9,* 1364–1366. doi: 10.1038/nn1785
Oliveira, F. T. P., & Ivry, R. B. (2008). The representation of action: Insights from bimanual coordination. *Current Directions in Psychological Science, 17,* 130–135. doi: 10.1111/j.1467-8721.2008.00562.x
Palmer, C. (1989). Mapping musical thought to musical performance. *Journal of Experimental Psychology: Human Perception and Performance, 15,* 331–346. doi: 10.1037/0096-1523.15.2.331
Repp, B. H. (1996). Patterns of note onset asynchronies in expressive piano performance. *The Journal of the Acoustical Society of America, 100,* 3917–3932. doi: 10.1121/1.417245
Ridding, M. C., Brouwer, B., & Nordstrom, M. A. (2000). Reduced interhemispheric inhibition in musicians. *Experimental Brain Research, 133,* 249–253. doi: 10.1007/s002210000428
Rokni, U., Steinberg, O., Vaadia, E., & Sompolinsky, H. (2003). Cortical representation of bimanual movements. *The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 23,* 11577–11586. doi: 10.1523/JNEUROSCI.23-37-11577.2003
Ryu, Y. U., & Buchanan, J. J. (2004). Amplitude scaling in a bimanual circle-drawing task: Pattern switching and end-effector variability. *Journal of Motor Behavior, 36,* 265–279. doi: 10.3200/JMBR.36.3.265-279
Sadato, N., Okada, T., Honda, M., & Yonekura, Y. (2002). Critical period for cross-modal plasticity in blind humans: A functional MRI study. *NeuroImage, 16,* 389–400. doi: 10.1006/nimg.2002.1111
Schlaug, G., Jäncke, L., Huang, Y., Staiger, J. F., & Steinmetz, H. (1995). Increased corpus callosum size in musicians. *Neuropsychologia, 33,* 1047–1055. doi: 10.1016/0028-3932(95)00045-5
Schmidt, R. A. (1975). A schema theory of discrete motor skill learning. *Psychological Review, 82,* 225–260. doi: 10.1037/h0076770
Serrien, D. J., & Brown, P. (2002). The functional role of interhemispheric synchronization in the control of bimanual timing tasks. *Experimental Brain Research, 147,* 268–272. doi: 10.1007/s00221-002-1253-2
Shaffer, L. H. (1981). Performances of Chopin, Bach, and Bartok: Studies in motor programming. *Cognitive Psychology, 13,* 326–376. doi: 10.1016/0010-0285(81)90013-X
Stephan, K. M., Binkofski, F., Halsband, U., Doehle, C., Wunderlich, G., Schnitzler, A., … Freund, H. J. (1999). The role of ventral medial wall motor areas in bimanual co-ordination. A combined lesion and activation study. *Brain, 122* (Pt 2), 351–368. doi: 10.1093/brain/122.2.351
van Vugt, F. T., Furuya, S., Vauth, H., Jabusch, H.-C., & Altenmüller, E. (2014). Playing beautifully when you have to be fast: Spatial and...
temporal symmetries of movement patterns in skilled piano performance at different tempi. *Experimental Brain Research, 232*, 3555–3567. doi: 10.1007/s00221-014-4036-4
van Vugt, F. T., Jabusch, H.-C., & Altenmüller, E. (2012). Fingers phrase music differently: Trial-to-trial variability in piano scale playing and auditory perception reveal motor chunking. *Frontiers in Auditory Cognitive Neuroscience, 3*, 495. doi: 10.3389/fpsyg.2012.00495
van Vugt, F. T., Jabusch, H.-C., & Altenmüller, E. (2013). Individuality that is unheard of: Systematic temporal deviations in scale playing leave an inaudible pianistic fingerprint. *Frontiers in Cognitive Science, 4*, 134. doi: 10.3389/fpsyg.2013.00134
Vernon, L. N. (1937). *Synchronization of chords in artistic piano music* [Dissertation, University of Iowa].
Wagner, C. (1971). The influence of the tempo of playing on the rhythmic structure studied at pianist’s playing scales. In J. Vredenbregt & J. Wartenweiler (Eds.), *Medicine and sport* (pp. 129–132). Basel, Switzerland: Karger.
Yokoi, A., Bai, W., & Diedrichsen, J. (2017). Restricted transfer of learning between unimanual and bimanual finger sequences. *Journal of Neurophysiology, 117*, 1043–1051. doi: 10.1152/jn.00387.2016
RECEIVED 12.07.2019 | ACCEPTED 01.082019 | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3576,
1
],
[
3576,
6864,
2
],
[
6864,
9951,
3
],
[
9951,
14616,
4
],
[
14616,
18889,
5
],
[
18889,
25428,
6
],
[
25428,
31412,
7
],
[
31412,
37102,
8
],
[
37102,
38385,
9
]
]
} |
9bf503be4ca1fa6abcf144408b07f3bd81f92b20 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 30,
"total-fallback-pages": 0,
"total-input-tokens": 114950,
"total-output-tokens": 23389,
"fieldofstudy": [
"Computer Science"
]
} | Sparse Estimation Using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models
Niels Lovmand Pedersen\textsuperscript{a}, Carles Navarro Manchón\textsuperscript{a}, Mihai-Alin Badiu\textsuperscript{a}, Dmitriy Shutin\textsuperscript{b}, Bernard Henri Fleury\textsuperscript{a}
\textsuperscript{a}Department of Electronic Systems, Aalborg University, Niels Jernes Vej 12, DK-9220 Aalborg, Denmark.
\textsuperscript{b}Institute of Communications and Navigation, German Aerospace Center, Oberpfaffenhofen, D-82234 Wessling, Germany.
Abstract
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper proposes a GSM model - the Bessel K model - that induces concave penalty functions for the estimation of complex sparse signals. The properties of the Bessel K model are analyzed when it is applied to Type I and Type II estimation. This analysis reveals that, by tuning the parameters of the mixing pdf different penalty functions are invoked depending on the estimation type used, the value of the noise variance, and whether real or complex signals are estimated. Using the Bessel K model, we derive a sparse estimator based on a modification of the expectation-maximization algorithm formulated for Type II estimation. The estimator includes as a special instance the algorithms proposed by Tipping and Faul \cite{1} and by Babacan et al. \cite{2}. Numerical results show the superiority of the proposed estimator over these state-of-the-art estimators in terms of convergence speed, sparseness, reconstruction error, and robustness in low and medium signal-to-noise ratio regimes.
Keywords:
Sparse Bayesian learning, sparse signal representations, underdetermined linear systems, hierarchical Bayesian modeling, sparsity-inducing priors.
\textsuperscript{✩}Parts of this work have previously been presented in conference proceedings \cite{3, 4}. Email addresses: [email protected] (Niels Lovmand Pedersen), [email protected] (Carles Navarro Manchón), [email protected] (Mihai-Alin Badiu), [email protected] (Dmitriy Shutin), [email protected] (Bernard Henri Fleury)
1. Introduction
Compressive sensing and sparse signal representation have attracted the interest of an increasing number of researchers over the recent years [5, 6, 7, 8]. This is motivated by the widespread applicability that such techniques have found in a large variety of engineering disciplines. Generally speaking, these disciplines consider the following signal model:
\[ y = \Phi w + n. \]
In this expression, \( y \) is an \( M \times 1 \) vector of measurement samples, \( \Phi = [\phi_1, \ldots, \phi_N] \) is an \( M \times N \) dictionary matrix with \( N > M \). The additive term \( n \) is an \( M \times 1 \) perturbation vector, which is assumed to be Gaussian distributed with zero-mean and covariance \( \lambda^{-1} I \), where \( \lambda > 0 \) denotes the noise precision and \( I \) is the identity matrix. The objective is to accurately estimate the unknown weight vector \( w = [w_1, \ldots, w_N]^T \), which is assumed \( K \)-sparse in the canonical basis.
We coin the signal model (1) as either real, when \( \Phi, w, \) and \( n \) are all real, or as complex, when \( \Phi, w, \) and \( n \) are all complex. Historically, real signal models have dominated the research in sparse signal representation and compressive sensing. However, applications seeking sparse estimation for complex signal models are not uncommon. An example is the estimation of multipath wireless channels [8, 9, 3, 4]. The extension of sparse representation from real signal models to complex models is not always straightforward, as we will discuss in this paper.
Many convex [10, 11], greedy [12, 13], and Bayesian methods have been proposed in the literature in recent years to devise sparse estimators. In this paper, we focus on Bayesian inference methods commonly referred to as sparse Bayesian learning (SBL) [14, 15]. In SBL, we design priors for \( w \) that induce sparse representations of \( \Phi w \). Instead of working directly with the prior probability density function (pdf) \( p(w) \), SBL typically uses a two-layer hierarchical prior model that involves a conditional prior pdf \( p(w|\gamma) \) and a hyperprior pdf \( p(\gamma) \). The goal is to select these pdfs in such a way that we can construct computationally tractable iterative algorithms that estimate both the hyperparameter vector \( \gamma \) and the weight vector \( w \) with the latter estimate being sparse.
A widely used two-layer prior model is the model where the entries of \( w \) are independent and identically distributed according to a Gaussian scale mixture (GSM) [10, 17, 18, 19, 20]. Specifically, \( w_i \) is modeled as \( w_i = \sqrt{\gamma_i} u_i \), where \( u_i \) is a standard Gaussian random variable and \( \gamma_i \) is a nonnegative random scaling factor, also known as the mixing variable [8]. The pdf \( p(\gamma_i) \) of the latter variable is called the mixing pdf of the GSM. Based on a careful selection of \( p(\gamma_i) \)
---
1 Obviously, one could also consider a mixed model where, e.g., \( \Phi \) and \( n \) are complex but \( w \) is real. In this paper we focus on the two most relevant cases of real and complex signal models as defined above.
2 In this configuration, \( \gamma_i \) can be seen as the variance of \( w_i \).
an inference algorithm is then constructed. The sparsity-inducing property of the resulting estimator does not only depend on $p(\gamma_i)$ but also on the type of inference method used, as discussed next.
In SBL two widespread inference approaches, referred to as Type I and Type II estimation following \[21\], have been used. In Type I estimation, the maximum-a-posteriori (MAP) estimate of $w$ is computed from the observation $y$:
$$\hat{w}_I(y) = \underset{w}{\arg \max} \ p(w|y)$$
$$= \underset{w}{\arg \max} \ \log \int p(y|w)p(w|\gamma)p(\gamma)d\gamma.$$ \hspace{1cm} (2)
Equivalently, the Type I estimator $\hat{w}_I$ is obtained as the minimizer of the Type I cost function
$$L_I(w) \triangleq \rho \|y - \Phi w\|_2^2 + \lambda^{-1} q_I(w).$$ \hspace{1cm} (3)
In the above expression, $\| \cdot \|_p, p \geq 1$, is the $\ell_p$-norm and the parameter $\rho$ takes values $\rho = 1/2$ when the signal model (1) is real and $\rho = 1$ when it is complex. The pdf $p(\gamma)$ is designed such that the penalization term $q_I(w) \propto -\log p(w)$ with $p(w) = \int p(w|\gamma)p(\gamma)d\gamma$ enforces a sparse estimate of the weight vector $w$.
In Type II estimation \[22\ \[14\ \[15\], the MAP estimate of $\gamma$ is computed from the observation $y$:
$$\hat{\gamma}_{II}(y) = \underset{\gamma}{\arg \max} \ p(\gamma|y)$$
$$= \underset{\gamma}{\arg \max} \ \log \int p(y|w)p(w|\gamma)p(\gamma)d\gamma.$$ \hspace{1cm} (4)
Thus, the estimator $\hat{\gamma}_{II}$ is the minimizer of
$$L_{II}(\gamma) \triangleq \rho y^H C^{-1} y + \rho \log |C| - \log p(\gamma)$$ \hspace{1cm} (5)
with $C \triangleq \lambda^{-1} I + \Phi \Gamma \Phi^H$ and $\Gamma = \text{diag}(\gamma)$. The Type II estimator of $w$ follows as
$$\hat{w}_{II}(y) = \langle w \rangle_{p(w|y;\hat{\gamma}_{II}(y))} = (\Phi^H \Phi + \lambda^{-1} \hat{\Gamma}_{II}^{-1})^{-1} \Phi^H y.$$ \hspace{1cm} (6)
where $\hat{\Gamma}_{II} = \text{diag}(\hat{\gamma}_{II}(y))$ and $\langle \cdot \rangle_{p(x)}$ denotes expectation over the pdf $p(x)$. The impact of $p(\gamma)$ on the estimator $\hat{w}_{II}$ is not straightforward. This complicates the task of selecting $p(\gamma)$ inducing a sparse estimate of $w$. In \[21\], the relationship between Type I and Type II estimation has been identified. This
---
3Here $x \propto y$ denotes $\exp(x) = \exp(\nu) \exp(y)$, and thus $x = \nu + y$, for some arbitrary constant $\nu$. We will also make use of $x \propto y$, which denotes $x = \nu y$ for some positive constant $\nu$.
\[3\]
result makes it possible to compare the two estimation methods. Invoking Theorem 2, \( \hat{w}_{II}(y) \) is equivalently the minimizer of the Type II cost function
\[
L_{II}(w) \triangleq \rho \| y - \Phi w \|_2^2 + \lambda^{-1} q_{II}(w)
\]
with penalty
\[
q_{II}(w) = \min_{\gamma} \{ \rho w^H \Gamma^{-1} w + \rho \log |C| - \log p(\gamma) \}.
\]
Specifically, \( \hat{w}_{II}(y) \) in (6) equals the global minimizer of \( L_{II}(w) \) iff \( \hat{\gamma}_{II}(y) \) equals the global minimizer of \( L_{II}(\gamma) \). Likewise, \( \hat{w}_{\star}(y) = \langle w \rangle_{p(w|\gamma_{\star}(y))} \) is a local minimizer of \( L_{II}(w) \) iff \( \hat{\gamma}_{\star}(y) \) is a local minimizer of \( L_{II}(\gamma) \).
The MAP estimates in (2) and (4) cannot usually be computed in closed-form and one must resort to iterative inference methods to approximate them. One method is the Relevance Vector Machine (RVM) [14, 15]. In RVM the mixing pdf \( p(\gamma) \) is equal to an improper constant prior. An instance of the expectation-maximization (EM) algorithm is then formulated to approximate the Type II estimator. Another method, devised for real signal models in [23], uses the EM algorithm to approximate two popular Type I estimators with respectively \( \ell_1 \)-norm and log-sum constrained penalization. These penalization terms arise from selecting the mixing pdf equal to an exponential pdf and the noninformative Jeffreys prior, respectively. In the former case, the marginal prior pdf \( p(w) \) is the product of Laplace pdfs and \( L_I(w) \) equals the cost function of Least Absolute Shrinkage and Selection Operator (LASSO) [10] or Basis Pursuit Denoising [11].
The sparse estimators in [14, 15, 23] inherit the limitation of the instances of the EM algorithm that they embed: high computational complexity and slow convergence [1]. To circumvent this shortcoming, a fast inference framework is proposed in [1] for RVM and later applied to derive the Fast Laplace algorithm [2]. The latter algorithm is derived based on an augmented probabilistic model obtained by adding a third layer to the real GSM model of the Laplace pdf; the third layer introduces a hyper-hyperprior for the rate parameter of the exponential pdf, which coincides with the regularization parameter of the \( \ell_1 \) penalization induced by the Laplace prior. However, as Fast Laplace is based on Type II estimation it cannot be seen as the adaptive Bayesian version of the \( \ell_1 \) re-weighted LASSO algorithm [24]. The Bayesian version of this latter estimator is proposed in [25, 26].
Even though the fast algorithms in [1] and [2] converge faster than their EM counterparts, they still suffer from slow convergence, especially in low and moderate signal-to-noise ratio (SNR) regimes as we will demonstrate in this paper. Furthermore, in these regimes the algorithms significantly overestimate the number of nonzero weights. We will show that this behavior is, in fact, a consequence of the prior models used to derive the algorithms.
\[^4\]Let us point out that the hierarchical representation resulting in the \( \ell_1 \)-norm presented in [23] is only valid for real-valued variables. In this paper, we extend this representation to cover complex-valued variables as well.
Coming back to the original motivation of this work, though complex GSM models have been proposed in the literature [27, 28], they have not been extensively applied within the framework of SBL. An example illustrating this fact is the hierarchical modeling of the $\ell_1$-norm in Type I estimation. While this penalty results from selecting the exponential mixing pdf for the entries in $\gamma$ in real GSM models, said pdf will not induce the $\ell_1$-norm penalty for complex models. Yet to the best of our knowledge, the complex GSM model realizing the $\ell_1$-norm penalty has not been established in the literature. Moreover, it is not evident what sparsity-inducing property the complex GSM model exhibits when applied in Type II estimation. Motivated by the relative scarcity of formal tools for sparse learning in complex models and inspired by the recent analysis of sparse Bayesian algorithms in [21], we propose and investigate an SBL approach that applies to both real and complex signal models.
Starting in Section 2, we first present a GSM model for both real and complex sparse signal representation where the mixing pdf $p(\gamma_i)$ is selected to be a gamma pdf. When $w$ is real, the marginal prior pdf $p(w)$ equals the product of Bessel K pdfs [17, 18, 19]. We extend the Bessel K model to cover complex weights and model for this extension several penalty functions previously introduced for inferring real sparse weights. One important example is the hierarchical prior modeling inducing the $\ell_1$-norm penalty for complex weights. We then analyze the Type I and Type II estimators derived from the Bessel K model. We show that a sparsity-inducing prior for Type I estimation does not necessarily have this property for Type II estimation and, interestingly, a sparsity-inducing prior for real weights is not necessarily sparsity-inducing for complex weights. In the particular case where the dictionary matrix $\Phi$ is orthonormal, we demonstrate, using the EM algorithm, that Type I and Type II estimators derived using the Bessel K model are generalizations of the soft-thresholding rule with degree of sparseness depending on the selection of the shape parameter of the gamma pdf $p(\gamma_i)$. Additionally, we show that this model has a strong connection to the Bayesian formalism of the group LASSO [26, 29]. Note that the Bessel K model has been previously introduced for sparse signal representation [30, 31]. However, these works were restricted to the inference of real weights and did not consider the relationship between Type I and Type II estimation.
In Section 3, we propose greedy, low-complexity estimators using the Bessel K model. The estimators are based on a modification of the EM algorithm for Type II estimation. As the Bessel K model encompasses the prior models used in [1] and [2], the iterative algorithms derived in these publications can be seen as instances of our estimators for particular settings of the associated parameters of the gamma mixing pdf.
Section 4 provides numerical results obtained via Monte Carlo simulations that reveal the superior performance of the proposed estimators in terms of convergence speed of the algorithms, sparseness, and mean-squared error (MSE) of
---
5 The Bessel K pdf is in turn a special case of even a larger class of generalized hyperbolic distributions [17], obtained when the mixing pdf is a Generalized Inverse Gaussian pdf.
the estimates. Furthermore, and of great importance in many engineering areas, the estimators show a significant robustness in low and moderate SNR regimes; a property not exhibited by the traditional SBL estimators, like [1] and [2], and other state-of-the-art non-Bayesian sparse estimators. This result opens for a potential application of our estimators in systems operating in these SNR regimes - e.g., receivers in wireless communications [3, 4]. Furthermore, the proposed estimators can inherently incorporate the estimation of the noise variance. In the literature this parameter is often learned from a training procedure or tuned for optimality. Since the algorithms in [1] and [2] only differ from ours in the choice of parameters of the mixing pdf, we can safely conclude that the observed performance benefits are a direct consequence of our proposed prior model.
Finally, we conclude the paper in Section 5.
2. The Bessel K Model for Real and Complex Signal Representation
In this section we present the Bessel K model for SBL. We first state the probabilistic model of the signal model (1). Based on this probabilistic model we analyze the Type I and Type II cost functions. We then show how to obtain various estimators with different sparsity-inducing properties by appropriately setting the parameters of the Bessel K model.
2.1. Probabilistic Model
We begin with the specification of the probabilistic model for (1) augmented with the two-layer prior model for \( w \):
\[
p(y, w, \gamma) = p(y|w)p(w|\gamma)p(\gamma).
\]
(9)
From (1), \( p(y|w) = N(y|\Phi w, \lambda^{-1}I) \) if the signal model is real and \( p(y|w) = CN(y|\Phi w, \lambda^{-1}I) \) if the model is complex.
The sparsity constraints on \( w \) are determined by the joint prior pdf \( p(w|\gamma)p(\gamma) \). Motivated by previous works on GSM modeling and SBL [14, 15, 23] we select the conditional prior pdf \( p(w|\gamma) \) to factorize in a product of zero-mean Gaussian pdfs: \( p(w|\gamma) = \prod_i p(w_i|\gamma_i) \) where
\[
p(w_i|\gamma_i) = \left( \frac{\rho}{\pi \gamma_i} \right)^\rho \exp \left( -\rho \frac{|w_i|^2}{\gamma_i} \right),
\]
(10)
In the above expression, \( \rho = 1/2 \) when \( w \) is real and \( \rho = 1 \) when \( w \) is complex. We choose the mixing pdf \( p(\gamma) \) to be a product of identical gamma pdfs, i.e.,
\[ N(\cdot|a, B) \] and \( CN(\cdot|a, B) \) denote respectively a multivariate real and a multivariate complex Gaussian pdf with mean vector \( a \) and covariance matrix \( B \). We shall also make use of the gamma pdf \( Ga(\cdot|a, b) = \frac{1}{\Gamma(a)} x^{a-1} \exp(-bx) \) with shape parameter \( a \) and rate parameter \( b \).
\[ p(\gamma) = \prod_i p(\gamma_i; \epsilon, \eta) \] with \( p(\gamma_i; \epsilon, \eta) \triangleq \text{Ga}(\gamma_i|\epsilon, \eta) \). The prior pdf for \( w \) is then given by \( p(w; \epsilon, \eta) = \int p(w|\gamma)p(\gamma; \epsilon, \eta) d\gamma = \prod_i p(w_i; \epsilon, \eta) \) with \( p(w_i; \epsilon, \eta) \triangleq \text{Ga}(w_i|\epsilon, \eta) \).
\[ p(w_i; \epsilon, \eta) = \frac{2(\rho \eta)^{\frac{\epsilon - 1}{2}}}{\pi^\epsilon \Gamma(\epsilon)} |w_i|^{-\rho} K_{\epsilon - \rho}(2\sqrt{\rho \eta}|w_i|). \] (11)
In this expression, \( K_\nu(\cdot) \) is the modified Bessel function of the second kind and order \( \nu \in \mathbb{R} \). In case \( w \) is real \((\rho = 1/2)\), we obtain the GSM model of the Bessel K pdf \[17, 18\]. We will keep the same terminology when \( w \) is complex \((\rho = 1)\).\footnote{To the authors’ best knowledge, the GSM model of the Bessel K pdf has only been presented for real variables.}
The Bessel K pdf (11) represents a family of prior pdfs for \( w \) parametrized by \( \epsilon \) and \( \eta \). By selecting different values for \( \epsilon \) and \( \eta \), we realize various penalty functions for Type I and Type II estimation as shown in the following.
2.2. Type I Cost Function
The Type I cost function \( L_I(w) \) induced by the Bessel K model is given by \( 3 \) with penalty \( q_I(w) = \sum_i q_I(w_i; \epsilon, \eta) \) where
\[ q_I(w_i; \epsilon, \eta) \triangleq -\log(|w_i|^{-\rho} K_{\epsilon - \rho}(2\sqrt{\rho \eta}|w_i|)). \] (12)
Special cases of Type I penalties resulting from the Bessel K pdf have already been considered in the literature for sparse regression when the weights are real \[30, 31\]. We review them together with introducing the corresponding extension to complex weights.
2.2.1. The \( \ell_1 \)-norm penalty
This penalty is of particular importance in sparse signal representation as the convex relaxation of the \( \ell_0 \)-norm\footnote{The \( \ell_0 \)-norm of the vector \( x \) is the number of nonzero entries in \( x \). Note that by abuse of terminology \( \| x \|_0 \) is coined a norm even though it does not fulfill all properties of a norm.}
When \( w \) is real, it is well-known that the Laplace prior induces the \( \ell_1 \)-norm penalty. The Bessel K pdf (11) encompasses the Laplace pdf as a special case with the selection \( \epsilon = 1 \) and \( \rho = 1/2 \).
\[ p(w_i; \epsilon = 1, \eta) = \sqrt{\frac{\eta}{2}} \exp(-\sqrt{2\eta}|w_i|), \quad w_i \in \mathbb{R}. \] (13)
The Laplace pdf for real weights is thereby the pdf of a GSM with an exponential mixing pdf \[10\].
The extension of (13) to \( w \) complex is not straightforward. One approach is to treat the real and imaginary parts of each \( w_i \) independently with both parts modeled according to the real GSM representation of the Laplace pdf. Doing so using (13) we obtain \( p(w_i) = \frac{\eta}{2} \exp(-\sqrt{2\eta}(|\text{Re}\{w_i\}| + |\text{Im}\{w_i\}|)) \). Obviously
\[ K_{12}(z) = \sqrt{\frac{\pi}{2z}} \exp(-z) \] \[32\].
this approach does not lead to the $\ell_1$-norm penalty for Type I estimation. The complex GSM model with a gamma mixing pdf with shape parameter $\epsilon = 3/2$ does induce this penalty. Indeed, with this setting, (11) becomes
$$p(w_i; \epsilon = 3/2, \eta) = \frac{2\eta}{\pi} \exp(-2\sqrt{\eta}|w_i|), \quad w_i \in \mathbb{C}. \quad (14)$$
Throughout the paper, we refer to the pdf in (14) as the Laplace pdf for complex weights.
In summary, the Bessel K model induces the $\ell_1$-norm penalty $q_I(w) = 2\sqrt{\rho\eta} \sum_i |w_i|$ with the selection $\epsilon = \rho + 1/2$. The introduced GSM model of the Laplace pdf for both real and complex variables is strongly connected with the group LASSO and its Bayesian interpretation [26, 29], where sparsity is enforced simultaneously over groups of $k$ variables. In the Bayesian interpretation of the group LASSO a gamma pdf with shape parameter $(k + 1)/2$ is employed to model the prior for each of the variables in a group. This choice of shape parameter is consistent with the choice of $\epsilon$ in the GSM model of the Laplace prior: in the real case a group consists of $k = 1$ variable and, thus, $(k + 1)/2 = 1$, whereas in the complex case, a group consists of the real and imaginary parts of a complex variable, hence, $k = 2$ and $(k + 1)/2 = 3/2$.
2.2.2. The log-sum penalty
The selection $\epsilon = \eta = 0$ in (11) entails the Jeffreys (improper) prior density $p(\gamma_i) \propto \gamma_i^{-1}$ and thereby the improper marginal prior density $p(w) \propto \prod_i |w_i|^{-2\rho}$. Thus, when the mixing density of the GSM is chosen to be noninformative, the log-sum penalization $q_I(w) = 2\rho \sum_i \log |w_i|$ is invoked in (3). This penalty has gained much interest in the literature, including [14, 15, 23, 24, 35], as it is known to strongly promote sparse estimates.
2.2.3. The Bessel K penalty
The Bessel K pdf can be used with arbitrary values of $\epsilon \geq 0$ controlling its sparsity-inducing property. To illustrate this, Fig. 1(a) depicts one contour line of the restriction of $q_I(w_1, w_2; \epsilon, \eta)$ in (12) for selected values of $\epsilon$. As $\epsilon$ approaches zero more probability mass concentrates along the $w$-axes; as a consequence, the mode of the resulting posterior pdf $p(w|y; \epsilon, \eta)$ is more likely to be close to the axes, thus encouraging a sparse estimate. The behavior of the $\ell_1$-norm penalty that results from the selection $\epsilon = \rho + 1/2 = 3/2$ is also clearly recognized.
---
10 The $\ell_1$-norm for the complex vector $x$ is defined as $\|x\|_1 = \sum_i |x_i| = \sum_i \sqrt{\text{Re}^2(x_i) + \text{Im}^2(x_i)}$ [33, 34].
11 Let $f$ denote a function defined on a set $A$. The restriction of $f$ to a subset $B \subset A$ is the function defined on $B$ that coincides with $f$ on this subset.
2.3. Type II Cost Function
We invoke Theorem 2 in [21] to obtain the Type II cost function induced by the Bessel K model (see (7) and (8)):
\[
L_{II}(w) \triangleq \rho \|y - \Phi w\|^2_2 + \lambda^{-1} q_{II}(w)
\]
(15)
with
\[
q_{II}(w; \epsilon, \eta) = \min \{ \rho w^H W^{-1} w + \rho \log|C| + (1 - \epsilon) \sum \log \gamma_i + \eta \sum \gamma_i \}.
\]
(16)
In contrast to \( q_I(w) \), \( q_{II}(w) \) is nonseparable. This makes an interpretation of \( q_{II}(w) \) as done for \( q_I(w) \) in Fig. 1(a) rather difficult. However, this interpretation becomes straightforward if \( \Phi \) is orthonormal, i.e., \( \Phi^H \Phi = I \). In this case \( q_{II}(w) \) is separable, i.e., \( q_{II}(w) = \sum_i q_{II}(w_i) \) with
\[
q_{II}(w_i; \epsilon, \eta) = \min \{ \frac{\|w_i\|^2}{\gamma_i} + \rho \log(\lambda^{-1} + \gamma_i) + (1 - \epsilon) \log \gamma_i + \eta \gamma_i \}.
\]
(17)
Fig. 1(b) shows the contours of the restriction to \( \mathbb{R}^2 \) of \( q_{II}(w_1, w_2; \epsilon, \eta) \) in (17) for different values of \( \epsilon \). Again, we observe the same increased concentration of mass around the \( w \)-axes for decreasing values of \( \epsilon \). Interestingly, \( q_{II}(w_1, w_2; \epsilon = 3/2, \eta) \) is no longer sparsity-inducing as compared to \( q_I(w_1, w_2; \epsilon = 3/2, \eta) \). Thus, a sparsity-inducing prior model for Type I estimation is not necessarily sparsity-inducing for Type II estimation. We further investigate this important result in Section 2.4.
Another important property of the Type II penalty is its dependency on the noise variance \( \lambda^{-1} \). Fig. 2(a) and Fig. 2(b) depict a single contour line of (17) for two values of \( \epsilon \) and two values of \( \lambda^{-1} \). Notice that \( q_{II}(w; \epsilon = 1/2, \eta = 1) \) resembles the log-sum penalty even in noisy conditions. For comparison purposes, we show in Fig. 2(c) the Type II penalty computed with the prior model...
in RVM \cite{14,15} which utilizes a constant prior pdf $p(\gamma_i) \propto 1$ (corresponding to setting $\epsilon = 1$ and $\eta = 0$ in \cite{16}). When $\lambda^{-1} = 0$ the RVM penalty equals the log-sum penalty. However, in noisy conditions the RVM penalty resembles the $\ell_1$-norm penalty. Note that we cannot simply set $\lambda^{-1}$ to some small value in order to obtain a strong sparsity-inducing penalty in RVM as $\lambda^{-1}$ acts as a regularization of $q_{II}(w)$ in \cite{15}. Based on this observation, we expect that the Type II estimator derived from the Bessel K model achieves improved sparsity performance as compared to RVM in noisy scenarios. The numerical results conducted in Section 4 demonstrate that this is indeed the case.
2.4. Type I and Type II Estimation
Having evaluated the impact of $\epsilon$ on $q_I(w)$ and $q_{II}(w)$, we now investigate its effect of this parameter on the corresponding Type I and Type II estimators. We demonstrated that as $\epsilon$ decreases, $q_I(w)$ and $q_{II}(w)$ become more and more sparsity-inducing which motivates the selection of a small $\epsilon$ for sparse estimation. On the other hand the Bessel K model for Type I and Type II estimation dominates the information contained in the observation $y$ for decreasing values of $\epsilon$. Specifically, in case of Type I, when $\epsilon \leq \rho$ then $\lim_{w_i \to 0} q_I(w_i) = -\infty$, hence, the Type I estimator does not exist as $L_I(w)$ has singularities. Likewise, this is the case for the Type II estimator when $\epsilon < 1$. The unbounded behavior of these penalties naturally questions the practicability of the Bessel K model in SBL. At least one would expect that we should refrain from selecting $\epsilon \leq \rho$ in case of Type I estimation and $\epsilon < 1$ for Type II estimation. Note, however, that utilizing unbounded penalties in SBL is not uncommon. Examples include \cite{30,31} as well as the popular GSM model realizing the log-sum penalty in e.g., \cite{23}. Furthermore, the sparsity-inducing behavior of the penalty curves in Fig. 1 and Fig. 2 provides a strong motivation for using the Bessel K model in SBL. The approach is to formulate approximate inference algorithms, such as EM, for Type I and Type II estimation that overcome the difficulty of the singularities in the objective functions.
Figure 2: One contour line of the restriction to $\mathbb{R}^2$ of (a) $q_{II}(w_1, w_2; \epsilon = 1/2, \eta = 1)$, (b) $q_{II}(w_1, w_2; \epsilon = 1, \eta = 1)$, and (c) $q_{II}(w_1, w_2; \epsilon = 1, \eta = 0)$ with $\Phi$ orthonormal and $\lambda^{-1}$ as a parameter. Note that $q_{II}(w_1, w_2; \epsilon = 1, \eta = 0)$ in (c) coincides with the penalty used in RVM \cite{14,15}.
2.4.1 Approximate Type I estimation
The EM algorithm approximating the Type I estimator makes use of the complete data \( \{\gamma, y\} \) for \( \mathbf{w} \). The M-step computes an estimate of \( \mathbf{w} \) as the maximizer of
\[
\langle \log p(y|\mathbf{w})p(\mathbf{w}|\gamma)p(\gamma) \rangle_{p(\gamma; \hat{\mathbf{w}})},
\]
(18)
where \( p(\gamma; \hat{\mathbf{w}}) \) is computed in the E-step. Notice that as \( p(\mathbf{w}|y, \gamma) \propto p(y|\mathbf{w})p(\mathbf{w}|\gamma) \) is proportional to a Gaussian pdf for \( \mathbf{w} \), (18) does not have any singularity in contrast to \( L_I(\mathbf{w}) \).
In order to get further insight into the impact of \( \epsilon \) on the EM algorithm, we follow [23] and let \( \Phi \) be orthonormal such that the EM update of the estimate of \( \mathbf{w} \) decouples into \( N \) independent scalar optimization problems. Fig. 3(a) visualizes the EM estimator for different values of \( \epsilon \). Clearly, the EM estimator approximates the soft-thresholding rule for large values of \( \text{Re}\{\phi_H^i y\} \) and as \( \epsilon \) decreases the threshold value increases, thus, encouraging sparsity.
When the Bessel K pdf equals the Laplace pdf (i.e., \( \epsilon = \rho + 1/2 \)), \( \hat{\mathbf{w}}_I \) coincides with the soft-thresholding rule, which can be computed in closed form:
\[
\hat{w}_{I,i}(y) = \text{sign}(\phi_i^* y) \max \left\{ 0, |\phi_i^* y| - \lambda^{-1} \sqrt{\frac{\eta}{\rho}} \right\}, \quad i = 1, \ldots, N.
\]
(19)
Here, \( \text{sign}(x) = x/|x| \) is the sign function. Notice that the EM estimator with \( \epsilon = \rho + 1/2 \) approximates (19) as depicted in Fig. 3(a).
2.4.2. Approximate Type II estimation
The EM algorithm approximating Type II estimation is devised using \( \{w, y\} \) as the complete data for \( \gamma \). The M-step computes an estimate of \( \gamma \) as the maximizer of
\[
\langle \log p(y|w)p(w|\gamma)p(\gamma) \rangle_{p(w;\hat{\gamma})},
\]
with \( p(w|\gamma) \) computed in the E-step. As \( p(\gamma|w) \propto p(w|\gamma)p(\gamma) \) is a Generalized Inverse Gaussian (GIG) pdf for \( \gamma \), \( 20 \) does not exhibit any singularity as opposed to \( \mathcal{L}_{II}(\gamma) \).
In Fig. 5(b), we show the EM estimate of \( w_i \) for different settings of \( \epsilon \). Similar to Type I, the Type II estimate approaches the soft-thresholding rule as \( \text{Re}\{\phi_H^i y\} \) becomes larger and as \( \epsilon \) decreases a sparser estimate is obtained. However, when \( \epsilon = 3/2 \), i.e., utilizing the Laplace GSM model for the complex weights, the Type I estimator coincides with the soft-threshold rule while the Type II estimator does not have this threshold-like behavior and is not sparse. This was already indicated by the behavior of \( q_{II}(w;\epsilon = 3/2, \eta) \) in Fig. 1(b).
From Fig. 6 we conclude that the EM-based Type I estimator is a sparse estimator for \( \epsilon \leq \rho+1/2 \), whereas the EM-based Type II estimator only exhibits this property for \( \epsilon \leq 1 \). In Fig. 7 we illustrate this important difference in the behavior of these estimators for real and complex signal representation when utilizing the GSM model of the Laplace prior: the EM-based Type I estimator achieves a sparse solution for both real and complex weights, whereas for the EM-based Type II estimator this is only the case for real weights.
3. Sparse Bayesian Inference
In this section we derive a Bayesian inference scheme that relies on the Bessel K model presented in Section 2. First, we obtain an EM algorithm that approximates the Type II estimator of the weight vector \( w \) in \( 11 \). Inspired
by [1] and [36] we then derive a fast algorithm based on a modification of the EM algorithm. We show that this algorithm actually encompasses the fast algorithms in [1] and [2] as special instances.
Naturally, the approach presented here can also be applied to derive algorithms approximating the Type I estimator. However, numerical investigations not reported here indicate that these algorithms often fail to produce sparse estimates of $w$ when small values of the parameter $\epsilon$ are selected. Hence, we restrict the discussion in this section to algorithms approximating the Type II estimator.
3.1. Sparse Bayesian Inference Using EM
We adapt the EM algorithm approximating the Type II estimator previously used for SBL [14, 1, 15, 37, 2] to the Bessel K model. As the value of $\lambda$ is in general unknown and has a significant impact on the sparsity-inducing property on $q_{II}(w)$ (see Section 2), we include the estimation of this parameter in the inference framework. We seek the MAP estimate of $\{\gamma, \lambda\}$, i.e., the maximizer of
$$L(\gamma, \lambda) = \log p(y, \gamma, \lambda) = \log(p(y|\gamma, \lambda)p(\gamma)p(\lambda)).$$
(21)
We use the EM algorithm to approximate the MAP estimator. We specify $\{w, y\}$ to be the complete data for $\{\gamma, \lambda\}$. With this choice the E-step of the EM algorithm computes the conditional expectation
$$\langle \log p(y, w, \gamma, \lambda) \rangle_{p(w|y, \gamma^{[t]}, \lambda^{[t]})}$$
with $p(w|y, \gamma^{[t]}, \lambda^{[t]}) = N(w|\mu^{[t]}, \Sigma^{[t]})$ or $p(w|y, \gamma^{[t]}, \lambda^{[t]}) = CN(w|\mu^{[t]}, \Sigma^{[t]})$ depending on whether the underlying signal model is real or complex. Here, $\langle \cdot \rangle^{[t]}$ denotes the estimate of the parameter given as an argument at iteration $t$.
In either case, the parameters of the conditional pdf of $w$ read
$$\Sigma^{[t]} = (\lambda^{[t]} \Phi^H \Phi + (\Gamma^{[t]})^{-1})^{-1},$$
(23)
$$\mu^{[t]} = \lambda^{[t]} \Phi^H y.$$
(24)
The M-step of the EM algorithm updates the estimate of $\{\gamma, \lambda\}$ as the maximizer of (22):
$$\gamma_i^{[t+1]} = \frac{\epsilon - \rho - 1 + \sqrt{(\epsilon - \rho - 1)^2 + 4\rho |\langle w_i^2 \rangle^{[t]}|}}{2\eta}, \quad i = 1, \ldots, N,$$
(25)
$$\lambda^{[t+1]} = \frac{M}{\|y - \Phi \mu^{[t]}\|_2^2 + \text{tr}(\Phi^H \Phi \Sigma^{[t]}))}.$$
(26)
Here, $\langle |w_i|^2 \rangle^{[t]}$ is the $i$th diagonal element of $\Sigma^{[t]} + \mu^{[t]}(\mu^{[t]})^H$ computed in the E-step and $\text{tr}(\cdot)$ is the trace operator.
3.2. Modified update of $\gamma_i^{[t+1]}$
One of the major drawbacks of the EM algorithm approximating the Type II estimator is its slow convergence, as observed in, e.g., [1] [2] [36]. In this section, we discuss a modification of the EM algorithm that improves the convergence speed. The proposed algorithm is inspired by [1] and [36]. To this end, we focus on the update of a single estimate of $\gamma_i$ and express this update as a (non-linear recurrent) function of the previous update. Then, we analyze the fixed points of this function for different settings of the hyperparameters $\epsilon$ and $\eta$ and formulate a new update rule for the estimate of $\gamma_i$ at iteration $t + 1$ based on these fixed points. From this point on, we restrict our analysis to the Bessel K model with $\epsilon \leq 1$ since, as discussed in Section 2, the setting $\epsilon > 1$ does not yield a sparse Type II estimator.
To begin, we consider the update in (25) for a single parameter $\gamma_i$ while considering the estimates $\gamma_k^{[t]}$, $k \neq i$, and $\lambda_i^{[t]}$ as fixed quantities. In Appendix B.1, we show that the dependency of $\langle |w_i|^2 \rangle$ on $\gamma_i^{[t]}$ is expressed as
$$\langle |w_i|^2 \rangle = \frac{(\gamma_i^{[t]})^2(q_i^{[t]} + |q_i^{[t]}|^2) + \gamma_i^{[t]}(s_i^{[t]})^2}{(\gamma_i^{[t]} + s_i^{[t]})^2}$$ \hspace{1cm} (27)
with $s_i^{[t]} \triangleq e_i^T \Sigma_i^{[t]} e_i$, $q_i^{[t]} \triangleq \lambda_i^{[t]} e_i^T \Sigma_i^{[t]} y$, $\Sigma_i^{[t]} \triangleq (\lambda_i^{[t]} \Phi^T + \sum_{k \neq i} (\gamma_k^{[t]})^{-1} e_k e_k^T)^{-1}$ and $e_i$ denoting an $N \times 1$ vector of all zeros but 1 at the $i$th position. By inserting (27) into (25), we obtain an update expression of the form
$$\gamma_i^{\text{new}} = \varphi_i^{[t]}(\gamma_i^{\text{old}})$$ \hspace{1cm} (28)
where the function $\varphi_i^{[t]}$ is parametrized by $\epsilon$, $\eta$, $s_i^{[t]}$, and $q_i^{[t]}$. Next, we want to explore the hypothetical behavior of the estimates of $\gamma_i$ that we would obtain by recursively applying $\varphi_i^{[t]}$ \textit{ad infinitum}. We do so by analyzing the existence of fixed points of the function $\varphi_i^{[t]}$. A fixed point $\tilde{\gamma}_i$ of $\varphi_i^{[t]}$ must fulfill
$$\tilde{\gamma}_i = \varphi_i^{[t]}(\tilde{\gamma}_i) = \frac{\epsilon - \rho - 1 + \sqrt{(\epsilon - \rho - 1)^2 + 4\rho \eta |(s_i^{[t]} + |q_i^{[t]}|^2) + \gamma_i^{[t]} s_i^{[t]}|^2}}{2\eta}$$ \hspace{1cm} (29)
where, for notational simplicity, we have dropped the iteration index for $s_i$ and $q_i$. By inspection of (29), it is clear that $\tilde{\gamma}_i = 0$ is always a fixed point of $\varphi_i^{[t]}$ when $\epsilon \leq 1$. We look for other positive fixed points by solving (29). These fixed points are solutions of the fourth order equation
$$0 = \gamma_i \left( \eta \gamma_i^3 + \gamma_i^2[2\eta s_i - (\epsilon - \rho - 1)] + \gamma_i[\eta s_i^2 - 2(\epsilon - \rho - 1)s_i - \rho(s_i + |q_i|^2)] - (\epsilon - 1)s_i^2 \right).$$ \hspace{1cm} (30)
\[14\] The selected mixing pdf also has a significant impact on the convergence speed as shown in Section 4.
Hence, if any strictly positive fixed point $\tilde{\gamma}_i$ of $\varphi_i^{[t]}$ exists, it must be a solution of the cubic equation
$$0 = \eta \gamma_i^3 + \gamma_i^2 [2 \eta s_i - (\epsilon - \rho - 1)] + \gamma_i [\eta s_i^2 - 2(\epsilon - \rho - 1)s_i - \rho(s_i + |q_i|^2)] - (\epsilon - 1)s_i^2.$$ \hspace{1cm} (31)
As we show in Appendix B.2, the positive solutions of (31) correspond, in fact, to the stationary points of (21) when all variables except $\gamma_i$ are kept fixed at their current estimates, i.e., of
$$\ell_i^{[t]}(\gamma_i) \propto \log(p(y|\gamma_i, \gamma_{-i}^{[t]}, \lambda^{[t]}p(\gamma_i)).$$ \hspace{1cm} (32)
Based on the above analysis, we formulate a new update rule for $\gamma_i$ at iteration $t + 1$. Given the values of all estimates at iteration $t$, we calculate the fixed points of the corresponding function $\varphi_i^{[t]}$ by solving (30). Then
- if no strictly-positive fixed points of $\varphi_i^{[t]}$ exist, we set $\hat{\gamma}_i^{[t+1]} = 0$, which, remember, is also a fixed point of $\varphi_i^{[t]}$.
- if strictly-positive fixed points of $\varphi_i^{[t]}$ exist, we select the fixed point $\tilde{\gamma}_i$ which yields the largest value $\ell_i^{[t]}(\tilde{\gamma}_i)$ among all strictly positive fixed points. We then set $\gamma_i^{[t+1]} = \tilde{\gamma}_i$.
Note that the above selection criterion for $\gamma_i^{[t+1]}$ is a heuristic choice. In fact, we have no guarantee that, by iteratively applying the recurrent function $\varphi_i^{[t]}$, convergence to the selected fixed point will occur. This is likely to depend on the initialization $\gamma_i^{[t]}$. Moreover, when $\epsilon < 1$, selecting a strictly-positive fixed point instead of 0 does not guarantee that the objective function (21) is increased, as (32) diverges to infinity when $\gamma_i$ tends to 0.15 With this selection, however, we hope to obtain an improved convergence speed at the expense of sacrificing the monotonicity property of the EM algorithm. The numerical results obtained with this heuristic choice, shown in Section 4, confirm the effectiveness of the approach.
Next we investigate the solutions of (30) for different selections of $\epsilon$ and $\eta$. We show that for some particular selections of these parameters, the modified update of $\gamma_i^{[t+1]}$ coincides with the updates in the algorithms presented in [1] and [2]. For brevity, we omit the algorithmic iteration index $t$ throughout the rest of the section.
3.2.1. Fixed points for $0 \leq \epsilon < 1$ and $\eta \geq 0$
We consider an arbitrary value of $\epsilon$ in the range $0 \leq \epsilon < 1$. First, as $-(\epsilon - 1)s_i^2 \geq 0$ for $\epsilon < 1$, (31) has at least one negative solution. If no positive solution exists we set $\hat{\gamma}_i = 0$. If (31) has at least one positive solution it is easily
15See the discussion in Section 2.4.
shown that it has exactly two, denoted by $\gamma_i^{(1)}$ and $\gamma_i^{(2)}$. If $\gamma_i^{(1)} = \gamma_i^{(2)}$ then this point is a saddle point of $\ell_i$ and therefore we set $\hat{\gamma}_i = 0$. If $\gamma_i^{(2)} > \gamma_i^{(1)}$ then $\hat{\gamma}_i = \gamma_i^{(2)}$ or if $\gamma_i^{(1)} > \gamma_i^{(2)}$ then $\hat{\gamma}_i = \gamma_i^{(1)}$ (the proof is straightforward and is omitted). Thus, we always select the right-most positive solution.
For the special case $\epsilon = \eta = 0$, i.e., when the mixing density coincides with the Jeffreys prior, (31) reduces to a quadratic equation. It is easy to show that in this case either two positive solutions exist or none exists.
### 3.2.2. Fixed points for $\epsilon = 1$ and $\eta = 0$
In this case the mixing density coincides with a constant improper prior, which leads to the same GSM model as used in RVM [14, 1, 15]. With this setting (31) simplifies to
$$\hat{\gamma}_i = |q_i|^2 - s_i.$$ \hspace{1cm} (33)
From (33), a positive solution of (31) exists if and only if $|q_i|^2 > s_i$. If this condition is not satisfied we set $\hat{\gamma}_i = 0$. It is interesting to note that (33) is independent of $\rho$ and thus is the same regardless of whether the signal model is real or complex.
Next, we show the equivalence between (33) and the corresponding update in Fast RVM [1]. In [1], the estimate of $\gamma_i$ is computed as the maximizer of the marginal log-likelihood function $\ell_i(\gamma_i, \epsilon = 1, \eta = 0)$ in (32). Hence, the estimate of $\gamma_i$ in [1] equals that in (33), because (33) maximizes $\ell_i(\gamma_i, \epsilon = 1, \eta = 0)$.
As the updates of $\mu$, $\Sigma$, and $\hat{\lambda}$ are identical to those in Fast RVM the two algorithms coincide when $\epsilon = 1$ and $\eta = 0$.
### 3.2.3. Fixed points for $\epsilon = 1$ and $\eta > 0$
In this case the mixing pdf coincides with an exponential pdf, so the GSM model is the same as that used in Fast Laplace [2]. The solution
$$\hat{\gamma}_i = -\frac{(2\eta s_i + \rho) + \sqrt{\rho^2 + 4\rho \eta |q_i|^2}}{2\eta}$$ \hspace{1cm} (34)
is positive if and only if $|q_i|^2 - s_i > \eta s_i^2 / \rho$ otherwise we set $\hat{\gamma}_i = 0$. The case $\epsilon = 1$ and $\rho = 1/2$ corresponds to the GSM model of the Laplace prior for real weights. Obviously, (34) can also be used for complex weights, with $\rho = 1$. Yet in this case the marginal prior for $w$ is no longer Laplacian, as showed in Section 2, but some other sparsity-inducing member of the Bessel K density family. The estimate of $\gamma_i$ in Fast Laplace [2] is the maximizer of $\ell_i(\gamma_i, \epsilon = 1, \eta)$ and, hence, is identical to the estimate in (34).
### 3.3. Fast Sequential Inference Scheme
The modified update of $\gamma_i^{[t+1]}$, $i = 1, \ldots, N$, described in Section 3.2 can be directly used to speed up the EM algorithm presented in Section 3.1. With this modification, every time an estimate of a given $\gamma_i$ is set to zero, we remove the
corresponding column vector $\phi_i$ from the dictionary matrix $\Phi$. This effectively reduces the model complexity “on the fly”. However, the first iterations still suffer from a high computational complexity due to the update (23). To avoid this, we follow the approach outlined in [1, Sec. 4], which consists of starting with an “empty” dictionary $\Phi$ and incrementally filling the dictionary by possibly adding one column vector at each iteration of the algorithm. Specifically, at a given iteration of the algorithm, each $\hat{\gamma}_i$, $i = 1, \ldots, N$, is computed from (30) and the one, say $\hat{\gamma}'_i$, that gives rise to the greatest increase in $\exp(\ell(\cdot))$ between two consecutive algorithmic iterations, is selected. Depending on the value of this $\hat{\gamma}'_i$, the corresponding vector $\phi'_i$ is then added, deleted, or kept. The quantities $\Sigma$, $\mu$, and $\hat{\lambda}$ are updated using (23), (24), and (26) together with $s_i$ and $q_i$, $i = 1, \ldots, N$. If the estimate of $\lambda$ is not updated between two consecutive iterations, $\Sigma$, $\mu$, $s_i$, and $q_i$ can be updated efficiently using the update procedures proposed in [1, 36].
We refer to the above sequential algorithm as Fast-BesselK.
4. Numerical Results
In this section we analyze the performance of the Fast-BesselK algorithm proposed in Section 3. The purpose is to characterize the impact of the prior model on the performance of the iterative algorithm in terms of MSE, sparseness of $\hat{w}$, and convergence speed. Section 3 shows that Fast-RVM [1], Fast-Laplace [2], and Fast-BesselK are all instances of the same greedy inference scheme each algorithm resulting from a particular selection of the parameters of the mixing (gamma) pdf. Hence, by comparing the performances of these algorithms we can draw conclusions on the sparsity-inducing property of their respective prior models.
4.1. Simulation Scenarios and Performance Metrics
The performance of the considered sparse algorithms (see Section 4.2) is evaluated by means of Monte Carlo simulations. In order to test the algorithms on a realistic benchmark, we use a random $M \times N$ dictionary matrix $\Phi$, with $M = 100$ and $N = 256$, whose entries are iid zero-mean complex symmetric Gaussian random variables with variance $M^{-1}$. The weight vector $w$ has $K$ nonzero entries with associated indices uniformly drawn without repetition from the set $\{1, 2, \ldots, N\}$. The set of these indices together with its cardinality $K$ are unknown to the algorithms. The nonzero entries in $w$ are independent and drawn from a zero-mean circular-symmetric complex Gaussian distribution with unit variance. Other distributions for the entries in $w$ are considered at the end of this section. All reported performance curves are computed based
\footnote{Naturally, the practical implementation of the inference schemes also impacts the performance. For the subsequent analysis, Fast-RVM, Fast-Laplace, and Fast-BesselK are all implemented based on the Matlab-code for Fast-RVM located at http://people.ee.duke.edu/~lcarin/BCS.html}
on a total of 1000 Monte Carlo trials. For each trial, new realizations of the
dictionary matrix $\Phi$, the vector $w$, and the random perturbation vector $n$ are
drawn independently.
All numerical investigations where replicated for an equivalent real-valued
signal model. Due to space limitations, we do not include the results of these
studies in this contribution, as most of the conclusions are similar to those
drawn from the complex-valued signal model. We will, however, shortly discuss
the relation between the performance of the estimators for real and complex
models at the end of this section.
The performance is evaluated with respect to the following metrics:
- **normalized mean-squared error** : $\text{NMSE} \triangleq \langle \| \hat{w} - w \|_2^2 \rangle / \langle \| w \|_2^2 \rangle$.
- **support error rate** : $\triangleq \# \{ i : \hat{w}_i = 0 \text{ and } w_i \neq 0 \} \cup \{ i : \hat{w}_i \neq 0 \text{ and } w_i = 0 \} \} / N$.
We also report the convergence speed, measured in terms of the number of
algorithmic iterations used, of the Bayesian inference methods as they share the
same computational complexity.
### 4.2. Inference Algorithms Considered
The proposed Fast-BesselK algorithm is tested with two settings for $\epsilon$ and $\eta$:
- **Fast-BesselK($\epsilon = 0$):** we set $\epsilon = 0$ and $\eta = 0$ corresponding to the use of
the Jeffreys prior as mixing density.
- **Fast-BesselK($\epsilon = 0.5$):** we set $\epsilon = 0.5$ and $\eta = 1$.
Instead of selecting a particular value of $\eta$, we could have included this parameter
in the inference framework as done in [2]. Our investigations, however, show
that for $\epsilon << 1$ the performance of Fast-BesselK becomes largely independent
of the choice of $\eta$, and we have therefore simply selected $\eta = 1$.
The performance of Fast-BesselK is contrasted with the state-of-the-art sparse estimators listed below:
1. **Fast-RVM [1, 37]:** is equivalent to Fast-BesselK with $\epsilon = 1$ and $\eta = 0$ (see Section 3).
2. **Fast-Laplace [2]:** is equivalent to Fast-BesselK with $\epsilon = 1$ when including
the update for $\eta$ in [2] (see Section 3).
---
17 In this paper we have not included an investigation on a specific application. We refer to
the work [4] where such a performance assessment is made.
18 We also considered Fast-BesselK with $\epsilon = 0$ and $\eta = 1$. However, this setting led to
similar performance to Fast-BesselK($\epsilon = 0, \eta = 0$).
19 If the Fast-BesselK is implemented with a “top-down” approach (starting out with the
full dictionary $\Phi$) including individual rate parameters $\eta_i$ for each $w_i$, $i = 1, \ldots, N$, may be
beneficial [3].
20 The software is available on-line at http://people.ee.duke.edu/~lcarin/BCS.html
21 The software is available on-line at http://ivpl.eecs.northwestern.edu/
3. OMP, see e.g., [12]: OMP terminates when the greedy algorithm has included \( K + 10 \) column vectors in \( \Phi \). We empirically observed that this choice induces a better NMSE performance than when including \( K \) columns only.
4. SpaRSA [34]: the sparse reconstruction by separable approximation (SpaRSA) algorithm for solving the LASSO cost function. Following [34], we use the adaptive continuation procedure for the regularization \( \kappa \) of the \( \ell_1 \)-norm penalty in the LASSO cost function. Here SpaRSA repeatedly solves the LASSO cost function with decreasing values for \( \kappa \) until a minimum value of \( \kappa \) is reached. The minimum value of \( \kappa \) is set through training. Specifically, we run 50 Monte Carlo trials for each specific settings of \( M, N, K, \) and SNR value. We then choose the value of \( \kappa \) from a set of 50 candidate values in the range \( [0.001 \| \Phi^H y \|_\infty, 0.1 \| \Phi^H y \|_\infty] \) that leads to the smallest error \( \| w - \hat{w} \|_2^2 \).
For brevity, we refer to Fast-RVM, Fast-Laplace, and Fast-BesselK as Bayesian algorithms. We initialize these algorithms as outlined in [1, Sec. 4]. They stop when either the stopping criterion \( \| \hat{\mu}^{[t+1]} - \hat{\mu}^{[t]} \|_\infty \leq 10^{-8} \) is fulfilled or the number of iterations has reached its max limit set to 1000.
As a reference, we also consider the performance of the oracle estimator of \( w \) [38] that “knows” the support of \( w \), denoted by \( \text{supp}(w) \triangleq \{ i : w_i \neq 0 \} \). The oracle estimate reads
\[
\hat{w}_o(y) = \begin{cases}
( \Phi_o^H \Phi_o )^{-1} \Phi_o^H y, & \text{on supp}(w) \\
0, & \text{elsewhere}
\end{cases}
\]
where \( \Phi_o \) is the \( M \times K \) dictionary matrix constructed from those columns of \( \Phi \) that correspond to the nonzero entries in \( w \).
4.3. Performance Comparison
As our analysis in Section 2 shows, the noise precision \( \lambda \) greatly impacts the sparsity property of the Type II penalty. We therefore investigate the impact of this parameter on the algorithms. First, we assume this quantity to be known to the Bayesian algorithms. Note that SpaRSA and OMP do not estimate \( \lambda \). In a next step, this parameter is considered unknown and estimated by the Bayesian algorithms.
4.3.1. Performance versus SNR
The goal of this investigation is to evaluate whether the algorithms can achieve sparse and accurate estimates in conditions of low and medium SNR. In these simulations, we set \( K = 25 \). In Fig. 3(a) and Fig. 5(c), \( \lambda \) is known by the Bayesian algorithms. Fig. 3(a) shows that Fast-BesselK(\( \epsilon = 0 \)) and Fast-BesselK(\( \epsilon = 0.5 \)) achieve the lowest NMSE among the algorithms across the whole SNR range. Their performance is close to that of the oracle estimator.
---
22The software is available on-line at [http://www.lx.it.pt/~mtf/SpaRSA/](http://www.lx.it.pt/~mtf/SpaRSA/).
in the high SNR regime, i.e., above 20 dB. These algorithms also achieve the lowest support error rate across the whole SNR range with a value close to zero as shown in Fig. 5(c).
We repeat the investigation for the Bayesian algorithms but this time with the noise precision \( \lambda \) unknown and being estimated alongside \( w \) and \( \gamma \) using (26). The estimate \( \hat{\lambda} \) is updated at every third iteration. We observe a significant performance degradation in NMSE and support error rate for Fast-RVM and Fast-Laplace in Fig. 5(b) and Fig. 5(d). The reason is that Fast-RVM and Fast-Laplace heavily overestimate \( \lambda \), thus, \( K \) is overestimated as well (results not shown). Consequently, the support error rate and NMSE is high. In contrast, the Fast-BesselK algorithms perform essentially the same as when \( \lambda \) is known.
In summary, the results presented in Fig. 5 corroborate the significant impact of the estimation of the noise precision on the performance of the Fast Bayesian algorithms. When \( \lambda \) is known, all algorithms achieve an acceptable performance, both in terms of NMSE and support error rate. However, when \( \lambda \) is unknown and estimated by the algorithms, only Fast-BesselK is able to produce accurate estimates of this parameter, resulting in greatly improved performance as compared to Fast-Laplace and Fast-RVM. This is an important result as, in
\[\text{In some cases, the sequence of estimates of } \lambda \text{ produced by Fast-RVM and Fast-Laplace did not converge. Due to this, a maximum of value of } 10^8 \text{ was set for } \lambda.\]
many applications, the noise precision parameter is not known in advance and, hence, needs to be estimated.
4.3.2. Performance versus $K$
We fix the SNR at 20 dB and compare the performance of the algorithms versus the number $K$ of nonzero entries in $w$. In Fig. 6(a) and Fig. 6(c) we assume $\lambda$ to be known to the Bayesian algorithms. The NMSE curves in Fig. 6(a) show that when $K \leq 40$ the algorithms achieve an accurate reconstruction of $w$. Fast-BesselK($\epsilon = 0$) and Fast-BesselK($\epsilon = 0.5$) yield the lowest NMSE which turns out to be close to that of the oracle estimator. In this range, these algorithms exhibit a support error rate close to zero as depicted in Fig. 6(c).
When $\lambda$ is estimated the NMSE and support error rate performance achieved by Fast-RVM and Fast-Laplace degrade as depicted in Fig. 6(c) and Fig. 6(d). Fast-BesselK($\epsilon = 0$) achieves the lowest NMSE but only for $K \leq 30$, as it only accurately estimates $\lambda$ in this range. Consequently, its support error rate decreases for $K > 30$. In turn, Fast-BesselK($\epsilon = 0.5$) achieves similar performance to when $\lambda$ is known. Hence, the selection of $\epsilon = 0.5$ seems to be a good trade-off between achieved sparseness and reconstruction error.
4.3.3. Number of performed algorithmic iterations
We evaluate the convergence speed for the Bayesian algorithms in terms of the number of performed algorithmic iterations. Fig. 7 reports the number of algorithmic iterations until either the stopping criterion is fulfilled or the number of iterations has reached its max limit of 1000 (see Section 4.2) versus SNR and $K$. The Fast-BesselK algorithms perform significantly less number of iterations across the whole SNR range as compared to Fast-RVM and Fast-Laplace, especially in low to medium SNR as seen from Fig. 7(a) and Fig. 7(b). The same superior performance is observed when $K$ is varied in Fig. 7(c) and Fig. 7(d). Notice that the iteration count of greedy algorithms inherently depends on $K$. As Fast-RVM and Fast-Laplace tend to heavily overestimate $K$, they inevitably require a larger number of iterations than algorithms achieving sparser estimates. The Fast-BesselK algorithms exhibit a modest increase of used iterations when $K \leq 40$ as they achieve good reconstruction error in this range, see Fig. 6. When $K \geq 40$, the different performance behavior for Fast-BesselK in Fig. 7(c) and Fig. 7(d) is attributed to the fact that Fast-BesselK significantly underestimates $\lambda$ in this range. In this case, the penalty $q_{II}(\mathbf{w})$ has a high impact on the estimate $\hat{\mathbf{w}}$, which leads to a very sparse estimate $\mathbf{w}$ and, thus, a low number of algorithmic iterations.
Figure 7: Number of used iterations versus SNR and $K$ when $\lambda$ is known ((a), (c)) and $\lambda$ is unknown and estimated ((b), (d)). Selected system parameter settings: $M = 100$, $N = 256$. In ((a), (b)) $K = 25$ and in ((c), (d)) the SNR is fixed at 20 dB.
4.3.4. Performance versus different distributions of the nonzero entries in $w$
We investigate the dependency of the performance of the considered algorithms on the underlying prior distribution of the non-zero entries in $w$. To this end we repeat the previous numerical studies while considering two additional prior distributions for these entries. The first distribution results from selecting the nonzero entries to be of the form $\exp(j\phi_k)$, $k = 1, \ldots, K$ with the phases $\{\phi_k\}$ drawn independently and uniformly on the interval $[0, 2\pi)$. The second distribution results from drawing the nonzero entries independently according to a complex Laplace distribution, see (14), with unit variance. In the next comparison, the nonzero entries are iid according to the complex Laplace distribution with pdf $[14]$ and variance one. We show results only for Fast-RVM, Fast-Laplace, and Fast-BesselK($\epsilon = 0.5$), as the performance gain achieved by Fast-BesselK($\epsilon = 0.5$) as compared to OMP and SpaRSA is similar to the performance observed in the previous investigations. We conclude from Fig. 8 and Fig. 9 that Fast-BesselK($\epsilon = 0.5$) still maintains its superior performance. Furthermore, we again observe the important fact that Fast-BesselK($\epsilon = 0.5$) achieves similar performance in scenarios with known or unknown noise precision. This is in direct contrast to the other Bayesian methods.
4.3.5. Performance for real signal models
We conclude this section by briefly commenting on the performance achieved by the considered algorithms when they are devised for and applied to real-valued signal models. To distinguish between the algorithms devised based on real signal model from those devised for a complex signal model, in the subsequent discussion we refer to the former (latter) as real (complex) algorithms.
In general, all considered complex algorithms perform better than their real variant. In particular, complex algorithms produce accurate results for less sparse weight vectors than their real counterpart. This is explained by the fact that the former use both real and imaginary parts to prune components in \( \hat{w} \), thus, improving the sparse signal representation.
The relative performances of the real algorithms compared to each other show the same trends as that observed for their complex variant. As an illustration, real Fast-BesselK(\( \epsilon = 0 \)) is especially sensitive to high values of \( K \); this is a well-known effect that arises when using the Jeffreys prior as the mixing density. This again emphasizes our conclusion that Fast-BesselK(\( \epsilon = 0.5 \)) is a good trade-off between sparseness and reconstruction error.
5. Conclusion
In this paper, we proposed a hierarchical prior model for sparse Bayesian learning (SBL) that applies to sparse signal representation in complex- and real-valued signal models. Our motivation was on the one hand to overcome the lack of sparsity-inducing prior models for complex signals and on the other hand to propose prior models that induce sparse, accurate, and robust signal representations in conditions of low and medium signal-to-noise ratio (SNR). Both aspects are of particular importance in many engineering applications of sparse signal representation, e.g., in wireless communications.
In the proposed hierarchical prior model the entries of the parameter vector of interest are modeled as independent complex Gaussian scale mixtures (GSMs) with mixing hyperparameters identically distributed according to a gamma distribution with shape parameter $\epsilon$ and rate parameter $\eta$. This model – we termed it the Bessel K model – comprises a family of hierarchical prior probability density functions (pdfs) indexed by these parameters.
We analyzed the properties of Type I and Type II estimators derived from the Bessel K model. Our analysis revealed that the ability of a given element in the density family to induce sparse estimates heavily depends on the inference method used and, interestingly, whether real or complex signals are inferred. In the case of Type I estimation, the Bessel K model invokes, with the right setting of parameters $\epsilon$ and $\eta$, classical penalties such as the $\ell_1$-norm or the log-sum as special cases. The hierarchical Bayesian formulation of the $\ell_1$-norm penalty in the complex case is especially interesting as, to the authors’ knowledge, it has not been proposed before. In the case of Type II estimation, the resulting penalties are also strongly influenced by the variance of the measurement noise, as pointed out by [21]. Nonetheless, we showed that the Bessel K model with $\epsilon < 1$ promotes sparse Type II estimators even when the noise variance is high. In contrast, traditional prior models lose this property in such conditions.
Finally, we derived a greedy algorithm of low complexity based on a modification of the expectation-maximization algorithm formulated for Type II estimation. As the Bessel K model encompasses as special cases previously proposed prior models, the algorithm generalizes existing fast SBL methods, allowing us to directly compare the impact of the different prior models on the performance of the resulting estimators.
The numerical results demonstrated that the Bessel K model with $\epsilon < 1$ leads to estimators with superior convergence speed, sparseness, and lower mean-squared estimation error as compared to state-of-the-art sparse Bayesian estimators. We showed a significant robustness compared to the latter estimators in low and moderate SNR regimes. This is in agreement with the superior sparsity-inducing property of the Bessel K model with $\epsilon < 1$ for highly noisy measurements, as shown in Section 2. Furthermore, the results corroborate that the proposed estimators effectively include the estimation of the noise variance, thus avoiding the need for a training procedure for this parameter.
Appendix A. Approximate Type I Estimation Using EM
Remember that the Type I estimator is the maximizer of
\[ \mathcal{L}(\mathbf{w}) = \log(p(\mathbf{y}|\mathbf{w}, \lambda)p(\mathbf{w})). \]
We formulate the EM algorithm approximating the Type I estimator by selecting \( \{\gamma, \mathbf{y}\} \) to be the complete data for \( \mathbf{w} \). The E-step of the EM algorithm computes the conditional expectation
\[ \langle \log p(\mathbf{y}, \mathbf{w}, \gamma) \rangle_{p(\gamma; \hat{\mathbf{w}})} \]
with
\[ p(\gamma; \hat{\mathbf{w}}) \propto \prod_i \gamma_i^{\epsilon - \rho - 1} \exp \left( - \frac{\gamma_i^{-1} \rho |\hat{w}_i|^2 - \gamma_i \eta}{} \right) \]
computed in the E-step. The right-hand side expression in (A.3) is recognized as the product of GIG pdfs [39], i.e.,
\[ p(\gamma_i; \nu, a, b_i) = \frac{(a/b_i)^{\nu/2}}{2K_\nu(\sqrt{ab_i})} \gamma_i^{\nu - 1} \exp\left( - \frac{a^2 \gamma_i - b_i \gamma_i^{-1}}{\nu} \right) \]
with order \( \nu = \epsilon - \rho \) and parameters \( a = 2\eta \) and \( b_i = 2\rho |\hat{w}_i|^2 \). The moments of the GIG distribution are given in closed form [39]:
\[ \langle \gamma_i^n \rangle = \left( \frac{\rho |\hat{w}_i|^2}{\eta} \right)^n \frac{K_{\nu+n}(2\sqrt{\rho \eta |\hat{w}_i|})}{K_{\nu}(2\sqrt{\rho \eta |\hat{w}_i|})}, \quad n \in \mathbb{R}. \]
The M-step of the EM algorithm updates the estimate of \( \mathbf{w} \) as the maximizer of (A.2):
\[ \hat{\mathbf{w}} = \left( \Phi^H \Phi + \lambda^{-1} (\Gamma^{-1}) \right)^{-1} \Phi^H \mathbf{y}. \]
In case we use the Laplace GSM model \( (\nu = \epsilon - \rho = 1/2) \), (A.4) with \( n = -1 \) simplifies to
\[ \langle \gamma_i^{-1} \rangle = \frac{\sqrt{\eta/\rho}}{|\hat{w}_i|}, \]
where we have invoked the identity \( K_{\nu}(\cdot) = K_{-\nu}(\cdot) \) [32].
Appendix B. Results for Section 3.2
This appendix contains the derivations of some results used in Section 3.2.
Appendix B.1. Computation of $\langle |w_i|^2 \rangle$
We follow the approach in [40] to compute $\langle |w_i|^2 \rangle$. We can express $\langle |w_i|^2 \rangle$ as $\langle |w_i|^2 \rangle = e_i^T(\Sigma + \mu \mu^H)e_i$ with $e_i$ being an $N \times 1$ vector of all zeros with $1$ at the $i$th position. First, we consider the dependency of $\Sigma$ in (23) on a single parameter $\gamma_i$. We note that $\Sigma = (\lambda \Phi \Phi^H + \sum_{k \neq i} \gamma_k^{-1} e_k e_k^T + \gamma_i^{-1} e_i e_i^T)^{-1}$. Making use of the matrix inversion lemma [40] we recast $\Sigma$ as
$$\Sigma = \Sigma_{-i} - \frac{\Sigma_{-i} e_i e_i^T \Sigma_{-i}}{\gamma_i + e_i^T \Sigma_{-i} e_i},$$
(B.1)
where $\Sigma_{-i} \triangleq (\lambda \Phi \Phi^H + \sum_{k \neq i} \gamma_k^{-1} e_k e_k^T)^{-1}$. After some straightforward algebraic manipulations, $\langle |w_i|^2 \rangle$ can be expressed as
$$\langle |w_i|^2 \rangle = \frac{\gamma_i^2(s_i + |q_i|^2) + \gamma_i s_i^2}{(\gamma_i + s_i)^2}$$
(B.2)
with the definitions $s_i \triangleq e_i^T \Sigma_{-i} e_i$ and $q_i \triangleq \lambda e_i^T \Sigma_{-i} \Phi^H y$.
Appendix B.2. Computation of the stationary points of $\ell_i(\gamma_i)$
We define
$$\ell_i(\gamma_i) \triangleq \epsilon \log(p(y|\gamma_i, \gamma_{-i}, \lambda)p(\gamma_i)).$$
(B.3)
Following the steps in [1] we can write $\ell(\gamma_i)$ as
$$\ell_i(\gamma_i) \triangleq -\rho \log |1 + \gamma_i \hat{s}_i| + \rho \frac{|\hat{q}_i|^2}{\gamma_i + \hat{s}_i} + (\epsilon - 1) \log \gamma_i - \eta \gamma_i$$
(B.4)
with the definitions $\hat{s}_i \triangleq \phi_i^H C_{-i}^{-1} \phi_i$, $\hat{q}_i \triangleq y^H C_{-i}^{-1} \phi_i$, and $C_{-i} \triangleq \lambda^{-1} I + \sum_{k \neq i} \gamma_k \Phi_k \Phi_k^H$. Taking the derivative of $\ell$ with respect to $\gamma_i$ and equating the result to zero yields
$$(\epsilon - \rho - 1) \hat{s}_i^2 + \gamma_i [2\eta \hat{s}_i - (\epsilon - \rho - 1) \hat{s}_i^2] + \gamma_i [\eta + \rho (\hat{s}_i - |\hat{q}_i|^2) - 2(\epsilon - 1) \hat{s}_i] - (\epsilon - 1).$$
(B.5)
Making use of the matrix inversion lemma for $C_{-i}^{-1}$, we show the identities $s_i = \hat{s}_i^{-1}$ and $|q_i|^2 = |\hat{q}_i|^2 / \hat{s}_i$ [39]. By substituting these identities into (B.5), we arrive at the cubic equation in (B.5). Thus, the positive solutions of (B.5) are the stationary points of (B.4).
Acknowledgment
This work was supported by the 4GMCT cooperative research project funded by Intel Mobile Communications, Agilent Technologies, Aalborg University and the Danish National Advanced Technology Foundation.
References
[1] M. E. Tipping, A. C. Faul, Fast marginal likelihood maximisation for sparse Bayesian models, in: Proc. 9th International Workshop on Artificial Intelligence and Statistics, 2003.
[2] S. D. Babacan, R. Molina, A. K. Katsaggelos, Bayesian compressive sensing using Laplace priors, IEEE Trans. on Image Processing 19 (1) (2010) 53–63.
[3] N. L. Pedersen, C. N. Manchón, D. Shutin, B. H. Fleury, Application of Bayesian hierarchical prior modeling to sparse channel estimation, in Proc. IEEE Int. Communications Conf. (ICC) (2012) 3487–3492.
[4] N. L. Pedersen, C. N. Manchón, B. H. Fleury, A fast iterative Bayesian inference algorithm for sparse channel estimation, in Proc. IEEE Int. Communications Conf. (ICC) (2013) 4591 – 4596.
[5] R. Baraniuk, Compressive sensing, IEEE Signal Processing Magazine 24 (4) (2007) 118–121.
[6] E. J. Candes, M. B. Wakin, An introduction to compressive sampling, IEEE Signal Process. Mag. 25 (2) (2008) 21–30.
[7] D. G. Tzikas, A. C. Likas, N. P. Galatsanos, The variational approximation for Bayesian inference, IEEE Signal Process. Mag. 25 (6) (2008) 131–146.
[8] W. Bajwa, J. Haupt, A. Sayeed, R. Nowak, Compressed channel sensing: A new approach to estimating sparse multipath channels, Proceedings of the IEEE 98 (6) (2010) 1058–1076.
[9] D. Shutin, B. H. Fleury, Sparse variational Bayesian SAGE algorithm with application to the estimation of multipath wireless channels, IEEE Trans. on Signal Proc. 59 (2011) 3609–3623.
[10] R. Tibshirani, Regression shrinkage and selection via the LASSO, J. R. Statist. Soc. 58 (1994) 267–288.
[11] S. S. Chen, D. L. Donoho, M. A. Saunders, Atomic decomposition by basis pursuit, SIAM Journal on Scientific Computing 20 (1998) 33–61.
[12] J. A. Tropp, Greed is good: Algorithmic results for sparse approximation, IEEE Trans. on Inf. Theory 50 (2004) 2231–2242.
[13] D. Needell, J. Tropp, CoSaMP: Iterative signal recovery from incomplete and inaccurate samples, Applied and Computational Harmonic Analysis 26 (3) (2009) 301–321.
[14] M. Tipping, Sparse Bayesian learning and the relevance vector machine, Journal of Machine Learning Research 1 (2001) 211–244.
[15] D. P. Wipf, B. D. Rao, Sparse Bayesian learning for basis selection, IEEE Trans. on Sig. Proc. 52 (8) (2004) 2153 – 2164.
[16] D. F. Andrews, C. L. Mallows, Scale mixtures of normal distributions, Journal of the Royal Statistical Society. Series B (Methodological) 36 (1974) 99–102.
[17] O. Barndorff-Nielsen, J. Kent, M. Sorensen, Normal variance-mean mixtures and z distributions, International Statistical Review 50 (1982) 145–159.
[18] T. Gneiting, Normal scale mixtures and dual probability densities, Journal of Statistical Computation and Simulation 59 (1997) 375–384.
[19] T. Eltoft, T. Kim, T.-W. Lee, Multivariate scale mixture of gaussians modeling, Lecture Notes in Computer Science 3889 (2006) 799–806.
[20] J. A. Palmer, D. P. Wipf, K. Kreutz-Delgado, B. D. Rao, Variational EM algorithm for non-Gaussian latent variable models, in: Advances in Neural Information Processing Systems, NIPS, 2006.
[21] D. P. Wipf, B. D. Rao, S. Nagarajan, Latent variable Bayesian models for promoting sparsity, IEEE Trans. on Information Theory, 57 (9) (2011) 6236–6255.
[22] D. J. C. MacKay, Bayesian interpolation, in: Neural Computation, Vol. 4, 1992, pp. 415–447.
[23] M. Figueiredo, Adaptive sparseness for supervised learning, IEEE Trans. on Pattern Analysis and Machine Intel. 25 (9) (2003) 1150–1159.
[24] E. J. Candes, M. B. Wakin, S. Boyd, Enhancing sparsity by reweighted $\ell_1$ minimization, Journal of Fourier Analysis and Applications 14 (5) (2008) 877–905.
[25] J. E. Griffin, P. J. Brown, Bayesian adaptive lassos with non-convex penalization, (Technical Report). Dept. of Statistics, University of Warwick, 2007.
[26] A. Lee, F. Caron, A. Doucet, C. Holmes, A hierarchical Bayesian framework for constructing sparsity-inducing priors (2010) arXiv:1009.1914.
[27] J. A. Palmer, D. P. Wipf, K. Kreutz-Delgado, B. D. Rao, Probabilistic formulation of independent vector analysis using complex Gaussian scale mixtures, in: Advances in Neural Information Processing Systems, NIPS, 2009.
[28] Y. Rakvongthai, A. Vo, S. Oraintara, Complex Gaussian scale mixtures of complex wavelet coefficients, IEEE Trans. on Signal Proc. 58 (7) (2010) 3545–3556.
[29] M. Kyung, J. Gill, M. Ghosh, G. Casella, Penalized regression, standard errors, and Bayesian lassos, Bayesian Analysis 5(2) (2010) 369–412.
[30] F. Caron, A. Doucet, Sparse bayesian nonparametric regression, in: Proc. of the 25th international conference on Machine learning, 2008, pp. 88–95.
[31] J. E. Griffin, P. J. Brown, Inference with normal-gamma prior distributions in regression problems, Bayesian Analysis 5 (1) (2010) 171–188.
[32] M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, 1972.
[33] S.-J. Kim, K. Koh, M. Lustig, S. Boyd, D. Gorinevsky, An interior-point method for large-scale $\ell_1$-regularized least squares, IEEE Journal of Selected Topics in Signal Proc. 1 (4) (2007) 606–617.
[34] S. J. Wright, R. D. Nowak, M. A. T. Figueiredo, Sparse reconstruction by separable approximation, IEEE Trans. on Signal Proc. 57 (7) (2009) 2479–2493.
[35] D. P. Wipf, S. Nagarajan, Iterative reweighted $\ell_1$ and $\ell_2$ methods for finding sparse solutions, IEEE Journal of Selected Topics in Signal Processing 4 (2) (2010) 317–329.
[36] D. Shutin, T. Buchgraber, S. R. Kulkarni, H. V. Poor, Fast variational sparse Bayesian learning with automatic relevance determination for superimposed signals, IEEE Trans. on Signal Proc. 59 (12) (2011) 6257–6261.
[37] S. Ji, Y. Xue, L. Carin, Bayesian compressive sensing, IEEE Trans. on Signal Proc. 56 (6) (2008) 2346–2356.
[38] E. J. Candes, T. Tao, The Dantzig selector: statistical estimation when $p$ is much larger than $n$, Annals of Statistics 36 (6) (2007) 2313–2351.
[39] B. Jorgensen, Statistical Properties of the Generalized Inverse Gaussian Distribution (Lecture Notes in Statistics 9), Springer-Verlag New York Inc, 1982.
[40] K. V. Mardia, J. T. Kent, J. M. Bibby., Multivariate Analysis, Vol. Probability and Mathematical Statistics, Academic Press, 1979. | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2338,
1
],
[
2338,
5612,
2
],
[
5612,
8143,
3
],
[
8143,
11435,
4
],
[
11435,
14873,
5
],
[
14873,
17573,
6
],
[
17573,
20632,
7
],
[
20632,
23494,
8
],
[
23494,
25480,
9
],
[
25480,
28236,
10
],
[
28236,
29925,
11
],
[
29925,
31939,
12
],
[
31939,
34501,
13
],
[
34501,
37660,
14
],
[
37660,
40554,
15
],
[
40554,
43581,
16
],
[
43581,
46718,
17
],
[
46718,
49600,
18
],
[
49600,
52589,
19
],
[
52589,
54224,
20
],
[
54224,
55510,
21
],
[
55510,
57255,
22
],
[
57255,
58696,
23
],
[
58696,
59978,
24
],
[
59978,
63228,
25
],
[
63228,
65163,
26
],
[
65163,
67756,
27
],
[
67756,
69920,
28
],
[
69920,
72096,
29
],
[
72096,
74009,
30
]
]
} |
9dc645bbe822ea1c5d26a7685985e42afded351c | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 5,
"total-fallback-pages": 0,
"total-input-tokens": 21721,
"total-output-tokens": 5979,
"fieldofstudy": [
"Computer Science"
]
} | Binary Classification with Positive Labeling Sources
Jieyu Zhang
University of Washington
Seattle, United States
[email protected]
Yujing Wang
Microsoft Research Asia
Beijing, China
[email protected]
Yaming Yang
Microsoft Research Asia
Beijing, China
[email protected]
Yang Luo
Microsoft Research Asia
Beijing, China
[email protected]
Alexander Ratner
University of Washington
Snorkel AI, Inc.
Seattle, United States
[email protected]
ABSTRACT
To create a large amount of training labels for machine learning models effectively and efficiently, researchers have turned to Weak Supervision (WS) [25], which uses programmatic labeling sources rather than manual annotation. Existing works of WS for binary classification typically assume the presence of labeling sources that are able to assign both positive and negative labels to data in roughly balanced proportions. However, for many tasks of interest where there is a minority positive class, negative examples could be too diverse for developers to generate indicative labeling sources. Thus, in this work, we study the application of WS on binary classification tasks with positive labeling sources only. We propose Weapo, a simple yet competitive WS method for producing training labels without negative labeling sources. On 10 benchmark datasets, we show Weapo achieves the highest averaged performance in terms of both the quality of synthesized labels and the performance of the final classifier supervised with these labels. We incorporated the implementation of Weapo into WRENCH [40], an existing benchmarking platform.
CCS CONCEPTS
• Computing methodologies → Semi-supervised learning settings.
KEYWORDS
Weak supervision; data programming; binary classification
ACM Reference Format:
Jieyu Zhang, Yujing Wang, Yaming Yang, Yang Luo, and Alexander Ratner. 2022. Binary Classification with Positive Labeling Sources. In Proceedings of the 31st ACM International Conference on Information and Knowledge Management (CIKM ’22), October 17–21, 2022, Atlanta, GA, USA. ACM, New York, NY, USA, 5 pages. https://doi.org/10.1145/3511808.3557552
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].
CIKM ’22, October 17–21, 2022, Atlanta, GA, USA
© 2022 Copyright held by the owner/author(s). Publication rights licensed to ACM.
ACM ISBN 978-1-4503-9236-5/22/10...$15.00
https://doi.org/10.1145/3511808.3557552
1 https://github.com/JieyuZ2/wrench/blob/main/wrench/labelmodel/weapo.py
1 INTRODUCTION
Weak Supervision (WS), one recent paradigm [25] for overcoming the challenge of low availability of training labels, has achieved remarkable success in various real-world applications [1, 13]. Specifically, in WS, expensive, time-consuming manual annotations are replaced with programmaticaly-generated labeling sources, called labeling functions (LFs), applied to unlabeled data. The usable labeling sources include but not limited to heuristics, knowledge bases, and pretrained models- they are typically cheaper than hand-labeling and able to provide potentially noisy labels to unlabeled data at scale. Despite the efficacy and efficiency of WS framework, it heavily relies on high-quality labeling sources to achieve satisfactory performance [39, 40]. In some real-world scenarios, in particular ones with a minority “positive” and majority “negative” class, the data of certain label could be highly diverse, making it difficult for practitioners to create labeling sources. For example, in bot detection where the user aim to detect bots from normal users, it is non-trivial even for experts to create labeling sources that identify the patterns of normal users, since the user behavior could be arbitrary. Note that such a motivation indeed drives the long-standing research problem of Positive-Unlabeled learning [3]. With regard to the importance of labeling sources and the difficulty of generating them for certain applications, in this work, we study the effectiveness of WS approaches under the setting where the labeling source of certain data class is absent. Specifically, we focus on binary classification with positive labeling sources only; in other words, the labeling source at-hand could only assign positive or abstain on any given data point.
We propose Weapo, a simple yet effective method for binary classification with positive labeling sources only. In particular, it is based on the intuition that data receiving more positive votes from the labeling sources are, in expectation, more likely to be positive examples. We formulate this simple idea as constraints on the inferred labels and construct a constrained optimization problem that seeks for a solution satisfying the constraints and minimizing the ℓ-2 regularization loss. On 10 benchmark binary classification datasets, we empirically demonstrate the efficacy of Weapo by showing that it offers highest performance on average. Specifically, we conduct experiments regarding both the quality of generated labels and the performance of a final classifier supervised with the labels. In both batches of experiments, we compare Weapo with modified versions of several existing WS methods as their
We denote scalar and generic items as lowercase letters, vectors as lowercase bold letters, and matrices as bold uppercase letters. For a vector \( \mathbf{v} \), we use \( v_i \) to represent its \( i \)-th value.
In binary classification, we aim to learn a scoring function \( g \) that could be used to build a binary classifier \( h(x) = \text{sign}(g(x) - \pi) \), where \( \pi \) is a threshold and \( x \) is a data point. In other words, the classifier \( h(x) \) maps data \( x \in X \) into binary label \( y \in \mathcal{Y} = \{-1, +1\} \). In standard supervised learning, we are given the ground truth label \( y = [y_1, y_2, ..., y_N] \) of the dataset \( D = \{x_i\}_{i \in [N]} \) for learning an optimal scorer \( g \), where \( N \) is the size of the dataset. However, for many classification tasks of interest, the collection of ground truth labels could be expensive and time-consuming. To tackle the challenge of low availability of ground truth labels, researchers have resorted to Weak Supervision [25, 37], which leverages programmatically generated, potentially noisy and correlated labeling sources to synthesize training labels. In this work, we follow this Weak Supervision setup and do not assume any ground truth label.
Formally, we have access to \( M \) labeling sources \( S = \{\lambda_j\}_{j \in [M]} \). For concreteness, we follow the general convention of Weak Supervision [25] and refer to these sources as labeling functions (LFs). Different from existing studies of Weak Supervision for binary classification that typically assume LFs could assign positive (+1), negative (-1), or abstain (0) to each data point, we are interested in the setting wherein we do not have negative LFs. We argue that such a setting is of importance because in real-world scenarios (1) high negative-class diversity may make constructing LFs prohibitively difficult [3], or (2) negative data may not be systematically recorded in some domains [2] and therefore it is difficult for developers to summarize labeling heuristics. Thus, in our setting, each LF \( \lambda_j \) either assigns positive label (+1) to a data or abstains (0), resulting in a label matrix \( L \in \{0, 1\}^{M \times N} \). Additionally, we assume the class prior \( p_+ = p(y = 1) \) is known following the convention of Weak Supervision [26]. We use \( \Lambda(x) \) to represent the output of LFs on data \( x \). We also use \( S^d \) to represent \( \{0, 1\}^d \) and \( \Lambda(x) \in \mathcal{B}^M \).
Given these LFs, our goal is to learn a label model \( f_0(\Lambda(x)) \) (short for \( f_0(x) \)), which is also a scoring function similar to \( g \) but inputs \( \Lambda(x) \) instead. It could be used to either directly make predictions on test data or provide supervisions for training a more complex end model \( g \) which inputs the data feature.
## 4 THE PROPOSED APPROACH
### 4.1 Conditional Moment Statistics
First, given a parameterized scoring function \( f_0(x) \) and a possible output of all the LFs \( v \in \mathcal{B}^M \), we define a moment statistic conditional on \( \Lambda(x) = v \) as
\[
E_{x:\Lambda(x)=v}[f_0(x)],
\]
which is the averaged score of \( f_0(x) \) over the set of data where \( \Lambda(x) = v \). Empirically, given the dataset \( D \) at-hand, the conditional moment statistics can be similarly defined as
\[
E_{x_i \in D, \Lambda(x_i)=v}[f_0(x_i)] = E_{x_i \in D_v}[f_0(x_i)] = \frac{1}{|D_v|} \sum_{x_i \in D_v} f_0(x_i),
\]
where \( D_v = \{x_i \in D | \Lambda(x_i) = v\} \).
### 4.2 A Partial Ordering of LFs Output
Then we introduce the covering relation between two binary vector \( v_1, v_2 \in \mathcal{B}^M \).
**Definition 4.1 (Covering Relation).** For \( v_1, v_2 \in \mathcal{B}^M \), \( v_1 \) is covered by \( v_2 \) if \( \forall i \in [M], v_2[i] \geq v_1[i] \) and \( \exists j \in [M], v_2[j] > v_1[j] \). We represent this covering relation using operator \( \triangleright \), e.g., \( v_2 \triangleright v_1 \).
For example, \( v_1 \) is covered by \( v_2 \) if \( v_1 = [1, 0, 0] \) and \( v_2 = [1, 1, 0] \); however for \( v_3 = [0, 0, 1] \), there is no covering relation between \( v_2 \) and \( v_3 \). Hence, the covering relation defines a partial ordering of elements in \( \mathcal{B}^M \).
### 4.3 Constrained Optimization
Now we describe our intuition. We expected that (in expectation) data have more positive votes should be more likely to be positive. Notably, we do not simply count the number of LFs assigning positive label as LF could be noisy, instead we resort to the covering
We simply parametrize the scoring function $f_\theta(x)$ as
$$f_\theta(x) = \Lambda(x) \theta^T,$$
(7)
where $\theta \in \Delta^M$ and $\Lambda(x) \theta^T$ is a convex combination of LFs output. Such a simple parametrization restricts the range of $f_\theta(x)$ to be $[0, 1]$ and therefore $f_\theta(x)$ could be interpreted as $P(y = 1|\Lambda(x))$. Then, we could further incorporate the label prior $p_+$ as a constraint. Specifically, we expect $\frac{1}{N} \sum_{i=1}^N f_\theta(x_i) = p_+$ and the final optimization problem becomes:
$$\min_{\theta \in \Delta^M} \lambda ||\theta||_2^2 + \sum_{i=1}^d \max(A_i f(x; \theta)^T, 0) + \left| \frac{1}{N} \sum_{i=1}^N f_\theta(x_i) - p_+ \right|$$
(8)
Such an optimization problem can be readily and efficiently solved by existing library, e.g., CVXPy [8].
5 EXPERIMENTS
5.1 Datasets
Throughout the experiments, we use the following 10 binary classification datasets from WRENCH [40], a comprehensive benchmark platform for Weak Supervision: **Census, Mushroom, Spambase, PhishingWebsites, Bioresponse, BankMarketing, CDR, SMS, Yelp, and IMDb**. Note that the first 6 datasets are tabular dataset while the remaining ones are textual datasets. For all the datasets, we only use the positive labeling functions provided by WRENCH. For textual datasets, we use pretrained BERT [7] to extract features.
5.2 Compared Methods
We compare **WEapo**, as well as its variant that does not leverage the label prior (**WEapo-prior**), with the following label models in the literature. **MV**: We adopt the classic majority voting (MV) algorithm as one label model. Notably, the abstaining LF, i.e., $\lambda_i = 0$ won’t contribute to the final votes. **DS [6]**: Dawid-Skene (DS) model estimates the accuracy of each LF with expectation maximization (EM) algorithm by assuming a naive Bayes distribution over the LFs’ votes and the latent ground truth. **MeTel [26]**: MeTel models the distribution via a Markov Network and recover the parameters via a matrix completion-style approach. **FS [14]**: FlyingSquid (FS) models the distribution as a binary Ising model, where each LF is represented by two random variables. A Triplet Method is used to recover the parameters and therefore no learning is needed, which makes it much faster than DS and MeTel. However, all existing label models assume the presence of negative LF that is absent in our setting. Thus, we treat the abstain (0) as negative (-1) so that existing label models are applicable.
5.3 Evaluation Protocol
First, we compare the performance of label models on test set. Notably, there is a subset of data not covered by any LF and therefore the label models have no information on them. Thus, we only evaluate the performance of label models on the covered subset of test data. We also found it is beneficial to treat these uncovered data as negative example when training the end model, since covered data are more likely to be positive, leaving the uncovered more likely to be negative.
Then, we compare the performance of end model trained with signals produced by label model. Notably, throughout the experiments, we do not use any clean labels as validation set for model selection, as it contradicts to our setting of absence of clean labels. We found that in such a setup the kernel ridge regression model with RBF kernel outperforms other options, e.g., linear regression, logistic regression, multi-layer perceptron classifier and so on.
For both evaluations, we adopt two common metrics for binary classification, namely, the Area Under the Receiver Operating Characteristic Curve (ROC-AUC score) and the Area Under the Precision-Recall curve (PR-AUC score), since they can be used to directly evaluate the scoring function $f_\theta(x)$.
5.4 Results: Label Models
The main results of label model comparison are presented in Table 1. First of all, we can see that **WEapo** achieves the highest averaged performance under both evaluation metrics and its variant **WEapo-prior** has the second best performance. This demonstrates the efficacy of **WEapo** as well as incorporating label prior as a constraint. However, **WEapo** does not outperform all the baselines on every datasets, which aligns with the recent results in a benchmarking study [40] that it is unlikely to have a universally-best label model.
Table 1: Label model comparison on covered test data. We highlight the best performing method in bold.
| Method | Census | Mushroom | Spambase | Phishing Websites | Bioreponse | Bank Marketing | CDR | SMS | Yelp | IMDb | Average |
|----------|--------|----------|----------|-------------------|------------|----------------|-----|-----|------|------|---------|
| MV | 58.28 | 66.02 | 68.25 | 65.41 | 57.73 | 67.97 | 57.81| 49.00| 66.31| 55.59| 60.44 |
| DS | 37.19 | 66.71 | 64.73 | 30.96 | 57.99 | 48.92 | 47.26| 37.50| 69.13| 61.86| 52.22 |
| Snorkel | 52.07 | 53.05 | 68.31 | 38.47 | 57.59 | 63.44 | 57.54| 32.50| 68.90| 50.66| 54.24 |
| FS | 56.76 | 65.91 | 75.27 | 53.97 | 63.71 | 71.12 | 55.98| 32.50| 64.14| 49.05| 58.84 |
| **Weapo** | **64.91** | **62.58** | **71.10** | **57.52** | **59.21** | **62.98** | **62.01**| **72.50**| **67.80**| **50.07**| **63.07** |
| **Weapo** | **56.72** | **68.58** | **75.15** | **67.22** | **63.71** | **64.88** | **62.94**| **75.83**| **65.64**| **61.19**| **66.19** |
Table 2: End model comparison on test data. We highlight the best performing method in bold.
| Method | Census | Mushroom | Spambase | Phishing Websites | Bioreponse | Bank Marketing | CDR | SMS | Yelp | IMDb | Average |
|----------|--------|----------|----------|-------------------|------------|----------------|-----|-----|------|------|---------|
| Gold | 89.03 | 100.00 | 96.56 | 99.24 | 80.70 | 91.10 | 81.21| 99.90| 95.67| 89.32| 92.27 |
| Gold-covered | 83.71 | 100.00 | 89.40 | 97.90 | 72.96 | 89.88 | 81.13| 98.40| 94.81| 88.75| 89.69 |
| Gold-slice | 81.96 | 98.32 | 85.26 | 90.10 | 70.11 | 62.63 | 78.12| 98.30| 88.33| 85.81| 85.86 |
| Gold-train | 72.75 | 87.63 | 83.54 | 84.34 | 69.76 | 62.18 | 74.91| 96.16| 90.07| 85.42| 80.66 |
| MV | 78.74 | 90.85 | 82.66 | **78.08** | 69.71 | **84.48** | 76.95| 92.92| 85.68| 84.38| 82.45 |
| DS | 76.55 | 91.02 | **83.33** | 60.21 | 69.33 | 76.89 | 75.27| 90.76| **87.68**| **85.35**| 79.64 |
| Snorkel | 80.50 | 85.25 | 82.95 | 67.62 | 69.62 | 80.66 | 77.24| **97.80**| **85.79**| **83.35**| 81.08 |
| FS | 80.48 | 92.21 | 82.89 | 72.27 | 69.71 | 82.06 | 77.29| 97.63| 85.34| 83.93| 82.38 |
| **Weapo** | **79.30** | **90.59** | **82.44** | **77.37** | **69.79** | **83.87** | **73.96**| **96.03**| **85.99**| **83.88**| **82.18** |
| **Weapo** | **79.12** | **91.98** | **83.15** | **78.01** | **69.50** | **84.48** | **78.01**| **96.82**| **86.40**| **84.93**| **83.24** |
5.5 Results: End Models
For evaluation of end models, we additionally include four methods involving ground truth label for understanding the upper-bound performance we could achieve. Gold: it use all the ground truth labels of training data to train the end model; Gold-cover: it use the ground truth labels of covered training data to train the end model, since for uncovered data we do not have information for their underlying labels as no LF fires; Gold-slice: because label model inputs only the votes of LF, a group of data sharing the same votes would receive the same output from the label model, Gold-slice assigns the most-likely label for such a group of data, which is more close to the upper-bound performance any label model could offer; Gold-train: it use all the ground truth label to train a label model $f_0$ with the same model class as Weapo, i.e., $\theta \in \Delta^M$.
For the results in Table 2, we can first see that Weapo still achieve the highest averaged performance and again, it is not the best method for every dataset as observed in the label model comparison. Surprisingly, we found that Weapo is slightly better than Gold-train in terms of averaged performance, which further indicates the efficacy of our design. Finally, we conclude that even with positive labeling sources only. We propose Weapo, a simple yet effective method for such a novel setting. It leverages the intuition that data receiving more votes from positive labeling sources are in expectation more likely to be positive. Empirically, we compare Weapo with several baselines modified for this setting and show that it offers highest averaged performance.
REFERENCES
[1] Stephen H Bach, Daniel Rodriguez, Yintao Liu, Chong Luo, Haidong Shao, Cassandra Xia, Souvik Sen, Alex Ratner, Braden Hancock, Houman Alborzi, et al.
| 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
5748,
1
],
[
5748,
10330,
2
],
[
10330,
14678,
3
],
[
14678,
19464,
4
],
[
19464,
19464,
5
]
]
} |
b00c9166ec6f7f409eb1456838e7b494ce5bbe7b | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 58,
"total-fallback-pages": 0,
"total-input-tokens": 173523,
"total-output-tokens": 57506,
"fieldofstudy": [
"Medicine"
]
} | Veettil SK, Wong TY, Loo YS, et al. Role of diet in colorectal cancer incidence: umbrella review of meta-analyses of prospective observational studies. JAMA Netw Open. 2021;4(2):e2037341. doi:10.1001/jamanetworkopen.2020.37341
eAppendix. Supplementary Methods
eTable 1. Search Strategy
eFigure. Study Flow Diagram
eTable 2. Excluded Studies
eTable 3. Descriptive Characteristics of Included Meta-analyses
eTable 4. Associations With Nonsignificant Evidence
eTable 5. Sensitivity Analyses for Associations With Class I, II, or III Evidence
eTable 6. Evidence Criteria: Difference Between and Comparison of WCRF and Present Review
eTable 7. Summary Estimates for Concordance in Meta-analyses: Red Meat Intake and Incidence of CRC
eReferences.
This supplemental material has been provided by the authors to give readers additional information about their work.
eAppendix. Supplementary Methods
We followed relevant sections of the Meta-analysis of Observational Studies in Epidemiology (MOOSE) guidelines.
Umbrella reviews are useful tools that provide a comprehensive overview of evidence of published systematic reviews and meta-analyses on a specific topic. They can elucidate the strength of evidence and the precision of the estimates, and evaluate risk of bias of the published reports. Our objective in this study is to grade the evidence from published meta-analyses of prospective observational studies that assessed the association between dietary patterns, specific foods, food groups, beverages (including alcohol), macronutrients, and micronutrients and incidence of colorectal cancer (CRC). Definition of different dietary patterns is provided below:
**Research questions:** 1) Which dietary factors are associated with the incidence of colorectal cancer in the general adult population? 2) How credible is the evidence behind these associations in published meta-analyses of prospective observational studies?
**Eligibility criteria:** PICO characteristics: population-adults of any age; exposure-any dietary patterns, pre-specified diet quality indices, specific foods, food groups, beverages (including alcohol), macronutrients (i.e., carbohydrate, fat, protein), and micronutrients (vitamins, minerals, antioxidants, polyphenols); comparison of this study-1) exposed group to any of the aforementioned factors versus the non-exposed group and 2) high intake of any of the aforementioned diet groups versus a low intake group; and primary outcome-incidence of colorectal cancer.
Studies were included that met the following criteria: 1) meta-analysis of prospective observational studies (i.e., cohort design) among adults with multivariable-adjusted summary risk estimates and corresponding 95% confidence intervals; and 2) investigated the association of dietary factor(s) with the incidence of CRC. Studies were excluded if they were primary studies, or if no summary estimate was reported (e.g., systematic reviews without meta-analysis). We also excluded (1) meta-analyses of studies with other study designs; and (2) meta-analyses that provided insufficient or inadequate data for quantitative synthesis. We also excluded meta-analyses published in languages other than English. When more than one meta-analysis on the same research question was eligible, only one meta-analysis was selected for each exposure to avoid the inclusion of duplicate studies. In that case, the meta-analysis with the largest number of primary studies was selected. If more than one published meta-analysis on the same exposure included an equal number of studies, the one with the largest number of CRC cases was chosen. If more than one published meta-analysis fulfilled both criteria, the one with more comprehensive information on primary studies was selected.
**Search strategy:** We searched Medline, Embase and the Cochrane Library from database inception to September 2019. We also manually searched the cited references of the retrieved articles and reviews.
**Data extraction:** Data were extracted by two authors (Y.S. and T.Y.) and double-checked by a third author (S.V.). From each eligible article, we recorded the following: name of the first author, publication year, diet exposure, number of included studies, the total number of CRC cases and participants, type of comparison (e.g., high versus low), study-specific summary risk estimates (i.e., risk ratio (RR), odds ratio (OR), hazard ratio (HR), or incident rate ratio (IRR)) together with the corresponding confidence intervals, and estimates of publication bias. For each primary study included in the published meta-analysis, we noted whether relevant confounders were accounted for in adjusted summary estimates and reported. We communicated with authors to obtain data for evidence synthesis if it was not clearly reported in the published meta-analysis.
**Definition of important dietary patterns:**
| Dietary pattern | Study | Exposure definition |
|-------------------------|---------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------|
| Dietary calcium | Meng 2019[218] | The comparison of elemental intake of dietary calcium from each study included in the meta-analysis classified as highest categories (Q3, Q4, and Q5 [up to 2057 mg/day]) and the lowest categories (Q1 and Q2 [<228 mg/day]). |
| Dietary glycemic load | Reynolds 2019[182] | Based on WHO Nutrition Guidance Expert Advisory Group |
| Dietary glycemic load | Reynolds 2019[182] | Based on WHO Nutrition Guidance Expert Advisory Group |
| Healthy diet | Feng 2017[179] | High intakes of vegetables, fruits, whole grains, olive oil, fish, soy, poultry, and low-fat dairy |
| Heavy alcohol drinking | Fedirko 2011[201] | Consumption of ≥4 drinks/day (≥50 g/day of ethanol) |
| Light alcohol drinking | Fedirko 2011[201] | Consumption of ≤1 drink/day (≤12.5 g/day of ethanol) |
| Mediterranean diet | Schwingshackl 2017[178] | High consumption of plant-based foods, especially whole grain products, vegetables, fruits, nuts, and legumes with regular intake of fish and seafood. Eggs, red and processed meat as well as high-fat dairy products are consumed in low amounts |
| Moderate alcohol drinking| Fedirko 2011[201] | Consumption of 2–3 drinks/day (12.6–49.9 g/day of ethanol) |
| Western diet | Feng 2017 | High consumption of red and/or processed meat, refined grains, sweets, high-fat dairy products, butter, potatoes and high-fat gravy, and low intake of fruits and vegetables |
| Non-vegetarian diet | Godos 2016[181] | Eating meat more than once per week |
| Pesco-vegetarian diet | Godos 2016[181] | Consumption of fish more than once per month in those following vegetarian diet |
| Semi-vegetarian diet | Godos 2016[181] | Low consumption of meat (more than once per month but less than once per week) |
| Suppemental calcium | Heine-Bröring 2015[216] | Use of calcium in supplement form. Mean level of intake:145 mg/day to 1,130 mg/day |
| Unhealthy diet | Grosso 2017[180] | High intakes of red and processed meat, sugary drinks and salty snacks, starchy foods, and refined carbohydrates |
| Vegetarian diet | Godos 2016[181] | Eating meat less than once per month |
### eTable 1. Search Strategy
| No. | Search term | Embase 1974 | CDSR | MEDLINE |
|-----|----------------------------------------------------------------------------|-------------|-------|----------|
| 1 | exp Systematic Review/*CDSR: systematic review.mp. | 219179 | 7127 | 112213 |
| 2 | systematic review.ti,ab. | 170483 | 794 | 130108 |
| 3 | exp Meta Analysis/*CDSR: meta analysis.mp. | 171779 | 8406 | 104669 |
| 4 | meta-analysis.ti,ab. | 174319 | 1843 | 127415 |
| 5 | exp Colorectal Neoplasms/*CDSR: Colorectal Neoplasms.mp. | 27509 | 60 | 192528 |
| 6 | exp Colonic Neoplasms/*CDSR: Colonic Neoplasms.mp. | 304714 | 12 | 72783 |
| 7 | exp Rectal Neoplasms/*CDSR: Rectal Neoplasms.mp. | 240553 | 27 | 45779 |
| 8 | exp Adenomatous Polyps/*CDSR: Adenomatous Polyps.mp. | 8868 | 19 | 7822 |
| 9 | exp Adenocarcinoma/*CDSR: Adenocarcinoma.mp. | 208037 | 286 | 365492 |
| 10 | exp Intestinal Polyps/*CDSR: Intestinal Polyps.mp. | 30058 | 3 | 14332 |
| 11 | exp Colonic Polyps/*CDSR: Colonic Polyps.mp. | 19381 | 9 | 8126 |
| 12 | colorectal cancer$.tw. | 143433 | 280 | 92873 |
| 13 | colorectal tumo$.tw. | 9331 | 18 | 6648 |
| 14 | colorectal neoplas$.tw. | 5617 | 64 | 3574 |
| 15 | colon cancer$.tw. | 65894 | 103 | 44261 |
| 16 | colon tumo$.tw. | 6699 | 11 | 4907 |
| 17 | colon neoplas$.tw. | 599 | 5 | 380 |
| 18 | colonic cancer$.tw. | 3567 | 10 | 2808 |
| 19 | colonic tumo$.tw. | 2450 | 1 | 1759 |
| 20 | colonic neoplas$.tw. | 1679 | 19 | 1183 |
| 21 | rectal cancer$.tw. | 34633 | 70 | 21678 |
| 22 | rectal tumo$.tw. | 3399 | 11 | 2160 |
| 23 | rectal neoplas$.tw. | 560 | 31 | 370 |
| 24 | rectum cancer$.tw. | 929 | 18 | 520 |
| 25 | rectum tumo$.tw. | 171 | 11 | 92 |
| 26 | rectum neoplas$.tw. | 23 | 0 | 13 |
| 27 | polyps$.tw. | 39414 | 110 | 268025 |
| 28 | adenoma$.tw. | 108700 | 129 | 80009 |
| 29 | adenomatous$.tw. | 19048 | 40 | 13997 |
| 30 | exp Adenoma/*CDSR: Adenoma.mp. | 110273 | 79 | 98362 |
| 31 | or/1-4 | 377143 | 9104 | 236427 |
| 32 | or/5-30 | 667370 | 689 | 898844 |
| 33 | 31 and 32 | 12909 | 663 | 8899 |
| 34 | Limit “33” to humans | 1661 | (exclude MEDLINE journals) | 7954 |
Screening Records after duplicates removed (n = 9954)
Records identified through database searching
MEDLINE = 7954
Embase = 1661
CDSR = 663
Records screened (n = 9954)
Records excluded based on title and abstract (n = 9732)
Full-text articles assessed for eligibility (n = 222)
Full-text articles excluded (n = 177)
23 Not a relevant study design
38 Outcome of interest on incidence of colorectal cancer not reported
69 Not the largest systematic review or meta-analysis investigating outcome of interest
20 Exposure of interest not reported
21 No meta-analysis
4 Non-English publication
2 Insufficient data reported
Studies included in quantitative synthesis (n = 45 meta-analyses)
### eTable 2. Excluded Studies
| Reason | References |
|---------------------------------------------|------------|
| Outcome of interest on incidence of colorectal cancer not reported | (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38) |
| Not a relevant study design | (39)(40)(41)(42)(43)(44)(45)(46)(47)(48)(49)(50)(51)(52)(53)(54)(55)(56)(57)(58)(59)(60)(61) |
| No meta-analysis | (62)(63)(64)(65)(66)(67)(68)(69)(70)(71)(72)(73)(74)(75)(76)(77)(78)(79)(80)(81)(82) |
| Exposure of interest not reported | (83)(84)(85)(86)(87)(88)(89)(90)(91)(92)(93)(94)(95)(96)(97)(98)(99)(100)(101)(102) |
| Non-English publication | (103)(104)(105)(106) |
| Not the largest systematic review or meta-analysis investigating outcome of interest | (107)(108)(109)(110)(111)(112)(113)(114)(115)(116)(117)(118)(119)(120)(121)(122)(123)(124)(125)(126)(127)(128)(129)(130)(131)(132)(133)(134)(135)(136)(137)(138)(139)(140)(141)(142)(143)(144)(145)(146)(147)(148)(149)(150)(151)(152)(153)(154)(155)(156)(157)(158)(159)(160)(161)(162)(163)(164)(165)(166)(167)(168)(169)(170)(171)(172)(173)(174)(175) |
| Insufficient data reported | (176)(177) |
### eTable 3. Descriptive Characteristics of Included Meta-analyses
| Exposure | Author; publication year | No. of primary studies | No. of participant cases | No. of cases | Duration of follow-up (range in years; mean in years) | Adjustment for confounding variables |
|----------|--------------------------|------------------------|--------------------------|--------------|--------------------------------------------------------|-------------------------------------|
| Dietary behaviours or diet quality indices |
| Adherence to Mediterranean diet | Schwingshackl 2017(178) | 6 | 1410030 | 1610 | 5 - 26; 15.5 | Age, sex, race/ethnicity, BMI, physical activity, educational level, socioeconomic status, smoking status, alcohol intake, family history of CRC, use of aspirin or other NSAIDs, colonoscopy, history of polyps, multivitamin use, energy intake, menopausal status, HRT use |
| Adherence to healthy diet | Feng 2017(179) | 15 | 1182930 | 1153 | 1.7 - 14; 8.5 | Age, sex, race/ethnicity, educational level, occupation, diabetes, BMI, smoking status, alcohol intake, physical activity, colorectal adenoma history, extent of colon resection, family history of CRC, energy intake, use of aspirin, use of HRT, multivitamin use, endoscopy |
| Adherence to unhealthy diet | Grosso 2017(180) | 7 | 979243 | 9104 | 5 - 14; 9.5 | Age, sex, race/ethnicity, BMI, energy intake, diabetes, educational level, smoking status, alcohol intake, occupation, physical activity, family history of CRC, use of aspirin or other NSAIDs, use of HRT |
| Adherence to Western diet | Feng 2017(179) | 15 | 1182930 | 1153 | 1.7 - 14; 8.5 | Age, sex, race/ethnicity, BMI, diabetes, smoking status, colorectal adenoma history, extent of colon resection, alcohol intake, educational level, occupation, physical activity, family history of CRC, energy intake, use of aspirin, menopausal status, use of HRT, multivitamin use, endoscopy |
| Adherence to alcohol drinking | Feng 2017(179) | 9 | 718248 | 3965 | 5 - 16; 9.7 | Age, sex, race/ethnicity, BMI, family history of CRC, educational level, smoking status, energy intake, physical activity, meat intake (red or processed meat), consumption of vegetables, fruit intake, use of aspirin, multivitamin use including dietary folate, total milk intake; intakes of fibre, fat, calcium |
| Vegetarian diet | Godos 2016(181) | 3 | 149516 | 1506 | 7.3 - 20.3; 14.2 | Age, sex, race/ethnicity, BMI, educational level, smoking status, alcohol intake, physical activity, family history of CRC, history of peptic ulcer, history of inflammatory bowel disease, treatment for diabetes mellitus within the past year, aspirin use, statin therapy, prior colonoscopy or flexible sigmoidoscopy, supplemental calcium consumption, supplemental vitamin D, energy intake, use of HRT, fibre intake |
| Pesco-vegetarian diet | Godos 2016(181) | 3 | 149516 | 1506 | 7.3 - 20.3; 14.2 | Age, sex, race/ethnicity, BMI, educational level, smoking status, alcohol intake, physical activity, family history of CRC, history of peptic ulcer, history of inflammatory bowel disease, treatment for diabetes mellitus within the past year, aspirin use, statin therapy, |
prior colonoscopy or flexible sigmoidoscopy, supplemental calcium consumption, supplemental vitamin D, energy intake, use of HRT, fibre intake
| Food groups or foods | Dietary glycaemic index | Dietary glycaemic load | Eating frequency (3 vs <3 daily meals) | Eating frequency (4 vs <3 daily meals) | Eating frequency (≥5 vs <3 daily meals) |
|---------------------|-------------------------|-----------------------|---------------------------------------|---------------------------------------|---------------------------------------|
| Semi-vegetarian diet | Godos 2016<sup>(181)</sup> | 3 | 580175 | 4062 | 5 - 20.3; 10.9 |
| | | | Age, sex, race/ethnicity, total energy intake, smoking status, alcohol intake, BMI, physical activity, educational level, family history of CRC, history of peptic ulcer, history of inflammatory bowel disease, treatment for diabetes mellitus within the past year, aspirin use, statin therapy, prior colonoscopy or flexible sigmoidoscopy, supplemental calcium consumption, supplemental vitamin D, HRT use, intake of fibre |
| Dietary glycaemic index | Reynolds 2019<sup>(182)</sup> | 10 | 941652 | 1121 | 6.9 - 15.7; 11.2 |
| | | | Age, sex, race/ethnicity, BMI, educational level, alcohol consumption, smoking status, BMI, use of NSAIDs, history of diabetes, colorectal screening, family history of any cancer, physical activity, energy intake, menopausal status, HRT use, multivitamin use, waist:hip ratio, calcium |
| Dietary glycaemic load | Reynolds 2019<sup>(182)</sup> | 12 | 1181780 | 1421 | 6.9 - 16.5; 11.4 |
| | | | Age, sex, race/ethnicity, educational level, alcohol consumption, smoking status, BMI, history of diabetes, family history of any cancer, history of colorectal polyp, physical activity, colorectal screening, menopausal status, hormone therapy (OC or HRT), parity, energy intake, use of NSAIDs, multivitamin use including folic acid, waist:hip ratio, calcium, red meat |
| Eating frequency (3 vs <3 daily meals) | Liu 2014<sup>(183)</sup> | 2 | 77641 | 550 | 5.8 - 10; 7.9 |
| | | | Age, sex, race/ethnicity, educational level, BMI, physical activity, smoking status, energy intake, calcium intake, vitamin D intake, alcohol intake, fruit intake, vegetable intake, red/processed meat intake, use of aspirin or other NSAIDs, family history of CRC, history of sigmoidoscopy/colonoscopy, total fat |
| Eating frequency (4 vs <3 daily meals) | Liu 2014<sup>(183)</sup> | 3 | 112609 | 1133 | 5.8 - 14; 9.9 |
| | | | Age, sex, race/ethnicity, educational level, BMI, physical activity, smoking status, energy intake, calcium intake, alcohol intake, fruit intake, vegetable intake, meat intake (red or processed meat), use of aspirin or other NSAIDs, family history of CRC, history of sigmoidoscopy or colonoscopy, total fat, use of supplements containing antioxidants, vitamin intake (dietary folate, vitamin D), dietary approaches to stop hypertension (DASH) score |
| Eating frequency (≥5 vs <3 daily meals) | Liu 2014<sup>(183)</sup> | 2 | 77641 | 550 | 5.8 - 10; 7.9 |
| | | | Age, sex, race/ethnicity, educational level, BMI, physical activity, smoking status, energy intake, calcium intake, vitamin D intake, alcohol intake, fruit intake, vegetable intake, meat intake (red or processed meat), use of aspirin or other NSAIDs, family history of CRC, history of sigmoidoscopy/colonoscopy, total fat |
| Food Type | Reference | N | Year | Study ID | Ages | Age-adjusted HR (95% CI) |
|--------------|--------------------|----|------|----------|------|--------------------------|
| Red meat | Schwingshackl 2018 | 21 | 2018 | 2154027 | 6 | 4.8 - 32; 11.3 |
| Processed | Schwingshackl 2018 | 15 | 2018 | 1910983 | 6 | 4.8 - 20; 10.2 |
| Beef | Carr 2016 | 4 | 2016 | 654521 | 6 | 4.8 - 13.4; 10.1 |
| Pork | Carr 2016 | 4 | 2016 | 654521 | 6 | 4.8 - 13.4; 10.1 |
| Poultry | Carr 2016 | 13 | 2016 | 1492358 | 6 | 4.8 - 32; 11.3 |
| Fish | Wu 2012 | 18 | 2012 | 1083264 | 6 | 4.8 - 24; 11.5 |
Age, sex, race/ethnicity, energy intake, educational level, BMI, waist circumference, family history of CRC, history of colorectal polyps, diabetes, smoking status, alcohol intake, physical activity, screening and examinations, multivitamin use (vitamin B6, folate, vitamin D), use of aspirin or other NSAIDs, use of hormone therapy (OC or HRT), menopausal status, fruits, vegetables, grain foods including cereal, fibre intake, dietary calcium, dietary fat intake, tea consumption, intake of dried and salted fish.
| Group | Study Year | Study ID | Study Size | Age Range | Variables |
|----------------------|------------|----------|------------|-----------|-----------------------------------------------------------------------------------------------------|
| Fruits and vegetables| Aune 2011 | 1522363 | 11543 | 4.3 - 16; 9.5 | Age, sex, race/ethnicity, family history of CRC, history of colorectal polyps, menopausal status, HRT use, energy intake, BMI, physical activity, smoking status, alcohol consumption, meat intake (red and processed meat), fish intake, dietary fibre from cereal sources, educational level, dietary calcium, aspirin use, multivitamin use (including folate, vitamin D), consumption of dairy products, sigmoidoscopy |
| Fruits | Schwingshackl 2018 | 1924385 | 19114 | 5 - 26; 11 | Age, sex, race/ethnicity, diabetes, BMI, smoking status, alcohol intake, educational level, physical activity, energy intake, family history of CRC, multivitamin use (including folate, vitamin D), use of aspirin or other NSAIDs, intake of grains and cereal, meat intake including red and processed meat, calcium, screening and examinations, history of polyps or adenoma, menopausal status, HRT use, vegetable intake, intake of dairy products, fish intake, year of follow-up |
| Vegetables | Schwingshackl 2018 | 1924385 | 19114 | 5 - 26; 11 | Age, sex, race/ethnicity, diabetes, BMI, smoking status, alcohol intake, educational level, physical activity, energy intake, family history of CRC, multivitamin use (including folate, vitamin D), use of aspirin or other NSAIDs, intake of grains and cereal, meat intake including red and processed meat, calcium, screening and examinations, history of polyps or adenoma, menopausal status, HRT use, vegetable intake, intake of dairy products, fish intake, year of follow-up |
| Cruciferous vegetables| Wu 2013 | 1117353 | 8021 | 4.3 - 20; 9 | Age, race/ethnicity, family history of CRC, history of colorectal polyp, smoking status, BMI, physical activity, use of aspirin or other NSAIDs, multivitamin use (including folate, vitamin D), menopausal status, HRT use, energy intake, alcohol consumption, red meat, calcium, educational level, CRC screening, intake of fruits, consumption of grains |
| Broccoli | Wu 2013 | 278338 | 2807 | 5 - 8.5; 6.9 | Age, race/ethnicity, family history of CRC, history of colorectal polyp, BMI, smoking status, physical activity, use of aspirin or other NSAIDs, multivitamin use (including folate, vitamin D), HRT use, energy intake, alcohol consumption, red meat, calcium, intake of fruits, grain intake, educational level |
| Allium vegetables | Zhu 2014 | 552180 | 5458 | 3.3 - 24; 14 | Age, sex, energy intake, occupation, income, history of colorectal polyps, diabetes, BMI, physical activity, alcohol intake, smoking status, use of aspirin or other NSAIDs, HRT use, intake of calcium, fruits, vegetables, meat intake (including red or processed meat), family history of CRC or intestinal cancers, educational level, history of chronic intestinal disease or cholecystectomy, screening and examinations, fibre intake, multivitamin use (including folate, vitamin C, vitamin D) |
| Garlic | Chiavarini 2016 | 330731 | 4141 | 5 - 24; 12.3 | Age, sex, BMI, smoking status, family history, endoscopy, use of aspirin or other NSAIDs, physical activity, HRT use, meat intake (red or processed meat), alcohol consumption, calcium, energy intake, consumption of fruits, vegetable intake, previous polyps, vitamin intake (including folate, vitamin D) |
| Food Group | Study Reference | N | Age, Sex Distribution | Smoking Status | BMI | Alcohol Intake | Family History | Physical Activity | Energy Intake | Other Relevant Factors |
|------------|-----------------|---|-----------------------|----------------|-----|---------------|---------------|-------------------|---------------|-----------------------|
| Onion | Turati 2014 | 2 | 4 - 10; 7 | | | | | | 1321 | Age, educational level, BMI, smoking status, alcohol intake, beta-carotene; history of cholecystectomy, chronic intestinal disease, colorectal polyps; family history of CRC, physical activity, energy intake, red meat, calcium, fibre, multivitamin use including vitamin C, aspirin use, sigmoidoscopy, HRT use |
| Legumes | Zhu 2015 | 13| 5 - 16; 8.9 | | | | | | 1782607 | Age, sex, BMI, energy intake, history of colorectal polyps, physical activity, family history of CRC, smoking status, alcohol consumption, use of aspirin or other NSAIDs, sigmoidoscopy, menopausal status, HRT use, multivitamin use (including folate, vitamin D), meat intake (red or processed meat, pork), educational level; intakes of fruits, grains, calcium, dairy products, vegetables, fish, fibre; coffee intake, income, diabetes |
| Nuts | Schwingshackl 2018 | 6 | 4.8 - 30; 13.1 | | | | | | 1152672 | Age, sex, BMI, alcohol intake, family history of CRC, physical activity, aspirin use, history of colorectal polyps, smoking status, energy intake, multivitamin use, fruit intake, intake of dietary fibre, HRT use, screening and examinations, history of ulcerative colitis, cholesterol and triglyceride |
| Soy products | Lu 2017 | 5 | 8 - 13; 10 | | | | | | 281425 | Age, sex, race/ethnicity, educational level, household income, physical activity, BMI, menopausal status, HRT use, family history of CRC, energy intake; intakes of fruits, vegetables, non-soy calcium, non-soy fibre; vitamin use (non-soy folic acid, vitamin D), dairy products, meat intake including red meat, fish intake, smoking status, alcohol consumption, diabetes, coffee intake |
| Whole grains | Schwingshackl 2018 | 9 | 5 - 26; 14.1 | | | | | | 970927 | Age, sex, BMI, smoking status, educational level, alcohol consumption, fibres from foods other than whole-grain bread, calcium, energy intake, HRT use, family history of CRC, physical activity, aspirin use, colonoscopy, history of polyps, multivitamin use including folate; intakes of saturated fats, fruits, vegetables; meat intake (red or processed meat) |
| Refined grains | Schwingshackl 2018 | 2 | 14 - 14.8; 14.4 | | | | | | 72431 | Age, race/ethnicity, BMI, physical activity, smoking status, educational level, energy intake; intakes of saturated fat, calcium, red meat, fruits, vegetables; family history of CRC, endoscopy, aspirin use |
| Eggs | Schwingshackl 2018 | 3 | 7.4 - 32; 18.8 | | | | | | 94181 | Age, sex, BMI, educational level, occupation, smoking status, geographic region, energy intake; intakes of vegetables, fruits, cereals; tea consumption, use of NSAIDs, fibre intake, alcohol consumption |
| Dairy products | Schwingshackl 2018 | 17 | 3.3 - 26; 11.7 | | | | | | 1629366 | Age, sex, race/ethnicity, occupation, geographical area, diabetes at baseline, smoking status, BMI, alcohol intake, educational level, physical activity, family history of CRC, energy intake, use of aspirin or other NSAIDs, colonoscopy, history of polyps, multivitamin use (including vitamin B6, folate, vitamin D), history of gallbladder surgery, intake of fat, dietary fibre, meat intake (red or processed meat), intake of fruits, vegetable intake, tea consumption, menopausal status, use of hormone therapy (OC or HRT) |
| Cheese | Aune 2012 | 7 | 3.3 - 19.6; 11.2 | | | | | | 234759 | Age, sex, BMI, occupation, smoking status, geographical area, energy intake, family history of CRC, fat intake, dietary fibre, gallbladder surgery, alcohol intake, physical activity, educational level, red meat, history of colon polyps, multivitamin use (including vitamin B6, folate), HRT use, menopausal status, diabetes, aspirin use, intake of fruits, vegetable intake |
| Beverage | Study Year | Study ID | n | Mean Age | Characteristics |
|------------------------|------------|----------|------|----------|---------------------------------------------------------------------------------|
| Yogurt | Zhang 2019 | 698366 | 5 | 3.3 - 12; 7.7 | Age, sex, family history of CRC or other cancers, previous polyp, screening, smoking status, alcohol intake, aspirin use, physical activity, BMI, meat intake (including red or processed meat), fat intake, dietary fibre, gallbladder surgery, energy intake, educational level, menopausal status, hormone therapy (OC or HRT), dietary calcium, simple sugars, history of diabetes, vegetables, fruits, nuts and legumes, cereals, fish |
| Beverages | | | | | |
| Tea | Chen 2017 | 1208316 | 15 | 1 - 15; 8.6 | Age, sex, race/ethnicity, family history of CRC, BMI, intake of fibre, coffee intake, alcohol intake, diabetes, educational level, smoking status, physical activity, intake of fruits, vegetable intake, calcium, energy intake, meat intake (including red meat and pork), radiation exposure, use of aspirin or other NSAIDs, fat intake, vitamin supplement intake, menopausal status, HRT use, household income, history of colorectal polyps and chronic ulcerative colitis, occupation, colorectal screening |
| Green tea | Wang 2012 | 352275 | 5 | 6 - 15; 9.2 | Age, sex, family history of CRC, smoking status, alcohol intake, BMI, meat consumption including red meat, intake of black tea, intake of fruits, vegetable intake, coffee consumption, radiation exposure, menopausal status, use of NSAIDs, vitamin supplement use, history of colorectal polyps and chronic ulcerative colitis, energy intake |
| Black tea | Sun 2006 | 274975 | 6 | 8 - 20; 13 | Age, sex, race/ethnicity, educational level, family history of CRC, history of sigmoidoscopy or colonoscopy, BMI, smoking status, physical activity, aspirin use, vitamin supplement intake, alcohol consumption, red meat consumption, total energy intake, menopausal status, HRT use; intakes of fat, fibre, calcium; fruit intake, vegetable intake, waist/hip circumference ratio |
| Coffee | Gan 2017 | 2046575 | 19 | 4.5 - 18; 10.1 | Age, sex, race/ethnicity, BMI, smoking status, alcohol intake, educational level, serum cholesterol, physical activity, calcium intake, tea consumption, energy intake, family history of CRC, use of aspirin or other NSAIDs, colorectal screening, vitamin intake (including vitamin B6, folic acid, vitamin C, vitamin D), fat intake, fibre intake, menopausal status, HRT use, diabetes, fruits, vegetables, meat intake including red or processed meat and pork, number of pregnancies and deliveries, age at menarche, age at first delivery, intake of dairy products |
| Non-fermented milk | Ralston 2014 | 892569 | 14 | 5 - 24; 11.3 | Age, sex, race/ethnicity, occupation, smoking status, geographical area, BMI, total energy intake, family history of CRC, previous intestinal polyp, screening, use of aspirin or other NSAIDs, physical activity, saturated fat, dietary fibre intake, alcohol intake, red meat consumption, educational level, history of diabetes, fruits, vegetables, multivitamin use |
| Food | Source | N | Median Age or Range | OES or N | Variables |
|----------------------|----------------------|------|---------------------|-----------|---------------------------------------------------------------------------|
| Fermented milk | Ralston 2014 | 7 | 328750 | 1876 | Age, sex, occupation, smoking status, geographical area, BMI, total energy intake, family history of CRC, previous intestinal polyp, screening, aspirin use, physical activity, saturated fat, dietary fibre intake, alcohol intake, red meat consumption, educational level, history of diabetes, fruits, vegetables, multivitamin use (including folic acid, vitamin C, vitamin D), menopausal status, HRT use |
| Alcohol (Moderate) | Fedirko 2011 | 22 | 2798092 | 1912 | Age, sex, race/ethnicity, smoking status, BMI, coffee intake, educational level, cholesterol, history of gall bladder surgery, energy intake; intakes of fats, protein, dietary fibre; family history of CRC, physical activity, history of polyps, multivitamin use (including folate and vitamin D), meat intake (including poultry/non-poultry meat, processed meat), seafood intake, calcium, occupation, intake of vegetables, fruit intake, diabetes, menopausal status, use of hormone therapy (OC or HRT), socioeconomic status, aspirin use, screening and examinations |
| Alcohol (Heavy) | Fedirko 2011 | 7 | 738539 | 5078 | Age, sex, family history of CRC, BMI, smoking status, physical activity, educational level, sedentary work, consumption of vegetables, meat consumption (including red or processed meat), fruit intake, energy intake, aspirin use, screening and examinations, intake of calcium, multivitamins (including folate, vitamin D) |
| Beer | Zhang 2015 | 7 | 805177 | 5149 | Age, sex, race/ethnicity, family history of CRC, smoking status, coffee intake, total serum cholesterol, educational level, BMI, non-contraceptive oestrogen use, physical activity, history of colorectal polyps, energy intake, intake of fats, dietary fibre, calcium, other types of alcohol |
| Wine | Xu 2019 | 9 | 973286 | 7511 | Age, sex, race/ethnicity, smoking status, coffee intake, total serum cholesterol, educational level, BMI, non-contraceptive oestrogen use, history of colorectal polyps, physical activity, intake of other types of alcohol, meat consumption including poultry, seafood consumption, multivitamin use, energy intake, family history of CRC, intake of fat, dietary fibre, calcium, fruit intake, vegetable intake, diabetes |
| Wine (Light to moderate) | Xu 2019 | 4 | 676331 | 4559 | Age, sex, race/ethnicity, smoking status, BMI, intake of other types of alcohol, physical activity, educational level, energy intake, family history of CRC, intake of fat, dietary fibre, calcium, fruit intake, vegetable intake, meat intake, multivitamin use, diabetes |
| Wine (Heavy) | Xu 2019<sup>(203)</sup> | 5 | 686749 | 4670 | 5.3 - 14.7; 9.9 | Age, sex, race/ethnicity, smoking status, BMI, intake of other types of alcohol, educational level, meat consumption including poultry, seafood consumption, multivitamin use, history of colonic polyps, physical activity, energy intake, family history of CRC, intake of fat, dietary fibre, calcium, fruit intake, vegetable intake, diabetes |
| --- | --- | --- | --- | --- | --- | --- |
| **Macronutrients** | | | | | | |
| Total dietary fat | Liu 2011<sup>(204)</sup> | 13 | 459910 | 3635 | 3 - 32; 11.5 | Age, sex, BMI, energy intake, parity, fibre intake, smoking status, educational level, alcohol intake, physical activity, calcium intake, geographical area, occupation; consumption of fruits, vegetables, cereals; family history of CRC, history of colorectal polyps, hormone therapy, diabetes, vitamin use (including vitamin A, vitamin E) |
| Saturated fatty acids | Liu 2011<sup>(204)</sup> | 12 | 451956 | 3182 | 3 - 32; 9.9 | Age, sex, total energy intake, parity, fibre intake, BMI, smoking status, education, alcohol consumption, physical activity, calcium intake, geographical area, occupation; intakes of fruits, vegetables, cereals; family history of CRC, history of colorectal polyps, hormone therapy, diabetes, vitamin use (vitamin A, vitamin E) |
| Monounsaturated fatty acids | Liu 2011<sup>(204)</sup> | 11 | 399687 | 3048 | 3 - 32; 11.9 | Age, sex, total energy intake, parity, fibre intake, BMI, smoking status, education, alcohol consumption, physical activity, calcium intake, geographical area, occupation; intakes of fruits, vegetables, cereals; family history of CRC, history of colorectal polyps, hormone therapy, diabetes, vitamin use (vitamin A, vitamin E) |
| Polyunsaturated fatty acids | Kim 2018<sup>(205)</sup> | 14 | 933712 | 1003 | 3.3 - 32; 13 | Age, sex, race/ethnicity, dietary fibre intake, Dutch Healthy Diet index, energy intake, BMI, educational level, family history of CRC, screening and examinations, use of aspirin or other NSAIDs, intake of alcohol, smoking status, physical activity, hormone therapy, calcium, multivitamin use (including folate, vitamin D), fruit intake, vegetable intake, meat intake (red or processed meat), history of polyps, cereal intake, cardiovascular disease, memory loss, use of cholesterol-lowering drugs, omega-6 (linoleic + arachidonic) intake, menopausal status, past history of or medication use for diabetes, intake of low-fat dairy products, geographical area, occupation |
| Total n-3 polyunsaturated fatty acids | Chen 2015<sup>(206)</sup> | 8 | 579427 | 6807 | 4.8 - 22; 10.8 | Age, sex, parity, total energy intake, BMI, smoking status, alcohol intake, educational level, physical activity, calcium intake, meat intake (red or processed meat), dietary fibre, intake of fat (saturated fat, monounsaturated fat, n-6 PUFA), diabetes, family history of CRC, menopausal status, use of hormone therapy, multivitamin use (including vitamin A, folate, vitamin C, vitamin D, vitamin E), use of aspirin or other NSAIDs, screening and examinations, low-fat dairy products, fruits, vegetables |
© 2021 Veettil SK et al. JAMA Network Open.
| Dietary Factor | Study Reference | N | Median Age (Range) | Covariates | Notes |
|----------------------------------------|-----------------------|----|--------------------|----------------------------------------------------------------------------|----------------------------------------------------------------------|
| Marine n-3 polyunsaturated fatty acids | Chen 2015[206] | 10 | 666713 | Age, sex, race/ethnicity, BMI, educational level, alcohol intake, energy intake, dietary fibre, calcium, fat intake (saturated fat, monounsaturated fat, n-6 PUFA), family history of CRC, history of colorectal polyps, physical activity, smoking status, hormone therapy, multivitamin use (including folate, vitamin C, vitamin D), diabetes, use of aspirin or other NSAIDs, menopausal status, low-fat dairy products, fruits, vegetables, cardiovascular disease, memory loss, use of cholesterol-lowering drugs, screening and examinations, meat intake (red or processed meat) | |
| Cholesterol | Liu 2011[204] | 7 | 261260 | Age, sex, total energy intake, parity, educational level, BMI, smoking status, alcohol consumption, physical activity, calcium intake, family history of CRC, history of colorectal polyps, hormone therapy, occupation, geographical area; consumption of vegetables, fruits, cereals; vitamin intake (vitamin A, vitamin E) | |
| Carbohydrate | Aune 2012[207] | 11 | 806647 | Age, race/ethnicity, educational level, income, BMI, physical activity, family history of CRC, hormone therapy (OC or HRT), total energy intake, colorectal polyps, smoking status, use of aspirin or other NSAIDs, multivitamin use (including folate, vitamin D), alcohol intake, meat intake (red or processed meat), calcium, dietary fibre, diabetes, colorectal screening, magnesium, total fat, parity | |
| Sucrose | Aune 2012[207] | 5 | 831687 | Age, race/ethnicity, BMI, family history of CRC or other cancers, smoking status, educational level, physical activity, total energy intake, alcohol intake, colorectal polyps, use of aspirin or other NSAIDs, multivitamin use (including folate, vitamin D), hormone therapy (OC or HRT), meat intake (red or processed meat), calcium, dietary fibre, diabetes, prior endoscopy screening, total fat | |
| Fructose | Aune 2012[207] | 4 | 640683 | Age, race/ethnicity, BMI, family history of CRC or other cancers, smoking status, educational level, physical activity, total energy intake, alcohol intake, colorectal polyps, use of aspirin or other NSAIDs, multivitamin use (including folate, vitamin D), diabetes, prior endoscopy screening, use of aspirin or other NSAIDs, calcium, meat intake (red or processed meat), hormone therapy (OC or HRT), total fibre, total fat | |
| Dietary protein | Lai 2017[208] | 3 | 207068 | Age, sex, energy intake, dietary fibre intake, supplement intake, smoking status, BMI, alcohol intake, educational level, physical activity, calcium intake (except for milk protein and milk products) | |
| Total dietary fibre | Reynolds 2019 | 21 | 2259486 | Age, sex, race/ethnicity, physical activity, smoking status, meat intake (red and processed meat), total energy intake, calcium, BMI, educational level, alcohol intake, family history, colorectal polyp, use of multivitamin (including folate, vitamin C, vitamin D), aspirin or other anti-inflammatory use, hormone therapy (OC or HRT), menopause, colonoscopy, dietary assessment, fat | |
| Cereal fibre | Aune 2011[209] | 7 | 1471756 | Age, sex, race/ethnicity, family history of CRC, history of colorectal polyps, smoking status, BMI, physical activity, use of aspirin or other NSAIDs, multivitamin use (including folate, vitamin D), meat intake (red and processed meat), menopausal status, HRT use, alcohol intake, calcium intake, energy intake, educational level, sigmoidoscopy or colonoscopy, glycaemic load, consumption of dairy products | |
© 2021 Veetil SK et al. JAMA Network Open.
| Nutrient Type | Source | Study Year | Participants | Follow-Up | Age and Other Covariates |
|---------------|--------|------------|--------------|-----------|--------------------------|
| Fruit fibre | Aune 2011 | 2011 | 8 | 1514871 | 9930; 4.5 - 16; 9.3 |
| | | | | | Age, sex, race/ethnicity, family history of CRC, history of colorectal polyps, smoking status, BMI, physical activity, use of aspirin or other NSAIDs, multivitamin use (including folate, vitamin D), alcohol intake, menopausal status, HRT use, meat intake (red or processed meat, pork), calcium intake, energy intake, education, sigmoidoscopy or colonoscopy, glycaemic load, consumption of dairy products |
| Vegetable fibre | Aune 2011 | 2011 | 8 | 1514871 | 9930; 4.5 - 16; 9.3 |
| | | | | | Age, sex, race/ethnicity, family history of CRC, history of colorectal polyps, smoking status, BMI, physical activity, use of aspirin or other NSAIDs, multivitamin use (including folate, vitamin D), alcohol intake, menopausal status, HRT use, meat intake (red or processed meat, pork), calcium intake, energy intake, education, sigmoidoscopy or colonoscopy, glycaemic load, consumption of dairy products |
| Legume fibre | Reynolds 2019 | 2019 | 4 | 1104339 | 5651; 5 - 12.1; 8.3 |
| | | | | | Age, sex, physical activity, smoking status, menopause, HRT use, meat intake (red or processed meat), folate, calcium, energy intake, alcohol intake, educational level, BMI, family history, history of colon polyps, aspirin use |
| Soluble fibre | Reynolds 2019 | 2019 | 3 | 204243 | 2580; 7.6 - 11.7; 9.1 |
| | | | | | Age, sex, energy intake, BMI, educational level, family history, colonoscopy, anti-inflammatory use, consumption of alcohol, smoking status, physical activity, HRT use, calcium, red meat, vitamin intake (folate, vitamin D) |
| Insoluble fibre | Reynolds 2019 | 2019 | 3 | 204243 | 2580; 7.6 - 11.7; 9.1 |
| | | | | | Age, sex, energy intake, BMI, educational level, family history, colonoscopy, anti-inflammatory use, consumption of alcohol, smoking status, physical activity, HRT use, calcium, red meat, vitamin intake (folate, vitamin D) |
### Micronutrients
| Micronutrient Type | Source | Study Year | Participants | Follow-Up | Age and Other Covariates |
|--------------------|--------|------------|--------------|-----------|--------------------------|
| Flavonoids | Bo 2016 | 2016 | 6 | 188135 | 6609; 6.1 - 28; 14.2 |
| | | | | | Age, race/ethnicity, BMI, occupation, geographic area, family history of CRC, history of colorectal polyps, prior sigmoidoscopy screening, physical activity, smoking status, alcohol consumption, intake of meat, intake of fruits, vegetables, intake of fibre, total fat, total energy, calcium, vitamin use (folate, vitamin C, vitamin E), aspirin use, HRT use |
| Flavonols | Chang 2018 | 2018 | 5 | 729461 | 9720; 11 - 28; 18.9 |
| | | | | | Age, sex, geographic area, occupation, smoking, physical activity, education, BMI, history of CRC, history of endoscopy, alcohol consumption, total energy intake, total fat, intake of meat, fibre, calcium intake, menopausal status, hormone therapy (OC or HRT), regular aspirin use, vitamin intake (vitamin C, vitamin D, vitamin E) |
| Quercetin | Grosso 2017 | 2017 | 2 | 117266 | 463; 10 - 28; 19 |
| | | | | | Age, sex, geographic area, occupation, smoking status, BMI, family history of CRC, history of colorectal polyps, prior sigmoidoscopy screening, physical activity, alcohol consumption, meat intake, total energy intake, total calcium intake, total fibre intake, aspirin use, vitamin intake, HRT use |
| Kaempferol | Grosso 2017 | 2017 | 2 | 117266 | 472; 10 - 28; 19 |
| | | | | | Age, sex, geographic area, occupation, smoking status, BMI, family history of CRC, history of colorectal polyps, prior sigmoidoscopy screening, physical activity, alcohol consumption, meat intake, total energy intake, total calcium intake, total fibre intake, aspirin use, vitamin intake, HRT use |
| Phytochemicals | Authors | Year | n | OCP | Age Group | Variables Studied |
|----------------|---------|------|----|-----|-----------|-------------------|
| Myricetin | Grosso 2017 | 2 | 117266 | 466 | 10 - 28; 19 | Age, sex, geographic area, occupation, smoking status, BMI, family history of CRC, history of colorectal polyps, prior sigmoidoscopy screening, physical activity, alcohol consumption, meat intake, total energy intake, total calcium intake, total fibre intake, aspirin use, vitamin intake, HRT use |
| Flavones | Chang 2018 | 3 | 598744 | 7091 | 11 - 26; 17.7 | Age, sex, history of CRC, history of endoscopy, smoking status, physical activity, education, BMI, alcohol consumption, total energy, total fat, intake of meat, fibre intake, calcium intake, menopausal status, hormone therapy (OC or HRT), regular aspirin use, vitamin intake (vitamin C, vitamin D, vitamin E) |
| Flavanones | Chang 2018 | 4 | 608609 | 7181 | 11 - 28; 20.3 | Age, sex, geographic area, occupation, history of CRC, history of endoscopy, smoking, physical activity, education, BMI, alcohol consumption, total energy, total fat, intake of meat, fibre intake, calcium intake, menopausal status, hormone therapy (OC or HRT), regular aspirin use, vitamin intake (vitamin C, vitamin D, vitamin E) |
| Flavan-3-ols | Chang 2018 | 4 | 719596 | 9576 | 11 - 26; 16.6 | Age, sex, family history of CRC, history of CRC, history of endoscopy, smoking, physical activity, education, BMI, alcohol consumption, total energy, total fat, intake of meat, fibre intake, calcium intake, menopausal status, hormone therapy (OC or HRT), regular aspirin use, vitamin intake (vitamin C, vitamin D, vitamin E) |
| Catechin | Grosso 2017 | 2 | 155503 | 3249 | 13 - 13.3; 13.2 | Age, occupation, BMI, family history of CRC, waist-to-hip ratio, physical activity, smoking, alcohol intake, total fruit intake, vegetable consumption, meat intake, total energy intake |
| Flavanols | He 2016 | 3 | 242284 | 5059 | 13.3 - 26; 18.5 | Age, BMI, family history of CRC, history of endoscopy, alcohol consumption, physical activity, smoking, fibre intake, meat intake, total energy intake, use of NSAIDs, dietary supplement (calcium, n-3 polyunsaturated fatty acids, manganum, riboflavin, vitamin C, vitamin E, folate) |
| Anthocyanins | He 2016 | 2 | 121432 | 2574 | 16.2 - 26; 21.1 | Age, BMI, family history of CRC, history of endoscopy, alcohol consumption, physical activity, smoking, fibre intake, meat intake, total energy intake, use of NSAIDs, dietary supplement (calcium, n-3 polyunsaturated fatty acids, manganum, riboflavin, folate, vitamin C, vitamin E) |
| Anthocyanidins | Chang 2018 | 3 | 598744 | 7091 | 11 - 26; 17.7 | Age, sex, history of CRC, history of endoscopy, smoking, physical activity, education, BMI, alcohol consumption, total energy, total fat, intake of meat, fibre intake, calcium intake, menopausal status, hormone therapy (OC or HRT), regular aspirin use, vitamin intake (vitamin C, vitamin D, vitamin E) |
| Phyto-oestrogens| Jiang 2017 | 5 | 275443 | 2485 | 6.4 - 19; 10.2 | Age, sex, household income, dialect group, diabetes at baseline, smoking, BMI, alcohol intake, education, physical activity, family history of CRC, daily energy intake, menopausal status, average intakes of fruits, vegetables, meat intake, fibre intake, non-soya calcium, fats, vitamin intake (non-soya folic acid, vitamin D), use of NSAIDs, hormone therapy |
| Isoflavones | Grosso 2017 | 5 | 292616 | 2587 | 6.4 - 19; 10.2 | Age, education, alcohol intake, smoking status, BMI, physical activity, household income, family history of CRC, history of diabetes mellitus, total energy intake, intakes of fruits, vegetables, meat, non-soya calcium, fibre, coffee intake, fats, dairy products, individual phytoestrogens, menopausal status, HRT use, vitamin intake (folic acid, vitamin D) |
| Component | Study | N | Year | Code | Age, sex, race/ethnicity, education level, family history of CRC, BMI, physical activity, smoking status, alcohol consumption, energy intake, dietary factor, use of NSAIDs, menopausal status |
|----------------------------|------------------------|----|--------|--------|----------------------------------------------------------------------------------------------------------------------------------|
| Combined carotenoids | Panic 2017(215) | 2 | 2017 | 196383 | 2673 8.2 - 11; 9.6 Age, education level, smoking status, BMI, physical activity, family history of CRC, history of intestinal polyps, alcohol intake, total energy intake, total fat intake, meat intake, dietary fibre intake, total calcium intake, hormone therapy (HRT), use of NSAIDs, vitamin intake (folate, vitamin D) |
| Alpha-carotene | Panic 2017(215) | 3 | 2017 | 223334 | 2857 8 - 11; 9.1 Age, education level, smoking status, BMI, physical activity, family history of CRC, history of intestinal polyps, serum cholesterol, alcohol consumption, total energy intake, total fat intake, meat intake, dietary fibre intake, total calcium intake, HRT use, use of NSAIDs, vitamin intake (folate, vitamin D) |
| Beta-carotene | Panic 2017(215) | 4 | 2017 | 279666 | 3605 8 - 11; 9.5 Age, education level, smoking status, BMI, physical activity, family history of CRC, history of intestinal polyps, serum cholesterol, alcohol intake, total energy intake, meat intake, dietary fibre intake, total calcium intake, hormone therapy (HRT), use of NSAIDs, vitamin intake (folate, vitamin D) |
| Lycopene | Panic 2017(215) | 3 | 2017 | 223334 | 2857 8 - 11; 9.1 Age, education level, smoking status, BMI, physical activity, family history of CRC, history of intestinal polyps, serum cholesterol, alcohol consumption, total energy intake, total fat intake, meat intake, dietary fibre intake, total calcium intake, hormone therapy (HRT), use of NSAIDs, vitamin intake (folate, vitamin D) |
| Beta-cryptoxanthin | Panic 2017(215) | 2 | 2017 | 196383 | 2673 8.2 - 11; 9.6 Age, education level, smoking status, BMI, physical activity, family history of CRC, history of intestinal polyps, alcohol intake, total energy intake, total fat intake, meat intake, dietary fibre intake, total calcium intake, hormone therapy (HRT), use of NSAIDs, vitamin intake (folate, vitamin D) |
| Lutein and zeaxanthin | Panic 2017(215) | 3 | 2017 | 223334 | 2857 8 - 11; 9.1 Age, education level, smoking status, BMI, physical activity, family history of CRC, history of intestinal polyps, serum cholesterol, alcohol consumption, total energy intake, total fat intake, meat intake, dietary fibre intake, total calcium intake, hormone therapy (HRT), use of NSAIDs, vitamin intake (folate, vitamin D) |
| Multivitamin | Heine-Bröring 2015(216) | 7 | 2015 | 670513 | 8737 5 - 24; 12.7 Age, sex, race/ethnicity, education, family history of CRC, BMI, physical activity, smoking status, alcohol consumption, energy intake, dietary factor, use of NSAIDs, menopausal status |
| Multivitamin | Liu 2015(217) | 5 | 2015 | 522507 | 3584 5 - 16; 9 Age, race/ethnicity, BMI, education level, alcohol consumption, smoking status, physical activity, family history of CRC, meat intake, total energy intake, fruit intake, vegetable intake, intake of saturated fat, dietary fibre, vitamin intake (vitamin B6, folate, vitamin C, vitamin E), calcium, menopausal status, hormone therapy, aspirin use |
| Vitamin A | Heine-Bröring 2015(216) | 2 | 2015 | 46796 | 443 8 - 10; 9 Age, smoking status, energy intake |
| Vitamin A | Liu 2015(217) | 6 | 2015 | 208536 | 1206 4.5 - 10; 7 Age, smoking status, education level, physical activity, alcohol consumption, family history of CRC, menopausal status, total energy intake, intake of meat, hormone therapy (HRT) |
| Vitamin B2 | Liu 2015(217) | 5 | 2015 | 392184 | 4939 5.74 - 13.3; 10 Age, educational level, BMI, household income, smoking status, alcohol intake, physical activity, family history of CRC, diabetes history, energy intake, vegetables, fruits, meat, calcium, fibre, iron, fats, menopausal status, hormone therapy (HRT), use of NSAIDs |
| Vitamin | Reference | Sample Size | Study Population |
|---------------|--------------------------------|-------------|-----------------------------------------------------------------------------------|
| Vitamin B3 | Liu 2015<sup>(217)</sup> | 2 | Age, educational level, BMI, household income, smoking status, alcohol intake, physical activity, family history of CRC, diabetes history, energy intake, vegetables, fruits, meat, calcium, fibre, iron, fats, menopausal status, hormone therapy (HRT), use of NSAIDs |
| Vitamin B6 | Liu 2015<sup>(217)</sup> | 11 | Age, sex, BMI, education, household income, smoking status, alcohol consumption, physical activity, family history of CRC, diabetes history, total intake of energy, intake of vegetables, fruits, meat, fats, iron, calcium, use of aspirin or other NSAIDs, vitamin use (vitamin B, vitamin E), hormone therapy (HRT), menopausal status |
| Folic acid | Liu 2015<sup>(217)</sup> | 19 | Age, sex, BMI, education, household income, smoking status, alcohol consumption, physical activity, family history of CRC, diabetes history, past medical history of colonoscopy, total intake of energy, intake of vegetables, fibre, fruits, meat, fats, iron, calcium, use of aspirin or other NSAIDs, vitamin use (vitamin B, vitamin C, vitamin E), hormone therapy (HRT), menopausal status |
| Vitamin B12 | Liu 2015<sup>(217)</sup> | 5 | Age, BMI, race/ethnicity, past medical history of colonoscopy, smoking status, physical activity, alcohol consumption, diabetes history, energy intake, intake of vegetables, fruits, meat, calcium, use of NSAIDs, vitamin use, hormone therapy (HRT), menopausal status |
| Vitamin C | Heine-Bröring 2015<sup>(216)</sup> | 3 | Age, BMI, educational level, physical activity, smoking status, alcohol consumption, energy intake, dietary factors, menopausal status |
| Vitamin C | Liu 2015<sup>(217)</sup> | 9 | Age, BMI, occupation, education level, smoking level, alcohol consumption, physical activity, family history of CRC, energy intake, intake of fibre, vegetables, multivitamin intake, menopausal status, serum cholesterol concentration, hormone therapy (HRT), use of aspirin |
| Vitamin D | Heine-Bröring 2015<sup>(216)</sup> | 5 | Age, race/ethnicity, sex, family history of CRC, BMI, physical activity, smoking status, alcohol intake, energy intake, dietary factors, menopausal status, use of NSAIDs |
| Vitamin D | Liu 2015<sup>(217)</sup> | 14 | Age, sex, geographical area, occupation, race/ethnicity, BMI, physical activity, smoking status, educational level, total energy intake, fruits, meat, vegetables, alcohol intake, fat intake, dietary fibre intake, calcium intake, CRC screening, menopausal status, family history of CRC, history of intestinal polyps, use of aspirin or other NSAIDs, hormone therapy (HRT), vitamin use |
| Vitamin E | Heine-Bröring 2015<sup>(216)</sup> | 4 | Age, BMI, family history of CRC, physical activity, smoking status, educational level, energy intake, alcohol consumption, dietary factors, menopausal status, use of NSAIDs |
| Vitamin E | Liu 2015<sup>(217)</sup> | 10 | Age, sex, BMI, educational level, alcohol intake, smoking status, physical activity, family history of CRC, history of colorectal polyps, serum cholesterol, energy intake, intake of meat, vegetable consumption, intake of fibre, vitamin intake, hormone therapy (HRT), menopausal status, aspirin use |
| Dietary calcium | Meng 2019<sup>(218)</sup> | 8 | 1449526 | 13640 | 7 - 16.4; 10 | Age, sex, race/ethnicity, BMI, waist:hip ratio, education, smoking status, tea intake, alcohol consumption, physical activity, family history of CRC or other cancers, history of intestinal polyps, CRC screening, diabetes, total energy intake, fat intake, intake of meat, intake of fruits, vegetables, whole grains, fibre, intake of phosphorus, retinol, sodium, potassium, zinc, use of calcium supplement, multivitamin use, use of ginseng, menopausal status, hormone therapy (OC or HRT), statin use, use of aspirin or other NSAIDs |
| Supplemental calcium | Heine-Bröring 2015<sup>(216)</sup> | 7 | 1064458 | 9862 | 3.3 - 16; 8.4 | Age, race/ethnicity, BMI, physical activity, educational level, family history of CRC, smoking status, alcohol consumption, energy intake, dietary factors, menopausal status, use of NSAIDs |
| Supplemental calcium | Heine-Bröring 2015<sup>(216)</sup> | 6 | 929116 | 8837 | 5 - 10; 8 | Age, race/ethnicity, BMI, physical activity, educational level, family history of CRC, smoking status, alcohol consumption, energy intake, dietary factors, menopausal status, use of NSAIDs |
| Heme iron | Qiao 2013<sup>(219)</sup> | 6 | 646901 | 8022 | 7.2 - 22; 15.7 | Age, sex, BMI, education level, physical activity, smoking status, alcohol consumption, family history of CRC, history of endoscopy, diabetes, intake of total energy, fat, calcium, fibre, zinc, magnesium, hormone therapy (HRT), regular aspirin use, menopausal status, vitamin intake |
| Magnesium | Chen 2012<sup>(220)</sup> | 7 | 336463 | 7435 | 7.9 - 28; 15.9 | Age, sex, BMI, geographic region, alcohol intake, physical activity, education, smoking status, diabetes, history of CRC, screening for CRC, magnesium, calcium, fibre intake, fat intake, total energy intake, vitamin intake (vitamin B6, folate, vitamin B12, vitamin D, vitamin E), HRT use, use of aspirin or other NSAIDs |
| Zinc | Li 2014<sup>(221)</sup> | 5 | 350507 | 5676 | 9.5 - 22; 15.7 | Age, BMI, geographic region, alcohol intake, physical activity, education, smoking status, diabetes, history of CRC, screening for CRC, magnesium, calcium, fibre intake, fat intake, total energy intake, vitamin intake (vitamin B6, folate, vitamin B12, vitamin D, vitamin E), HRT use, use of aspirin or other NSAIDs |
| Methionine | Zhou 2013<sup>(222)</sup> | 7 | 431029 | 6331 | 5.8 - 22; 13.3 | Age, income, waist:hip ratio, BMI, physical activity, smoking status, education, alcohol consumption, family history of CRC, history of CRC, history of colorectal polyps, screening, diabetes, energy intake, calcium, meat, fat intake, fibre intake, iron, vegetables, fruits, vitamin intake (vitamin B6, folate, vitamin D, vitamin E), menopausal status, hormone therapy (OC or HRT), use of aspirin or other NSAIDs |
| Garlic supplement | Chiavarini 2016<sup>(110)</sup> | 4 | 304677 | 2703 | 3.3 - 24; 9.8 | Age, sex, BMI, smoking status, educational level, family history, history of chronic intestinal disease or cholecystectomy, screening, physical activity, fruits, vegetables, total energy intake, alcohol intake, calcium, meat, hormone therapy (HRT), vitamin intake (folate, vitamin C, vitamin D), use of aspirin or other NSAIDs |
**Abbreviations:** BMI, body mass index; CRC, colorectal cancer; HRT, hormone replacement therapy; NSAIDs, non-steroidal anti-inflammatory drugs; OC, oral contraceptive; PUFA, polyunsaturated fatty acid
| Exposure | Author; year | Comparison | Summargy metric | Credibility assessment | AMSTAR-2 |
|----------------------------------------------|--------------|------------|-----------------|------------------------|----------|
| | | | | | 2 |
| Dietary glycaemic index | Reynolds 2019 | High vs low | RR 1.10 (0.99-1.22) | p-value 0.08955 | I² 56.0% | Largest study (95% CI) 1.06-1.27 | Predictive interval (95% CI) 0.81-1.47 | Egger's p-value 0.868 | Excess significance test O/E 3/NA | Quality of evidence p-value NA | NS | High |
| Dietary glycaemic load | Reynolds 2019 | High vs low | RR 0.93 (0.85-1.01) | p-value 0.080955 | I² 32.0% | Largest study (95% CI) 0.70-0.95 | Predictive interval (95% CI) 0.76-1.14 | Egger's p-value 0.139 | Excess significance test O/E 2/NA | Quality of evidence p-value NA | NS | High |
| Eating frequency (3 vs <3 daily meals) | Liu 2014 | High vs low | RR 0.85 (0.66-1.31) | p-value 0.47531 | I² 63.4% | Largest study (95% CI) 0.78-1.36 | Predictive interval (95% CI) NA | Egger's p-value NA | Excess significance test O/E 0/NA | Quality of evidence p-value NA | NS | Moderate |
| Eating frequency (4 vs <3 daily meals) | Liu 2014 | High vs low | RR 0.88 (0.65-1.19) | p-value 0.40383 | I² 65.7% | Largest study (95% CI) 0.91-1.32 | Predictive interval (95% CI) 0.03-24.69 | Egger's p-value 0.069 | Excess significance test O/E 0/NA | Quality of evidence p-value NA | NS | Moderate |
| Eating frequency | Liu 2014 (183) | High vs low | RR | 0.75 (0.54-1.05) | 0.09413 | 0.0% | 0.51-1.14 | NA | NA | 0/NA | NA | NS | Moderate |
|-----------------------------------------------|----------------|-------------|-----|-----------------|---------|------|-----------|-----|-----|-------|-----|-------|----------|
| Vegetarian diet | Godos 2016 (181) | Yes vs no | RR | 0.88 (0.74-1.05) | 0.14873 | 21.3% | 0.64-0.98 | 0.21-3.67 | 0.919 | 1/NA | NA | NS | Low |
| Food groups or foods | | | | | | | | | | | | | |
|-----------------------------------------------|----------------|-------------|-----|-----------------|---------|------|-----------|-----|-----|-------|-----|-------|----------|
| Nuts | Schwingshackl 2018 (184) | High vs low | RR | 0.96 (0.90-1.02) | 0.15397 | 3.7% | 0.85-1.02 | 0.87-1.05 | 0.478 | 0/NA | NA | NS | High |
| Refined grains | Schwingshackl 2018 (184) | High vs low | RR | 1.46 (0.80-2.67) | 0.21776 | 71.4% | 0.85-1.50 | NA | NA | 1/NA | NA | NS | High |
| Cruciferous vegetables | Wu 2013 (188) | High vs low | RR | 0.96 (0.86-1.08) | 0.50786 | 39.6% | 0.86-1.09 | 0.73-1.27 | 0.398 | 0/NA | NA | NS | Moderate |
| Broccoli | Wu 2013 (188) | High vs low | RR | 0.91 (0.80-1.03) | 0.14492 | 0.0% | 0.80-1.08 | 0.39-2.10 | 0.920 | 0/NA | NA | NS | Moderate |
| Beef | Carr 2016 (185) | High vs low | RR | 1.10 (0.98-1.23) | 0.12048 | 13.7% | 0.86-1.24 | 0.80-1.51 | 0.458 | 1/NA | NA | NS | Low |
| Poultry | Carr 2016 (185) | High vs low | RR | 0.97 (0.89-1.07) | 0.57776 | 44.2% | 0.86-1.01 | 0.75-1.26 | 0.302 | 2/NA | NA | NS | Low |
| Fish | Wu 2012 (186) | High vs low | OR | 0.93 (0.82-1.05) | 0.22129 | 37.2% | 0.54-0.88 | 0.64-1.34 | 0.817 | 3/NA | NA | NS | Low |
| Fruits and vegetables | Aune 2011 (187) | High vs low | RR | 0.93 (0.86-1.01) | 0.08766 | 28.1% | 0.85-1.09 | 0.77-1.12 | 0.492 | 1/NA | NA | NS | Low |
| Soy products | Lu 2017(193) | High vs low | RR 0.86 (0.72-1.03) | 0.10126 | 44.7 % | 0.78-1.16 | 0.55-1.36 | 0.422 | 2/NA | NA | NS | Low |
|--------------|--------------|-------------|----------------------|---------|--------|----------|---------|-------|------|-----|-----| |
| Cheese | Aune 2012(194) | High vs low | RR 0.94 (0.75-1.18) | 0.59378 | 38.5 % | 0.56-1.12 | 0.54-1.65 | 0.122 | 1/NA | NA | NS | Low |
| **Beverages** | | | | | | | | | | | | |
| Wine | Xu 2019(203) | Yes vs no | RR 1.01 (0.90-1.13) | 0.89148 | 59.0 % | 0.93-1.11 | 0.75-1.35 | 0.257 | 2/NA | NA | NS | Moderate |
| Wine | Xu 2019(203) | <2 drinks/d vs non-drinkers | RR 0.94 (0.84-1.05) | 0.27068 | 25.4 % | 0.83-1.08 | 0.67-1.32 | 0.226 | 0/NA | NA | NS | Moderate |
| Wine | Xu 2019(203) | ≥2 drinks/d vs non-drinkers | RR 1.03 (0.85-1.24) | 0.79103 | 41.8 % | 1.04-1.40 | 0.62-1.71 | 0.439 | 1/NA | NA | NS | Moderate |
| Coffee | Gan 2017(199) | High vs low | RR 0.98 (0.90-1.06) | 0.63354 | 41.4 % | 0.95-1.18 | 0.77-1.24 | 0.764 | 3/NA | NA | NS | Moderate |
| Fermented milk | Ralston 2014(200) | High vs low | RR 1.01 (0.89-1.15) | 0.83901 | 0.0% | 0.86-1.34 | 0.86-1.19 | 0.351 | 0/NA | NA | NS | Moderate |
| Tea | Chen 2017(196) | High vs low | OR 0.94 (0.86-1.03) | 0.17801 | 32.7 % | 0.90-1.05 | 0.74-1.20 | 0.328 | 3/NA | NA | NS | Moderate |
| Green tea | Wang 2012(197) | High vs low | RR 0.93 (0.77-1.12) | 0.44432 | 59.2 % | 0.97-1.45 | 0.53-1.62 | 0.653 | 2/NA | NA | NS | Critically low |
| Black tea | Sun 2006(198) | High vs low | OR 1.05 (0.75-1.46) | 0.77918 | 75.1 % | 0.83-1.22 | 0.37-2.99 | 0.704 | 2/NA | NA | NS | Critically low |
© 2021 Veetil SK et al. *JAMA Network Open.*
| Nutrition Factor | Study Reference | Consumption Comparison | RR (95% CI) | %Change | 95% Lower CI | 95% Upper CI | P Value | Risk Classification |
|-----------------------------------|-----------------|-------------------------|---------------|---------|--------------|--------------|---------|---------------------|
| Legume fibre | Reynolds 2019 | High vs low | 0.91 (0.81-1.02) | 38.0% | 0.83-1.04 | 0.60-1.36 | 0.214 | High |
| Soluble fibre | Reynolds 2019 | High vs low | 0.84 (0.67-1.05) | 38.2% | 0.69-1.03 | 0.10-7.29 | 0.904 | High |
| Insoluble fibre | Reynolds 2019 | High vs low | 0.86 (0.74-1.01) | 0.0% | 0.72-1.06 | 0.31-2.39 | 0.893 | High |
| Dietary protein | Lai 2017 | High vs low | 0.94 (0.73-1.21) | 0.0% | 0.64-1.44 | 0.54-1.63 | 0.454 | Moderate |
| Polyunsaturated fatty acids | Kim 2018 | High vs low | 0.99 (0.93-1.04) | 22.0% | 0.98-1.03 | 0.85-1.14 | 0.965 | Moderate |
| Monounsaturated fatty acids | Liu 2011 | High vs low | 1.04 (0.93-1.16) | 0.0% | 0.87-1.29 | 0.92-1.18 | 0.214 | Low |
| Saturated fatty acids | Liu 2011 | High vs low | 1.00 (0.90-1.12) | 0.0% | 0.77-1.14 | 0.89-1.13 | 0.037 | Low |
| Total dietary fat | Liu 2011 | High vs low | 0.99 (0.89-1.11) | 6.9% | 0.78-1.17 | 0.84-1.17 | 0.092 | Low |
| Total n-3 polyunsaturated fatty acids | Chen 2015 | High vs low | 1.00 (0.93-1.07) | 8.6% | 0.92-1.17 | 0.89-1.13 | 0.773 | Low |
| Marine n-3 polyunsaturated fatty acids | Chen 2015 | High vs low | 1.00 (0.93-1.07) | 0.0% | 0.89-1.20 | 0.92-1.08 | 0.728 | Low |
| Cholesterol | Liu 2011 | High vs low | 1.14 (0.88-1.47) | 49.8% | 0.70-1.60 | 0.56-2.30 | 0.057 | Low |
| Carbohydrate | Aune 2012 | High vs low | 0.93 (0.84-1.04) | 39.8% | 0.75-1.10 | 0.70-1.25 | 0.049 | Low |
| Sucrose | Aune 2012 | High vs low | 1.01 (0.87-1.17) | 63.5% | 0.97-1.20 | 0.65-1.56 | 0.949 | Low |
| Fructose | Aune 2012(207) | High vs low | RR | 1.06 (0.87-1.28) | 0.5765 (0.87-1.28) | 72.5% | 0.90-1.13 | 0.56-1.99 | 0.353 | 2/NA NA NS Low |
|---------------------|----------------|-------------|-----|------------------|-------------------|-------|-----------|-----------|-------|---------------|
| Fruit fibre | Aune 2011(209) | High vs low | RR | 0.94 (0.85-1.04) | 0.2080 (0.85-1.04) | 39.1% | 0.95-1.23 | 0.73-1.20 | 0.913 | 2/NA NA NS Low |
| Vegetable fibre | Aune 2011(209) | High vs low | RR | 0.98 (0.91-1.06) | 0.6317 (0.91-1.06) | 0.0% | 0.89-1.15 | 0.90-1.07 | 0.514 | 0/NA NA NS Low |
**Micronutrients**
| Garlic supplement | Chiavarini 2016(190) | Yes vs no | RR | 1.07 (0.91-1.26) | 0.4170 (0.91-1.26) | 27.8% | 1.01-1.81 | 0.74-1.55 | 0.634 | 1/NA NA NS Moderate |
|---------------------|-----------------------|------------|-----|------------------|-------------------|-------|-----------|-----------|-------|---------------------|
| Flavanols | He 2016(213) | High vs low | OR | 1.00 (0.66-1.28) | 0.9558 (0.66-1.28) | 41.3% | 0.95-1.21 | 0.22-4.68 | 0.924 | 0/NA NA NS Moderate |
| Anthocyanins | He 2016(213) | High vs low | OR | 0.92 (0.66-1.28) | 0.6205 (0.66-1.28) | 17.0% | 0.81-1.91 | NA | NA | 0/NA NA NS Moderate |
| Quercetin | Grosso 2017(212) | High vs low | OR | 0.98 (0.75-1.29) | 0.8941 (0.75-1.29) | 29.6% | 0.75-1.36 | 0.08-11.45 | 0.430 | 0/NA NA NS Low |
| Kaempferol | Grosso 2017(212) | High vs low | OR | 1.12 (0.91-1.38) | 0.2893 (0.91-1.38) | 0.0% | 0.85-1.53 | 0.29-4.32 | 0.984 | 0/NA NA NS Low |
| Myricetin | Grosso 2017(212) | High vs low | OR | 1.10 (0.82-1.48) | 0.5096 (0.82-1.48) | 42.4% | 0.67-1.18 | 0.06-19.82 | 0.541 | 0/NA NA NS Low |
| Catechin | Grosso 2017(212) | High vs low | OR | 0.89 (0.71-1.11) | 0.3047 (0.71-1.11) | 57.0% | 0.77-1.21 | 0.36-2.17 | 0.271 | 1/NA NA NS Low |
| Phyto-oestrogens | Jiang 2017(214) | High vs low | RR | 0.93 (0.83-1.05) | 0.2313 (0.83-1.05) | 0.0% | 0.79-1.14 | 0.78-1.12 | 0.993 | 0/NA NA NS Low |
| Nutrient | Study | Outcome | RR | 95% CI | p-value | I² % | RR | 95% CI | p-value | I² % | RR | 95% CI | p-value | I² % | Whether Significant
|-------------------------------|----------------------------|------------------------|------|---------------|---------|------|------|---------------|---------|------|------|---------------|---------|------|------------------|
| Isoflavones | Grosso 2017(212) | High vs low | OR 0.92 (0.82-1.03) | 0.1522 4 | 0.0% | 0.79-1.14 | 0.78-1.08 | 0.668 | 0/NA | NA | NS Low |
| Combined carotenoids | Panic 2017(215) | High vs low | RR 1.08 (0.93-1.26) | 0.3171 1 | 0.0% | 0.93-1.28 | NA | NA | 0/NA | NA | NS Low |
| Alpha-carotene | Panic 2017(215) | High vs low | RR 1.05 (0.92-1.21) | 0.4647 7 | 0.0% | 0.88-1.20 | 0.43-2.59 | 0.190 | 0/NA | NA | NS Low |
| Beta-carotene | Panic 2017(215) | High vs low | RR 0.98 (0.87-1.11) | 0.7854 2 | 0.0% | 0.78-1.08 | 0.74-1.30 | 0.090 | 0/NA | NA | NS Low |
| Lycopene | Panic 2017(215) | High vs low | RR 1.08 (0.94-1.23) | 0.2601 1 | 0.0% | 0.94-1.26 | 0.45-2.56 | 0.309 | 0/NA | NA | NS Low |
| Beta-cryptoxanthin | Panic 2017(215) | High vs low | RR 0.99 (0.74-1.34) | 0.9585 7 | 38.8% | 0.78-1.06 | NA | NA | 0/NA | NA | NS Low |
| Lutein and zeaxanthin | Panic 2017(215) | High vs low | RR 1.05 (0.91-1.20) | 0.5221 0 | 0.0% | 0.88-1.20 | 0.43-2.57 | 0.585 | 0/NA | NA | NS Low |
| Multivitamin | Liu 2015(217) | High vs low | RR 0.83 (0.65-1.05) | 0.1211 6 | 68.5% | 0.83-1.17 | 0.42-1.62 | 0.121 | 2/NA | NA | NS Low |
| Vitamin A | Liu 2015(217) | High vs low | RR 0.89 (0.77-1.03) | 0.1323 0 | 0.0% | 0.70-1.50 | 0.75-1.06 | 0.304 | 1/NA | NA | NS Low |
| Vitamin B2 | Liu 2015(217) | High vs low | RR 0.89 (0.78-1.00) | 0.0572 3 | 4.2% | 0.66-0.99 | 0.72-1.08 | 0.159 | 1/NA | NA | NS Low |
| Vitamin B3 | Liu 2015(217) | High vs low | RR 1.18 (0.76-1.84) | 0.4568 3 | 31.0% | 0.70-1.60 | NA | NA | 0/NA | NA | NS Low |
| Vitamin B12 | Liu 2015(217) | High vs low | RR 1.10 (0.92-1.32) | 0.3114 5 | 49.1% | 0.72-1.08 | 0.67-1.80 | 0.018 | 0/NA | NA | NS Low |
| Vitamin C | Heine-Bröring 2015(216) | Yes vs no | RR 0.92 (0.75-1.11) | 0.3779 9 | 42.2% | 0.73-1.49 | 0.55-1.53 | 0.231 | 1/NA | NA | NS Low |
| Vitamin | Author | High vs low | RR | 95% CI | p | O/E | OR | 95% CI | p | O/E | NA | NS | Score | Critical \( p \) |
|-------------|-------------------|-------------|--------|----------------|-------|-----|--------|----------------|-------|-----|----|----------|-------|------------------|
| Vitamin C | Liu 2015(217) | High vs low | 0.92 | (0.80-1.07) | 0.3068| 40.0%| 0.73-1.09 | 0.62-1.38 | 0.954 | 2/NA | NA | NS | Low |
| Vitamin D | Heine-Bröring 2015(216) | Yes vs no | RR | 0.90 (0.81-1.02) | 0.0939| 46.3%| 0.80-1.06 | 0.67-1.23 | 0.487 | 2/NA | NA | NS | Low |
| Vitamin E | Liu 2015(217) | High vs low | 0.88 | (0.75-1.04) | 0.1217| 49.3%| 0.85-1.38 | 0.54-1.43 | 0.264 | 1/NA | NA | NS | Low |
| Flavonoids | Bo 2016(210) | High vs low | OR | 1.10 (0.95-1.28) | 0.1933| 5.0% | 0.95-1.50 | 0.87-1.40 | 0.825 | 1/NA | NA | NS | Critically low |
| Flavonols | Chang 2018(212) | High vs low | RR | 1.00 (0.92-1.08) | 0.9497| 6.6% | 0.89-1.14 | 0.85-1.17 | 0.777 | 0/NA | NA | NS | Critically low |
| Flavones | Chang 2018(212) | High vs low | RR | 1.02 (0.94-1.12) | 0.6262| 0.0% | 0.92-1.17 | 0.58-1.80 | 0.202 | 0/NA | NA | NS | Critically low |
| Flavanones | Chang 2018(212) | High vs low | RR | 0.99 (0.91-1.06) | 0.7128| 0.0% | 0.91-1.10 | 0.83-1.17 | 0.485 | 0/NA | NA | NS | Critically low |
| Flavan-3-ols| Chang 2018(212) | High vs low | RR | 1.02 (0.93-1.12) | 0.6260| 20.4% | 0.95-1.21 | 0.78-1.34 | 0.908 | 0/NA | NA | NS | Critically low |
| Anthocyanidins | Chang 2018(212) | High vs low | RR | 1.00 (0.91-1.09) | 0.9457| 0.0% | 0.91-1.13 | 0.54-1.83 | 0.125 | 0/NA | NA | NS | Critically low |
| Methionine | Zhou 2013(222) | High vs low | RR | 0.89 (0.77-1.03) | 0.1118| 29.1%| 0.76-1.28 | 0.64-1.24 | 0.632 | 2/NA | NA | NS | Critically low |
NA = not applicable because of non-significant effect estimate/data unavailability; NS = not significant; O/E = observed/expected number of studies with significant results; OR = odds ratio; RR = risk ratio
### eTable 5. Sensitivity Analyses for Associations With Class I, II, or III Evidence
| Exposure | Author; year | No. of primary studies | No. of study participants | No. of cases | Comparison | Summary metric | Credibility assessment | AMSTAR-2 |
|-------------------|--------------|------------------------|---------------------------|--------------|------------|---------------|------------------------|-----------|
| Alcohol (Moderate) | Fedirko 2011(201) | 17 | 2754534 | 18420 | >1-3 drinks/d vs non/occasion drinkers | RR 1.17 (1.08-1.26) | 0.0000 6 | 37.3 % | 1.01-1.13 | 0.96-1.42 | 0.014 | 5/2.5 | 1.00 | Class III Moderate |
| Supplemen- tal calcium | Heine-Börning 2015(216) | 6 | 1029242 | 9621 | Yes vs no | RR 0.89 (0.84-0.95) | 0.0005 1 | 47.5 % | 0.88-1.05 | 0.73-1.09 | 0.252 | 2/3.2 | NP | Class III Low |
| Whole grains | Schwingshackle 2018(184) | 7 | 932818 | 8943 | High vs low | RR 0.87 (0.82-0.94) | 0.0001 1 | 48.3 % | 0.88-0.99 | 0.73-1.04 | 0.018 | 4/0.9 | 0.06 | Class III High |
**Exclusion of primary studies with number of study participants lower than 25th percentile** (applicable to those meta-analyses with evidence of small-study effects in primary analysis)
Primary studies adjusted for confounding variables
| Study Description | Authors | Year | Participants | High vs Low | RR | 95% CI | P Value | % Change | 95% CI | Class | Critically low |
|------------------------------------------|----------------|------|--------------|-------------|-----|----------|---------|----------|----------|-------|----------------|
| Adherence to Mediterranean diet | Schwingshackl | 2017 | 16102 | High vs low | 0.86| (0.80-0.92)|<10^-6 | 29.7 | 0.80-0.99| 0.74-1.00| 0.841 | 3/5.0 |
| Adherence to Western diet | Feng | 2017 | 11537 | High vs low | 1.28| (1.13-1.45)|<10^-4 | 72.2 | 1.09-1.44| 0.79-2.07| 0.173 | 8/6.5 |
| Adherence to healthy diet | Feng | 2017 | 11537 | High vs low | 0.84| (0.76-0.92)|<10^-4 | 56.2 | 0.69-0.90| 0.60-1.17| 0.602 | 5/7.5 |
| Pesco-vegetarian diet | Godos | 2016 | 1506 | Yes vs no | 0.67| (0.53-0.83)|<10^-3 | 0.0 | 0.48-0.94| 0.15-2.89| 0.437 | 2/1.7 |
| Semi-vegetarian diet | Godos | 2016 | 4062 | Yes vs no | 0.86| (0.79-0.94)|<10^-2 | 0.0 | 0.76-0.95| 0.72-1.04| 0.964 | 1/1.2 |
| Red meat | Schwingshackl | 2018 | 21326 | High vs low | 1.13| (1.08-1.19)|<10^-8 | 20.5 | 1.15-1.19| 1.02-1.26| 0.175 | 3/6.0 |
| Processed meat | Schwingshackl | 2018 | 18646 | High vs low | 1.14| (1.07-1.23)|<10^-3 | 25.9 | 1.09-1.32| 0.97-1.35| 0.981 | 4/6.9 |
| Whole grains | Schwingshackl | 2018 | 9223 | High vs low | 0.88| (0.83-0.94)|<10^-6 | 34.9 | 0.88-0.99| 0.77-1.01| 0.067 | 4/1.0 |
| Dairy products | Schwingshackl | 2018 | 16910 | High vs low | 0.83| (0.76-0.89)|<10^-6 | 60.3 | 0.83-0.95| 0.65-1.04| 0.170 | 8/4.0 |
| Yogurt | Zhang | 2019 | 5432 | High vs low | 0.81| (0.76-0.86)|<10^-6 | 0.0 | 0.75-0.87| 0.72-0.90| 0.835 | 2/1.8 |
© 2021 Veettil SK et al. JAMA Network Open.
| Variable | Study | N | HR 5/20 | Adherence | RR 9/20 | P-value | Class | Study quality |
|----------------------------------|-----------------------------------------------------------------------|----|----------|------------|-----------|---------|-------|---------------|
| Alcohol (Moderate) | Fedirko 2011 | 22 | RR 1.24 | <10\(^{-6}\) | 49.3% | 0.95-1.61 | | Class II Moderate |
| | Fedirko 2011 | 22 | RR 1.24 | <10\(^{-6}\) | 49.3% | 0.95-1.61 | | Class II Moderate |
| Alcohol (Heavy) | Fedirko 2011 | 7 | RR 1.58 | <10\(^{-6}\) | 0.0% | 1.27-2.16 | Class I | Moderate |
| Non-fermented milk | Ralston 2014 | 14 | RR 0.85 | 0.0004 | 0.0% | 0.78-1.18 | Class III | Moderate |
| Total dietary fibre | Reynolds 2019 | 21 | RR 0.84 | <10\(^{-6}\) | 18.1% | 0.65-0.85 | Class I | High |
| Dietary calcium | Meng 2019 | 8 | HR 0.77 | <10\(^{-6}\) | 0.0% | 0.75-0.94 | Class I | Moderate |
| Supplementation calcium | Heine-Bröning 2015 | 7 | RR 0.88 | 0.0009 | 51.7% | 0.88-1.05 | Class III | Low |
| Supplementation calcium | Heine-Bröning 2015 | 6 | RR 0.80 | 0.0002 | 30.9% | 0.72-1.02 | Class III | Low |
| **Primary studies with high quality** | | | | | | | | |
| Adherence to Mediterranean diet* | Schwingshack 2017 | 6 | RR 0.86 | 8.4 \times 10^{-6} | 29.7% | 0.80-0.99 | Class III | Critically Low |
© 2021 Veettil SK et al. *JAMA Network Open.*
| Dietary Pattern | Source | N | Cases | Controls | High vs low | OR | 95% CI | P | Adjustment | N | NP | Class | Moderate |
|---------------------------------------|--------------------|-------|----------|----------|-------------|--------|---------|-----------|------------|--------|------|-------|----------|
| Adherence to Western diet | Feng 2017(179) | 13 | 1181915 | 11449 | High vs low | OR 1.23 (1.09-1.40) | 0.0001 | 71.6% | 1.09-1.44 | 0.78-1.95 | 0.457 | 6/6.9 | Class III | Moderate |
| Pescovegetarian diet | Godos 2016(181) | 3 | 149516 | 1506 | Yes vs no | RR 0.67 (0.53-0.83) | 0.0004 | 0.0% | 0.48-0.94 | 0.15-2.89 | 0.437 | 2/1.7 | Class III | Low |
| Semi-vegetarian diet | Godos 2016(181) | 3 | 580175 | 4062 | Yes vs no | RR 0.86 (0.79-0.94) | 0.0007 | 0.0% | 0.76-0.95 | 0.72-1.04 | 0.964 | 1/1.2 | NP | Class III Low |
| Red meat* | Schwingshackle 2018(184) | 21 | 2154027 | 21326 | High vs low | RR 1.13 (1.08-1.19) | <10^-6 | 20.5% | 1.15-1.19 | 1.02-1.26 | 0.175 | 3/6.0 | NP | Class I High |
| Processed meat* | Schwingshackle 2018(184) | 15 | 1910983 | 18646 | High vs low | RR 1.14 (1.07-1.23) | 0.0001 | 25.9% | 1.09-1.32 | 0.97-1.35 | 0.981 | 4/6.9 | NP | Class III High |
| Whole grains* | Schwingshackle 2018(184) | 9 | 970927 | 9223 | High vs low | RR 0.88 (0.83-0.94) | 0.00006 | 34.9% | 0.88-0.99 | 0.77-1.01 | 0.067 | 4/1.0 | 0.26 | Class III High |
| Dairy products* | Schwingshackle 2018(184) | 17 | 1629366 | 16910 | High vs low | RR 0.83 (0.76-0.89) | <10^-6 | 60.3% | 0.83-0.95 | 0.65-1.04 | 0.170 | 8/4.0 | 0.99 | Class II High |
| Yogurt* | Zhang 2019(195) | 5 | 698366 | 5432 | High vs low | OR 0.81 (0.76-0.86) | <10^-6 | 0.0% | 0.75-0.87 | 0.72-0.90 | 0.835 | 2/1.8 | 1.00 | Class I Low |
| Alcohol (Moderate) | Fedirko 2011(201) | 10 | 1061631 | 7809 | >1-3 drinks/d vs non/occasional drinkers | RR 1.36 (1.16-1.58) | 0.00013 | 55.3% | 0.93-1.29 | 0.88-2.10 | 0.016 | 5/1.4 | 0.29 | Class III Moderate |
© 2021 Veettil SK et al. *JAMA Network Open.*
| Alcohol (Heavy) | Fedirko 2011 (201) | 4 | 637367 | 3724 | ≥4 drinks/d vs non/occasion al drinkers | RR | 1.73 (1.47–2.04) | <10⁻⁶ | 0.0% | 1.27–2.16 | 1.21–2.49 | 0.248 | 4/3.5 | 0.90 | Class I | Moderate |
|----------------|-------------------|---|--------|------|----------------------------------------|----|-----------------|-------|------|-----------|-----------|------|------|------|---------|---------|
| Non-fermented milk | Ralston 2014 (200) | 10 | 751312 | 4184 | High vs low | RR | 0.83 (0.74–0.94) | 0.0034 | 27.9% | 0.78–1.18 | 0.63–1.10 | 0.577 | 3/0.6 | 0.42 | Class III | Moderate |
| Total dietary fibre | Reynolds 2019 (182) | 17 | 2071669 | 20961 | High vs low | RR | 0.85 (0.79–0.90) | <10⁻⁶ | 10.5% | 0.65–0.85 | 0.76–0.95 | 0.642 | 5/10.5 | NP | Class I | High |
| Dietary calcium* | Meng 2019 (218) | 8 | 1449526 | 13640 | High vs low | HR | 0.77 (0.73–0.82) | <10⁻⁶ | 0.0% | 0.75–0.94 | 0.72–0.83 | 0.598 | 5/3.9 | 1.00 | Class I | Moderate |
| Supplemen tal calcium* | Heine-Bröring 2015 (216) | 7 | 1064458 | 9862 | Yes vs no | RR | 0.88 (0.82–0.94) | 0.0000 | 51.7% | 0.88–1.05 | 0.70–1.09 | 0.071 | 3/3.4 | NP | Class III | Low |
| Supplemen tal calcium* | Heine-Bröring 2015 (216) | 6 | 929116 | 8837 | High vs low | RR | 0.80 (0.72–0.89) | 0.0000 | 30.9% | 0.72–1.02 | 0.63–1.01 | 0.884 | 4/2.7 | 0.95 | Class III | Low |
* Not performed due to limited number of primary studies
*Sensitivity analysis is not possible because no information on quality assessment of primary studies
* Sensitivity analysis is not possible because meta-analysis only included good-quality studies
NP = not pertinent, because estimated number is larger than observed, and there is no evidence of excess significance based on assumption made for plausible effect size; O/E = observed/expected number of studies with significant results; OR = odds ratio; RR = risk ratio.
### eTable 6: Evidence Criteria: Difference Between WCRF and Present Review
| WCRF<sup>(223)</sup> | Umbrella review |
|------------------------|----------------|
| • Evidence from more than one study | • Number of cases >1,000 |
| • Evidence from at least two independent cohort studies | • p <10<sup>−6</sup> |
| • No substantial heterogeneity | • I<sup>2</sup> <50% |
| • Good quality studies to exclude with confidence the possibility that the observed association results from random or systematic error, including confounding, measurement error, and selection bias | • 95% prediction interval excluding the null |
| • Dose-response relationship | • No small-study effects |
| • Strong and plausible experimental evidence | • No excess significance bias |
### eTable 6.1: Comparison with WCRF meta-analyses for associations with class I evidence in primary analysis
| Association | WCRF<sup>(223)</sup> | Present review |
|-------------|-------------------------|----------------|
| | Author (Year) | Number of studies reported | Author (Year) | Number of studies reported |
| Red meat | Alexander (2015) | 17 | Schwingshakl (2018) | 21 |
| | Chan (2011) | 8 | | |
| Alcohol beverages (heavy intake) | Only dose-response meta-analysis found | - | Fedirko (2011) | 7 |
| Total dietary fibre | Aune (2011) | 16 | Reynolds (2019) | 21 |
| Dietary calcium | Only dose-response meta-analysis found | - | Meng (2019) | 8 |
| Yogurt | Only dose-response meta-analysis found | - | Zhang (2019) | 5 |
**Explanation:**
Although WCRF is the latest report, the meta-analyses they used for the intake of red meat and total dietary fibre are different from ours. According to the published methodology by WCRF, the search for articles was updated to April 2015. For our current review paper, a systematic literature search up to September 2019 was performed. Hence, the meta-analyses included for the intake of red meat, total dietary fibre, yogurt, and dietary calcium are from recent papers published between 2018 to 2019, except for heavy alcohol intake which was published in 2011. The meta-analyses included in our review are chosen based on specified selection criteria: meta-analysis with the largest number of primary studies and the one with the largest number of colorectal cancer cases. However, the selection criteria
in the WCRF report are unclear. We followed exactly the protocol as suggested by recent umbrella reviews for selection of meta-analysis for evidence grading. We excluded the meta-analyses used by WCRF and they are shown in the exclusion references in this supplementary material. For all of the associations, we used summary estimates for high versus low intake instead of dose-response meta-analysis.
eTable 7. Summary Estimates for Concordance in Meta-analyses: Red Meat Intake and Incidence of CRC
| Author | Year | RR | 95% CI | P-value | Class of evidence |
|-----------------|------|-----|--------------|---------|---------------------------|
| Larsson(175) | 2006 | 1.20| 1.11 - 1.31 | >10^-6 | Class III |
| Chan (173) | 2011 | 1.17| 1.09 - 1.25 | >10^-6 | Class III |
| Pham(141) | 2014 | 1.18| 0.92- 1.53 | NS | Not significant (only Japanese population included): excluded in this comparison |
| Alexander(168) | 2015 | 1.16| 1.10 - 1.23 | NA | Data not available to grade the evidence |
| Schwingshackl(184) | 2018 | 1.14| 1.07 - 1.23 | >10^-6 | Class III |
**Abbreviations:** NA: not available; RR, relative risk; 95% CI, 95% confidence interval
*Please note: Dose-response meta-analyses were not included in our review.*
eReferences
1. Godos J, Bella F, Torrisi A, Sciacca S, Galvano F, Grosso G. Dietary patterns and risk of colorectal adenoma: a systematic review and meta-analysis of observational studies. J Hum Nutr Diet [Internet]. 2016;29(6):757–67. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med12&NEWS=N&AN=27412573
2. Yoon H, Benamouzig R, Little J, Francois-Collange M, Torme D. Systematic review of epidemiological studies on meat, dairy products and egg consumption and risk of colorectal adenomas. Eur J Cancer Prev [Internet]. 2000;9(3):151–64. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med4&NEWS=N&AN=10954254
3. Wang Y-M, Zhou Q-Y, Zhu J-Z, Zhu K-F, Yu C-H, Li Y-M. Systematic Review with Meta-Analysis: Alcohol Consumption and Risk of Colorectal Serrated Polyp. Dig Dis Sci [Internet]. 2015;60(7):1889–902. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=25618311
4. Zhu J-Z, Wang Y-M, Zhou Q-Y, Zhu K-F, Yu C-H, Li Y-M. Systematic review with meta-analysis: alcohol consumption and the risk of colorectal adenoma. Aliment Pharmacol Ther [Internet]. 2014;40(4):325–37. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=24943329
5. Wang J, Wang H, Chen Y, Hao P, Zhang Y. Alcohol ingestion and colorectal neoplasia: a meta-analysis based on a Mendelian randomization approach. Colorectal Dis [Internet]. 2011;13(5):e71-8. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=21114754
6. Bagnardi V, Blangiardo M, La Vecchia C, Corrao G. A meta-analysis of alcohol drinking and cancer risk. Br J Cancer [Internet]. 2001;85(11):1700–5. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med4&NEWS=N&AN=11742491
7. Yao Y, Suo T, Andersson R, Cao Y, Wang C, Lu J, et al. Dietary fibre for the prevention of recurrent colorectal adenomas and carcinomas [Internet]. 2017. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=coch&NEWS=N&AN=00075320-100000000-02504
8. Ben Q, Sun Y, Chai R, Qian A, Xu B, Yuan Y. Dietary fiber intake reduces risk for colorectal adenoma: a meta-analysis. Gastroenterology [Internet]. 2014;146(3):689–699.e6. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=24216326
9. Jacobs ET, Lanza E, Alberts DS, Hsu C-H, Jiang R, Schatzkin A, et al. Fiber, sex, and colorectal adenoma: results of a pooled analysis. Am J Clin Nutr [Internet]. 2006;83(2):343–9. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN=16469993
10. Veettil SK, Ching SM, Lim KG, Saokaew S, Phisalprapa P, Chaiyakunapruk N. Effects of calcium on the incidence of recurrent colorectal adenomas: A systematic review with meta-analysis and trial sequential analysis of randomized controlled trials. Medicine (Baltimore) [Internet]. 2017;96(32):e7661. Available from:
11. Keum N, Lee DH, Greenwood DC, Zhang X, Giovannucci EL. Calcium intake and colorectal adenoma risk: dose-response meta-analysis of prospective observational studies. Int J Cancer [Internet]. 2015;136(7):1680–7. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medc1&NEWS=N&AN=25 156950
12. Shaukat A, Scouras N, Schunemann HJ. Role of supplemental calcium in the recurrence of colorectal adenomas: a metaanalysis of randomized controlled trials. Am J Gastroenterol [Internet]. 2005;100(2):390–4. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN=156 67497
13. Z, Z, Z, Y, Z, H, C, Z. Association between red and processed meat intake and colorectal adenoma incidence and recurrence: A systematic review and meta-analysis. Oncotarget [Internet]. 2018;9(64):32373–82. Available from: http://www.oncotarget.com/index.php?journal=oncotarget&page=article&op=download&path%5B%5D=23561&path%5B%5D=74195
14. Carroll C, Cooper K, Papaioannou D, Hind D, Pilgrim H, Tappenden P. Supplemental calcium in the chemoprevention of colorectal cancer: a systematic review and meta-analysis. Clin Ther [Internet]. 2010;32(5):789–803. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=206 85491
15. Cao H, Wang C, Chai R, Dong Q, Tu S. Iron intake, serum iron indices and risk of colorectal adenomas: a meta-analysis of observational studies. Eur J Cancer Care (Engl) [Internet]. 2017;26(5). Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN=26 956572
16. Q, D, S, T, H, C, Z. W. Meta-analysis of the association between cruciferous vegetables intake and colorectal adenoma risk. Int J Clin Exp Med [Internet]. 2017;10(6):9288–97. Available from: http://www.ijcem.com/files/ijcem0024790.pdf
17. Bjelakovic G, Nikolova D, Simonetti RG, Gluud C. Antioxidant supplements for preventing gastrointestinal cancers [Internet]. 2008. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=coch&NEWS=N&AN=000 75320-100000000-03125
18. Figueiredo JC, Mott LA, Giovannucci E, Wu K, Cole B, Grainge MJ, et al. Folic acid and prevention of colorectal adenomas: a combined analysis of randomized clinical trials. Int J Cancer [Internet]. 2011;129(1):192–203. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=211 70989
19. Fife J, Raniga S, Hider PN, Frizelle FA. Folic acid supplementation and colorectal cancer risk: a meta-analysis. Colorectal Dis [Internet]. 2011;13(2):132–7. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=198 63600
20. Kennedy DA, Stern SJ, Moretti M, Matok I, Sarkar M, Nickel C, et al. Folate intake and the risk of colorectal cancer: a systematic review and meta-analysis. Cancer Epidemiol [Internet]. 2011;35(1):2–10. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN
21. Ibrahim EM, Zekri JM. Folic acid supplementation for the prevention of recurrence of colorectal adenomas: metaanalysis of interventional trials. Med Oncol [Internet]. 2010;27(3):915–8. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=19757214
22. S.-X. D, S.-Y. H, W. A, J. G. Folic acid supplementation in prevention of colorectal adenoma recurrence: A meta-analysis. Acad J Second Mil Med Univ [Internet]. 2010;31(9):984–9. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=emed11&NEWS=N&AN=35971118
23. Xu X, Yu E, Liu L, Zhang W, Wei X, Gao X, et al. Dietary intake of vitamins A, C, and E and the risk of colorectal adenoma: a meta-analysis of observational studies. Eur J Cancer Prev [Internet]. 2013;22(6):529–39. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=24064545
24. Woo HD, Park S, Oh K, Kim HJ, Shin HR, Moon HK, et al. Diet and cancer risk in the Korean population: a meta-analysis. Asian Pac J Cancer Prev [Internet]. 2014;15(19):8509–19. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medc&NEWS=N&AN=25339056
25. Wei MY, Garland CF, Gorham ED, Mohr SB, Giovannucci E. Vitamin D and prevention of colorectal adenoma: a meta-analysis. Cancer Epidemiol Biomarkers Prev [Internet]. 2008;17(11):2958–69. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med6&NEWS=N&AN=18990737
26. Weingarten MA, Zalmanovici A, Yaphe J, Weingarten AM, Zalmanovici Trestioreanu A, Yaphe J, et al. Dietary calcium supplementation for preventing colorectal cancer and adenomatous polyps. Cochrane database Syst Rev [Internet]. 2008;(1):CD003548. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med6&NEWS=N&AN=18254022
27. Asano T, McLeod RS. Dietary fibre for the prevention of colorectal adenomas and carcinomas. Cochrane database Syst Rev [Internet]. 2002;(2):CD003430. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med4&NEWS=N&AN=12076480
28. Bailie L, Loughrey MB, Coleman HG. Lifestyle Risk Factors for Serrated Colorectal Polyps: A Systematic Review and Meta-analysis. Gastroenterology [Internet]. 2017;152(1):92–104. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN=2763904
29. Jin H, Leng Q, Li C. Dietary flavonoid for preventing colorectal neoplasms [Internet]. 2012. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=coch&NEWS=N&AN=00753020-100000000-07736
30. Bergsm-Kadijk JA, van ’t Veer P, Kampman E, Burema J. Calcium does not protect against colorectal neoplasia. Epidemiology [Internet]. 1996;7(6):590–7. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med4&NEWS=N&AN=8899384
31. Singh S, Singh PP, Murad MH, Singh H, Samadder NJ. Prevalence, risk factors, and outcomes of interval colorectal cancers: a systematic review and meta-analysis. Am J Gastroenterol [Internet]. 2014;109(9):1375–89. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=24 957158
32. Aune D, Chan DSM, Vieira AR, Navarro Rosenblatt DA, Vieira R, Greenwood DC, et al. Red and processed meat intake and risk of colorectal adenomas: a systematic review and meta-analysis of epidemiological studies. Cancer Causes Control [Internet]. 2013;24(4):611–27. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=233 80943
33. Xu B, Sun J, Sun Y, Huang L, Tang Y, Yuan Y. No evidence of decreased risk of colorectal adenomas with white meat, poultry, and fish intake: a meta-analysis of observational studies. Ann Epidemiol [Internet]. 2013;23(4):215–22. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=233 75344
34. Jacobs DRJ, Marquart L, Slavin J, Kushi LH. Whole-grain intake and cancer: an expanded review and meta-analysis. Nutr Cancer [Internet]. 1998;30(2):85–96. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med4&NEWS=N&AN=958 9426
35. Ben Q, Zhong J, Liu J, Wang L, Sun Y, Yv L, et al. Association Between Consumption of Fruits and Vegetables and Risk of Colorectal Adenoma: A PRISMA-Compliant Meta-Analysis of Observational Studies. Medicine (Baltimore) [Internet]. 2015;94(42):e1599. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=26 496264
36. Wang Y, Wang Z, Fu L, Chen Y, Fang J. Legume consumption and colorectal adenoma risk: a meta-analysis of observational studies. PLoS One [Internet]. 2013;8(6):e67335. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=238 26270
37. Ben Q, Wang L, Liu J, Qian A, Wang Q, Yuan Y. Alcohol drinking and the risk of colorectal adenoma: a dose-response meta-analysis. Eur J Cancer Prev [Internet]. 2015;24(4):286–95. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=25 162969
38. Anonymous. Antioxidants don’t prevent colorectal cancer. South African Fam Pract [Internet]. 2006;48(8):12. Available from: http://www.tandfonline.com/loi/ojfp20
39. Galeone C, Pelucchi C, La Vecchia C. Added sugar, glycemic index and load in colon cancer risk. Curr Opin Clin Nutr Metab Care [Internet]. 2012;15(4):368–73. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med8&NEWS=N&AN=225 10682
40. Dahm CC, Keogh RH, Spencer EA, Greenwood DC, Key TJ, Fentiman IS, et al. Dietary fiber and colorectal cancer risk: a nested case-control study using food diaries. J Natl Cancer Inst [Internet]. 2010;102(9):614–26. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=204 07088
© 2021 Veettil SK et al. JAMA Network Open.
41. Bristow SM, Bolland MJ, MacLennan GS, Avenell A, Grey A, Gamble GD, et al. Calcium supplements and cancer risk: a meta-analysis of randomised controlled trials. Br J Nutr [Internet]. 2013;110(8):1384–93. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=23601861
42. Qin X, Cui Y, Shen L, Sun N, Zhang Y, Li J, et al. Folic acid supplementation and cancer risk: a meta-analysis of randomized controlled trials. Int J Cancer [Internet]. 2013;133(5):1033–41. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=23338728
43. Qin T, Du M, Du H, Shu Y, Wang M, Zhu L. Folic acid supplements and colorectal cancer risk: meta-analysis of randomized controlled trials. Sci Rep [Internet]. 2015;5:12044. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=26131763
44. Morita M, Yin G, Yoshimitsu S, Ohnaka K, Toyomura K, Kono S, et al. Folate-related nutrients, genetic polymorphisms, and colorectal cancer risk: the fukuoka colorectal cancer study. Asian Pac J Cancer Prev [Internet]. 2013;14(11):6249–56. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medc&NEWS=N&AN=24377513
45. Bjelakovic G, Gluud LL, Nikolova D, Whitfield K, Krstic G, Wetterslev J, et al. Vitamin D supplementation for prevention of cancer in adults [Internet]. 2014. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=coch&NEWS=N&AN=00075320-100000000-06085
46. Arain MA, Abdul Qadeer A. Systematic review on “vitamin E and prevention of colorectal cancer”. Pak J Pharm Sci [Internet]. 2010;23(2):125–30. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=20363687
47. Cai X, Wang C, Yu W, Fan W, Wang S, Shen N, et al. Selenium Exposure and Cancer Risk: an Updated Meta-analysis and Meta-regression using a comprehensive list of selenium/ selenium supplement/ serum/plasma selenium/ toenail selenium/ anti-oxidant/ minerals And cancer/ breast cancer/ lung cancer/ esophageal. Sci Cit Index, Web Sci [Internet]. 2015 [cited 2019 Nov 11]; Available from: www.nature.com/scientificreports
48. Petimar J, Smith-Warner SA, Fung TT, Rosner B, Chan AT, Hu FB, et al. Recommendation- based dietary indexes and risk of colorectal cancer in the Nurses’ Health Study and Health Professionals Follow-up Study. Am J Clin Nutr [Internet]. 2018 Nov 1 [cited 2019 Nov 11]:108(5):1092–103. Available from: https://academic.oup.com/ajcn/article/108/5/1092/5115702
49. Ibanez-Sanz G, Diez-Villanueva A, Vilorio-Marques L, Gracia E, Aragones N, Olmedo-Requena R, et al. Possible role of chondroitin sulphate and glucosamine for primary prevention of colorectal cancer. Results from the MCC-Spain study. Sci Rep [Internet]. 2018;8(1):2040. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medcl&NEWS=N&AN=29391578
50. Vollset SE, Clarke R, Lewington S, Ebbing M, Halsey J, Lonn E, et al. Effects of folic acid supplementation on overall and site-specific cancer incidence during the randomised trials: meta-analyses of data on 50,000 individuals. Armitage J Clarke R, Parish S, Peto R, Collins R, Lonn E, Yusuf S, Manson JE, Glynn R, Grodstein F, Albert CM, Cook NR, Hankey G, Eikelboom JW, Toole J, Malinow MR, Chambless LE, Spence JD, Pettigrew
LC, Howard VJ, Sides EG, Wang CH, Stampfer M, Galan P, BL, editor. Lancet (London, England) [Internet]. 2013;381(9871):1029–36. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=233 52552
51. Shi Y, Yu P-W, Zeng D-Z. Dose-response meta-analysis of poultry intake and colorectal cancer incidence and mortality. Eur J Nutr [Internet]. 2015;54(2):243–50. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=24 788671
52. Tian C, Wang W, Hong Z, Zhang X. Coffee consumption and risk of colorectal cancer: a dose- response analysis of observational studies. Cancer Causes Control [Internet]. 2013;24(6):1265–8. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=235 46611
53. Li G, Ma D, Zhang Y, Zheng W, Wang P. Coffee consumption and risk of colorectal cancer: a meta-analysis of observational studies. Public Health Nutr [Internet]. 2013;16(2):346–57. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=226 94939
54. Galeone C, Turati F, La Vecchia C, Tavani A. Coffee consumption and risk of colorectal cancer: a meta-analysis of case-control studies. Cancer Causes Control [Internet]. 2010;21(11):1949–59. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=206 80435
55. Sun N-H, Huang X-Z, Wang S-B, Li Y, Wang L-Y, Wang H-C, et al. A dose-response meta-analysis reveals an association between vitamin B12 and colorectal cancer risk. Public Health Nutr [Internet]. 2016;19(8):1446–56. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med12&NEWS=N&AN=26 373257
56. Keum N, Aune D, Greenwood DC, Ju W, Giovannucci EL. Calcium intake and colorectal cancer risk: dose-response meta-analysis of prospective observational studies. Int J cancer [Internet]. 2014;135(8):1940–8. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=24 623471
57. Zhao G-H, Jiang S, Yan L-H, Xie L-F, Yang H, Wang Y. Is poultry intake associated with colorectal cancer?. Int J Colorectal Dis [Internet]. 2016;31(5):1087–8. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med12&NEWS=N&AN=26 519150
58. Mizoue T, Tanaka K, Tsuji I, Wakai K, Nagata C, Otani T, et al. Alcohol drinking and colorectal cancer risk: an evaluation based on a systematic review of epidemiologic evidence among the Japanese population. Jpn J Clin Oncol [Internet]. 2006;36(1):25–39. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN=168 70695
59. Gorham ED, Garland CF, Garland FC, Grant WB, Mohr SB, Lipkin M, et al. Vitamin D and prevention of colorectal cancer. J Steroid Biochem Mol Biol [Internet]. 2005;97(1–2):179–94. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN=162 36494
© 2021 Veettil SK et al. JAMA Network Open.
60. Papaioannou D, Cooper KL, Carroll C, Hind D, Squires H, Tappenden P, et al. Antioxidants in the chemoprevention of colorectal cancer and colorectal adenomas in the general population: a systematic review and meta-analysis. Colorectal Dis [Internet]. 2011;13(10):1085–99. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=20412095
61. Pais R, Dumitrascu DL. Do antioxidants prevent colorectal cancer? A meta-analysis. Rom J Intern Med [Internet]. 2013;51(3–4):152–63. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=24620628
62. Richardson A, Hayes J, Frampton C, Potter J. Modifiable lifestyle factors that could reduce the incidence of colorectal cancer in New Zealand. N Z Med J [Internet]. 2016;129(1447):13–20. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med12&NEWS=N&AN=27977648
63. Thies F, Masson LF, Boffetta P, Kris-Etherton P. Oats and bowel disease: a systematic literature review. Br J Nutr [Internet]. 2014;112 Suppl:S31-43. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=25267242
64. Yip CSC, Lam W, Fielding R. A summary of meat intakes and health burdens. Eur J Clin Nutr [Internet]. 2018;72(1):18–29. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med1&NEWS=N&AN=28792013
65. T. M. Nutrition in the chemoprevention of gastrointestinal cancer: Where we are in the new millennium. Pract Gastroenterol [Internet]. 2004;28(3):52–64. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=emed8&NEWS=N&AN=39163072
66. Nuri Faruk Aykan. Red meat and colorectal cancer.
67. de Menezes RF, Bergmann A, Thuler LCS. Alcohol consumption and risk of cancer: a systematic literature review. Asian Pac J Cancer Prev [Internet]. 2013;14(9):4965–72. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medc&NEWS=N&AN=24175760
68. Tavani A, La Vecchia C. Coffee, decaffeinated coffee, tea and cancer of the colon and rectum: a review of epidemiological studies, 1990-2003. Cancer Causes Control [Internet]. 2004;15(8):743–57. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN=15456988
69. Gerber M. Omega-3 fatty acids and cancers: a systematic update review of epidemiological studies. Br J Nutr [Internet]. 2012;107 Suppl:S228-39. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med8&NEWS=N&AN=22591896
70. Yusof AS, Isa ZM, Shah SA. Dietary patterns and risk of colorectal cancer: a systematic review of cohort studies (2000-2011). Asian Pac J Cancer Prev [Internet]. 2012;13(9):4713–7. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medc&NEWS=N&AN=23167408
71. Sakai M, Kakutani S, Horikawa C, Tokuda H, Kawashima H, Shibata H, et al.
Arachidonic acid and cancer risk: a systematic review of observational studies. BMC Cancer [Internet]. 2012;12:606. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med8&NEWS=N&AN=232 49186
72. Lampe JW. Dairy products and cancer. J Am Coll Nutr [Internet]. 2011;30(5 Suppl 1):464S–70S. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=220 81693
73. Grant WB, Garland CF. A critical review of studies on vitamin D in relation to colorectal cancer. Vol. 48, Nutrition and Cancer. Lawrence Erlbaum Associates Inc.; 2004. p. 115–23.
74. Tabung FK. Inaccurate data in meta-analysis “Dietary patterns and colorectal cancer risk: a meta-analysis”. Eur J Cancer Prev [Internet]. 2019;28(1):58–9. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medl&NEWS=N&AN=294 24754
75. Asano KT, McLeod RS. Vitamins and minerals for the prevention of colorectal adenomas and carcinomas [Internet]. 2012. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=coch&NEWS=N&AN=000 75320-100000000-03322
76. Le NT. Meat Mutagens and Colorectal Adenoma and Cancer: A Problem with a Recently Published Systematic Review and Meta-Analysis. Nutrients [Internet]. 2018;10(3). Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medl&NEWS=N&AN=295 09700
77. Giammanco M, Di Majo D, La Guardia M, Aiello S, Crescimannno M, Flandina C, et al. Vitamin D in cancer chemoprevention. Pharm Biol [Internet]. 2015;53(10):1399–434. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=25 856702
78. Farinetti A, Zurlo V, Manenti A, Coppi F, Mattioli AV. Mediterranean diet and colorectal cancer: A systematic review. Nutrition [Internet]. 2017;43–44:83–8. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN=28 935150
79. Alicandro G, Tavani A, La Vecchia C. Coffee and cancer risk. Eur J Cancer Prev [Internet]. 2017 Sep [cited 2019 Nov 11];26(5):424–32. Available from: http://insights.ovid.com/crossref?an=00008469-201709000-00010
80. Li D. Omega-3 polyunsaturated fatty acids and non-communicable diseases: meta-analysis based systematic review. Asia Pac J Clin Nutr [Internet]. 2015;24(1):10–5. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=25 740737
81. Boehm K HM. Cochrane Database of Systematic Reviews Green tea (Camellia sinensis) for the prevention of cancer (Review). 2016 [cited 2019 Nov 11]. Available from: www.cochranelibrary.com
82. El Kinany K, Deoula M, Hatime Z, Bennani B, El Rhazi K. Dairy products and colorectal cancer in middle eastern and north African countries: a systematic review. BMC Cancer [Internet]. 2018;18(1):233. Available from:
83. Kantor ED, Zhang X, Wu K, Signorello LB, Chan AT, Fuchs CS, et al. Use of glucosamine and chondroitin supplements in relation to risk of colorectal cancer: Results from the Nurses’ Health Study and Health Professionals follow-up study. Int J cancer [Internet]. 2016;139(9):1949–57. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med12&NEWS=N&AN=27 357024
84. Vieira AR, Abar L, Chan DSM, Vingeliene S, Polemiti E, Stevens C, et al. Foods and beverages and colorectal cancer risk: a systematic review and meta-analysis of cohort studies, an update of the evidence of the WCRF-AICR Continuous Update Project. Ann Oncol Off J Eur Soc Med Oncol [Internet]. 2017;28(8):1788–802. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN=28 407090
85. Choi Y, Giovannucci E, Lee JE. Glycaemic index and glycaemic load in relation to risk of diabetes-related cancers: a meta-analysis. Br J Nutr [Internet]. 2012;108(11):1934–47. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med8&NEWS=N&AN=231 67978
86. Jayedi A, Emadi A, Shab-Bidar S. Dietary Inflammatory Index and Site-Specific Cancer Risk: A Systematic Review and Dose-Response Meta-Analysis. Adv Nutr [Internet]. 2018;9(4):388–403. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medc&NEWS=N&AN=300 32224
87. Y. F, X. J, C. M, Z. G. Meta-analysis of the association between the inflammatory potential of diet and colorectal cancer risk. Oncotarget [Internet]. 2017;8(35):59592–600. Available from: http://www.impactjournals.com/oncotarget/index.php?journal=oncotarget&page=article&op=download&path%5B%5D=19233&path%5B%5D=61578
88. Chiavarini M, Bertarelli G, Minelli L, Fabiani R. Dietary Intake of Meat Cooking-Related Mutagens (HCAs) and Risk of Colorectal Adenoma and Cancer: A Systematic Review and Meta-Analysis. 2017 [cited 2019 Nov 11]; Available from: www.mdpi.com/journal/nutrients
89. Shivappa N, Godos J, Hebert JR, Wirth MD, Piuri G, Speciani AF, et al. Dietary Inflammatory Index and Colorectal Cancer Risk-A Meta-Analysis. Nutrients [Internet]. 2017;9(9). Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medc1&NEWS=N&AN=28 930191
90. Sardo Molmenti CL, Steck SE, Thomson CA, Hibler EA, Yang J, Shivappa N, et al. Dietary Inflammatory Index and Risk of Colorectal Adenoma Recurrence: A Pooled Analysis. Nutr Cancer. 2017 Feb 17;69(2):238–47.
91. Fan Y, Jin X, Man C, Gao Z, Wang X. Meta-analysis of the association between the inflammatory potential of diet and colorectal cancer risk [Internet]. Vol. 8. 2017 [cited 2019 Nov 11]. Available from: www.impactjournals.com/oncotarget
92. Berrino F. Life style prevention of cancer recurrence: the yin and the yang. Cancer Treat Res [Internet]. 2014;159:341–51. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN
93. Badger TM, Ronis MJJ, Simmen RCM, Simmen FA. Soy protein isolate and protection against cancer. J Am Coll Nutr [Internet]. 2005;24(2):146S–149S. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN=15798082
94. Zock PL, Katan MB. Linoleic acid intake and cancer risk: a review and meta-analysis. Am J Clin Nutr [Internet]. 1998;68(1):142–53. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med4&NEWS=N&AN=9665108
95. Xie L, Mo M, Jia H-X, Liang F, Yuan J, Zhu J. Association between dietary nitrate and nitrite intake and site-specific cancer risk: evidence from observational studies [Internet]. Vol. 7. 2016 [cited 2019 Nov 11]. Available from: www.impactjournals.com/oncotarget
96. Yang B, Wang F-L, Ren X-L, Li D. Biospecimen long-chain N-3 PUFA and risk of colorectal cancer: a meta-analysis of data from 60,627 individuals. PLoS One [Internet]. 2014;9(11):e110574. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=25375637
97. Kohler LN, Garcia DO, Harris RB, Oren E, Roe DJ, Jacobs ET. Adherence to Diet and Physical Activity Cancer Prevention Guidelines and Cancer Outcomes: A Systematic Review. Cancer Epidemiol Biomarkers Prev [Internet]. 2016;25(7):1018–28. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med12&NEWS=N&AN=27340121
98. Andersen V, Holst R, Vogel U. Systematic review: diet-gene interactions and the risk of colorectal cancer. Aliment Pharmacol Ther [Internet]. 2013;37(4):383–91. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=23216531
99. Schwingshackl L, Bogensberger B, Hoffmann G. Diet Quality as Assessed by the Healthy Eating Index, Alternate Healthy Eating Index, Dietary Approaches to Stop Hypertension Score, and Health Outcomes: An Updated Systematic Review and Meta-Analysis of Cohort Studies. J Acad Nutr Diet. 2018 Jan 1;118(1):74–100.e11.
100. Steck SE, Guinter M, Zheng J, Thomson CA. Index-Based Dietary Patterns and Colorectal Cancer Risk: A Systematic Review. Adv Nutr. 2015 Nov 1;6(6):763–73.
101. Zhang C, Wang W, Zhang D. Association between dietary inflammation index and the risk of colorectal cancer: A meta-analysis. Vol. 70, Nutrition and Cancer. Routledge; 2018. p. 14–22.
102. Namazi N, Larijani B, Azadbakht L. Association between the dietary inflammatory index and the incidence of cancer: a systematic review and meta-analysis of prospective studies. Public Health [Internet]. 2018;164:148–56. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medl&NEWS=N&AN=30321762
103. Castillo-Lancellotti C, Tur Mari JA, Uauy Dagach R. [Folic acid supplementation and colorectal adenoma recurrence: systematic review]. Supl con acido folico y Prev recurrencia adenomas Color Revis Sist [Internet]. 2012;27(1):13–21. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med8&NEWS=N&AN=22566300
104. Ryan-Harshman Walid Aldoori MB BCh MPA ScD MR. Vol 53: noVember • noVembre 2007 Canadian Family Physician • Le Médecin de famille canadien 1913 Diet and colorectal cancer Review of the evidence. Vol. 53, Can Fam Physician. 2007.
105. Azeem S, Wasif G, Siddiqui AA, Jandrapalli SB. 16.xx.XXXX Diet and Colorectal Cancer Risk in Asia: A Systematic Review Asian Pac. Asian Pacific J Cancer Prev [Internet]. 2015 [cited 2019 Nov 11];16(xx):XXXX–XXXX. Available from: http://dx.doi.org/10.7314/
106. Aranceta Bartrina J, Pérez Rodrigo C. [Association between sucrose intake and cancer: a review of the evidence]. Nutr Hosp [Internet]. 2013 Jul [cited 2019 Nov 11];28 Suppl 4:95–105. Available from: http://www.ncbi.nlm.nih.gov/pubmed/23834098
107. Schwingshackl L, Hoffmann G. Adherence to Mediterranean diet and risk of cancer: a systematic review and meta-analysis of observational studies. Int J cancer [Internet]. 2014;135(8):1884–97. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=24599882
108. Schwingshackl L, Hoffmann G. Adherence to Mediterranean diet and risk of cancer: an updated systematic review and meta-analysis of observational studies. Cancer Med [Internet]. 2015;4(12):1933–47. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=26471010
109. G.H. S. Meat consumption is a risk factor for colorectal cancer: Meta-analysis of case-control studies. Pakistan J Nutr [Internet]. 2006;5(3):230–3. Available from: http://pjbs.org/pjnonline/fin425.pdf
110. Norat T, Lukanova A, Ferrari P, Riboli E. Meat consumption and colorectal cancer risk: dose-response meta-analysis of epidemiological studies. Int J cancer [Internet]. 2002;98(2):241–56. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medc&NEWS=N&AN=11857415
111. Norat T, Lukanova A, Ferrari P, Riboli E. Meat consumption and colorectal cancer risk: an estimate of attributable and preventable fractions. IARC Sci Publ [Internet]. 2002;156:223–5. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med4&NEWS=N&AN=12484173
112. Sandhu MS, White IR, McPherson K. Systematic review of the prospective cohort studies on meat consumption and colorectal cancer risk: a meta-analytical approach. Cancer Epidemiol Biomarkers Prev [Internet]. 2001;10(5):439–46. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN=11352852
113. Geelen A, Schouten JM, Kamphuis C, Stam BE, Burema J, Renkema JMS, et al. Fish consumption, n-3 fatty acids, and colorectal cancer: a meta-analysis of prospective cohort studies. Am J Epidemiol [Internet]. 2007;166(10):1116–25. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med6&NEWS=N&AN=17823383
114. Haas P, Machado MJ, Anton AA, Silva ASS, de Francisco A. Effectiveness of whole grain consumption in the prevention of colorectal cancer: meta-analysis of cohort studies. Int J Food Sci Nutr [Internet]. 2009;60 Suppl 6:1–13. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=11932630
115. Koushik A, Hunter DJ, Spiegelman D, Beeson WL, van den Brandt PA, Buring JE, et al. Fruits, vegetables, and colon cancer risk in a pooled analysis of 14 cohort studies. J Natl Cancer Inst [Internet]. 2007;99(19):1471–83. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN=178 95473
116. Kashino I, Mizoue T, Tanaka K, Tsuji I, Tamakoshi A, Matsuo K, et al. Vegetable consumption and colorectal cancer risk: an evaluation based on a systematic review and meta-analysis among the Japanese population. Sasazuki S Inoue M, Iwasaki M, Otani T, Sawada N, Shimazu T, Yamaji T, Tsuji I, Tsubono Y, Nishino Y, Tamakoshi A, Matsuo K, Ito H, Wakai K, Nagata C, Mizoue T, Tanaka K TS, editor. Jpn J Clin Oncol [Internet]. 2015;45(10):973–9. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=26 450957
117. Tse G, Eslick GD. Cruciferous vegetables and risk of colorectal neoplasms: a systematic review and meta-analysis. Nutr Cancer [Internet]. 2014;66(1):128–39. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=24 341734
118. Hu J-Y, Hu Y-W, Zhou J-J, Zhang M-W, Li D, Zheng S. Consumption of garlic and risk of colorectal cancer: an updated meta-analysis of prospective studies. World J Gastroenterol [Internet]. 2014;20(41):15413–22. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=25 386091
119. Magalhaes B, Peleteiro B, Lunet N. Dietary patterns and colorectal cancer: systematic review and meta-analysis. Eur J Cancer Prev [Internet]. 2012;21(1):15–23. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med8&NEWS=N&AN=219 46864
120. Fleischauer AT, Poole C, Arab L. Garlic consumption and cancer prevention: meta-analyses of colorectal and stomach cancers. Am J Clin Nutr [Internet]. 2000;72(4):1047–52. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med4&NEWS=N&AN=110 10950
121. Wu L, Wang Z, Zhu J, Murad AL, Prokop LJ, Murad MH. Nut consumption and risk of cancer and type 2 diabetes: a systematic review and meta-analysis. Nutr Rev [Internet]. 2015;73(7):409–25. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=26 081452
122. Yu Y, Jing X, Li H, Zhao X, Wang D. Soy isoflavone consumption and colorectal cancer risk: a systematic review and meta-analysis. Sci Rep [Internet]. 2016;6:25939. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med12&NEWS=N&AN=27 170217
123. Yan L, Spitznagel EL, Bosland MC. Soy consumption and colorectal cancer risk in humans: a meta-analysis. Cancer Epidemiol Biomarkers Prev [Internet]. 2010;19(1):148–58. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=200 56634
124. Huncharek M, Muscat J, Kupelnick B. Colorectal cancer risk and dietary intake of calcium, vitamin D, and dairy products: a meta-analysis of 26,335 cases from 60 observational studies. Nutr Cancer [Internet]. 2009;61(1):47–69. Available from: http://ovidsp.ovid.com/ovidweb.cgi?qf=JS&PAGE=reference&D=med6&NEWS=N&AN=191 16875
125. Cho E, Smith-Warner SA, Spiegelman D, Beeson WL, van den Brandt PA, Colditz GA, et al. Dairy foods, calcium, and colorectal cancer: a pooled analysis of 10 cohort studies. J Natl Cancer Inst [Internet]. 2004;96(13):1015–22. Available from: http://ovidsp.ovid.com/ovidweb.cgi?qf=JS&PAGE=reference&D=medc2&NEWS=N&AN=15 240785
126. Zhang X, Albanes D, Beeson WL, van den Brandt PA, Buring JE, Flood A, et al. Risk of colon cancer and coffee, tea, and sugar-sweetened soft drink intake: pooled analysis of prospective cohort studies. J Natl Cancer Inst [Internet]. 2010;102(11):771–83. Available from: http://ovidsp.ovid.com/ovidweb.cgi?qf=JS&PAGE=reference&D=med7&NEWS=N&AN=204 53203
127. Yu F, Jin Z, Jiang H, Xiang C, Tang J, Li T, et al. Tea consumption and the risk of five major cancers: a dose-response meta-analysis of prospective studies. BMC Cancer [Internet]. 2014;14:197. Available from: http://ovidsp.ovid.com/ovidweb.cgi?qf=JS&PAGE=reference&D=med10&NEWS=N&AN=24 636229
128. Sartini M, Bragazzi NL, Spagnolo AM, Schinca E, Ottria G, Dupont C, et al. Coffee Consumption and Risk of Colorectal Cancer: A Systematic Review and Meta-Analysis of Prospective Studies. Nutrients [Internet]. 2019;11(3). Available from: http://ovidsp.ovid.com/ovidweb.cgi?qf=JS&PAGE=reference&D=medl&NEWS=N&AN=309 09640
129. Kashino I, Akter S, Mizoue T, Sawada N, Kotemori A, Matsuo K, et al. Coffee drinking and colorectal cancer and its subsites: A pooled analysis of 8 cohort studies in Japan. Int J cancer [Internet]. 2018;143(2):307–16. Available from: http://ovidsp.ovid.com/ovidweb.cgi?qf=JS&PAGE=reference&D=medl&NEWS=N&AN=294 46077
130. Gnagnarella P, Gandini S, La Vecchia C, Maisonneuve P. Glycemic index, glycemic load, and cancer risk: a meta-analysis. Am J Clin Nutr [Internet]. 2008;87(6):1793–801. Available from: http://ovidsp.ovid.com/ovidweb.cgi?qf=JS&PAGE=reference&D=med6&NEWS=N&AN=185 41570
131. Nakagawa-Senda H, Ito H, Hosono S, Oze I, Tanaka H, Matsuo K. Coffee consumption and the risk of colorectal cancer by anatomical subsite in Japan: Results from the HERPACC studies. Int J cancer [Internet]. 2017;141(2):298–308. Available from: http://ovidsp.ovid.com/ovidweb.cgi?qf=JS&PAGE=reference&D=med13&NEWS=N&AN=28 425092
132. Akter S, Kashino I, Mizoue T, Matsuo K, Ito H, Wakai K, et al. Coffee drinking and colorectal cancer risk: an evaluation based on a systematic review and meta-analysis among the Japanese population. Jpn J Clin Oncol [Internet]. 2016;46(8):781–7. Available from: http://ovidsp.ovid.com/ovidweb.cgi?qf=JS&PAGE=reference&D=med12&NEWS=N&AN=27 174958
133. Je Y, Liu W, Giovannucci E. Coffee consumption and risk of colorectal cancer: a systematic review and meta-analysis of prospective cohort studies. Int J cancer [Internet].
134. Choi Y-J, Myung S-K, Lee J-H. Light Alcohol Drinking and Risk of Cancer: A Meta-Analysis of Cohort Studies. Cancer Res Treat [Internet]. 2018;50(2):474–87. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN =28 546524
135. Jayasekara H, MacInnis RJ, Room R, English DR. Long-Term Alcohol Consumption and Breast, Upper Aero-Digestive Tract and Colorectal Cancer Risk: A Systematic Review and Meta-Analysis. Alcohol Alcohol [Internet]. 2016;51(3):315–30. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med12&NEWS=N&AN =26 400678
136. Y. W, H. D, H. Y. A pooled analysis of alcohol intake and colorectal cancer. Int J Clin Exp Med [Internet]. 2015;8(5):6878–89. Available from: http://www.ijcem.com/files/ijcem0006962.pdf
137. Cai S, Li Y, Ding Y, Chen K, Jin M. Alcohol drinking and the risk of colorectal cancer death: a meta-analysis. Eur J Cancer Prev [Internet]. 2014;23(6):532–9. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN =25 170915
138. Mizoue T, Inoue M, Wakai K, Nagata C, Shimazu T, Tsuji I, et al. Alcohol drinking and colorectal cancer in Japanese: a pooled analysis of results from five cohort studies. Tsugane S Sasazuki S, Iwasaki M, Otani T, Kurahashi N, Shimazu T, Tsuji I, Tsubono Y, Nishino Y, Wakai K, Matsuo K, Nagata C, Mizoue T, Tanaka K I M, editor. Am J Epidemiol [Internet]. 2008;167(12):1397–406. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med6&NEWS=N&AN =184 20544
139. Moskal A, Norat T, Ferrari P, Riboli E. Alcohol intake and colorectal cancer risk: a dose- response meta-analysis of published cohort studies. Int J Cancer [Internet]. 2007;120(3):664– 71. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN=17 0 96321
140. Cho E, Smith-Warner SA, Ritz J, van den Brandt PA, Colditz GA, Folsom AR, et al. Alcohol intake and colorectal cancer: a pooled analysis of 8 cohort studies. Ann Intern Med [Internet]. 2004;140(8):603–13. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medc&NEWS=N&AN =150 96331
141. Pham NM, Mizoue T, Tanaka K, Tsuji I, Tamakoshi A, Matsuo K, et al. Meat consumption and colorectal cancer risk: an evaluation based on a systematic review of epidemiologic evidence among the Japanese population. Sasazuki S Inoue M, Iwasaki M, Otani T, Sawada N, Shimazu T, Yamaji T, Tsuji I, Tsubono Y, Nishino Y, Tamakoshi A, Matsuo K, Ito H, Wakai K, Nagata C, Mizoue T, Tanaka K TS, editor. Jpn J Clin Oncol [Internet]. 2014;44(7):641–50. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN =24 842864
142. Longnecker MP, Orza MJ, Adams ME, Vioque J, Chalmers TC. A meta-analysis of alcoholic beverage consumption in relation to risk of colorectal cancer. Cancer Causes Control [Internet]. 1990;1(1):59–68. Available from:
143. Alexander DD, Cushing CA, Lowe KA, Sceurman B, Roberts MA. Meta-analysis of animal fat or animal protein intake and colorectal cancer. Am J Clin Nutr [Internet]. 2009;89(5):1402–9. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med6&NEWS=N&AN=19261724
144. Shen X-J, Zhou J-D, Dong J-Y, Ding W-Q, Wu J-C. Dietary intake of n-3 fatty acids and colorectal cancer risk: a meta-analysis of data from 489 000 individuals. Br J Nutr [Internet]. 2012;108(9):1550–6. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med8&NEWS=N&AN=22906228
145. Huang J, Pan G, Jiang H, Li W, Dong J, Zhang H, et al. A meta-analysis between dietary carbohydrate intake and colorectal cancer risk: evidence from 17 observational studies. Biosci Rep [Internet]. 2017;37(2). Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN=28298476
146. M. M. Dietary fibre protective against colorectal cancer patients in Asia: A meta-analysis. Open Access Maced J Med Sci [Internet]. 2019;7(10):1723–7. Available from: http://www.id-press.eu/mjms/article/download/2827/3427
147. Ma Y, Hu M, Zhou L, Ling S, Li Y, Kong B, et al. Dietary fiber intake and risks of proximal and distal colon cancers: A meta-analysis. Medicine (Baltimore) [Internet]. 2018;97(36):e11678. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN=30200062
148. Gianfredi V, Salvatori T, Villarini M, Moretti M, Nucci D, Realdon S. Is dietary fibre truly protective against colon cancer? A systematic review and meta-analysis. Int J Food Sci Nutr [Internet]. 2018;69(8):904–15. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=29516760
149. Park Y, Hunter DJ, Spiegelman D, Bergkvist L, Berrino F, van den Brandt PA, et al. Dietary fiber intake and risk of colorectal cancer: a pooled analysis of prospective cohort studies. JAMA [Internet]. 2005;294(22):2849–57. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN=16352792
150. Woo HD, Kim J. Dietary flavonoid intake and risk of stomach and colorectal cancer. World J Gastroenterol [Internet]. 2013;19(7):1011–9. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=23467443
151. L. L, Y. Y, H. H, E. C, L. D, J. D. Flavan-3-ols consumption and cancer risk: A meta-analysis of epidemiologic studies. Oncotarget [Internet]. 2016;7(45):73573–92. Available from: http://www.impactjournals.com/oncotarget/index.php?journal=oncotarget&page=article&op=d ownload&path%5B%5D=12017&path%5B%5D=39641
152. Johnson CM, Wei C, Ensom JE, Smolenski DJ, Amos CI, Levin B, et al. Meta-analyses of colorectal cancer risk factors. Cancer Causes Control [Internet]. 2013;24(6):1207–22. Available from:
153. Keum N, Kim H, Giovannucci EL. Calcium as a chemopreventive agent against colorectal neoplasm: does obesity play a role?. Cancer Causes Control [Internet]. 2017;28(8):853–6. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=23563998
154. Bastide NM, Pierre FHF, Corpet DE. Heme iron from meat and risk of colorectal cancer: a meta-analysis and a review of the mechanisms involved. Cancer Prev Res (Phila) [Internet]. 2011;4(2):177–84. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=21209396
155. Ko HJ, Youn CH, Kim HM, Cho YJ, Lee GH, Lee WK. Dietary magnesium intake and risk of cancer: a meta-analysis of epidemiologic studies. Nutr Cancer [Internet]. 2014;66(6):915–23. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=24910891
156. Qu X, Jin F, Hao Y, Zhu Z, Li H, Tang T, et al. Nonlinear association between magnesium intake and the risk of colorectal cancer. Eur J Gastroenterol Hepatol [Internet]. 2013;25(3):309–18. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=23222473
157. Wark PA, Lau R, Norat T, Kampman E. Magnesium intake and colorectal tumor risk: a case-control study and meta-analysis. Am J Clin Nutr [Internet]. 2012;96(3):622–31. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med8&NEWS=N&AN=22854408
158. Mannisto S, Yaun S-S, Hunter DJ, Spiegelman D, Adami H-O, Albanes D, et al. Dietary carotenoids and risk of colorectal cancer in a pooled analysis of 11 cohort studies. Am J Epidemiol [Internet]. 2007;165(3):246–55. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN=17158857
159. Druesne-Pecollo N, Latino-Martel P, Norat T, Barrandon E, Bertrais S, Galan P, et al. Beta-carotene supplementation and cancer risk: a systematic review and meta-analysis of randomized controlled trials. Int J cancer [Internet]. 2010;127(1):172–84. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=19876916
160. Sanjoaquin MA, Allen N, Couto E, Roddam AW, Key TJ. Folate intake and colorectal cancer risk: a meta-analytical approach. Int J cancer [Internet]. 2005;113(5):825–8. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN=15499620
161. Burr NE, Hull MA, Subramanian V. Folic Acid Supplementation May Reduce Colorectal Cancer Risk in Patients With Inflammatory Bowel Disease: A Systematic Review and Meta-Analysis. J Clin Gastroenterol [Internet]. 2017;51(3):247–53. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN=26905603
162. Larsson SC, Orsini N, Wolk A. Vitamin B6 and risk of colorectal cancer: a meta-analysis
163. Jia K, Wang R, Tian J. Vitamin B6 Intake and the Risk of Colorectal Cancer: A Meta-Analysis of Prospective Cohort Studies. Nutr Cancer [Internet]. 2017;69(5):723–31. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN=204 95462
164. Alexander DD, Miller AJ, Cushing CA, Lowe KA. Processed meat and colorectal cancer: a quantitative review of prospective epidemiologic studies. Eur J Cancer Prev [Internet]. 2010;19(5):328–41. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=208 20901
165. Park Y, Spiegelman D, Hunter DJ, Albanes D, Bergkvist L, Buring JE, et al. Intakes of vitamins A, C, and E and use of multiple vitamin supplements and risk of colon cancer: a pooled analysis of prospective cohort studies. Cancer Causes Control [Internet]. 2010;21(11):1745–57. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=218 76081
166. Li Y, Yang H, Cao J. Association between alcohol consumption and cancers in the Chinese population--a systematic review and meta-analysis. PLoS One [Internet]. 2011;6(4):e18776. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=215 26212
167. Ma Y, Zhang P, Wang F, Yang J, Liu Z, Qin H. Association between vitamin D and risk of colorectal cancer: a systematic review of prospective studies. J Clin Oncol [Internet]. 2011;29(28):3775–82. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=218 76081
168. Alexander DD, Weed DL, Miller PE, Mohamed MA. Red Meat and Colorectal Cancer: A Quantitative Update on the State of the Epidemiologic Science. J Am Coll Nutr [Internet]. 2015;34(6):521–43. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=25 941850
169. Wang X, Yang HH, Liu Y, Zhou Q, Chen ZH. Lycopene Consumption and Risk of Colorectal Cancer: A Meta-Analysis of Observational Studies. Nutr Cancer. 2016 Oct 2;68(7):1083–96.
170. Kim D-H, Smith-Warner SA, Spiegelman D, Yaun S-S, Colditz GA, Freudenheim JL, et al. Cancer Causes Control. 2010;21(11):1919–30.
171. Tse G, Eslick GD. Soy and isoflavone consumption and risk of gastrointestinal cancer: a systematic review and meta-analysis. Eur J Nutr [Internet]. 2016;55(1):63–73. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med12&NEWS=N&AN=25 547973
172. Barrubés L, Babio N, Becerra-Tomás N, Rosique-Esteban N, Salas-Salvadó J. Association Between Dairy Product Consumption and Colorectal Cancer Risk in Adults: A Systematic Review and Meta-Analysis of Epidemiologic Studies. Adv Nutr [Internet]. 2019 May 1 [cited 2019 Nov 12];10(suppl_2):S190–211. Available from:
173. Chan DSM, Lau R, Aune D, Vieira R, Greenwood DC, Kampman E, et al. Red and processed meat and colorectal cancer incidence: meta-analysis of prospective studies. PLoS One [Internet]. 2011;6(6):e20456. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN =216 74008
174. K. S. Risk of colorectal cancer in relation to frequency and total amount of red meat consumption. Systematic review and meta-analysis. Arch Med Sci [Internet]. 2010;6(4):605–10. Available from: http://www.termedia.pl/Journal/-19/pdf-15186-10?filename=Riskofcolorect.pdf
175. Larsson SC, Wolk A. Meat consumption and risk of colorectal cancer: a meta-analysis of prospective studies. Int J cancer [Internet]. 2006;119(11):2657–64. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN =169 91129
176. Touvier M, Chan DSM, Lau R, Aune D, Vieira R, Greenwood DC, et al. Meta-analyses of vitamin D intake, 25-hydroxyvitamin D status, vitamin D receptor polymorphisms, and colorectal cancer risk. Cancer Epidemiol Biomarkers Prev [Internet]. 2011;20(5):1003–16. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN =213 78269
177. Yu XF, Wang YQ, Zou J, Dong J. A meta-analysis of the effects of energy intake on risk of digestive cancers. World J Gastroenterol. 2012;18(48):7362–70.
178. Schwingshackl L, Schwedhelm C, Galbete C, Hoffmann G. Adherence to Mediterranean Diet and Risk of Cancer: An Updated Systematic Review and Meta-Analysis. Nutrients [Internet]. 2017;9(10). Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN =28 954418
179. Feng Y-L, Shu L, Zheng P-F, Zhang X-Y, Si C-J, Yu X-L, et al. Dietary patterns and colorectal cancer risk: a meta-analysis. Eur J Cancer Prev [Internet]. 2017;26(3):201–11. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medc1&NEWS=N&AN =26 945285
180. Grosso G, Bella F, Godos J, Sciaccia S, Del Rio D, Ray S, et al. Possible role of diet in cancer: systematic review and multiple meta-analyses of dietary patterns, lifestyle factors, and cancer risk. Nutr Rev [Internet]. 2017;75(6):405–19. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN =28 969358
181. Godos J, Bella F, Sciaccia S, Galvano F, Grosso G. Vegetarianism and breast, colorectal and prostate cancer risk: an overview and meta-analysis of cohort studies. J Hum Nutr Diet [Internet]. 2017;30(3):349–59. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medc1&NEWS=N&AN =27 709695
182. Reynolds A, Mann J, Cummings J, Winter N, Mete E, Te Morenga L. Carbohydrate quality and human health: a series of systematic reviews and meta-analyses. Lancet (London, England) [Internet]. 2019;393(10170):434–45. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medc&NEWS=N&AN =306 38909
© 2021 Veettil SK et al. JAMA Network Open.
183. Liu Y, Tang W, Zhai L, Yang S, Wu J, Xie L, et al. Meta-analysis: eating frequency and risk of colorectal cancer. Tumour Biol [Internet]. 2014;35(4):3617–25. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=24 307626
184. Schwingshackl L, Schwedhelm C, Hoffmann G, Knuppel S, Laure Preterre A, Iqbal K, et al. Food groups and risk of colorectal cancer. Int J cancer [Internet]. 2018;142(9):1748–58. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=292 10053
185. Carr PR, Walter V, Brenner H, Hoffmeister M. Meat subtypes and their association with colorectal cancer: Systematic review and meta-analysis. Vol. 138, International Journal of Cancer. Wiley-Liss Inc.; 2016. p. 293–302.
186. Wu S, Feng B, Li K, Zhu X, Liang S, Liu X, et al. Fish consumption and colorectal cancer risk in humans: a systematic review and meta-analysis. Am J Med [Internet]. 2012;125(6):551–9.e5. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med12&NEWS=N&AN=225 13196
187. Aune D, Lau R, Chan DSM, Vieira R, Greenwood DC, Kampman E, et al. Nonlinear reduction in risk for colorectal cancer by fruit and vegetable intake based on meta-analysis of prospective studies. Gastroenterology [Internet]. 2011;141(1):106–18. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=216 00207
188. Wu QJ, Yang Y, Vogtmann E, Wang J, Han LH, Li HL, et al. Cruciferous vegetables intake and the risk of colorectal cancer: a meta-analysis of observational studies. Ann Oncol Off J Eur Soc Med Oncol [Internet]. 2013;24(4):1079–87. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=232 11939
189. Zhu B, Zou L, Qi L, Zhong R, Miao X. Allium vegetables and garlic supplements do not reduce risk of colorectal cancer, based on meta-analysis of prospective studies. Clin Gastroenterol Hepatol [Internet]. 2014;12(12):1991-e121. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=24 681077
190. Chiavarini M, Minelli L, Fabiani R. Garlic consumption and colorectal cancer risk in man: a systematic review and meta-analysis. Public Health Nutr [Internet]. 2016;19(2):308–17. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=25 945653
191. Turati F, Guercio V, Pelucchi C, La Vecchia C, Galeone C. Colorectal cancer and adenomatous polyps in relation to allium vegetables intake: a meta-analysis of observational studies. Mol Nutr Food Res [Internet]. 2014;58(9):1907–14. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med10&NEWS=N&AN=24 976533
192. Zhu B, Sun Y, Qi L, Zhong R, Miao X. Dietary legume consumption reduces risk of colorectal cancer: evidence from a meta-analysis of cohort studies. Sci Rep [Internet]. 2015;5:8797. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=25 739376
193. Lu D, Pan C, Ye C, Duan H, Xu F, Yin L, et al. Meta-analysis of Soy Consumption and Gastrointestinal Cancer Risk. Sci Rep [Internet]. 2017;7(1):4048. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medl&NEWS=N&AN=286 42459
194. Aune D, Lau R, Chan DSM, Vieira R, Greenwood DC, Kampman E, et al. Dairy products and colorectal cancer risk: a systematic review and meta-analysis of cohort studies. Ann Oncol Off J Eur Soc Med Oncol [Internet]. 2012;23(1):37–45. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med8&NEWS=N&AN=21 6 17020
195. Zhang K, Dai H, Liang W, Zhang L, Deng Z. Fermented dairy foods intake and risk of cancer. Int J cancer [Internet]. 2019;144(9):2099–108. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medl&NEWS=N&AN=303 74967
196. Chen Y, Wu Y, Du M, Chu H, Zhu L, Tong N, et al. An inverse association between tea consumption and colorectal cancer risk. Oncotarget [Internet]. 2017;8(23):37367–76. Available from: http://www.impactjournals.com/oncotarget/index.php?journal=oncotarget&page=article&op=download&path%5B%5D=16959&path%5B%5D=54265
197. Wang Z-H, Gao Q-Y, Fang J-Y. Green tea and incidence of colorectal cancer: evidence from prospective cohort studies. Nutr Cancer [Internet]. 2012;64(8):1143–52. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med8&NEWS=N&AN=231 63842
198. Sun C-L, Yuan J-M, Koh W-P, Yu MC. Green tea, black tea and colorectal cancer risk: a meta-analysis of epidemiologic studies. Carcinogenesis [Internet]. 2006;27(7):1301–9. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med5&NEWS=N&AN=166 38787
199. Y. G, J. W, S. Z, L. L, S. C, N. M, et al. Association of coffee consumption with risk of colorectal cancer: A meta-analysis of prospective cohort studies. Oncotarget [Internet]. 2017;8(12):18699–711. Available from: http://www.impactjournals.com/oncotarget/index.php?journal=oncotarget&page=article&op=download&path%5B%5D=8627&path%5B%5D=25797
200. Ralston RA, Truby H, Palermo CE, Walker KZ. Colorectal cancer and nonfermented milk, solid cheese, and fermented milk consumption: a systematic review and meta-analysis of prospective studies. Crit Rev Food Sci Nutr [Internet]. 2014;54(9):1167–79. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medc1&NEWS=N&AN=24 499149
201. Fedirko V, Tramacere I, Bagnardi V, Rota M, Scotti L, Islami F, et al. Alcohol drinking and colorectal cancer risk: an overall and dose-response meta-analysis of published studies. Ann Oncol Off J Eur Soc Med Oncol [Internet]. 2011;22(9):1958–72. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=213 07158
202. Zhang C, Zhong M. Consumption of beer and colorectal cancer incidence: a meta-analysis of observational studies. Cancer Causes Control [Internet]. 2015;26(4):549–60. Available from:
203. Xu W, Fan H, Han Z, Liu Y, Wang Y, Ge Z. Wine consumption and colorectal cancer risk: a meta-analysis of observational studies. Eur J Cancer Prev [Internet]. 2019;28(3):151–8. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=25 677844
204. Liu L, Zhuang W, Wang R-Q, Mukherjee R, Xiao S-M, Chen Z, et al. Is dietary fat associated with the risk of colorectal cancer? A meta-analysis of 13 prospective cohort studies. Eur J Nutr [Internet]. 2011;50(3):173–84. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=206 97723
205. Kim M, Park K. Dietary Fat Intake and Risk of Colorectal Cancer: A Systematic Review and Meta-Analysis of Prospective Studies. Nutrients [Internet]. 2018;10(12). Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN=305 45042
206. Chen G-C, Qin L-Q, Lu D-B, Han T-M, Zheng Y, Xu G-Z, et al. N-3 polyunsaturated fatty acids intake and risk of colorectal cancer: meta-analysis of prospective studies. Cancer Causes Control [Internet]. 2015;26(1):133–41. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=25 416450
207. Aune D, Chan DSM, Lau R, Vieira R, Greenwood DC, Kampman E, et al. Carbohydrates, glycemic index, glycemic load, and colorectal cancer risk: a systematic review and meta-analysis of cohort studies. Cancer Causes Control [Internet]. 2012;23(4):521–35. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med8&NEWS=N&AN=224 18776
208. Lai R, Bian Z, Lin H, Ren J, Zhou H, Guo H. The association between dietary protein intake and colorectal cancer risk: a meta-analysis. World J Surg Oncol [Internet]. 2017;15(1):169. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN=28 886717
209. Aune D, Chan DSM, Lau R, Vieira R, Greenwood DC, Kampman E, et al. Dietary fibre, whole grains, and risk of colorectal cancer: systematic review and dose-response meta-analysis of prospective studies. BMJ [Internet]. 2011;343:d6617. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med7&NEWS=N&AN=220 74852
210. Bo Y, Sun J, Wang M, Ding J, Lu Q, Yuan L. Dietary flavonoid intake and the risk of digestive tract cancers: a systematic review and meta-analysis. Sci Rep [Internet]. 2016;6:24836. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med12&NEWS=N&AN=27 112267
211. Chang H, Lei L, Zhou Y, Ye F, Zhao G. Dietary Flavonoids and the Risk of Colorectal Cancer: An Updated Meta-Analysis of Epidemiological Studies. Nutrients [Internet]. 2018;10(7). Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN=30 041489
© 2021 Veettil SK et al. JAMA Network Open.
212. Grosso G, Godos J, Lamuela-Raventos R, Ray S, Micek A, Pajak A, et al. A comprehensive meta-analysis on dietary flavonoid and lignan intake and cancer risk: Level of evidence and limitations. Mol Nutr Food Res [Internet]. 2017;61(4). Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN=27943649
213. He X, Sun L-M, X. H, He X, Sun L-M, X. H. Dietary intake of flavonoid subclasses and risk of colorectal cancer: Evidence from population studies. Oncotarget [Internet]. 2016;7(18):26617–27. Available from: http://www.impactjournals.com/oncotarget/index.php?journal=oncotarget&page=article&op=donload&path%5B%5D=8562&path%5B%5D=25493
214. Jiang R, Botma A, Rudolph A, Husing A, Chang-Claude J. Phyto-oestrogens and colorectal cancer risk: a systematic review and dose-response meta-analysis of observational studies. Br J Nutr [Internet]. 2016;116(12):2115–28. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med12&NEWS=N&AN=28091359
215. Panic N, Nedovic D, Pastorino R, Boccia S, Leoncini E. Carotenoid intake from natural sources and colorectal cancer: a systematic review and meta-analysis of epidemiological studies. Eur J Cancer Prev [Internet]. 2017;26(1):27–37. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med13&NEWS=N&AN=26960163
216. Heine-Broring RC, Winkels RM, Renkema JMS, Kragt L, van Orten-Luiten A-CB, Tighchelaar EF, et al. Dietary supplement use and colorectal cancer risk: a systematic review and meta-analyses of prospective cohort studies. Int J Cancer [Internet]. 2015;136(10):2388–401. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=25335850
217. Liu Y, Yu Q, Zhu Z, Zhang J, Chen M, Tang P, et al. Vitamin and multiple-vitamin supplement intake and incidence of colorectal cancer: a meta-analysis of cohort studies. Med Oncol [Internet]. 2015;32(1):434. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med11&NEWS=N&AN=25491145
218. Meng Y, Sun J, Yu J, Wang C, Su J. Dietary Intakes of Calcium, Iron, Magnesium, and Potassium Elements and the Risk of Colorectal Cancer: a Meta-Analysis. Biol Trace Elem Res [Internet]. 2019;189(2):325–35. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=medl&NEWS=N&AN=30171595
219. Qiao L, Feng Y. Intakes of heme iron and zinc and colorectal cancer incidence: a meta-analysis of prospective studies. Cancer Causes Control [Internet]. 2013;24(6):1175–83. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=23568532
220. Chen G-C, Pang Z, Liu Q-F. Magnesium intake and risk of colorectal cancer: a meta-analysis of prospective studies. Eur J Clin Nutr [Internet]. 2012;66(11):1182–6. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med8&NEWS=N&AN=23031849
221. Li P, Xu J, Shi Y, Ye Y, Chen K, Yang J, et al. Association between zinc intake and risk of digestive tract cancers: a systematic review and meta-analysis. Clin Nutr [Internet].
222. Zhou Z-Y, Wan X-Y, Cao J-W. Dietary methionine intake and risk of incident colorectal cancer: a meta-analysis of 8 prospective studies involving 431,029 participants. PLoS One [Internet]. 2013;8(12):e83588. Available from: http://ovidsp.ovid.com/ovidweb.cgi?T=JS&PAGE=reference&D=med9&NEWS=N&AN=24340103
223. Aicr, WCRF. Diet, nutrition, physical activity and colorectal cancer.
224. Kato I, Akhmedkanov A, Koenig K, Toniolo PG, Shore RE, Riboli E. Prospective study of diet and female colorectal cancer: The New York University Women’s Health Study. Nutr Cancer [Internet]. 1997 [cited 2020 Jul 21];28(3):276–81. Available from: https://www.tandfonline.com/doi/abs/10.1080/01635589709514588
225. Pietinen P, Malila N, Virtanen M, Hartman TJ, Tangrea JA, Albanes D, et al. Diet and risk of colorectal cancer in a cohort of Finnish men. Cancer Causes Control [Internet]. 1999 [cited 2020 Jul 21];10(5):387–96. Available from: https://link.springer.com/article/10.1023/A:1008962219408
226. Järvinen R, Knekt P, Hakulinen T, Rissanen H, Heliövaara M. Dietary fat, cholesterol and colorectal cancer in a prospective study. Br J Cancer [Internet]. 2001 Aug 3 [cited 2020 Jul 21];85(3):357–61. Available from: http://www.bjcancer.com
227. Wie GA, Cho YA, Kang HH, Ryu KA, Yoo MK, Kim YA, et al. Red meat consumption is associated with an increased overall cancer risk: A prospective cohort study in Korea. Br J Nutr [Internet]. 2014 Jul 28 [cited 2020 Jul 21];112(2):238–47. Available from: https://doi.org/10.1017/S0007114514000683
228. Chen J, Stampfer MJ, Hough HL, Garcia-Closas M, Willett WC, Hennekens CH, et al. A Prospective Study of N-Acetyltransferase Genotype, Red Meat Intake, and Risk of Colorectal Cancer. Cancer Res. 1998;58(15). | 2025-03-06T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
860,
1
],
[
860,
3770,
2
],
[
3770,
8614,
3
],
[
8614,
12852,
4
],
[
12852,
13541,
5
],
[
13541,
14893,
6
],
[
14893,
18057,
7
],
[
18057,
22452,
8
],
[
22452,
23730,
9
],
[
23730,
27465,
10
],
[
27465,
32316,
11
],
[
32316,
35780,
12
],
[
35780,
38922,
13
],
[
38922,
42115,
14
],
[
42115,
47021,
15
],
[
47021,
51711,
16
],
[
51711,
55623,
17
],
[
55623,
60055,
18
],
[
60055,
63705,
19
],
[
63705,
67170,
20
],
[
67170,
68807,
21
],
[
68807,
71208,
22
],
[
71208,
73057,
23
],
[
73057,
75637,
24
],
[
75637,
77804,
25
],
[
77804,
80731,
26
],
[
80731,
82901,
27
],
[
82901,
84255,
28
],
[
84255,
86531,
29
],
[
86531,
88801,
30
],
[
88801,
91188,
31
],
[
91188,
93073,
32
],
[
93073,
95456,
33
],
[
95456,
95858,
34
],
[
95858,
96801,
35
],
[
96801,
99756,
36
],
[
99756,
102703,
37
],
[
102703,
105497,
38
],
[
105497,
108467,
39
],
[
108467,
111793,
40
],
[
111793,
114728,
41
],
[
114728,
117585,
42
],
[
117585,
120367,
43
],
[
120367,
123273,
44
],
[
123273,
126236,
45
],
[
126236,
129350,
46
],
[
129350,
132171,
47
],
[
132171,
135274,
48
],
[
135274,
138189,
49
],
[
138189,
141005,
50
],
[
141005,
143792,
51
],
[
143792,
146520,
52
],
[
146520,
149481,
53
],
[
149481,
152466,
54
],
[
152466,
155400,
55
],
[
155400,
158192,
56
],
[
158192,
161247,
57
],
[
161247,
162996,
58
]
]
} |
10a47f3762fb76814b897437247a2ea954cd12ac | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 13,
"total-fallback-pages": 0,
"total-input-tokens": 37032,
"total-output-tokens": 11400,
"fieldofstudy": [
"Medicine"
]
} | Validation of an Arabic Version of the Adherence to Refills and Medications Scale (ARMS)
Ghaida Alammari 1,†, Hawazin Alhazzani 1, Nouf AlRajhi 1, Ibrahim Sales 1,‡, Amr Jamal 2,‡, Turky H. Almigbal 2, Mohammed A. Batais 2, Yousif A. Asiri 1, and Yazed AlRuthia 1,3,*,†
Citation: Alammari, G.; Alhazzani, H.; AlRajhi, N.; Sales, I.; Jamal, A.; Almigbal, T.H.; Batais, M.A.; Asiri, Y.A.; AlRuthia, Y. Validation of an Arabic Version of the Adherence to Refills and Medications Scale (ARMS). Healthcare 2021, 9, 1430. https://doi.org/10.3390/healthcare9111430
Abstract: Background: Medication non-adherence is a complex multifactorial phenomenon impacting patients with various health conditions worldwide. Therefore, its detection can improve patient outcomes and minimize the risk of adverse consequences. Even though multiple self-reported medication adherence assessment scales are available, very few of them exist in Arabic language. Therefore, the aim of this study was to validate a newly translated Arabic version of the Adherence to Refills and Medications Scale (ARMS) among patients with chronic health conditions. Methods: This is a single-center cross-sectional study that was conducted between October 10th 2018 and March 23rd 2021. ARMS was first translated to Arabic using the forward-backward translation method. The translated scale was then piloted among 21 patients with chronic health conditions (e.g., diabetes, hypertension, etc.) to examine its reliability and comprehensibility using the test-retest method. Thereafter, the Arabic-translated ARMS was self-administered to adult patients aged ≥18 years with chronic health conditions visiting the primary care clinics of a university-affiliated tertiary care hospital in Riyadh, Saudi Arabia. Construct validity was examined using factor analysis with varimax rotation. Results: Of the 264 patients who were invited to participate, 202 (76.5%) consented and completed the questionnaire. Most of the participants were males (69.9%), married (75.2%), having a college degree or higher (50.9%), retired or unemployed (65.2%), aged ≥50 years (65.2%), and are diabetic (95.9%). The 12-item Arabic-translated ARMS mean score was 17.93 ± 4.90, and the scale yielded good internal consistency (Cronbach’s alpha = 0.802) and test-retest reliability (Intraclass correlation coefficient = 0.97). Two factors were extracted explaining 100% of the total variance (factor 1 = 52.94% and factor 2 = 47.06%). Conclusions: The 12-item Arabic version of ARMS demonstrated good validity and reliability. Therefore, it should help in the detection of medication non-adherence among Arabic-speaking patient population and minimize the risk of adverse consequences.
Keywords: medication non-adherence; self-reports; validation studies; surveys and questionnaires; 12-item ARMS
1. Introduction
Medication non-adherence is a globally recognized multifactorial phenomenon impacting patients with various health conditions [1]. The World Health Organization (WHO) defines medication adherence as “the extent to which a person’s behavior—taking medication, following a diet and/or executing lifestyle changes, corresponds with agreed
recommendations from a health care provider.” [1]. Its prevalence among patients with chronic health conditions in the developed countries was estimated to be as high as 50%, and is believed to be higher in the developing countries [1,2]. In the United States, approximately half of patients with chronic illnesses are not believed to take their medications as prescribed resulting in over 100 billion United States dollars (USD) of avoidable healthcare costs [3,4]. Moreover, higher rates of hospital admissions and emergency department visits, disease progression, and poor clinical outcomes are believed to be direct consequences of poor medication adherence [3,5,6].
Even though multiple studies examined medication adherence among different patient populations worldwide, very few studies explored medication adherence levels among patients in the Middle East [7–10]. In Saudi Arabia, it was reported that up to 65% of patients with diabetes visiting primary care clinics in Al Hasa province are not adherent to their prescription medications [10]. Another questionnaire-based, cross-sectional, single-center study has estimated that 41.7% and 33% of patients with cardiovascular disease had medium and low levels of adherence to their prescription medications, respectively [9].
Multiple barriers to medication adherence have been identified in the literature [1]. Those barriers can be social (e.g., stigma associated mental illnesses) [11,12], economic factors (e.g., high copayments) [13], older age and polypharmacy [14], and poor health literacy [14]. Therefore, identifying reliable and efficient tools to assess medication adherence especially among patients with chronic health conditions became an area of research with great importance [15]. However, no gold standard medication adherence measure that can be relied upon exists so far due to the complexity of this phenomenon [16]. There are direct (e.g., face-to-face observation, and assessment of biological markers) and indirect (e.g., pill counts, and self-report questionnaires) medication adherence assessment methods with variable degrees of reliability and efficiency [16–19]. The direct medication adherence assessment tools are accurate to a great extent, however, they are somewhat invasive and impractical to use on a regular basis [19]. On the other hand, self-report questionnaires are non-invasive, less expensive, and easy to administer, albeit they are not as accurate as the direct assessment measures [20].
The studies that assessed medication adherence among Arabic-speaking patients have either used descriptive self-report questionnaires that have not been validated before or used the Arabic version of the 8-item Morisky Medication Adherence Scale (MMAS-8) which requires permission from the scale developer and administration fees [9,21]. Even though several other self-report medication adherence scales have been validated in different languages, such as Medication Adherence Questionnaire (MAQ), Brief Medication Questionnaire (BMQ), and Self-efficacy for Appropriate Medication Use Scale (SEAMS) [22–25], these scales have not been validated in Arabic.
The Adherence to Refills and Medications Scale (ARMS) is a 12-item widely used medication adherence assessment tool with proven reliability and validity among English-speaking patient population [26]. The scale was translated and validated in Turkish [27], Korean [28], Chinese [29] and Polish languages [30], among patients with chronic health conditions, such as diabetes and hypertension. However, this scale has not been validated among Arabic-speaking patients. Therefore, the aim of this study was to translate and validate ARMS into Arabic among Arabic-speaking patients with chronic health conditions.
2. Methods
2.1. Study Design
This was a single-center cross-sectional study that was conducted between October 10th 2018 and March 23rd 2021 at the primary care clinics of King Khalid University Hospital (KKUH) in Riyadh, Saudi Arabia. KKUH is a university-affiliated hospital providing primary and tertiary care to family members and relatives of King Saud University employees as well as citizens referred by the ministry of health.
2.2. Inclusion and Exclusion Criteria
The study included Arabic speaking adult patients aged \( \geq 18 \) years with chronic health conditions (e.g., diabetes, hypertension, dyslipidemia, etc.) who regularly visit the primary care clinics at KKUH every six months, and have active electronic medical records (e.g., they are still eligible to receive care from the hospital). Patients without active electronic medical records, those whose native language is not Arabic, patients who do not fill their medications at KKUH pharmacy, and those with cognitive disabilities, such as dementia and Alzheimer’s diseases, were excluded.
2.3. Population and Data Source
Two-hundred and sixty-four patients who met the inclusion criteria were identified by reviewing their electronic medical records and ensuring that they meet the inclusion criteria. Patients’ health conditions are documented in text under the physicians’ notes. Those patients were selected systematically by selecting every 10th patient from the electronic lists of patients scheduled for regular follow-up appointments with their primary care physicians between October 2018 and March 2021 in E-Sihi database, which is the electronic health system at KKUH. The patients were recruited by three pharmacy interns who were trained to recruit patients by following a standardized protocol specifying every step on how to approach patients, explaining the purpose of the study, and inviting them to participate by asking for their consent prior to inclusion in the study.
2.4. Research Instrument Translation and Validation
ARMS is a 12-item self-reported medication adherence scale that was developed in English language, and consists of two subscales (adherence with filling medications and adherence with taking medications). The original scale consisted of 14 items, however, it was shortened based on the psychometric analysis conducted by the scale developers to ensure high internal consistency and reliability [26]. Adherence with filling medications subscale consists of four items, and the remaining eight items comprise the other subscale (adherence with taking medications). Each item is scored using a 4-point Likert-scale (1 = none, 2 = some, 3 = most and 4 = All). The ARMS can range from 12 to 48 with higher scores indicating poor adherence [26]. This scale has been validated among different patient populations with various chronic health conditions, such as diabetes and hypertension, and was translated to different languages [28–30]. Moreover, a score of \( \geq 16 \) was used as a cut-off point to categorize surveyed patients into non-adherent (e.g., \( \geq 16 \)) and adherent (e.g., <16) [30].
In order to translate and validate the 12-item ARMS into Arabic, the permission to independently translate and validate the ARMS was obtained from the developers. Forward-backward translation method was used to translate the ARMS into Arabic. Two authors whose native language is Arabic and are proficient in English language translated ARMS into Arabic. The first draft of the translated ARMS was then reviewed for its face and content validity before being checked by a certified English language translator. Backward translation was then conducted by a native English speaker who is proficient in Arabic language, and no major issues were noticed. The pre-final version of the Arabic-ARMS was then piloted among a group of 21 patients with chronic health conditions (e.g., diabetes, hypertension, and dyslipidemia) to check its comprehensibility. The same questionnaire, which takes 10 to 15 min to complete, was re-introduced to the same group of patients two weeks later to examine its reliability using the test-retest method. No major changes were made and the final Arabic-ARMS was administered to patients who fit the inclusion criteria (Appendix A).
2.5. Study Variables
Sociodemographic characteristics (e.g., age, gender, monthly income, marital status, employment status, educational level, and whether the patient is enrolled in a private health insurance) were abstracted in the questionnaire. Moreover, health literacy was
assessed using the single item literacy screener (SILS) developed by Morris et al. [31], and was translated and validated into Arabic by Al-Jumaili et al. [32]. The SILS enquires about the need of the surveyee for someone’s help to read and understand medical or medication-related instructions with five possible responses on a Likert scale (1-never, 2-rarely, 3-sometimes, 4-often, 5-always). Those who responded with “sometimes”, “often”, and “always” are believed to have marginal or limited health literacy, and those who responded with “never” or “rarely” are believed to have adequate health literacy [31,32]. On the other hand, the medical characteristics of the participants (e.g., chronic health conditions and number of prescription medications) were also collected from the patients’ electronic health records.
2.6. Sample Size Estimation
Even though a sample of 100 participants is deemed sufficient to conduct most self-reported scales validation [33], the minimum sample size was estimated to be 192 subjects using GPower® software version 3.1 for a medium effect size (e.g., Cohen’s d = 0.3), \( \alpha = 0.05 \), \( \beta = 0.2 \), a power of 85%. Therefore, a response rate of 72.73% out of the systematically created list of 264 patients who met the inclusion criteria needs to be attained. This sample size also ensures the minimum sample needed for principal component analysis using the item to response theory [34].
2.7. Statistical Analysis
Descriptive statistics using frequencies and percentages, and mean ± standard deviation (SD) are shown for the participants’ characteristics and the scores of the 12-item Arabic-ARMS, respectively. In order to examine the Arabic-ARMS construct validity, principal component analysis with varimax rotation was conducted. Factors with eigenvalues greater than one were extracted [35]. Basic confirmatory factor analysis was conducted alongside the root mean square error of approximation (RMSEA) and Bentler comparative fit index (CFI) to examine the goodness of fit. Models with good fit have RMSEA \( \leq 0.06 \) and CFI \( \geq 0.9 \) [36]. Kaiser-Meyer-Olkin (KMO) measure was used to ensure sampling adequacy to conduct factor analysis with values above 0.5 considered satisfactory [37]. The reliability was examined using Intraclass Correlation Coefficient (ICC) for the test-retest method, and Cronbach’s alpha method. Scales with ICCs values above 0.8 [38,39] and a Cronbach’s alpha above 0.7 are generally considered reliable [40]. Convergent validity was examined using the composite reliability with a cut-off point of \( \geq 0.6 \); whereas, the discriminant validity was ensured if the square root of the average variance extracted (AVE) is greater than the correlation coefficient between the different extracted factors [41,42]. Homogeneity was checked using item-total correlations, and Spearman’s correlation coefficient (rho) was calculated to examine the association between the ARMS score and different sociodemographic and medical characteristics. All statistical analyses were conducted using SAS® version 9.4 (SAS institute, Cary, NC, USA).
2.8. Ethical Approval
The study protocol was approved by the ethics committee of King Saud University College of Medicine (E-19-3721), and all respondents verbally consented to participate in the study. No patient identifiers were collected and the data were anonymized and coded. The study adhered to the ethical principles of Helsinki declaration [43].
3. Results
3.1. Participants’ Characteristics
Out of 264 patients who fit the inclusion criteria and were invited to participate, 202 patients (76.5%) filled out the questionnaire (Figure 1). Most of the participants were males (69.9%), married (75.2%), having a college degree (e.g., a technical college diploma or bachelor’s degree) or higher (50.9%), retired or unemployed (65.2%), aged \( \geq 50 \) years (65.2%), and 40.1% had a monthly income between 5000–10,000 SAR (USD 1333.33–USD
With regard to the medical characteristics of the participants, the vast majority of them (96.4%) had diabetes (e.g., 34.1% with diabetes type I and 62.3% with diabetes type II), 48% had dyslipidemia, 40% had hypertension, and 10.4% had hypothyroidism. Approximately 58% of participants reported taking six or more medications and only 12.8% had medical insurance as shown in Table 2.
Figure 1. Flowchart of patient recruitment.
Table 1. Study participants’ sociodemographic characteristics (n = 202).
| Gender | Number | Percentage |
|--------------|--------|------------|
| Male | 141 | (69.8) |
| Female | 61 | (30.2) |
| Age group (years) | | |
| 18–25 | 22 | (10.8) |
| 26–33 | 11 | (5.4) |
| 34–41 | 14 | (6.9) |
| 42–49 | 23 | (11.3) |
| 50–57 | 34 | (16.8) |
| 58–65 | 58 | (28.7) |
| 66–73 | 31 | (15.3) |
| ≥74 | 9 | (4.4) |
Marital status
| Status | Number | Percentage |
|-------------|--------|------------|
| Single | 30 | (14.8) |
| Married | 152 | (75.2) |
| Divorced | 7 | (3.4) |
| Widowed | 13 | (6.4) |
Table 1. Cont.
| Educational level | |
|--------------------------------------------------------|--------|
| No official education | 24 (11.8) |
| Completed few years of elementary school | 8 (3.9) |
| Elementary school diploma | 13 (6.4) |
| Middle school diploma | 15 (7.4) |
| Secondary school diploma or equivalent (industrial or commercial diplomas) | 39 (19.3) |
| Post-secondary school diploma or technical college | 15 (7.4) |
| University degree | 76 (37.6) |
| Graduate degree or equivalent (masters, doctorate, medical fellowship) | 12 (5.9) |
| Employment status | |
|--------------------------------------------------------|--------|
| Government sector employee | 51 (25.2) |
| Private sector employee | 11 (5.4) |
| Freelancer | 8 (3.9) |
| Retired | 70 (34.6) |
| Unemployed | 62 (30.6) |
| Monthly income * | |
|--------------------------------------------------------|--------|
| Less than 5000 | 49 (24.2) |
| 5000–10,000 | 81 (40.1) |
| 10,000–15,000 | 37 (18.3) |
| 15,000–20,000 | 22 (10.8) |
| More than 20,000 | 13 (6.4) |
| Health literacy | |
|--------------------------------------------------------|--------|
| Adequate | 160 (79.2) |
| Marginal\limited | 42 (20.7) |
*Presented in Saudi Arabian Riyals (3.75 SAR = 1 USD).
Table 2. Participants’ medical characteristics (n = 202).
| Number of Medications Taken | |
|------------------------------------------------------|--------|
| One | 14 (6.9) |
| Two | 18 (8.9) |
| Three | 13 (6.4) |
| Four | 22 (10.8) |
| Five | 18 (8.9) |
| Six and more | 117 (57.9) |
| Chronic Diseases | |
|-------------------------------------------------------|--------|
| Hypertension | 99 (49.01) |
| Hypothyroidism | 21 (10.4) |
| Cardiovascular disease | 12 (5.9) |
| Dyslipidemia | 97 (48) |
| Diabetes mellitus type I | 69 (34.1) |
| Diabetes mellitus type II (no insulin use) | 122 (60.4) |
| Diabetes mellitus type II (with insulin use) | 4 (1.9) |
Table 2. Cont.
| Medical Conditions | Number |
|------------------------------|---------|
| Psychiatric disorders | 3 (1.4) |
| Pulmonary diseases | 15 (7.4)|
| Other | 26 (12.9)|
Number of chronic health conditions
| Number of Conditions | Number |
|----------------------|---------|
| 1–2 | 113 (55.9) |
| 3–4 | 80 (39.6) |
| 5–6 | 9 (4.45) |
Medical insurance
| Medical Conditions | Number |
|--------------------|---------|
| Yes | 26 (12.8) |
| No | 176 (87.1) |
Values are presented as n (%) unless otherwise specified.
3.2. Reliability and Internal Consistency
Using the test-retest method, the ICC for the Arabic-ARMS was 0.97 indicating good reliability. The item-total correlation coefficients for Arabic-ARMS ranged between 0.217 and 0.619, and Cronbach’s alpha values if each of the 12 items is removed ranged between 0.772 and 0.824. Overall, the Arabic-ARMS demonstrated good internal consistency with a Cronbach’s alpha of 0.802. The mean scores for the Arabic-ARMS 12 items alongside their standard deviation are shown in Table 3.
Table 3. Item Analysis of Arabic-ARMS.
| Item Description | Mean ± SD | Item–Total Correlation | Cronbach’s Alpha if Item Removed |
|----------------------------------------------------------------------------------|-----------|-------------------------|-------------------------------|
| 1. How often do you forget to take your medicine? | 1.50 ± 0.74 | 0.510 | 0.78 |
| 2. How often do you decide not to take your medicine? | 1.29 ± 0.63 | 0.532 | 0.78 |
| 3. How often do you forget to get prescriptions filled? | 1.35 ± 0.61 | 0.473 | 0.78 |
| 4. How often do you run out of medicine? | 1.72 ± 0.89 | 0.459 | 0.78 |
| 5. How often do you skip a dose of your medicine before you go to the doctor? | 1.25 ± 0.61 | 0.524 | 0.78 |
| 6. How often do you miss taking your medicine when you feel better? | 1.29 ± 0.64 | 0.529 | 0.78 |
| 7. How often do you miss taking your medicine when you feel sick? | 1.31 ± 0.74 | 0.528 | 0.78 |
| 8. How often do you miss taking your medicine when you are careless? | 1.28 ± 0.65 | 0.612 | 0.77 |
| 9. How often do you change the dose of your medicines to suit your needs (like when you take more or less pills than you’re supposed to)? | 1.66 ± 0.78 | 0.385 | 0.80 |
| 10. How often do you forget to take your medicine when you are supposed to take it more than once a day? | 1.38 ± 0.69 | 0.572 | 0.77 |
| 11. How often do you put off refilling your medicines because they cost too much money? | 1.58 ± 0.82 | 0.363 | 0.79 |
| 12. How often do you plan ahead and refill your medicines before they run out? * | 2.25 ± 1.22 | 0.217 | 0.82 |
* This item was reverse-coded.
3.3. Factor Analysis
The KMO for sampling adequacy was 0.8 indicating sufficient sample to run factor analysis. Using principal components analysis with varimax rotation, two factors were revealed with eigenvalues greater than one as shown in Table 4. The first factor (adherence with taking medications) consisted of eight items (e.g., item-1, item-2, item-5, item-6, item-7, item-8, item-9, and item-10) explaining 52.94% of variance and having a mean score of 12.59 and a standard deviation of 3.92. On the other hand, the second factor (adherence with filling medications) consisted of four items (e.g., item-3, item-4, item-11, and item-12) explaining 47.06% of variance and having a mean score of 6.93 and a standard deviation of 2.19. The Cronbach’s alpha values for the adherence with taking medications and
adherence with filling medications subscales were 0.804 and 0.665, respectively. The two extracted factors demonstrated goodness of fit using the confirmatory factor analysis with a CFI of 0.964 and RMSEA < 0.001. The composite reliabilities for the first and second factors were 0.85 and 0.64, respectively, which ensures the convergent validity. The root square of AVEs for factors one and two were 0.66 and 0.56, which are higher than the correlation coefficient between the two factors (e.g., correlation coefficient = 0.499) indicating good level of discriminant validity.
Table 4. Factor Analysis of the Arabic-ARMS (Varimax rotation method).
| % variance explained | Factor 1 | Factor 2 |
|----------------------|----------|----------|
| Items | | |
| 1. How often do you forget to take your medicine? | 52.94 | 47.06 |
| 2. How often do you decide not to take your medicine? | | 0.808 |
| 3. How often do you forget to get prescriptions filled? | 0.588 | |
| 4. How often do you run out of medicine? | | 0.337 |
| 5. How often do you skip a dose of your medicine before you go to the doctor? | 0.607 | 0.639 |
| 6. How often do you miss taking your medicine when you feel better? | 0.648 | |
| 7. How often do you miss taking your medicine when you feel sick? | 0.646 | |
| 8. How often do you miss taking your medicine when you are careless? | 0.803 | |
| 9. How often do you change the dose of your medicines to suit your needs (like when you take more or less pills than you’re supposed to)? | 0.338 | |
| 10. How often do you forget to take your medicine when you are supposed to take it more than once a day? | 0.755 | |
| 11. How often do you put off refilling your medicines because they cost too much money? | | 0.402 |
| 12. How often do you plan ahead and refill your medicines before they run out? | | 0.446 |
3.4. Adherence Scores
The mean ± SD score of the Arabic-ARMS was 17.93 ± 4.90, and its median (Q1-Q3) score was 17.00 (15.00–20.00). Using a score of ≥16 as cut-off point to categorize participants into adherent (e.g., <16) and non-adherent (e.g., ≥16), 36.14% of the participants were considered adherent and 63.86% were non-adherent. Older age (Spearman’s rank correlation coefficient (rho) = −0.157; p-value = 0.025), and employed patients (rho = −0.191; p-value = 0.006) were less likely to be non-adherent (e.g., ARMS score of ≥16). Additionally, older age (rho = −0.207; p-value = 0.003) but not the employment status (rho = −0.134; p-value = 0.056) was associated with lower total ARMS scores. On the other hand, male patients were more likely to be non-adherent in comparison to their female counterparts (rho = 0.223; p-value = 0.0014). Number of prescription medications (rho = 0.021; p-value = 0.768), number of chronic health conditions (rho = 0.035; p-value = 0.626), and health literacy (rho = −0.106; p-value = 0.132) were not associated with higher ARMS scores. Nonetheless, health literacy was negatively associated with the total ARMS score (rho = −0.211; p-value = 0.002), which means that those with adequate health literacy tend to have lower rates of non-adherence in comparison to their counterparts with limited health literacy levels.
4. Discussion
The ARMS is a widely used self-report questionnaire that has been used to assess medication adherence among diverse patient populations, particularly among older adults [26]. Additionally, it has been validated and culturally adapted to different languages, which makes it an attractive, easy to administer, free of charge, and reliable medication adherence scale [27–30]. However, the absence of a validated Arabic version of ARMS or other widely used and valid medication adherence scales that can be administered free of charge makes it hard to assess adherence to prescription medications among the Arabic-speaking patient population [15,17,21]. Therefore, translating and validating the ARMS into Arabic, which is a language spoken by more than 400 million people [44], should facilitate the assess-
ment of medication adherence among Arabic-speaking patient population, particularly among those with chronic health conditions, such as diabetes and hypertension, which are prevalent in the Arab world [45–47]. This study is to the best of our knowledge the first to validate ARMS to Arabic among a cohort of patients with chronic health conditions in Saudi Arabia. The majority of the participants had diabetes and many of them had hypertension and dyslipidemia, which represents to a great extent the characteristics of patients with chronic health conditions in Saudi Arabia [46]. Additionally, the psychometric analysis showed good reliability and construct validity of the Arabic-ARMS.
The reliability of the Arabic-ARMS was assessed by two methods (test-retest and Cronbach’s alpha methods), and in the two methods the Arabic-ARMS demonstrated good reliability [38–40]. The Cronbach’s alpha for the 12-item Arabic-ARMS was 0.8 which is acceptable and comparable to the original scale and the other translated versions [26–30,48]. In addition, the two revealed factors in the factor analysis are similar to the ones identified in the original scale. The first factor consisted of eight items that assess patients’ adherence to taking their prescription medications; whereas, the second factor consists of four items and assesses patients’ adherence to filling their prescription medications. However, the variance explained by each factor and the item loadings differed from that found in the psychometric analysis of the original scale [26]. Kripalani et al. reported two factors in the original 12-item ARMS, factor 1 consisted of eight items that evaluated adherence to taking medications correctly, had an eigenvalue of 4.209 and explained 35.1% of the variance, and factor 2, consisted of four items that evaluated the participants’ ability to refill medications on schedule, had an eigenvalue of 1.199 and explained 10.0% of the variance [26]. In this study, factor analysis identified the same number of factors identified in the original scale, however the distribution of items under the factors did not match that of the original scale. Additionally, the loadings of item number 3 and item number 9 are below cutoff point of >0.4 needed for any item to be attributed to a factor [49]. This is expected since the psychometric analyses of different validated versions of ARMS revealed different percentages of variance explained by these two factors [27–29]. Moreover, the Korean version identified an additional factor which represented the persistence with refilling medicines [28]. Additionally, the Chinese version omitted items 4 and 11 to accommodate the nature of their patient population, which resulted in higher Cronbach’s alpha for factor 1 (α = 0.90) and factor 2 (α = 0.77) in comparison to the original scale [29]. Therefore, making appropriate adjustments to fit the patient population may generate better estimates and help in identifying unique characteristics of the targeted patient population leading to a better understanding of the reasons behind medication non-adherence.
The ARMS was originally developed among patients with low health literacy, which makes an attractive tool to assess medication non-adherence among patients with various levels of health literacy due to its high level of comprehensibility [26]. Marginal health literacy was associated with poor adherence to prescription medications in most published research studies that explored the association between medication non-adherence and different patient sociodemographic and medical characteristics [26,29,50]. Even though patients with limited health literacy were leaning toward being non-adherent (e.g., ARMS score ≥ 16), the association between health literacy and Arabic-ARMS score was not significant. This can be due to the study’s small sample or the fact that health literacy was assessed using the SILS which is not as reliable as other longer scales, such as Test of Functional Health Literacy (TOFHL) and Rapid Estimate of Adult Literacy in Medicine (REALM) [51]. However, adequate health literacy was negatively associated with the total ARMS score, which means that patients with adequate health literacy were more likely to adhere to their prescription medications. Therefore, different cut-off points for non-adherence using ARMS score should be explored.
Even though this is the first study to the best of our knowledge that translated and validated an Arabic version of the ARMS, several limitations must be acknowledged. First, patient recruitment was planned to end by March 2020, however, the COVID-19 pandemic has resulted in many appointments being postponed. Second, this is a single center
study that explored the validity of a newly Arabic translated version of ARMS among patients with chronic health conditions. Therefore, the generalizability of its findings might be limited. Furthermore, since we included every 10th patient this might introduce some selection bias. Additionally, the scale was validated among a sample of patients who are largely Saudi. Thus, cultural and dialectal differences may make this Arabic translated version of ARMS not as comprehensible to non-Saudi patients as well as other Saudi patients from different geographic regions who were not represented in this study. Nonetheless, the scale was translated using Arabic terms that are understandable to anyone speaking the language. In addition, non-response bias cannot be excluded since not all patients who were invited to participate consented to participate and completed the questionnaire. Furthermore, the associations between different patient characteristics (e.g., beliefs about medications, patient medical and sociodemographic characteristics) and the ARMS score were not examined. In addition, the Arabic version of ARMS was not validated against other well-known medication adherence measures, such as pill count and medication possession ratio (MPR).
5. Conclusions
The findings of this study demonstrated good validity and reliability of the Arabic-ARMS, which makes it a feasible and accessible scale to many healthcare providers and researchers to assess medication adherence among patients with various health conditions. Future research should examine different cut-off points for non-adherence as well as cross-check the results with other Arabic translated scales, such as MMAS-8. Furthermore, the psychometric properties of the Arabic-ARMS should be examined among larger samples of patients with various chronic health conditions, and in different healthcare settings and cultures. Moreover, the Arabic version of ARMS should be validated against other medication adherence measures, such as pill count. Additionally, examining the relationship between different predictors of medication non-adherence (e.g., depression, beliefs about medications, polypharmacy, and older age) and the Arabic version of ARMS score should be conducted.
Author Contributions: Concept and design, G.A., H.A., N.A. and Y.A.; acquisition, analysis, and/or interpretation of data, Y.A., G.A., H.A., N.A., Y.A.A. and I.S.; drafting of the manuscript, G.A., Y.A., I.S., A.J., T.H.A., M.A.B. and I.S.; Critical revision of the manuscript for important intellectual content, all authors; statistical analyses, Y.A. and I.S.; administrative, technical, and/or material support, Y.A., N.A., G.A., H.A., I.S., A.J., T.H.A., M.A.B. and Y.A.A. All authors have read and agreed to the published version of the manuscript.
Funding: The authors acknowledge the financial support received from the Researchers Supporting Project number (RSP-2021/16), King Saud University, Riyadh, Saudi Arabia.
Institutional Review Board Statement: The study protocol was approved by the ethics committee of King Saud University College of Medicine (E-19-3721), and the study was conducted according to the guidelines of the Declaration of Helsinki.
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study, and no written consent for publication was required since no identifiable personal information are published.
Data Availability Statement: The data are available upon reasonable request from the corresponding author (Yazed AlRuthia).
Acknowledgments: The authors would like to thank Sunil Kripalani for granting us the permission to translate and validate the ARMS into Arabic. The copyright in ARMS is owned by Emory University.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
The Adherence to Refills and Medications Scale (ARMS)
مقياس الإلتزام بتناول الدواء وإعادة التعبئة
إله من السالمان أن ينوت الناس تناول دوائهم من وقت لآخر أو أن لا يتهكموا بالتعليمات والإرشادات العلاجية عند أخذهم لدوائهم. أود أن أسألكم على الإلتزام بالدواء، يرجى الإجابة على الأسئلة التالية.
| الأسان (1) | الأسان (2) | الأسان (3) | الأسان (4) |
|------------|------------|------------|------------|
| | | | |
- ما هو معدل نسبي تناول الدواء؟
- ما هو معدل إخلاء الدواء في الوقت؟
- ما هو معدل نسبي تناول الدواء؟
- ما هو معدل نسبي تناول الدواء؟
- ما هو معدل عدم تناول الدواء عند شرب السوائل؟
- ما هو معدل عدم تناول الدواء عند شرب السوائل؟
- ما هو معدل عدم تناول الدواء؟
- ما هو معدل عدم تناول الدواء؟
- ما هو معدل عدم تناول الدواء؟
- ما هو معدل نسبي تناول الدواء؟
- ما هو معدل نسبي تناول الدواء؟
- ما هو معدل نسبي تناول الدواء؟
References
1. Organization, W.H. Adherence to Long-Term Therapies: Evidence for Action; World Health Organization: Geneva, Switzerland, 2015.
2. Mohiuddin, A.K. Risks and reasons associated with medication non-adherence. J. Clin. Pharm. 2019, 1, 50–53.
3. Marcum, Z.A.; Sevick, M.A.; Handler, S.M. Medication nonadherence: A diagnosable and treatable medical condition. JAMA 2013, 309, 2105–2106. [CrossRef] [PubMed]
4. Kini, V.; Ho, P.M. Interventions to improve medication adherence: A review. JAMA 2018, 320, 2461–2473. [CrossRef] [PubMed]
5. Ho, P.M.; Bryson, C.L.; Rumsfeld, J.S. Medication adherence: Its importance in cardiovascular outcomes. Circulation 2009, 119, 3028–3035. [CrossRef]
6. Iuga, A.O.; McGuire, M.J. Adherence and health care costs. Risk Manag. Healthc. Policy 2014, 7, 35.
7. Zyoud, S.H.; Al-Jabi, S.W.; Sweileh, W.M.; Morisky, D.E. Relationship of treatment satisfaction to medication adherence: Findings from a cross-sectional survey among hypertensive patients in Palestine. Health Qual. Life Outcomes 2013, 11, 1–7. [CrossRef] [PubMed]
8. Menard, S.; Jbilou, J.; Lauzier, S. Family caregivers’ reported nonadherence to the controller medication of asthma in children in Casablanca (Morocco): Extent and associated factors. J. Asthma 2018, 55, 1362–1372. [CrossRef]
9. Altuwairqi, H.B. Barriers to medication adherence among cardiac patients following at King Fahad Medical City, Riyadh, Saudi Arabia. Saudi J. Health Sci. 2016, 5, 20. [CrossRef]
10. Khan, A.R.; Lateef, Z.N.A.-A.; Al Aithan, M.A.; Bu-Khamseen, M.A.; Al Ibraheim, I.; Khan, S.A. Factors contributing to non-compliance among diabetics attending primary health centers in the Al Hasa district of Saudi Arabia. J. Fam. Community Med. 2012, 19, 26. [CrossRef] [PubMed]
11. Rao, D.; Kekwatewwe, T.C.; Hosek, S.; Martinez, J.; Rodriguez, F. Stigma and social barriers to medication adherence with urban youth living with HIV. AIDS Care 2007, 19, 28–33. [CrossRef] [PubMed]
12. Blashill, A.J.; Perry, N.; Safren, S.A. Mental health: A focus on stress, coping, and mental illness as it relates to treatment retention, adherence, and other health outcomes. Curr. HIV/AIDS Rep. 2011, 8, 215–222. [CrossRef] [PubMed]
13. Fernandez-Lazaro, C.I.; Adams, D.P.; Fernandez-Lazaro, D.; Garcia-Gonzalez, J.M.; Caballero-Garcia, A.; Miron-Canelo, J.A. Medication adherence and barriers among low-income, uninsured patients with multiple chronic conditions. Res. Soc. Adm. Pharm. 2019, 15, 744–753. [CrossRef] [PubMed]
14. Pasina, L.; Brucato, A.; Falcone, C.; Cucchi, E.; Bresciani, A.; Sottocorno, M.; Taddei, G.C.; Casati, M.; Franchi, C.; Djdade, C.D.; et al. Medication non-adherence among elderly patients newly discharged and receiving polypharmacy. Drugs Aging 2014, 31, 283–289. [CrossRef] [PubMed]
15. Lam, W.Y.; Fresco, P. Medication adherence measures: An overview. BioMed Res. Int. 2015, 2015, 1–12. [CrossRef]
16. Kreys, E. Measurements of medication adherence: In search of a gold standard. J. Clin. Path. 2016, 2, 43–47.
17. Anghel, L.A.; Farcas, A.M.; Oprean, R.N. An overview of the common compliance used to measure treatment adherence. Med. Pharm. Rep. 2019, 9, 117. [CrossRef] [PubMed]
46. Tyrovolas, S.; El Bcheraoui, C.; Alghnam, S.A.; Alhabib, K.F.; Almadi, M.A.H.; Al-Raddadi, R.M.; Bedi, N.; Tantawi, M.E.; Krish, V.S.; Memish, Z.A.; et al. The burden of disease in Saudi Arabia 1990–2017: Results from the Global Burden of Disease Study 2017. *Lancet Planet. Health* 2020, 4, e195–e208. [CrossRef]
47. Mokdad, A.H.; Jaber, S.; Aziz, M.I.A.; AlBuhairan, F.; AlGhaithi, A.; AlHAmad, N.M.; Al-Hooti, S.N.; Al-Jasari, A.; AlMazroa, M.A.; AlQasmi, A.M.; et al. The state of health in the Arab world, 1990–2010: An analysis of the burden of diseases, injuries, and risk factors. *Lancet* 2014, 383, 309–320. [CrossRef]
48. Tavakol, M.; Dennick, R. Making sense of Cronbach’s alpha. *Int. J. Med. Educ.* 2011, 2, 53–55. [CrossRef]
49. Cutillo, L. Parametric and multivariate methods. In *Encyclopedia of Bioinformatics and Computational Biology*; Ranganathan, S., Nakai, K., Schonbach, C., Eds.; Elsevier: Amsterdam, Netherlands, 2019; pp. 738–746. [CrossRef]
50. Lee, Y.-M.; Yu, H.Y.; You, M.-A.; Son, Y.-J. Impact of health literacy on medication adherence in older people with chronic diseases. *Collegian* 2017, 24, 11–18. [CrossRef]
51. Tian, C.Y.; Xu, R.H.; Mo, P.K.-H.; Dong, D.; Wong, E.L.-Y. Generic health literacy measurements for adults: A scoping review. *Int. J. Environ. Res. Public Health* 2020, 17, 7768. [CrossRef] [PubMed] | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3186,
1
],
[
3186,
7387,
2
],
[
7387,
11513,
3
],
[
11513,
15497,
4
],
[
15497,
16759,
5
],
[
16759,
20053,
6
],
[
20053,
24418,
7
],
[
24418,
28597,
8
],
[
28597,
33320,
9
],
[
33320,
37138,
10
],
[
37138,
41203,
11
],
[
41203,
41203,
12
],
[
41203,
42562,
13
]
]
} |
37a0f4a62ed20a84fd992b0433a2d9345152faa2 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 2,
"total-fallback-pages": 0,
"total-input-tokens": 6958,
"total-output-tokens": 2297,
"fieldofstudy": [
"Medicine"
]
} | Editorial: Long-non coding RNAs in renal cell carcinoma
Zongping Wang\textsuperscript{1,2}, Song Wang\textsuperscript{1,2} and An Zhao\textsuperscript{2,3*}
\textsuperscript{1}Department of Urology, Cancer Hospital of University of Chinese Academy of Sciences (Zhejiang Cancer Hospital), Hangzhou, China, \textsuperscript{2}Institute of Cancer and Basic Medicine (ICBM), Chinese Academy of Sciences, Hangzhou, China, \textsuperscript{3}Experimental Research Center, Cancer Hospital of University of Chinese Academy of Sciences (Zhejiang Cancer Hospital), Hangzhou, China
KEYWORDS
long non-coding RNA, lncRNA, renal cell carcinoma, genitourinary cancers, oncology
Renal cell carcinoma (RCC) is one of the most common urological malignancies and is known for its complex genomic heterogeneity and natural drug resistance (1). Identifying the key regulatory mechanisms of RCC and developing biomarker-based diagnosis and treatment strategies for RCC have been expected in clinical practice (2, 3). Among the many kinds of tumor biomarkers, long non-coding RNAs (lncRNAs) has recently attracted considerable attention due to its various of functions in cellular processes (4, 5). Increasing evidence supports the role of lncRNA in tumor development, metastasis and drug resistance in RCC (6, 7). Therefore, lncRNAs have been suggested as biomarkers and topics in novel diagnostic and therapeutic strategies for RCC.
In this current topic, an overview of lncRNAs in RCC is provided through 4 original research papers by 23 authors, and these studies expand our understanding of the important roles of lncRNAs in the progression of RCC (8–11). Notably, Tan et al. reported the overexpressed lncRNA DUXAP9 was associated with poorer overall survival and progression-free survival in clear cell RCC (ccRCC). DUXAP9 knockdown can inhibit RCC cell proliferation, motility capacities and reverse epithelial-mesenchymal transition (EMT), whereas overexpression of DUXAP9 promoted RCC cells proliferation and motility capacities in vitro and induced EMT. Interesting, RNA immunoprecipitation and RNA stability assays showed that DUXAP9 was methylated at N6-adenosine and binds to IGF2BP2, which increases its stability. DUXAP9 activate PI3K/AKT pathway and Snail expression in RCC cells. DUXAP9 may be useful as a prognostic marker and/or therapeutic target in localized ccRCC.
The identification of RCC-associated lncRNAs using multi-omics and systems biology has been reported by serval groups. Chen et al. identified 4 key hypoxia-related lncRNAs (COMETT, EMX2OS, AC026462.3, and HAGLR) based on TCGA-KIRC datasets, and verified their relative expression via the qRT-PCR method, then they construct signature and nomogram to predict the prognosis of ccRCC patients. They also found that the 4-lncRNAs based-risk score was remarkably related to the infiltration...
levels of 6 tumor immune cells, they proposed that this study may be useful for medical decision-making and targeted therapy. Su et al. constructed a ceRNA network of key genes that are significantly associated with the distant metastasis and prognosis of patients with ccRCC. The distant metastasis-related lncRNAs were used to construct a risk score model through the univariate, least absolute shrinkage selection operator (LASSO), and multivariate Cox regression analyses, and the patients were divided into high- and low-risk groups according to the median of the risk score. The Kaplan–Meier survival analysis demonstrated that mortality was significantly higher in the high-risk group than in the low-risk group. qRT-PCR in the tissues and cells of ccRCC verified the high-expression level of three lncRNAs. Gene set enrichment analysis revealed that the lncRNA prognostic signature was mainly enriched in autophagy- and immune-related pathways. interestingly, Fang et al. identified the genome instability-related lncRNAs (GlnLncRNAs) and their clinical significances in RCC, based on the mutation data and lncRNA expression data on the TCGA database, they determined 11 GlnLncRNAs to construct a prognostic model, and found that this model was significantly associated with the RCC patients’ overall survival, their study provided theoretical support for the exploration of the formation and development of RCC.
In summary, this Research Topic provides novel insights into the regulatory network of lncRNAs in RCC, and these findings reveal the potential applications of lncRNAs in the diagnosis and therapy of RCC. We hereby appreciate all the authors for contributing to this Research Topic.
Author contributions
AZ drafted the editorial. ZW and SW edited the manuscript. All authors contributed to this work and gave approval to the final version.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
References
1. Dizman N, Philip E, Pacl S. Genomic profiling in renal cell carcinoma. Nat Rev Nephrol (2020) 16(8):435–51. doi: 10.1038/s41581-020-0310-x
2. Barbieri C, Chinnayani A, Lerner S, Swanton C, Rubin M. The emergence of precision urologic oncology: A collaborative review on biomarker-driven therapeutics. Eur Urol (2017) 71(2):237–46. doi: 10.1016/j.euro.2016.08.024
3. Yu M, Liu X, Xu H, Shen S, Wang F, Chen D, et al. Comprehensive evaluation of the mA regulator prognostic risk score in the prediction of immunotherapy response in clear cell renal cell carcinoma. Front Immunol (2022) 13:818120. doi: 10.3389/fimmu.2022.818120
4. Shaath H, Vishnubalaji R, Elango R, Kardousha A, Islam Z, Qureshi R, et al. Long non-coding RNA and RNA-binding protein interactions in cancer: Experimental and machine learning approaches. Semin Cancer Biol (2022) 51044:579X222100214-9. doi: 10.1016/j.semcancer.2022.05.013
5. Ebrahimi N, Parkhishde S, Samizadeh S, Esfahani A, Samsami S, Yazdani E, et al. Crosstalk between lncRNAs in the apoptotic pathway and therapeutic targets in cancer. Cytokine Growth factor Rev (2022) 65:61–74. doi: 10.1016/j.cytogfr.2022.04.003
6. Flippot R, Beine H, Boilève A, Vibert J, Malouf G. Long non-coding RNAs in genitourinary malignancies: a whole new world. Nat Rev Urol (2019) 16(8):844–504. doi: 10.1038/s41585-019-0195-1
7. Zhang W, Zheng X, Yu Y, Zheng L, Lan J, Wu Y, et al. Renal cell carcinoma-derived exosomes deliver IncARSR to induce macrophage polarization and promote tumor progression via STAT3 pathway. Int J Biol Sci (2022) 18(8):3209–22. doi: 10.7150/ijbs.70289
8. Tan L, Tang Y, Li H, Li P, Ye Y, Chen J, et al. N6-methyladenosine modification of LncRNA DXASP9 promotes renal cancer cells proliferation and motility by activating the PI3K/AKT signaling pathway. Front Oncol (2021) 11:641833. doi: 10.3389/fonc.2021.641833
9. Chen H, Pan Y, Jin X, Chen G. Identification of a four hypoxia-associated long non-coding RNA signature and establishment of a nomogram predicting prognosis of clear cell renal cell carcinoma. Front Oncol (2021) 11:713346. doi: 10.3389/fonc.2021.713346
10. Su Y, Zhang T, Tang J, Zhang L, Fan S, Zhou J, et al. Construction of competitive endogenous RNA network and verification of 3-key LncRNA signature associated with distant metastasis and poor prognosis in patients with clear cell renal cell carcinoma. Front Oncol (2021) 11:640150. doi: 10.3389/fonc.2021.640150
11. Fang X, Liu X, Lu I, Liu G. Identification of a somatic mutation-derived long non-coding RNA signatures of genomic instability in renal cell carcinoma. Front Oncol (2021) 11:728181. doi: 10.3389/fonc.2021.728181 | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2860,
1
],
[
2860,
7946,
2
]
]
} |
d3e9fa037eca4cd56ba137d2cf910a176fda19c0 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 33,
"total-fallback-pages": 0,
"total-input-tokens": 159379,
"total-output-tokens": 32014,
"fieldofstudy": [
"Mathematics"
]
} | A nonlinear dynamical system on the set of Laguerre entire functions
Yuri Kozitsky\textsuperscript{a,b,c,1} and Lech Wo\'owski\textsuperscript{a,d}
\textsuperscript{a}Institute of Mathematics, Marie Curie-Sk\'lodowska University, Lublin 20-031 Poland
\textsuperscript{b}Institute for Condensed Matter Physics, Lviv 290011 Ukraine
\textsuperscript{c}e-mail: [email protected]
\textsuperscript{d}e-mail: [email protected]
ABSTRACT: A nonlinear modification of the Cauchy problem $D_t f(t, z) = \theta D_z f(t, z) + z D_z^2 f(t, z)$, $t \in \mathbb{R}_+ = [0, +\infty)$, $z \in \mathfrak{C}$, $\theta \geq 0$, $f(0, z) = g(z) \in \mathcal{L}$ is considered. The set $\mathcal{L}$ consists of Laguerre entire functions, which one obtains as a closure of the set of polynomials having real nonpositive zeros only in the topology of uniform convergence on compact subsets of $\mathfrak{C}$. The modification means that the time half-line $\mathbb{R}_+$ is divided onto the intervals $I_n = [(n-1)\tau, n\tau]$, $n \in \mathbb{N}$, $\tau > 0$, and on each $I_n$ the evolution is to be described by the above equation but at the endpoints the function $f(t, z)$ is changed: $f(n\tau, z) \to [f(n\tau, z^\delta^{-1-\lambda})]^\delta$, with $\lambda > 0$ and an integer $\delta \geq 2$. The resolvent operator of such problem preserves the set $\mathcal{L}$. It is shown that for $t \to +\infty$, the asymptotic properties of $f(t, z)$ change considerably when the parameter $\tau$ reaches a threshold value $\tau_\ast$. The limit theorems for $\tau < \tau_\ast$ and for $\tau = \tau_\ast$ are proven. Certain applications, including limit theorems for weakly and strongly dependent random vectors, are given.
Keywords: Holomorphic Operators; Fixed Points; Stability; Convergence; Cauchy Problem
Mathematical Subject Classification: 30D15, 35K55, 58F39
\textsuperscript{1}Supported in part under the Grant KBN No 2 P03A 02915
1 Setup
1.1 Introduction
The Laguerre entire functions \( \mathcal{L} \) are obtained as uniform limits on compact subsets of \( \mathcal{C} \) of the sequences of polynomials possessing real nonpositive zeros only. These functions are being studied by many authors during this century in view of their various applications (see also \( \mathbb{R} \)). In \( \mathbb{R} \) the set of Laguerre entire functions \( \mathcal{L} \) was described in the framework of locally convex spaces of exponential type entire functions. In particular, it was shown that the Cauchy problem
\[
\frac{\partial f(t, z)}{\partial t} = \theta \frac{\partial f(t, z)}{\partial z} + z \frac{\partial^2 f(t, z)}{\partial z^2}, \quad t \in \mathbb{R}_+ \overset{\text{def}}{=} [0, +\infty), \quad z \in \mathcal{C},
\]
has a unique solution in \( \mathcal{L} \) at least for \( t \) small enough. This solution was obtained in an integral form and its possible asymptotic properties when \( t \to +\infty \) were considered. In this paper, a nonlinear modification of this problem is introduced and studied. We divide the time half-line onto the intervals \([(n - 1)\tau, n\tau], \quad n \in \mathbb{N} \) with certain \( \tau > 0 \). On each such an interval the evolution is to be described by the above equation but at the endpoints the function \( f(t, z) \) is changed
\[
f(n\tau, z) \to \left[ f(n\tau, z^{\delta^{-1-\lambda}}) \right]^\delta,
\]
with a fixed \( \lambda > 0 \) and an integer \( \delta \geq 2 \). For this dynamical system, we construct the evolution operator as a holomorphic nonlinear map between the Fréchet spaces of entire functions, which preserves the set of Laguerre entire functions. Here we use the properties of the operators having the form \( \varphi(\Delta_\theta) \) with \( \Delta_\theta = (\theta + zD)D \) and \( \varphi \in \mathcal{L} \) studied in \( \mathbb{R} \). For \( \lambda < 1/2 \), we show that, for sufficiently small values of \( \tau \), the asymptotic properties of \( f(t, z) \), \( t \to +\infty \) qualitatively are the same as in the case where the evolution is described only by the transformation \((1.1)\). At the same time, it is shown that there exists a threshold value \( \tau_* > 0 \) such that the asymptotic behaviour of \( f(t, z) \) changes drastically when \( \tau \) achieves this value. The description of this phenomenon is based upon the properties of the evolution operator fixed points. The results obtained are then used to describe a similar evolution on the sets of isotropic (i.e. \( O(N) \)-invariant) analytic functions and measures
defined on $\mathbb{R}^N$. In particular, the limit theorems for strongly and weakly dependent $N$-dimensional random vectors are proved.
Every statement given below in the form of Proposition either was proved in [6] or may be proven in an evident way.
1.2 Definitions and Main Results
Let $\mathcal{E}$ be the set of all entire functions $\mathfrak{C} \rightarrow \mathfrak{C}$. For $b > 0$, we define
$$\mathcal{B}_b = \{f \in \mathcal{E} | \|f\|_b < \infty\},$$
where
$$\|f\|_b = \sup_{k \in \mathbb{N}_0} \{b^{-k} | f^{(k)}(0) | \}, \quad f^{(k)}(0) = (D^k f)(0) = \frac{d^k f}{dz^k}(0),$$
(1.2)
and $\mathbb{N}_0$ stands for the set of nonnegative integers. For $a \geq 0$, let
$$\mathcal{A}_a = \bigcap_{b > a} \mathcal{B}_b = \{f \in \mathcal{E} | (\forall b > a) \|f\|_b < \infty\}.$$ (1.3)
**Proposition 1.1** $(\mathcal{B}_b, \| \cdot \|_b)$ is a Banach space, $\mathcal{A}_a$ equipped with the topology defined by the family $\{\| \cdot \|_b, \ b > a\}$ is a Fréchet space.
An equivalent topology on $\mathcal{A}_a$ may be introduced by means of the family $\{| \cdot |_b, \ b > a\}$ of the norms
$$|f|_b \overset{\text{def}}{=} \sup_{z \in \Phi} \{|f(z)| \exp(-b|z|)\}.$$
**Definition 1.1** A family $\mathcal{L}$ is formed by the entire functions possessing the representation
$$f(z) = Cz^m \exp(\alpha z) \prod_{j=1}^{\infty} (1 + \gamma_j z),$$
(1.4)
$$C \in \Phi', \ m \in \mathbb{N}_0, \ \alpha \geq 0, \ \gamma_j \geq \gamma_{j+1} \geq 0, \ \sum_{j=1}^{\infty} \gamma_j < \infty.$$
The elements of $\mathcal{L}$ are known as the Laguerre entire functions \cite{[3]}. Due to Laguerre and Pólya (see e.g. \cite{[3], [7]}), we know that $\mathcal{L}$ consists of the polynomials possessing real nonpositive zeros only as well as of their uniform limits on compact subsets of $\mathbb{C}$. Let $\mathcal{P}_L$ be the set of polynomials belonging to $\mathcal{L}$ and
$$
\mathcal{L}^+ \overset{\text{def}}{=} \{ f \in \mathcal{L} \mid f(0) > 0 \}, \quad \mathcal{L}^{(1)} \overset{\text{def}}{=} \{ f \in \mathcal{L} \mid f(0) = 1 \},
$$
(1.5)
$$
\mathcal{L}_a \overset{\text{def}}{=} \mathcal{L} \cap \mathcal{A}_a, \quad \mathcal{L}_a^+ \overset{\text{def}}{=} \mathcal{L}^+ \cap \mathcal{A}_a, \quad \mathcal{L}_a^{(1)} \overset{\text{def}}{=} \mathcal{L}^{(1)} \cap \mathcal{A}_a.
$$
(1.6)
Given $\theta \geq 0$, a map $\Delta_\theta : \mathcal{E} \to \mathcal{E}$ is defined to be
$$
(\Delta_\theta f)(z) = (\theta + zD)Df(z) = \theta \frac{df(z)}{dz} + z \frac{d^2 f(z)}{dz^2}.
$$
(1.7)
For $F(z) = f(z^2)$, one observes
$$
(\Delta_\theta f)(z^2) = \frac{1}{4} \left( \frac{2\theta - 1}{z} \frac{dF(z)}{dz} + \frac{d^2 F(z)}{dz^2} \right),
$$
(1.8)
which means that, for $\theta = N/2$, $N \in \mathbb{N}$, the map (1.7) is connected with the radial part of the $N$–dimensional Laplacian
$$
\Delta_r = \frac{N - 1}{r} \frac{\partial}{\partial r} + \frac{\partial^2}{\partial r^2}.
$$
Consider now the Cauchy problem:
$$
\frac{\partial f(t, z)}{\partial t} = (\Delta_\theta f)(t, z), \quad t \in \mathbb{R}_+, \quad z \in \mathbb{C},
$$
(1.9)
$$
f(0, z) = g(z),
$$
and let the initial condition have the form
$$
g(z) = \exp(-\varepsilon z)h(z), \quad h \in \mathcal{A}_a, \quad \varepsilon \geq 0.
$$
(1.10)
The following statement was proven in \cite{[3]} as Theorem 1.6.
**Proposition 1.2** (i) For every $\theta \geq 0$ and $g \in \mathcal{E}$ having the form (1.10), the problem (1.9) has a unique solution in $\mathcal{A}_\varepsilon$, which possesses the following integral representation
$$
f(t, z) = \exp \left( -\frac{z}{t} \right) \int_0^{+\infty} s^{\theta - 1} w_a \left( \frac{zs}{t} \right) e^{-s} g(ts) ds, \quad t > 0,
$$
(1.11)
\[
w_\theta(z) \overset{\text{def}}{=} \sum_{k=0}^{\infty} \frac{z^k}{k! \Gamma(\theta + k)}.
\]
(ii) If in \((1.10)\) \(\varepsilon > 0\), the solution \((1.11)\) converges in \(A_\varepsilon\) to zero when \(t \to +\infty\).
(iii) If in \((1.10)\) \(h \in L_0\) and \(\varepsilon = 0\), the solution \((1.11)\) also belongs to \(L_0\). It diverges when \(t \to +\infty\), which means \(M_f(t, r) \to +\infty\) for every \(r \in \mathbb{R}_+\). Here
\[
M_f(t, r) \overset{\text{def}}{=} \sup_{|z| \leq r} |f(t, z)|.
\]
By claim (ii), the so called stabilization of solutions holds (see e.g. [4] and [1]).
We modify the evolution described by the equation \((1.9)\) as follows. Let us divide the time half–line \(\mathbb{R}_+\) onto the intervals \([(n-1)\tau, n\tau], n \in \mathbb{N}\) with some \(\tau > 0\). On each such an interval, the evolution is to be described by \((1.9)\) but at the moments \(t = n\tau, n \in \mathbb{N}_0\) the function is changed as follows
\[
f(n\tau, z) \to [f(n\tau, z\delta^{-1-\lambda})]^{\delta},
\]
with a fixed \(\lambda > 0\) and an integer \(\delta \geq 2\). It is more convenient to deal with the sequence of functions depending on \(t\) from one such interval instead of considering one function with \(t\) varying on the sequence of intervals. In what follows, we consider the sequence of functions \(\{f_n(t, z), n \in \mathbb{N}_0\}\), each of which is a solution of the following Cauchy problem
\[
\frac{\partial f_n(t, z)}{\partial t} = \tau(\Delta_\theta f_n)(t, z), \quad \tau \geq 0, \quad t \in [0, 1], \quad z \in \mathcal{C}, \quad (1.13)
\]
\[
f_n(0, z) = [f_{n-1}(1, z\delta^{-1-\lambda})]^{\delta}, \quad n \in \mathbb{N},
\]
\[
f_0(1, z) = g(z) \in \mathcal{L}^+.
\]
Any \(g \in \mathcal{L}^+\) is described by the parameters \(C, \alpha, \{\gamma_j\}\) (see \((1.4)\) and \((1.5)\)) and one can show that \(g \in \mathcal{L}^+_\alpha\). For such functions, we define
\[
m_k(g) = \sum_{j=1}^{\infty} \gamma_j^k, \quad k \in \mathbb{N}, \quad (1.14)
\]
and
\[
I(g) = \begin{cases}
[0, (\delta^\lambda - 1)/\alpha], & \alpha > 0 \\
[0, \infty), & \alpha = 0
\end{cases} \quad (1.15)
\]
5
Proposition 1.2 implies the existence of solutions of (1.13) at least for \( g \in L_0 \).
The first of our theorems establishes the existence of these solutions for more general situations.
**Theorem 1.1** Let \( g \in L^+ \) and \( \tau \in I(g) \) be chosen. Then for every \( n \in \mathbb{N} \) and \( \theta \geq 0 \), the problem (1.13) has a unique solution \( f_n \), which belongs to \( L^\alpha_\theta \).
For \( \tau = 0 \), the sequence \( \{f_n\} \) can be found explicitly:
\[
f_n(t, z) = [g(z\delta^{-n(1+\lambda)})]^{[\delta^n].}
\]
(1.16)
If \( g \in L^{(1)} \), this sequence converges in \( A_\beta \) to the function \( f(t, z) \equiv 1 \). Thus one may expect that the same or similar convergence holds also for small positive values of \( \tau \). On the other hand, for large values of \( \tau \), claim (iii) of Proposition 1.2 suggests the divergence. Our aim in this work is to study the questions: (a) does there exist the intermediate value of \( \tau \), say \( \tau_* \), which separates such ”small” and ”large” values; (b) what would be the convergence of the sequence \( \{f_n\} \) for \( \tau = \tau_* \). The answer has been found for the values of \( \lambda \) restricted to the interval \( \lambda \in (0, 1/2) \) when the initial element \( g \) is being chosen in a subset of \( L^+ \) defined by \( \lambda \) as follows. Let
\[
\vartheta(\lambda) \overset{\text{def}}{=} \frac{1 - \delta^{-\epsilon}}{\delta^\lambda - \delta^{-\epsilon}}, \quad \epsilon = \frac{1 - 2\lambda}{4}.
\]
(1.17)
**Definition 1.2** A family \( L(\lambda) \) consists of the functions \( g \in L^{(1)} \) which are not constant and are such that
\[
\frac{m_2(g)}{[\alpha + m_1(g)]^2} \leq \frac{\delta^{1/2}}{\theta + 1} \vartheta(\lambda), \quad \frac{m_2(g)}{[m_1(g)]^2} \leq \frac{\delta^{1/2}}{\theta + 1}.
\]
(1.18)
Thereby, we state our main theorem.
**Theorem 1.2** For every \( \theta \geq 0 \) and \( g \in L(\lambda) \), there exist a positive \( \tau_* \in I(g) \) and a function \( C : [0, \tau_*] \to \mathbb{R}_+ \) such that
(i) for \( \tau < \tau_* \), the sequence of solutions of (1.13)
\[
\{f_n(t, z) \mid n \in \mathbb{N}_0, \ f_0(1, z) = C(\tau)g(z)\}
\]
converges in \( A_{\beta^{-1}} \), \( \beta_* \overset{\text{def}}{=} \tau_*/(\delta^\lambda - 1) \) to the function \( f(t, z) \equiv 1 \);
(ii) for \( \tau = \tau_* \), the sequence \( \{f_n(t, z) \mid n \in \mathbb{N}_0, \ f_0(1, z) = C(\tau_*)g(z)\} \)
converges in \( A_{\beta^{-1}} \), to
\[
f_*(t, z) = \delta^{-\delta\theta\lambda/(\delta - 1)}[1 - t(1 - \delta^{-\lambda})]^{-\theta} \exp \left( \frac{1}{\tau_*} \frac{1 - \delta^{-\lambda}}{1 - t(1 - \delta^{-\lambda})} z \right).
\]
(1.19)
Remark 1.1 The convergence to nontrivial (neither zero nor infinity) limits needs to control the constant $C$ in the representation (1.4) of the initial element of $\{f_n\}$. Otherwise one obtains only such trivial limits for "small" and "large" values of this constant.
1.3 Some Applications and Further Results
Let $E(N), N \in \mathbb{N}$ be the set of analytic functions $F: \mathbb{R}^N \to \mathbb{C}$. For appropriate $F \in E(N)$ and some $b > 0$, we set
$$
\|F\|_{b,N} \overset{\text{def}}{=} \sup_{x \in \mathbb{R}^N} \{|F(x)| \exp(-b|x|^2)\},
$$
(1.20)
where $|x|$ is the Euclidean norm of $x \in \mathbb{R}^N$. Let
$$
A_a^{(N)} \overset{\text{def}}{=} \{F \in E(N) \mid \|F\|_{b,N} < \infty, \forall b > a\}, \quad a \geq 0.
$$
(1.21)
This set equipped with the topology generated by the family $\{\|\cdot\|_{b,N}, b > a\}$ becomes a Fréchet space. Let $O(N)$ stand for the group of all orthogonal transformations of $\mathbb{R}^N$. A function $F \in E^{(N)}$ is said to be isotropic if for every $U \in O(N)$ and all $x \in \mathbb{R}^N$, $F(Ux) = F(x)$. The subset of $\mathcal{E}^{(N)}$ consisting of isotropic functions is denoted by $\mathcal{E}_{\text{isot}}^{(N)}$. Now let $\mathcal{P}_{\text{isot}}^{(N)} \subset \mathcal{E}_{\text{isot}}^{(N)}$ stand for the set of isotropic polynomials. The classical Study–Weyl theorem [9] (see also [8]) implies that there exists a bijection between the set of all polynomials of one complex variable $\mathcal{P}$ and $\mathcal{P}_{\text{isot}}^{(N)}$ established by
$$
\mathcal{P}_{\text{isot}}^{(N)} \ni P(x) = p((x,x)) \in \mathcal{P},
$$
where $(\cdot, \cdot)$ is the scalar product in $\mathbb{R}^N$. Obviously each a function $F$ having the form
$$
F(x) = f((x,x)),
$$
(1.22)
with certain $f \in \mathcal{E}$, belongs to $\mathcal{E}_{\text{isot}}^{(N)}$. Given a subset $\mathcal{X} \subset \mathcal{E}$, we write $\mathcal{X}(\mathbb{R}^N)$ for the subset of $\mathcal{E}_{\text{isot}}^{(N)}$ consisting of the functions obeying (1.22) with $f \in \mathcal{X}$. In this notation $\mathcal{P}_{\text{isot}}^{(N)} = \mathcal{P}(\mathbb{R}^N)$. Consider a map
$$
\mathcal{E}_{\text{isot}}^{(N)} \ni F \mapsto \left(\Delta + \frac{d}{(x,x)(x,\nabla)}\right)F \in \mathcal{E}_{\text{isot}}^{(N)},
$$
where ∆ and ∇ stand for the Laplacian and for the gradient in \( \mathbb{R}^N \). For a pair of functions \( F \) and \( f \) satisfying (1.22), one has (c.f. (1.8))
\[
\left( \Delta + \frac{d}{(x,x)}(x, \nabla) \right) F(x) = 4 (\Delta_\theta f)((x, x)),
\]
(1.23)
where \( \Delta_\theta \) is defined by (1.7) with \( \theta = N + \frac{d^2}{2} \).
(1.24)
Now let us consider the following Cauchy problem – an analog of (1.13):
\[
\frac{\partial F_n(t, x)}{\partial t} = \tau \left( \Delta + \frac{d}{(x,x)}(x, \nabla) \right) F_n(t, x), \quad t \in [0, 1], \quad x \in \mathbb{R}^N,
\]
\[
F_n(0, x) = \left[ F_{n-1}(1, x \delta^{-(1+\lambda)/2}) \right]^{\delta}, \quad n \in \mathbb{N},
\]
\[
F_0(1, x) = G(x) \in L^+(\mathbb{R}^N).
\]
(1.25)
For \( G \in L^+(\mathbb{R}^N) \), there exists \( g \in L^+ \) such that \( G \) and \( g \) satisfy (1.22), thus the interval (1.15) is defined for such \( G \). The direct corollary of Theorem 1.1 reads
**Theorem 1.3** For every \( d \geq -N \), \( G \in L^+(\mathbb{R}^N) \), \( \tau \in I(g) \), and \( n \in \mathbb{N} \), the problem (1.22) has a unique solution \( F_n \), which also belongs to \( L^+(\mathbb{R}^N) \).
For \( \lambda \in (0, 1/2) \), we have an analog of Theorem 1.2.
**Theorem 1.4** For every \( d \geq -N \) and \( g \in L(\lambda) \), there exist a positive \( \tau_* \in I(g) \) and \( C : [0, \tau_*] \rightarrow \mathbb{R}_+ \), such that
(i) for \( \tau < \tau_* \), the sequence of solutions of (1.22)
\[
\{ F_n(t, x) \mid n \in \mathbb{N}_0, \quad F_0(1, z) = C(\tau)g((x, x)) \}
\]
converges in \( A^{(N)}_{\beta_{-1}} \), \( \beta_* \defeq \tau_*/(\delta^\lambda - 1) \) to the function \( F(t, x) \equiv 1 \);
(ii) for \( \tau = \tau_* \), \( \{ F_n(t, x) \mid n \in \mathbb{N}_0, \quad F_0(1, x) = C(\tau_*)g((x, x)) \}
\]
converges in \( A^{(N)}_{\beta_*} \) to
\[
F_*(t, x) = \delta^{-\delta \theta \lambda/(\delta - 1)} [1 - t(1 - \delta^\lambda)]^{-\theta} \exp \left( \frac{1}{\tau_*} \frac{1 - \delta^{-\lambda}}{1 - t(1 - \delta^{-\lambda})} (x, x) \right),
\]
(1.26)
where \( \theta \) is given by (1.24).
8
Let $\mathcal{M}$ stand for the set of probability measures $\mu$ on $\mathbb{R}^N$ such that
\[ \int_{\mathbb{R}^N} \exp(\varepsilon(x, x)) \mu(dx) < \infty, \]
with certain $\varepsilon > 0$. For each such a measure, the function
\[ F_\mu(x) \overset{\text{def}}{=} \int_{\mathbb{R}^N} \exp((x, y)) \mu(dy), \tag{1.27} \]
belongs to $\mathcal{E}(N)$. For a Borel subset $B \subset \mathbb{R}^N$, we let
\[ B - x = \{ y \in \mathbb{R}^N \mid x + y \in B \}, \quad UB = \{ x \in \mathbb{R}^N \mid U^{-1}x \in B \}, \quad U \in O(N). \]
A measure $\mu \in \mathcal{M}$ is said to be isotropic if it is $O(N)$–invariant (i.e. $\mu(UB) = \mu(B)$), the subset $\mathcal{M}_{\text{isot}} \subset \mathcal{M}$ is to consist of such isotropic measures. Obviously, $F_\mu \in \mathcal{E}_{\text{isot}}(N)$ for $\mu \in \mathcal{M}_{\text{isot}}$. Now let $\mathcal{M}(\mathbb{R}^N)$ be the subset of $\mathcal{M}_{\text{isot}}$ consisting of the measures for which $F_\mu \in \mathcal{L}^{(1)}(\mathbb{R}^N)$. For a pair of measures $\mu, \nu \in \mathcal{M}$, their convolution is as usual
\[ (\mu \ast \nu)(B) = \int_{\mathbb{R}^N} \mu(B - x) \nu(dx). \tag{1.28} \]
Since $F_{\mu \ast \nu} = F_\mu F_\nu$, the measure $\mu \ast \nu$ belongs to $\mathcal{M}(\mathbb{R}^N)$ whenever $\mu$ and $\nu$ possess this property. Now let $\delta, \lambda, \text{ and } \tau$ be as in (1.13), (1.25). Consider the sequence $\{\mu_n, n \in \mathbb{N}_0\}$ defined
\[ \mu_n(dy) = \frac{1}{M_n(\tau)} \exp(\tau(y, y)) \mu_{n-1}^\delta(\delta^{(1+\lambda)/2}dy), \quad \mu_0 = \nu \in \mathcal{M}(\mathbb{R}^N), \tag{1.29} \]
where
\[ M_n(\tau) \overset{\text{def}}{=} \int_{\mathbb{R}^N} \exp(\tau(y, y)) \mu_{n-1}^\delta(\delta^{(1+\lambda)/2}dy), \]
and $\mu_{\ast\delta}$ is the convolution of $\delta$ copies of $\mu$. The measure $\mu_{n-1}^\delta(\delta^{(1+\lambda)/2})$ describes the probability distribution of the normalized sum of $\delta$ identically distributed independent random vectors. By means of the multiplier $\exp(\tau(y, y))$ in (1.29), we set these vectors being dependent, thus the measure $\mu_n$ describes the probability distribution of the following random vector
\[ X^{(n)} = \frac{1}{\sqrt{\delta}} \delta^{-\lambda/2} \left( X_1^{(n-1)} + \ldots + X_{\delta}^{(n-1)} \right). \tag{1.30} \]
The normalization of this sum is "abnormal" (more than normal) due to the additional factor $\delta^{-\lambda/2}$. Every $X(m)$ is the sum of $\delta^m$ vectors of the zero level. Such random vectors are known to be hierarchically dependent (see e.g. [4]). Their dependence is proportional to the parameter $\tau$ – it disappears if $\tau = 0$. Therefore, one may expect that, for small positive values of $\tau$, the dependence remains weak and the vectors obey the classical central limit theorem. In this case, due to the factors $\delta^{-\lambda/2}$, the sequence of measures $\{\mu_n\}$ ought to be asymptotically degenerate at zero, which means that the corresponding by (1.27) sequence $\{F_{\mu_n}\}$ converges to the function $F(x) \equiv 1$. But the functions $F_{\mu_n}$ may be obtained as solutions of the problem (1.25). To use this fact we construct the subset of $\mathcal{M}(\mathbb{R}^N)$ corresponding to $\mathcal{L}(\lambda)$ introduced by Definition (1.2). Choose $\lambda \in (0, 1/2)$. For a measure $\nu \in \mathcal{M}(\mathbb{R}^N)$, let $g \in \mathcal{L}(1)$ be the function such that $F_{\nu}(x) = g((x, x))$. Then
$$\mathcal{M}_\lambda(\mathbb{R}^N) \overset{\text{def}}{=} \{\nu \in \mathcal{M}(\mathbb{R}^N) \mid g \in \mathcal{L}(\lambda)\}. \quad (1.31)$$
The following assertion is a corollary of Theorem (1.4) for $d = 0$.
**Theorem 1.5** For every $N \in \mathbb{N}$ and $\nu \in \mathcal{M}_\lambda(\mathbb{R}^N)$, there exists $\tau_* > 0$ such that
(i) for $\tau < \tau_*$, the sequence of measures defined by (1.29)
$$\{\mu_n \mid n \in \mathbb{N}_0, \mu_0 = \nu\}$$
converges weakly to the measure degenerate at zero;
(ii) for $\tau = \tau_*$, this sequence converges weakly to the isotropic Gaussian measure with variance $2N(\delta^\lambda - 1)/\tau_*$.
It should be pointed out that the convergence to a nondegenerate measure for the abnormal normalization described by claim (ii) means the appearance of a strong dependence between the random vectors considered. For $\tau < \tau_*$, the dependence is weak and the classical central limit theorem ought to hold. To show this we introduce the classical normalization instead of (1.30). So we set along with (1.29):
$$\tilde{\mu}_n(dy) = \frac{1}{\tilde{M}_n(\tau)} \exp \left(\delta^{-n\lambda/2} \tau(y, y)\right) \tilde{\mu}_n(\sqrt{\delta}dy), \quad \mu_0 = \nu \in \mathcal{M}(\mathbb{R}^N),$$
$$\tilde{M}_n(\tau) = \int_{\mathbb{R}^N} \exp \left(\delta^{-n\lambda/2} \tau(y, y)\right) \tilde{\mu}_n(\sqrt{\delta}dy). \quad (1.32)$$
Theorem 1.6 Let $N$, $\nu$, and $\tau_*$ be as in Theorem 1.5. Then for $\tau < \tau_*$, the sequence of measures $\{\tilde{\mu}_n | n \in \mathbb{N}_0, \tilde{\mu}_0 = \nu\}$ defined by (1.32) converges weakly to an isotropic Gaussian measure.
2 Preliminaries
2.1 Laguerre Entire Functions and Evolution Operator
We start with the description of the Fréchet spaces $\mathcal{A}_a$. A subset $B \subset \mathcal{A}_a$ is said to be bounded in $\mathcal{A}_a$ if for every $b > a$, there exists $K_b > 0$ such that, for all $f \in B$, $\|f\|_b \leq K_b$.
Proposition 2.1 For every $a \geq 0$, the space $\mathcal{A}_a$ possesses the properties:
(i) the relative topology on bounded subsets of $\mathcal{A}_a$ coincides with the topology of uniform convergence on compact subsets of $\mathcal{C}$;
(ii) multiplication, i.e., $(f, g) \mapsto fg$ is a continuous map from $\mathcal{A}_a \times \mathcal{A}_b$ into $\mathcal{A}_{a+b}$;
(iii) differentiation, i.e. $f \mapsto f'$ is a continuous self-map of $\mathcal{A}_a$.
Remark 2.1 It can be easily shown that, for positive $a$ and $b$,
$$\|fg\|_{a+b} \leq \|f\|_a \|g\|_b,$$
thus $(f, g) \mapsto fg$ is a continuous map from $\mathcal{B}_a \times \mathcal{B}_b$ into $\mathcal{B}_{a+b}$, which implies claim (ii) of the latter statement.
Proposition 2.2 Every sequence $\{f_n, n \in \mathbb{N}\} \subset \mathcal{L}_a$, $a \geq 0$, that converges in $\mathcal{E}$ to a function $f \in \mathcal{A}_a$, which does not vanish identically, is a bounded subset of $\mathcal{A}_a$ and hence, by claim (i) of Proposition 2.1, it converges in $\mathcal{A}_a$ to $f \in \mathcal{L}$.
For $f \in \mathcal{L}^+$, one has $f(0) > 0$ (see (1.3)). Therefore, for such a function, there exists the neighborhood $\mathcal{D}$ of the origin in which $f \neq 0$, hence the following holomorphic function can be defined
$$\varphi(z) = \log f(z), \quad z \in \mathcal{D}. \tag{2.2}$$
In the sequel we use the notation
$$\varphi^{(k)} = (D^k \log f)(0), \quad k \in \mathbb{N}_0. \tag{2.3}$$
Proposition 2.3 [The sign rule] Let \( f \in \mathcal{L}^+ \), then
\[
(-1)^{k-1} \varphi^{(k)} \geq 0, \quad k \in \mathbb{N}.
\] (2.4)
Equalities hold simultaneously for all \( k \geq 2 \) and only for \( f(z) = C \exp(az) \).
Lemma 2.1 For a sequence \( \{ f_n(z) \mid n \in \mathbb{N}_0, f_n \in \mathcal{L}^+ \} \), let the derivatives (2.3) satisfy:
\( (i) \) \( \{ \varphi_n^{(k)} \} \) converges to \( \varphi^{(k)} \), \( k = 0, 1 \); (ii) \( \{ \varphi_n^{(2)} \} \) converges to zero. Then \( \{ f_n \} \) converges to \( \exp(\varphi^{(0)} + \varphi^{(1)} z) \) in \( \mathcal{A}_\psi \), \( \psi = \sup \varphi^{(1)}_n \).
**Proof.** By claim (ii) of Proposition 2.1 and Proposition 2.2, to prove this statement we only need to show that the sequence \( \{ f_n(z)/f_n(0) \} \) converges uniformly on compact subsets of \( \mathbb{C} \). Due to known Vitali’s theorem and to the fact that, for the functions considered, \( M_f(r) = f(r) \), we may do this by proving the pointwise convergence of \( \{ f_n(z)/f_n(0) \} \) on \( \mathbb{R}^+ \).
To this end we use the specific form of \( f \in \mathcal{L}^{(1)} \) given by (1.4). For each \( \gamma \geq 0 \), one has \( \exp(\gamma - \frac{1}{2} \gamma^2) \leq 1 + \gamma \leq \exp(\gamma) \). Hence for \( z \in \mathbb{R}^+ \),
\[
\exp(z\varphi^{(1)}_n + \frac{1}{2} z^2 \varphi^{(2)}_n) \leq \frac{f_n(z)}{f_n(0)} \leq \exp(z\varphi^{(1)}_n),
\] (2.5)
which yields the stated convergence.
For an entire function \( f \in \mathcal{E} \) and \( t \geq 0 \), we define
\[
(\exp(t\Delta_\theta)f)(z) = \sum_{k=0}^{\infty} \frac{t^k}{k!}(\Delta^k_\theta f)(z).
\] (2.6)
Proposition 2.4 For every positive \( a \) and \( t \) obeying \( at < 1 \), and \( \theta \geq 0 \),
\[
\| \exp(t\Delta_\theta)f \|_b \leq (1 - at)^{-\theta}\|f\|_a, \quad b = a/(1 - at),
\]
which means that (2.7) defines a continuous linear map
\[
\mathcal{A}_a \ni f \mapsto f_t \overset{\text{def}}{=} (\exp(t\Delta_\theta)f) \in \mathcal{A}_b, \quad b = a/(1 - at).
\] (2.7)
Corollary 2.1 For every positive \( a \) and \( t_0 \), a map \( (0, t_0) \ni t \mapsto f_t \in \mathcal{A}_{b_0} \), where \( b_0 = a/(1 - at_0) \) and \( f_t \) is defined by (2.7), is differentiable on \( (0, t_0) \) and
\[
\frac{\partial f_t}{\partial t} = \Delta_\theta f_t, \quad t \in (0, t_0).
\] (2.8)
One of the main results of [6] is Theorem 1.3 which asserts that the operators of the type of (2.6) preserves the class $L^\mathcal{L}$. In our case it reads as follows
**Proposition 2.5** Let $a$, $b$, $t$, and $\theta$ be as in Proposition 2.4. Then the operator (2.6), (2.7) maps $\mathcal{L}_a$ into $\mathcal{L}_b$.
The following statements have also been proven in [6].
**Proposition 2.6** For $t > 0$, the above operator has the integral form:
$$
(\exp(t\Delta_\theta)f)(z) = \exp\left(-\frac{z}{t}\right) \int_0^{+\infty} s^{\theta-1} w_\theta\left(\frac{z}{s}\right) e^{-s} f(ts) ds,
$$
where $w_\theta$ is defined by (1.12).
**Remark 2.2** Setting in (2.9) $z = 0$, one obtains for $f \in \mathcal{L}^+$ and $\theta > 0$: $(\exp(t\Delta_\theta)f)(0) > 0$. On the other hand, one has from (2.6)
$$
(\exp(t\Delta_\theta)f)(0) = \sum_{k=0}^{\infty} \frac{t^k}{k!} f^{(k)}(0) \frac{\Gamma(\theta+k)}{\Gamma(\theta)}. \tag{2.10}
$$
Passing here to the limit $\theta \to 0$ one gets
$$
(\exp(t\Delta_\theta)f)(0) = f(0) > 0. \tag{2.11}
$$
Below the case $\theta = 0$ is always understood as the above limit.
**Proposition 2.7** Let $v \in \mathbb{R}$ and $\exp(vz)h(z) \in \mathcal{A}_b$, ($b \geq 0$). For any $u \geq 0$ obeying the condition $ub < 1$,
$$
\exp(u\Delta_\theta)\exp(vz)h(z) = \exp\left(\frac{vz}{1-uv}\right) h_u(z), \tag{2.12}
$$
where
$$
h_u(z) = (1-uv)^{-\theta}\exp(u(1-uv)\Delta_\theta)h\left(\frac{z}{(1-uv)^2}\right). \tag{2.13}
$$
Moreover, if $h \in \mathcal{A}_a$, then $h_u \in \mathcal{A}_c$, where
$$
c = a(1-uv)^{-1}(1-(v+a)u)^{-1}. \tag{2.14}
$$
By means of (2.6), we construct the evolution operator which solves (1.13):
$$f_n(t, z) = \exp(t \Delta\phi) \left[ f_{n-1}(1, z\delta^{-1-\lambda}) \right]^\delta \overset{\text{def}}{=} T_t(f_{n-1}(t, \cdot))(z),$$
(2.15)
provided all $f_n(t, z)$ belong to the domain of $T_t$, $t \in [0, 1]$. For short we write
$$f_n(1, z) \overset{\text{def}}{=} f_n(z), \quad T_1 \overset{\text{def}}{=} T.$$
(2.16)
Thus one has
$$f_n = T(f_{n-1}).$$
(2.17)
We use such $T_t$ to define the operators between the Fréchet spaces $A_a$ and the Banach spaces $B_b$. In all such cases we denote them by $T_t$ pointing out if necessary between which spaces acts given $T_t$. Combining claim (ii) of Proposition 2.1 with Propositions 2.4 and 2.5 one has
**Proposition 2.8** For every $a < \frac{\delta^\lambda}{t\tau}$, the operator $T_t$ continuously maps: $B_a \rightarrow B_b, A_a \rightarrow A_b$, and $L_a \rightarrow L_b$, where $b = a\delta^{-\lambda}/(1 - a\tau\delta^{-\lambda})$.
**Proposition 2.9** Let the sequence $\{f_n(z) \mid n \in \mathbb{N}_0, \ f_0(z) = g(z) \in L^+\}$ defined by (2.17) converge in $A_a, a \geq 0$ to a function $f$. Then the sequence of solutions of (1.13) $\{f_n(t, z) \mid n \in \mathbb{N}_0, \ f_0(z) = g(z)\}$, defined by (2.15), converges in $A_a$ to the function
$$f(t, z) = (T_t f)(z).$$
(2.18)
To establish the existence and convergence of $\{f_n\}$ we use an analog of the Fréchet derivative of $T$ and then study the fixed points of $T$ and their stability. The following corollary of Proposition 2.8 allows to define the differentiability of $T$ acting between the Fréchet spaces. For $a \in [0, \tau\delta^{-\lambda})$, we set
$$b(a) \overset{\text{def}}{=} \frac{a\delta^{-\lambda}}{1 - a\tau\delta^{-\lambda}}.$$
(2.19)
**Corollary 2.2** Let $a < \frac{\delta^\lambda}{\tau}$, then there exists $\varepsilon > 0$ such that, for all $a' \in (a, a + \varepsilon)$, the operator $T$ continuously maps $B_{a'}$ into $B_{b(a')}$.
14
Definition 2.1 The operator $T : A_a \to A_{b(a)}$ is said to be differentiable on $A_a$ if for every $f \in A_a$, there exist $\varepsilon > 0$ and a continuous linear operator $T'[f] : A_a \to A_{b(a)}$ such that, for every $a' \in (a, a + \varepsilon)$, $T'[f]$ is the Fréchet derivative of $T$ considered as an operator between the Banach spaces $B_a$ and $B_{b(a)}$. The operator $T'[f]$ is said to be a derivative of $T$ at $f$.
Lemma 2.2 For $a < \delta^\lambda / \tau$, the operator $T : A_a \to A_{b(a)}$ is differentiable on $A_a$ and its derivative $T'[f]$ is the following operator
$$T'[f](h) = \delta \exp(\tau \Delta_\delta) \left( (f^\delta^{-1}h)(\delta^{-1-\lambda}z) \right). \tag{2.20}$$
Proof. For $a' \in (a, \delta^\lambda / \tau)$ and $f, h \in B_{a'}$, one has
$$T(f + h) = T(f) + \delta \exp(\tau \Delta_\delta) \left( (f^\delta^{-1}h)(\delta^{-1-\lambda}) \right) + R(f, h),$$
$$R(f, h) = \exp(\tau \Delta_\delta) \left( \sum_{k=2}^{\delta} \binom{\delta}{k} f^\delta^{-k}h^k \right)(\delta^{-1-\lambda}).$$
By means of Remark 2.1, (2.1), and Proposition 2.4, one obtains
$$\left\| \exp(\tau \Delta_\delta) \left( f^\delta^{-k}h^k \right)(\delta^{-1-\lambda}) \right\|_{b(a')} \leq (1 - a'\tau\delta^{-\lambda})^{-\theta} \|f\|_{a'\delta^{-k}} \|h\|_{a'k},$$
$$k = 1, 2, \ldots, \delta.$$
This gives for all $a' \in (a, \delta^\lambda / \tau)$,
$$\|R(f, g)\|_{b(a')} = o(\|h\|_{a'}),$$
and also for $T'$ defined by (2.20),
$$\|T'[f](h)\|_{b(a')} \leq \delta(1 - a'\tau\delta^{-\lambda})^{-\theta} \|f\|_{a'\delta^{-1}} \|h\|_{a'}.$$
By the latter estimate, $T'[f]$ continuously maps $B_{a'}$ into $B_{b(a')}$ whereas by the former one, this operator is the Fréchet derivative of $T : B_{a'} \to B_{b(a')}$. $\blacksquare$
The case of $\tau = 0$ was considered in (1.16), thus from now on we assume $\tau > 0$. It turns out that it is convenient to remove the explicit dependence on $\tau$ from the operator $T$. To this end we set
$$\tau \overset{\text{def}}{=} \beta(\delta^\lambda - 1), \tag{2.21}$$
15
and include $\beta$ into $z$. Then we consider the sequence $\{g_n(z)\}$
$$g_n(z) = Q(g_{n-1})(z), \quad n \in \mathbb{N},$$
where $g$ is the function which defines the starting element of $\{f_n\}$. To prove Theorem 1.6 we shall also use the sequence of functions from $\mathcal{L}^{(1)}$, $\{\tilde{g}_n(z) | n \in \mathbb{N}_0, \tilde{g}_0(z) = g(\beta z)\}$, where $g$ is as above, and
$$\tilde{g}_n(z) = \tilde{Q}_n(\tilde{g}_n)(z)$$
Comparing (2.15), (2.16) with (2.22) one obtains from Proposition 2.8 and Lemma 2.2.
**Proposition 2.10** For every $a < \delta^\lambda/(\delta^\lambda - 1)$, $Q$ is a differentiable (and hence continuous) operator, which maps: $\mathcal{A}_a \rightarrow \mathcal{A}_{b'}, \mathcal{L}^+ \rightarrow \mathcal{L}^+_{b'}$, where $b' = a[\delta^\lambda - a(\delta^\lambda - 1)]^{-1}$. Its derivative is
$$Q'[g](h)(z) = \exp \left( (\delta^\lambda - 1)\Delta_\theta \right) \left[ \left[ g^{\delta^{-1}h} \right](\delta^{-1}\lambda z) \right].$$
For $\tau \in I(g)$, $\beta$ varies in $J(g) \overset{\text{def}}{=} (0, 1/\alpha]$ (see (2.24) and (1.16)). Let $g \in \mathcal{L}^+$ be chosen. Then it possesses the representation (1.7) with $\alpha \geq 0$, which determines the intervals $I(g)$ (1.15) and $J(g)$, and $g \in \mathcal{L}^+_\alpha \subset \mathcal{A}_\alpha$.
**Lemma 2.3** For $\tau \in I(g)$, all the elements of $\{f_n | n \in \mathbb{N}_0, f_0 = g\}$ belong to $\mathcal{L}^+_\alpha \subset \mathcal{A}_\alpha$, all the elements of $\{g_n | n \in \mathbb{N}_0, g_0(z) = g(\beta z)\}$ belong to $\mathcal{L}^+_{\beta \alpha}$.
**Proof.** For $\tau \in I(g)$, $\alpha \leq (\delta^\lambda - 1)/\tau < \delta^\lambda/\tau$, thus by Corollary 2.3, $T$ maps $\mathcal{A}_\alpha$ into $\mathcal{A}_{b(\alpha)}$ with
$$b(\alpha) = \frac{\alpha \delta^{-\lambda}}{1 - \alpha \tau \delta^{-\lambda}} \leq \frac{\alpha \delta^{-\lambda}}{1 - 1 + \delta^{-\lambda}} = \alpha,$$
which means $T : \mathcal{A}_\alpha \rightarrow \mathcal{A}_{b(\alpha)}$. By Proposition 2.8, $T$ maps $\mathcal{L}$ into itself; by Remark 2.2, $(Tf)(0) > 0$ whenever $f(0) > 0$. The second part of Lemma concerning $\{g_n\}$ directly follows from the first one.
Since the starting element of $\{g_n\}$ is of the form $g_0(z) = g(\beta z)$, all its elements depend on $\beta$. Therefore, one may consider $g_n$ as a map from $J(g)$ into $\mathcal{A}_1$. To emphasize this fact we write sometimes $g_n(\cdot, \beta)$ instead of $g_n$.
16
Lemma 2.4 For every \( n \in \mathbb{N}_0 \), the map
\[
g_n : J(g) \to A_1
\]
is differentiable on \( \text{Int}J(g) \), its derivative at \( \beta \) is an entire function \( \dot{g}_n \in A_1 \).
**Proof.** Let us show that, for \( \beta \in \text{Int}J(g) \), there exists an entire function \( \dot{g}_n \in A_1 \) such that, for \( \beta \in \text{Int}J(g) \),
\[
g_n(\cdot, \beta) - g_n(\cdot, \beta) = \Delta \beta \dot{g}_n + r_n(\cdot, \Delta \beta), \quad \Delta \beta = \beta - \beta,
\]
where \( r_n(\cdot, \Delta \beta)/\Delta \beta \to 0 \) in \( A_1 \) when \( \Delta \beta \to 0 \). By claim (iii) of Proposition 2.1, differentiation is a continuous self-map of \( A_n \). Since \( g_0(z, \beta) = g(\beta z) \), the stated property obviously holds for \( n = 0 \). For some \( n \geq 1 \), let \( \dot{g}_{n-1} \) obey (2.26) and belong to \( A_1 \). Then
\[
g_n(\cdot, \beta) - g_n(\cdot, \beta) = Q(g_{n-1}(\cdot, \beta)) - Q(g_{n-1}(\cdot, \beta)) = Q((g_{n-1}(\cdot, \beta) + \Delta \beta \dot{g}_{n-1} + r_{n-1}(\cdot, \Delta \beta)) - Q(g_{n-1}(\cdot, \beta)).
\]
By means of the derivative (2.24), it can be written as
\[
g_n(\cdot, \beta) - g_n(\cdot, \beta) = \Delta \beta Q'[g_{n-1}](\dot{g}_{n-1}) + Q'[g_{n-1}](r_{n-1}(\cdot, \Delta \beta)) + R_{n-1},
\]
where for all \( a > 0 \),
\[
\|R_{n-1}\| = o(\Delta \beta\|\dot{g}_{n-1}\|_{c(a)} + \|r_{n-1}(\cdot, \Delta \beta)\|_{c(a)}).
\]
Since the operator \( Q'[g_{n-1}] \) is linear and continuous, the function
\[
Q'[g_{n-1}](r_{n-1}(\cdot, \Delta \beta)) + R_{n-1}
\]
obeys the conditions imposed on \( r_n \), thus \( \dot{g}_n \) exists and
\[
\dot{g}_n = Q'[g_{n-1}](\dot{g}_{n-1}).
\]
\[\blacksquare\]
Let \( g_n^{(k)} \equiv D_z^k g_n, k \in \mathbb{N} \), then claim (iii) of Proposition 2.1 implies
**Corollary 2.3** For every \( n \in \mathbb{N}_0 \) and \( k \in \mathbb{N} \), the map \( g_n^{(k)} : J(g) \to A_1 \) is differentiable on \( \text{Int}J(g) \), its derivative at \( \beta \) is an entire function \( \dot{g}_n^{(k)} \) from \( A_1 \). For every \( z_0 \in \mathcal{C} \), \( g_n^{(k)}(z_0, \beta) \) is \( \beta \)-differentiable on \( \text{Int}J(g) \) and
\[
\frac{\partial g_n^{(k)}(z_0, \beta)}{\partial \beta} = \dot{g}_n^{(k)}(z_0, \beta).
\]
2.2 Invariant Sets and Fixed Points
By Lemma 2.3, for chosen \( g \in \mathcal{L}^+ \) and \( \tau \in I(g) \), \( \mathcal{L}^+ \) is an invariant set of \( T \). It turns out that this set contains a subset which \( T \) maps into itself as well. Proposition 2.7 implies that such one is
\[
\mathcal{G} \overset{\text{def}}{=} \{ f(z) = C \exp(uz) \mid C > 0, \ u \geq 0 \} \subset \mathcal{L}^+.
\]
In fact
\[
T(C \exp(uz)) = C^\delta(1 - u\tau\delta^{-\lambda})^{-\theta} \exp \left( \frac{u\delta^{-\lambda}z}{1 - u\tau\delta^{-\lambda}} \right),
\]
which also yields that \( \mathcal{G} \) contains the following fixed points of \( T \):
\[
f_{i,*}(z) = C_{i,*} \exp(u_{i,*}z), \quad i = 1, 2,
\]
\[
C_{1,*} = 1, \ u_{1,*} = 0; \quad C_{2,*} = \delta^{-\lambda \theta / (\delta - 1)}, \ u_{2,*} = \frac{1}{\tau}(\delta^\lambda - 1).
\]
Consider the sequence \( \{ f_n \mid n \in \mathbb{N}_0, \ f_0 = C_0g = C_0\exp(\alpha z) \in \mathcal{G} \} \). By means of (2.31), one can calculate \( f_n \) explicitly
\[
f_n(z) = C_n \exp(u_n z),
\]
\[
C_n = C_0^{\delta^n} \Xi_n, \quad u_n = \frac{\alpha \delta^{-n\lambda}}{1 - \frac{\alpha \tau}{\delta^\lambda - 1}(1 - \delta^{-n\lambda})},
\]
\[
\Xi_n = \xi_n \prod_{l=1}^{n-1} (\xi_l(\delta^{-1})^{\delta^{n-1-l}} - 1), \quad \xi_l = \left[ 1 - \frac{\alpha \tau}{\delta^\lambda - 1}(1 - \delta^{-l\lambda}) \right]^{-\theta}.
\]
In this case we may check the validity of Theorem 1.2 directly. Set
\[
\tau_* \overset{\text{def}}{=} \frac{1}{\alpha}(\delta^\lambda - 1),
\]
\[
C(\tau) \overset{\text{def}}{=} \prod_{k=0}^{\infty} \left( \frac{\delta^\lambda - 1 - \alpha \tau + \alpha \tau \delta^{-(k-1)\lambda}}{\delta^\lambda - 1 - \alpha \tau + \alpha \tau \delta^{-k\lambda}} \right)^{\theta \delta^{-k-1}}.
\]
Then for \( \tau < \tau_* \), the sequence \( \{ f_n \mid n \in \mathbb{N}_0, \ f_0(z) = C(\tau) \exp(\alpha z) \} \) converges in \( \mathcal{A}_\alpha \) to \( f_{1,*} \equiv 1 \). If for such \( \tau \), one chooses \( f_0(z) = C_0\exp(\alpha z) \) with \( C_0 < C(\tau) \) (resp. \( C_0 > C(\tau) \)), then \( C_n \) in (2.34) tends to zero (resp. to infinity). For \( \tau = \tau_* \), one has in (2.36) and (2.34) respectively
\[
C(\tau_*) = C_{2,*},
\]
\[
C_n = C_0^{\delta^n} \exp \left( \lambda \delta^{\delta^n - 1} \log \delta \right), \ u_n = \alpha.
\]
Thus for all \( n \in \mathbb{N}_0, \ C_n = C_{2,*} \), if \( C_0 = C(\tau_s) = C_{2,*} \). For \( C_0 < C_{2,*} \) (resp. \( C_0 > C_{2,*} \)), \( C_n \) tends to zero (resp. to infinity). The fixed points of \( Q \) in \( \mathcal{G} \) are
\[
g_{i,*}(z) = C_{i,*} \exp(v_{i,z}), \quad v_{1,*} = 0, \quad v_{2,*} = 1. \tag{2.37}
\]
To describe the stability of the fixed points (2.32) we solve the eigenvalue problem
\[
T'[f_{i,*}](h) = \Lambda h. \tag{2.38}
\]
To this end we set
\[
h(z) = f_{i,*}(z)p(z) = C_{i,*} \exp(u_{i,z})p(z),
\]
with \( p \) being a polynomial, and obtain from (2.20) and Proposition 2.7
\[
T'[f_{i,*}](h) = \delta C_{i,*}^{\delta}(1 - u_{i,*}^{\delta - \lambda \tau})^{-\theta} \exp\left(\frac{u_{i,z}^{\delta - \lambda \tau}}{1 - u_{i,*}^{\delta - \lambda \tau}}\right) \exp\left(\tau(1 - u_{i,*}^{\delta - \lambda \tau})\Delta_\theta\right) p\left(\frac{z^{\delta - 1 - \lambda}}{(1 - u_{i,*}^{\delta - \lambda \tau})^2}\right).
\]
Suppose that \( \deg p = k, \ k \in \mathbb{N}_0 \) and apply the latter formula in (2.38). Since \( \exp(\ldots \Delta_\theta) \) maps such \( p \) into a polynomial \( q, \ \deg q = k, \) we may find \( \Lambda_k^{(i)} \) setting the coefficients in front of the \( k \)-th powers of \( z \) to be equal. This yields
\[
\Lambda_k^{(i)} = \frac{\delta^{-k\lambda-k+1}}{(1 - u_{i,*}^{\delta - \lambda \tau})^{2k}}, \quad k \in \mathbb{N}_0. \tag{2.39}
\]
For both \( f_{1,*}, \ \Lambda_0 = \delta > 1, \) which corresponds to their instability with respect to the variation of the constant multiplier \( C \). The rest of the eigenvalues which describe \( f_{1,*} \) are \( \Lambda_k^{(1)} = \delta^{-k\lambda-k+1} < 1. \) But for \( f_{2,*}, \) one has
\[
\Lambda_k^{(2)} = \delta^{\delta \lambda - k + 1}, \quad k \in \mathbb{N}_0. \tag{2.40}
\]
The eigenvalues of \( Q'[g_{i,*}] \) are exactly the same as given by (2.39). For \( \lambda \in (0, 1/2), \ \Lambda_2^{(2)} < 1. \) This means that, in the corresponding spaces \( \mathcal{A}_2, \ f_{2,*}, g_{2,*} \) have the stable manifolds of codim = 2 and \( f_{1,*}, g_{1,*} \) have those of codim = 1. This fact plays an important role in proving the convergence to these fixed points. The proof will be done by showing that there exist \( \beta_s > 0 \) and a function \( C : (0, \beta_s] \to \mathcal{R}_+ \) such that all elements of the sequence \( \{g_n \mid g_0(z) = C(\beta_s)g(\beta_s z)\} \) remain in the stable manifold of \( g_{2,*} \) and the elements of \( \{g_n \mid g_0(z) = C(\beta)g(\beta z), \ \beta < \beta_s\} \) remain in the stable manifold of \( g_{1,*}. \) The convergence of the corresponding sequences \( \{f_n\} \) will be obtained as a direct corollary.
3 Proofs
3.1 Main Lemmas
The case where the initials elements of the sequences considered are chosen in $\mathcal{G}$ has already been described, thus from now on we suppose that these functions are chosen outside of $\mathcal{G}$. We set (see (2.2), (2.3))
$$g_n(z) = C_n \exp(\varphi_n(z)), \quad \tilde{g}_n(z) = \exp(\tilde{\varphi}_n(z)), \quad \varphi_n(0) = \tilde{\varphi}_n(0) = 0,$$
and for $k \in \mathbb{N}$,
$$\varphi_n^{(k)} \equiv (D^k \varphi_n)(0), \quad \tilde{\varphi}_n^{(k)} \equiv (D^k \tilde{\varphi}_n)(0) = \delta^{n \lambda k} \varphi_n^{(k)}.$$ \hfill (3.2)
As it has been shown above (Lemma 2.4 and Corollary 2.3), all $\varphi_n^{(1)}$ are differentiable, and hence continuous, functions of $\beta \in J(g)$. For $\beta = 0$, all $\varphi_n^{(1)}$ are equal to zero, thus one may assume that, for every $n \in \mathbb{N}_0$, the following inequality
$$\varphi_n^{(1)} < (1 - \delta^{-\lambda})^{-1},$$ \hfill (3.3)
holds for $\beta$ small enough, say, for $\beta \in J_n = (0, \hat{\beta}_n)$. Below we obtain the estimates which allow to evaluate the intervals $J_n$. Thus we set
$$\nu_n = \frac{1}{1 - (1 - \delta^{-\lambda})\varphi_n^{(1)}}, \quad \kappa_n = \delta^{-\lambda} \nu_n.$$ \hfill (3.4)
Lemma 3.1 [Main estimates] For $\beta \in J_n$, the following estimates hold
$$C_n \geq C_{n-1}^\delta; \quad C_n \leq C_{n-1}^\delta \nu_n^\theta,$$
$$C_n \geq C_{n-1}^\delta \nu_n^\theta \exp \left\{ \frac{1}{2} \theta(\theta + 1) \kappa_n^2 (1 - \delta^{-\lambda})^2 \delta^{2\lambda - 1} \varphi_n^{(2)} \right\}.$$ \hfill (3.7)
Equalities hold in (3.3)–(3.7) only in the case $\theta = 0$. Further
$$\varphi_n^{(2)} > \delta^{2\lambda - 1} \kappa_n \varphi_n^{(2)}; \quad \varphi_n^{(1)} < \kappa_n \varphi_n^{(1)}; \quad \varphi_n^{(1)} > \kappa_n \varphi_n^{(1)} + (\theta + 1)(1 - \delta^{-\lambda}) \delta^{2\lambda - 1} \kappa_n^3 \varphi_n^{(2)}.$$ \hfill (3.8) \hfill (3.9) \hfill (3.10)
\[ \tilde{\varphi}_{n}^{(2)} > \delta^{-1}n\tilde{\varphi}^{(2)}_{n-1}; \quad (3.11) \]
\[ \tilde{\varphi}_{n}^{(1)} < \nu_n\tilde{\varphi}^{(1)}_{n-1}; \quad (3.12) \]
\[ \tilde{\varphi}_{n}^{(1)} > \nu_n\tilde{\varphi}^{(1)}_{n-1} + (\theta + 1)(1 - \delta^{-\lambda})\delta^{-1}n^3\delta^{-(n-1)\lambda}\tilde{\varphi}^{(2)}_{n-1}. \quad (3.13) \]
**Proof.** First we prove (3.5). Consider
\[ S(t, z) \overset{\text{def}}{=} \exp(t\Delta_\theta) \left[ g_{n-1}(z\delta^{-1-\lambda}) \right]^\delta, \quad t \in [0, \bar{t}] \], \quad \bar{t} \overset{\text{def}}{=} \delta^{-1}, \quad n \in \mathbb{N}. \quad (3.14) \]
Taking into account Corollary 2.1, (2.8), (2.22), and Lemma 2.3 one concludes that \( S \) belongs to \( \mathcal{L}^+ \) and satisfies the equation
\[ \frac{\partial S}{\partial t} = \Delta_\theta S, \quad S(0, z) = \left[ g_{n-1}(z\delta^{-1-\lambda}) \right]^\delta, \quad S(\bar{t}, z) = g_n(z). \quad (3.15) \]
We set
\[ S_k(t) \overset{\text{def}}{=} (D_z^k S)(t, 0), \quad k \in \mathbb{N}_0, \]
and obtain from (3.15) and (1.7)
\[ \frac{\partial S_0(t)}{\partial t} = \theta S_1(t). \]
Since \( S \in L^+, \) \( S_1(t) > 0 \) and for all \( t \in [0, \bar{t}], \)
\[ S_0(\bar{t}) > S_0(0) \quad \text{for} \ \theta > 0, \quad S_0(\bar{t}) = S_0(0) \quad \text{for} \ \theta = 0. \]
This estimate and the boundary conditions (3.15) gives (3.5). Now we set
\[ p_n(z) = \exp(-\varphi^{(1)}_n z)g_n(z), \quad (3.16) \]
insert \( g_{n-1}(z) = \exp(\varphi^{(1)}_{n-1} z)g_{n-1}(z) \) into (2.22), and use (2.12). Then
\[ g_n(z) = \nu_n^\theta \exp(\kappa_n\varphi^{(1)}_{n-1} z) \exp(t_n\kappa_n^{-2}\Delta_\theta) \left[ p_{n-1}(z\delta^{-1}\kappa_n^2) \right]^\delta, \quad (3.17) \]
where \( t_n = (1 - \delta^{-\lambda})\kappa_n. \) For \( t \in [0, t_n], \) we define
\[ \exp R(t, z) = \exp(t\Delta_\theta) \left[ p_{n-1}(z\delta^{-1}) \right]^\delta. \quad (3.18) \]
According to Proposition 2.7, the above function can be written in the form
\[ \exp R(t, z) = \exp(\tilde{u}z)\tilde{p}(z), \]
21
where \( \hat{u} < 0 \) and \( \hat{p} \) belongs to \( \mathcal{L}^+ \). Thus Proposition 2.3 yields for \( k \geq 2 \)
\[
(-1)^{k-1} R_k(t) = (-1)^{k-1} (D_z^k \log \hat{p}(0)) > 0. \tag{3.19}
\]
Besides, we have
\[
R(0, z) = \delta \log C_{n-1} - \delta^\lambda \varphi^{(1)}_{n-1} z + \delta \varphi_{n-1}(z \delta^{\lambda - 1}), \tag{3.20}
\]
which gives
\[
R_0(0) = \delta \log C_{n-1}, \quad R_1(0) = 0, \quad R_2(0) = \delta^{2\lambda - 1} \varphi^{(2)}_{n-1}. \tag{3.21}
\]
Comparing (3.18) and (3.17), one obtains
\[
R(t_n, z \kappa_n^2) = \varphi_n(z) - \kappa_n \varphi^{(1)}_{n-1} z + \log C_n - \theta \log \nu_n, \tag{3.22}
\]
which yields
\[
R_0(t_n) = \log C_n - \theta \log \nu_n, \quad R_1(t_n) = \kappa_n^{-2} (\varphi^{(1)}_n - \kappa_n \varphi^{(1)}_{n-1}), \tag{3.23}
\]
\[
R_2(t_n) = \kappa_n^{-4} \varphi^{(2)}_n.
\]
For \( R(t, z) \), we obtain from (3.18) an equation of the type of (1.9), (3.15)
\[
\frac{\partial R(t, z)}{\partial t} = \theta (D_z R)(t, z) + z\left[(D_z^2 R)(t, z) + (D_z R)^2(t, z)\right],
\]
with the initial condition given by (3.20). It yields in turn
\[
\frac{\partial R_0(t)}{\partial t} = \theta R_1(t), \tag{3.24}
\]
\[
\frac{\partial R_1(t)}{\partial t} = (\theta + 1) R_2(t) + R_1^2(t), \tag{3.25}
\]
\[
\frac{\partial R_2(t)}{\partial t} = (\theta + 2) R_3(t) + 4 R_1(t) R_2(t). \tag{3.26}
\]
By the sign rule (3.19), \( R_2(t) < 0 \), thus for every \( t_* \) such that \( R_1(t_*) = 0 \), one has from (3.25)
\[
\frac{\partial R_1}{\partial t}(t_*) < 0.
\]
Clearly, such \( t_* \) is at most one. Since \( R_1(0) = 0 \), one has \( t_* = 0 \) and
\[
R_1(t) < 0, \quad \forall t \in (0, t_n], \tag{3.27}
\]
22
which yields in (3.24)
\[ R_0(t_n) > R_0(0) \quad \text{for} \quad \theta > 0, \quad R_0(t_n) = R_0(0) \quad \text{for} \quad \theta = 0, \]
and \( R_1(t_n) < 0 \), implying (3.6) and (3.9) if the conditions (3.20) − (3.23) are taken into account. Applying again (3.19) and (3.27) in (3.26) we get
\[ \frac{\partial R_2(t)}{\partial t} > 0, \quad \forall t \in (0, t_n], \]
which yields in (3.25)
\[ R_1(t) > t(\theta + 1)R_2(0) \] (3.29)
and
\[ R_2(0) < R_2(t_n). \] (3.30)
The latter gives (3.8). Taking in (3.29) \( t = t_n \) one obtains (3.10). To obtain (3.4) one observes that (3.29) and (3.27) yield in (3.24) for \( \theta > 0 \)
\[ R_0(t_n) - R_0(0) > \frac{1}{2} t_n^2 \theta (\theta + 1)R_2(0). \]
For \( \theta = 0 \), we have already obtained \( R_0(t_n) = R_0(0) \). Finally, (3.11)−(3.13) follow directly from (3.8)−(3.10) and (3.2).
By the first condition in (1.18), there exists \( \sigma \in [\delta^{(2\lambda - 1)/4}, 1) \) such that
\[ \frac{m_2(g)}{(\alpha + m_1(g))^2} = \frac{\delta^{1/2} - \sigma}{\theta + 1} \frac{1 - \sigma}{\delta^\lambda - \sigma}. \] (3.31)
For such \( \sigma \), we set
\[ \Phi^{(1)} \equiv \frac{1 - \sigma \delta^{-\lambda}}{1 - \delta^{-\lambda}}, \] (3.32)
\[ \Phi^{(2)} \equiv -\Phi^{(1)} \frac{\delta^{1-\lambda} \sigma^2 (1 - \sigma)}{\theta + 1} \frac{\delta^\lambda - 1}{\delta^\lambda - 1}. \] (3.33)
Lemma 3.2 The following triple \( \mathcal{I}_n = (i_n^1; i_n^2; i_n^3) \) of statements:
\[ i_n^1 = \left\{ \exists \beta_n^+ \in J(g) : \varphi_n^{(1)} = \Phi^{(1)} \beta = \beta_n^+, \varphi_n^{(1)} < \Phi^{(1)}, \beta < \beta_n^+ \right\}, \]
\[ i_n^2 = \left\{ \exists \beta_n^- \in J(g) : \varphi_n^{(1)} = 1, \beta = \beta_n^-; \varphi_n^{(1)} < 1, \beta < \beta_n^- \right\}, \]
\[ i_n^3 = \left\{ \forall \beta \leq \beta_n^+ : \varphi_n^{(2)} \geq \Phi^{(2)} \right\}, \]
holds true for all \( n \in \mathbb{N}_0 \).
Proof. For \( n = 0 \), we have \( \varphi_0^{(1)} = \beta(\alpha + m_1(g)), \varphi_0^{(2)} = -\beta^2m_2(g) \). Thus we set
\[
\beta_0^- = \frac{1}{\alpha + m_1(g)}, \quad \beta_0^+ = \frac{\Phi^{(1)}}{\alpha + m_1(g)} > \beta_0^-.
\]
(3.34)
First let us prove that \( \beta_0^+ \in J(g) \). If \( \alpha = 0 \), \( \beta_0^+ \) needs only to be finite, which obviously holds. For \( \alpha > 0 \), the definitions (3.34) and (3.32) yield for \( \beta = \beta_0^+ \)
\[
\varphi_0^{(1)} = \Phi^{(1)} = \frac{\delta^{1/2}}{\delta^{1/2} - (\theta + 1)m_2(g)/[\alpha + m_1(g)]^2},
\]
thus
\[
\varphi_0^{(1)} = \frac{\delta^{1/2}}{\delta^{1/2} - (\theta + 1)(\beta_0^+)^2m_2(g)/[\varphi_0^{(1)}]^2}.
\]
This equation can be solved with respect to \( \varphi_0^{(1)} \)
\[
\varphi_0^{(1)} = \frac{1}{2}\{1 + [1 + 4\delta^{-1/2}(\theta + 1)(\beta_0^+)^2m_2(g)]^{1/2}\}.
\]
Hence making use of the second condition in (1.18) one gets
\[
\beta_0^+(\alpha + m_1(g)) = \varphi_0^{(1)} < \frac{1}{2}\{1 + [1 + 4\delta^{-1/2}(\theta + 1)(\beta_0^+)^2m_2(g)]^{1/2}\}
\]
\[
= 1 + [\delta^{-1/2}(\theta + 1)(\beta_0^+)^2m_2(g)]^{1/2} \leq 1 + \beta_0^+m_1(g).
\]
Therefore, \( \beta_0^+ \in J(g) \) and \( i_0^1, i_0^2 \) are true. To prove \( i_0^3 \) we to apply (3.31). Indeed, for \( \beta = \beta_0^+ \),
\[
\varphi_0^{(2)} = -(-\beta_0^+)^2m_2(g) = -\Phi^{(1)} \frac{m_2(g)}{[\alpha + m_1(g)]^2} = -\Phi^{(1)} \frac{\delta^{1/2} - 1 - \sigma}{\theta + 1 \delta - \sigma}
\]
\[
= \Phi^{(1)}(\Phi^{(1)})^{-2}\Phi^{(2)}\delta^{2\lambda-1}\sigma^2 \geq \Phi^{(2)}.
\]
This proves \( \mathcal{I}_0 \). Note that the estimate (3.3) with \( n = 0 \) holds for \( \beta \in (0, \beta_0^+) \).
To prove the implication \( \mathcal{I}_{n-1} \Rightarrow \mathcal{I}_n \), we remark that, for \( \beta = \beta_{n-1}^+ \), \( i_{n-1}^1 \) yields \( \varphi_{n-1}^{(1)} = \Phi^{(1)} \) and \( \kappa_n = \sigma^{-1} \) (see (3.4)). Now for \( \varphi_n^{(1)} \), we have the following possibilities: (a) the estimate (3.3) holds for \( \beta = \beta_{n-1}^+ \); (b) this estimate does not hold for such \( \beta \). In the case (a) one may apply Lemma (3.1). Then by means of \( i_{n-1}^3 \), (3.10), (3.32), and (obtain
\[
\varphi_n^{(1)} > \sigma^{-1}\Phi^{(1)} + (\theta + 1)(1 - \delta^{-\lambda})\sigma^{-3}\delta^{2\lambda-1}\Phi^{(2)} = \Phi^{(1)}.
\]
24
In the case (b) we simply have
\[ \varphi_n(1) \geq \frac{1}{1 - \delta - \lambda} \geq \frac{1 - \sigma \delta^{-\lambda}}{1 - \delta - \lambda} = \Phi(1). \]
For \( \beta = \beta_{n-1}^- \), we have \( \varphi_n^{(1)} = 1 \) and \( \kappa_n = 1 \). Therefore, \( \varphi_n^{(1)} < 1 \) for \( \beta \leq \beta_{n-1}^- \), as follows from \( i_{n-1}^2 \) and (3.9). By Corollary 2.3, \( \varphi_n^{(1)} \) is a continuous function of \( \beta \), thus there exists at least one value of \( \beta = \beta_n^+ \in (\beta_{n-1}^-, \beta_{n-1}^+) \) such that \( \varphi_n^{(1)} = \Phi(1) \). The smallest such one is set to be \( \beta_n^+ \). The existence of \( \beta_n^+ \) can be established in the same way. For \( \beta \leq \beta_n^+ \), we have \( \beta_n^+ \in (\beta_{n-1}^-, \beta_{n-1}^+) \) due to (3.35). By Corollary 3.1, the inequality (3.3) holds for \( \beta \leq \beta_n^+ \), thus \( J_n \) is nonempty.
**Lemma 3.3** There exists \( \beta_\ast \in J(g) \) such that, for \( \beta = \beta_\ast \),
\[ 1 < \varphi_n^{(1)} < \Phi(1), \quad \forall n \in \mathbb{N}_0. \quad (3.35) \]
For \( \beta < \beta_\ast \), the above upper estimate also holds and, moreover, there exists \( K = K(\beta) > 0 \), such that
\[ \varphi_n^{(1)} < K \delta^{-\lambda}, \quad \forall n \in \mathbb{N}_0. \quad (3.36) \]
**Proof.** Consider the set \( \Delta_n \overset{\text{def}}{=} \{ \beta \in (0, \beta_n^+) \mid 1 < \varphi_n^{(1)} < \Phi(1) \} \). Just above we have shown that \( \Delta_n \subseteq (\beta_n^- ; \beta_n^+) \), \( \Delta_n \) is nonempty and open. Let us prove that \( \Delta_n \subseteq \Delta_{n-1} \). Suppose there exists some \( \beta \in \Delta_n \) which does not belong to \( \Delta_{n-1} \). For this \( \beta \), either \( \varphi_n^{(1)} - 1 \leq 1 \) or \( \varphi_n^{(1)} - 1 \geq \Phi(1) \). Hence either \( \varphi_n^{(1)} < 1 \) or \( \varphi_n^{(1)} > \Phi(1) \) (it can be proved as above). This runs in counter with the supposition \( \beta \in \Delta_n \), hence \( \Delta_n \subseteq \Delta_{n-1} \). Now let \( D_n \) be the closure of \( \Delta_n \), then
\[ D_n = \{ \beta \in [\beta_n^- ; \beta_n^+] \mid 1 \leq \varphi_n^{(1)} \leq \Phi(1) \}. \quad (3.37) \]
\( D_n \) is nonempty and \( D_n \subseteq D_{n-1} \subseteq ... \subseteq D_0 \subseteq J(g) \). Let \( D_\ast = \bigcap_n D_n \), then \( D_\ast \) is also nonempty and closed, and \( D_\ast \subseteq J(g) \). Now let us show that, for
Finally, we apply (3.9) once again and obtain
\[ 1 \leq \phi_n^{(1)} \leq \Phi^{(1)}, \quad \forall n \in \mathbb{N}_0. \]
Suppose \( \phi_n^{(1)} = 1 \) for some \( n \in \mathbb{N}_0 \) and \( \beta \in D_s \), then \( \phi_m^{(1)} < 1 \) for all \( m > n \) (see (3.9)). The latter means that this \( \beta \) does not belong to all \( D_m \) with \( m > n \). This contradicts the supposition \( \beta \in D_s \). The case \( \phi_n^{(1)} = \Phi^{(1)} \) can be excluded similarly. Set \( \beta_* = \min D_s \). We have just proved that, for \( \beta = \beta_* \), (3.9) holds, thus it remains to prove the second part of Lemma. To this end we take \( \beta < \beta_* \). If \( \phi_n^{(1)} > 1 \) for all \( n \in \mathbb{N}_0 \), then either (3.9) holds or there exists such \( n_0 \) that \( \phi_{n_0}^{(1)} \geq \Phi^{(1)} \). This means either \( \beta \in D_* \) or \( \beta > \inf \beta_n^+ \).
Both these cases contradict the definition of \( \beta_* \). Hence there exists \( n_0 \) such that \( \phi_{n_0 - 1}^{(1)} \leq 1 \), then \( \phi_n^{(1)} < 1 \) for all \( n \geq n_0 \). In what follows, the definition (3.3) and the estimate (3.9) imply for the sequences \( \{ \phi_n^{(1)}, n \geq n_0 \} \) and \( \{ \kappa_n, n \geq n_0 \} \) to be strictly decreasing. Then for all \( n > n_0 \), one has (see (3.3))
\[ \phi_n^{(1)} < \kappa_n \phi_{n-1}^{(1)} < ... < \kappa_n \kappa_{n-1} ... \kappa_{n_0+1} \phi_{n_0}^{(1)} < (\kappa_{n_0+1})^{n-n_0}. \]
Since \( \kappa_{n_0+1} < 1 \), one has \( \sum_{n=0}^{\infty} \phi_n^{(1)} < \infty \). Thus there exists \( 0 < K_0 < \infty \) such that
\[ \prod_{n=1}^{\infty} \nu_n \overset{\text{def}}{=} K_0. \quad (3.38) \]
Finally, we apply (3.9) once again and obtain
\[ \phi_n^{(1)} < \delta^{-\lambda n} \nu_n \nu_{n-1} ... \nu_1 \phi_0^{(1)} < \delta^{-\lambda n} K_0 \phi_0^{(1)} \overset{\text{def}}{=} K \delta^{-\lambda n}, \quad \forall n \in \mathbb{N}_0. \quad (3.39) \]
Now we state the lemmas the proof of our theorems directly follows from. The first four lemmas describe the sequences \( \{ g_n \} \) defined by (2.22) whose elements have the form (3.1).
**Lemma 3.4** For every \( \theta \geq 0 \) and \( g \in \mathcal{L}(\lambda) \), there exists \( \beta_* \in J(g) \) such that,
(i) for \( \beta = \beta_* \), \( \lim_{n \to \infty} \phi_n^{(1)} = 1 \) and \( \lim_{n \to \infty} \phi_n^{(2)} = 0 \);
(ii) for \( \beta < \beta_* \), \( \lim_{n \to \infty} \phi_n^{(1)} = 0 \) and \( \lim_{n \to \infty} \phi_n^{(2)} = 0 \).
**Lemma 3.5** Let \( \theta, g \) and \( \beta_* \) be as above. Then there exists \( C : (0, \beta_*] \to \mathbb{R}_+ \) such that the sequence \( \{ C_n \mid n \in \mathbb{N}_0, C_n = g_n(0), C_0 = C(\beta) \} \), converges to \( C_{\beta_*} \) (resp. to \( C_{1,\beta} \)) given by (2.32) for \( \beta = \beta_* \) (resp. \( \beta < \beta_* \)). The sequence \( \{ C_n \mid C_0 > C(\beta) \} \) is divergent, the sequence \( \{ C_n \mid C_0 < C(\beta) \} \) tends to zero.
Lemma 3.6 Let $\theta$, $g$, $\beta_*$ and $C(\beta)$ be as above. Then for $\beta = \beta_*$, the sequence \( \{g_n \mid n \in N_0, \ g_0(z) = C(\beta_*)g(\beta z)\} \) converges in $A_1$ to $g_{2,*}(z) = C_{2,*}\exp(z)$ defined by (2.37).
Lemma 3.7 Let $\theta$, $g$, $\beta_*$ and $C(\beta)$ be as above. Then for every $\beta < \beta_*$
(i) the sequence \( \{g_n \mid n \in N_0, \ g_0(z) = C(\beta_*)g(\beta z)\} \) converges in $A_1$ to $g_{1,*}(z) \equiv 1$;
(ii) the sequence \( \{\bar{g}_n \mid n \in N_0, \ \bar{g}_0(z) = g(\beta z)\} \) defined by (2.23) converges in $A_{\varphi}$ to $\bar{g}_*(z) = \exp(\varphi z)$ with certain $\varphi = \varphi(\beta) > 0$.
Directly from the definitions (2.15), (2.16), and (2.22) one has the following corollary of the above lemmas.
Lemma 3.8 For every $\theta \geq 0$ and $g \in L(\lambda)$, there exist $\tau_* \in I(g)$ and a function $C : [0, \tau_*] \to \mathbb{R}_+$, such that:
(i) for $\tau < \tau_*$, the sequence \( \{f_n \mid n \in N_0, \ f_0(z) = C(\tau)g(z)\} \) converges in $A_{\beta_*^{-1}}$ to $f_{1,*}(z) \equiv 1$;
(ii) for $\tau = \tau_*$, the sequence \( \{f_n \mid n \in N_0, \ f_0(z) = C(\tau_*)g(z)\} \) defined by (2.13), (2.16), and (2.17) converges in $A_{\beta_*^{-1}}$, $\beta_* = \tau_*(\delta^{\lambda} - 1)^{-1}$ to $f_{2,*}(z) = \delta^{-\lambda\theta/\delta - 1}\exp(\beta_*^{-1}z)$.
3.2 Proof of Theorems
Proof of Theorem 1.1. As it has already been established, the function $f_n(t, z)$ defined by (2.13) gives the solution of the problem (1.13) provided all $f_m, m = 0, 1, \ldots, n - 1$ belong to the domain of the operators $T_t, t \in [0, 1]$. The latter fact follows from Lemma 2.3 and Proposition 2.8.
Proof of Theorem 1.2. Proposition 2.3 and Lemma 3.8 yield that, for $\tau < \tau_*$, the sequence \( \{f_n(t, z)\} \) converges in $A_{\beta_*^{-1}}$ to $T_t(f_{1,*})$, which may be easily calculated to be identically one. For $\tau = \tau_*$, one has the same convergence to $T_t(f_{2,*})$, which can be calculated explicitly by means of Proposition 2.7. The proof of Theorems 1.3 and 1.4 follows directly from Theorems 1.1 and 1.2 respectively on the base of the identity (1.23).
Proof of Theorem 1.5 and Theorem 1.6. By the continuity theorem (see e.g. [4], p.27), the convergence of the sequence of the transforms (1.27) \( \{F_{\mu_n}\} \) in a certain $A_2^{(N)}$ implies the weak convergence of the sequence \( \{\mu_n\} \). But for the measures defined by (1.29), the transforms (1.27) are the isotropic
functions $F_{\mu_n} \in A_0^{(N)}$ and for any of them, there exists an entire function $f_{\mu_n} \in A_0$ obeying (1.23). Moreover, (1.24) implies
$$f_{\mu_n}(z) = T(f_{\mu_{n-1}})(z) \left[ T(f_{\mu_{n-1}})(0) \right]^{-1}, \quad n \in \mathbb{N}.$$
Now if one chooses the starting element $\mu_0 = \nu$ such that
$$\int_{\mathbb{R}^N} \exp((x,y))\nu(dy) = g((x,x)),$$
where $g$ is the starting element of $\{f_n\}$ described by Lemma 3.8, then the validity of Theorem 1.5 follows from this Lemma. The assertion regarding the variance in claim (ii) may be checked directly. Similarly, the transforms
$$F_{\tilde{\mu}_n} \quad \text{of} \quad \tilde{\mu}_n, \quad \text{defined by (1.27)}, \quad \text{and the elements of the sequence} \quad \{\tilde{g}_n\}, \quad \text{defined by (2.23)} \quad \text{and described by claim (ii) of Lemma 3.7},$$
obey the relation
$$F_{\tilde{\mu}_n}(\sqrt{\beta x}) = \tilde{g}_n((x,x)), \quad n \in \mathbb{N}, \quad F_{\tilde{\mu}_0}(x) = g((x,x)).$$
Then the validity of Theorem 1.6 follows directly from claim (ii) of Lemma 3.7.
3.3 Proof of Lemmas
**Proof of Lemma 3.4.** Consider the case $\beta = \beta_*$, where (3.33) holds and $\varphi^{(2)}_0 \geq \Phi^{(2)}$ by statement $i_3$ of Lemma 3.2. First we prove that $\varphi^{(2)}_n \to 0$. Here we have such two possibilities:
(a) $\sigma > \delta^{(2\lambda-1)/4}$. From (3.4) and (3.35) we obtain $\kappa_n < \sigma^{-1}$. Thus
$$\delta^{2\lambda-1} \kappa_n^4 < \delta^{2\lambda-1} \sigma^{-4} < 1 \quad (3.40)$$
Applying this estimate in (3.8) one gets
$$| \varphi_n^{(2)} | < \delta^{2\lambda-1} \sigma^{-4} | \hat{\varphi}_{n-1}^{(2)} | < \cdots < (\delta^{2\lambda-1} \sigma^{-4})^n | \hat{\varphi}_0^{(2)} | \leq (\delta^{2\lambda-1} \sigma^{-4})^n | \Phi^{(2)} | .$$
In view of (3.40), this gives
$$\varphi_n^{(2)} \to 0, \quad n \to +\infty.$$
(b) $\sigma = \delta^{(2\lambda-1)/4}$. In this case we have only
$$\delta^{2\lambda-1} \kappa_n^4 < \delta^{2\lambda-1} \sigma^{-4} = 1. \quad (3.41)$$
Making use of (3.8) one obtains
\[ 0 > \varphi^{(2)}_n > \delta^{2\lambda - 1} \kappa_n^4 \varphi^{(2)}_{n-1} > \varphi^{(2)}_{n-1} > ... > \varphi^{(2)}_0 \geq \Phi^{(2)} \]
Hence \{\varphi^{(2)}_n\} is strictly increasing and bounded. Then it is convergent and its limit, say \( \varphi^{(2)} \), obeys the condition \( \varphi^{(2)} > \Phi^{(2)} \). Assume now that \( \varphi^{(2)} \neq 0 \).
Combining (3.8) and (3.41) one obtains (recall that \( \varphi^{(2)}_n < 0 \))
\[ \varphi^{(2)}_n \varphi^{(2)}_{n-1} < \delta^{2\lambda - 1} \kappa_n^4 - 1, \]
which means \( \kappa_n \to \delta^{(1-2\lambda)/4} \). The latter as well as the definitions of \( \kappa_n \) and \( \Phi^{(1)} \) immediately yield
\[ \varphi^{(1)}_n \to \Phi^{(1)}. \]
Passing to the limit \( n \to +\infty \) in (3.10) one obtains
\[ \Phi^{(1)} \geq \delta^{(1-2\lambda)/4} \Phi^{(1)} + (\theta + 1)(1 - \delta^{-\lambda})\delta^{2\lambda - 1}\delta^{3(1-2\lambda)/4} \varphi^{(2)}, \]
which yields in turn
\[ \varphi^{(2)} \leq -\Phi^{(1)} \frac{(1 - \sigma)\sigma^2 \delta^{1-\lambda}}{(\theta + 1)(\delta^\lambda - 1)} = \Phi^{(2)}. \]
The latter gives the following contradictory inequalities
\[ \Phi^{(2)} < \varphi^{(2)} \leq \Phi^{(2)}. \]
Thus \( \varphi^{(2)} = 0 \). To show that \( \varphi^{(1)}_n \to 1 \), we set
\[ b_n = (\theta + 1)(1 - \delta^{-\lambda})\delta^{2\lambda - 1} \kappa_n^3 \varphi^{(2)}_{n-1}. \]
Since \{\kappa_n\} is bounded and \( \varphi^{(2)}_n \to 0 \), one has \( b_n \to 0 \). By the estimate (3.35), \{\varphi^{(1)}_n\} is bounded. Then it contains a subsequence \{\varphi^{(1)}_{n_i}\} convergent to a certain \( a \in [1, \Phi^{(1)}] \). From (3.9) and (3.10) one has
\[ 0 > \varphi^{(1)}_{n_i} - \kappa_n \varphi^{(1)}_{n-1} > b_n, \]
which yields
\[ \lim_{i \to \infty} (\varphi^{(1)}_{n_i} - \kappa_n \varphi^{(1)}_{n-1}) = 0. \]
The latter can be rewritten as (see 3.4)
\[ a - \frac{\delta - \lambda a}{1 - (1 - \delta - \lambda)a} = 0. \]
Since \( \lambda > 0 \), the above equation has only one solution on \([1, \Phi^{(1)}]\), it is \( a = 1 \).
In what follows, the bounded sequence \( \{\varphi^{(1)}_n\} \) has only one accumulation point, hence it converges to \( a = 1 \) itself. In the case \( \beta < \beta^*_s \) the estimate \( (3.36) \) yields \( \varphi^{(1)}_n \to 0 \). Then \( \kappa_n \) given by \( (3.4) \) tends to \( \delta - \lambda \) which immediately gives in \( (3.8) \) \( \varphi^{(2)}_n \to 0 \).
**Proof of Lemma 3.5.** From the definitions \( (2.22) \) and \( (3.1) \) one obtains
\[ C_n = C_{n-1}^\delta \Psi_{n-1}(\beta), \]
\[ \Psi_n(\beta) \overset{\text{def}}{=} \{ \exp \left( (\delta - 1) \Delta_\theta \right) \exp \left( \delta \varphi_n(\delta^{-1} \cdot) \right) \} (0). \]
For \( \theta = 0 \), \( \Psi_n(\beta) = 1 \) (see Remark 2.2) and the situation with \( C_n \) is obvious. Consider the case \( \theta > 0 \). Then
\[ C_n = C_0^\delta \Xi_n(\beta), \quad \Xi_n(\beta) \overset{\text{def}}{=} \Psi_{n-1}(\beta) \Psi_{n-2}(\beta) \cdots \Psi_0^\delta(\beta). \quad (3.43) \]
Now we put \( C_0 = \zeta > 0 \), then \( C_n = C_n(\zeta, \beta) \). By the above representation, for every fixed \( \beta > 0 \), \( C_n \) is a monotone convex differentiable function of \( \zeta \) and
\[ C_n(\zeta, \beta) = \zeta^n \Xi_n(\beta), \quad \frac{\partial C_n}{\partial \zeta} = \delta^n \zeta^{-1} C_n. \quad (3.44) \]
By Lemma 3.3, \( \varphi^{(1)}_n < \Phi^{(1)} \) for all \( n \in \mathbb{N}_0 \) and \( \beta \in (0, \beta^*_s] \). This gives in \( (3.4) \)
\[ \kappa_n < \sigma^{-1} \leq \delta(1-2\lambda)/4 \] for such \( \beta \) and \( n \). We set
\[ \zeta^- = \delta^{-\theta(1+2\lambda)/4(\delta-1)}, \]
\[ \Upsilon = [\zeta^-, 1] \subset \mathbb{R}_+. \quad (3.45) \]
For a fixed \( \beta \in (0, \beta^*_s] \), let us prove that the following inductive statements hold true for all \( n \in \mathbb{N}_0 \)
\[ i^+_n = \{ \exists \zeta^+_n \in \Upsilon : C_n(\zeta^+_n, \beta) = 1 \}, \]
\[ i^-_n = \{ \exists \zeta^-_n \in \Upsilon : C_n(\zeta^-_n, \beta) = \zeta^- \}. \quad (3.47) \]
Since \( C_n \) is a monotone convex function of \( \zeta \) \( (3.44) \), such \( \zeta^+_n \) are unique. We set \( \zeta^+_0 = 1 \), \( \zeta^- = \zeta^- \). Then \( C_0 = \zeta \) obeys the above conditions, thus \( i^+_0 \) are true. Now suppose that \( i^+_n \) are true. Then \( (3.5) \) and \( (3.3) \) yield for \( \theta > 0 \)
\[ C_n(\zeta^+_n, \beta) > 1, \quad C_n(\zeta^-_n, \beta) < \zeta^-. \]
Taking into account that $C_n$ depends on $\zeta$ as given by (3.44) one concludes that there exist $\zeta_n^\pm$ such that
\[ \zeta_n^- < \zeta_n^- < \zeta_n^+ < \zeta_n^- - 1, \]
and the statements $i_n^\pm$ hold true. Set
\[ \Upsilon_n = [\zeta_n^-, \zeta_n^+]. \]
Then
\[ \Upsilon_n \subset \Upsilon_{n-1} \subset \ldots \subset \Upsilon, \]
and there exists $\tilde{\zeta}_n \in \Upsilon_n$ such that
\[ \zeta_n^+ - \zeta_n^- = (1 - \zeta^+) \left[ \frac{\partial C_n(\tilde{\zeta}_n, \beta)}{\partial \zeta} \right]^{-1}. \]
Let
\[ \Upsilon^* = \bigcap_{n \in \mathbb{N}_0} \Upsilon_n, \]
which is closed and nonempty. For $\zeta \in \Upsilon^*$, all $C_n$ belong to $\Upsilon$. Hence the sequence $\{C_n\}$ is separated from zero for such $\zeta$. This yields that the derivative given by (3.44) tends to $+\infty$ when $n \to \infty$. Taking into account all these facts one concludes
\[ \Upsilon^* = \{\zeta^*\}, \quad \zeta^* \in \Upsilon \]
and, for all $n \in \mathbb{N}_0$,
\[ C_n(\zeta^*, \beta) \in \Upsilon. \]
It should be pointed out that $\zeta^* = \zeta^*(\beta)$. Choose $\zeta = \zeta^*$. Then by (3.51), the sequence $\{C_n\}$ is bounded, hence it contains a convergent subsequence. For $\beta = \beta_*$, by means of (3.32) and (3.37) one may show that such a subsequence converges to $C_{2_*} = \delta^{-\lambda \theta/(\delta-1)}$. As in the case of $\{\varphi_n^{(1)}\}$ considered above, this fact implies the convergence of the whole sequence to this limit. For $\beta < \beta_*$, one employs (3.33) and (3.34) and shows similarly the convergence of $\{C_n\}$ to $C_{1_*} = 1$. Thus we choose the function $C(\beta)$ to be $C(\beta) = \zeta^*(\beta)$. \(\blacksquare\)
Proof of Lemma 3.6. It follows from Lemmas 2.1, 3.4, and 3.5. \(\blacksquare\)
Proof of Lemma 3.7. Claim (i) follows from the lemmas just mentioned. To prove claim (ii) we fix $\beta < \beta_*$ and show the convergence of $\{\varphi_n^{(2)}\}$ to zero. Indeed, (3.11) and (3.38) imply
\[ \left| \varphi_n^{(2)} \right| < \delta^{-n}(\nu_0 \nu_{n-1} \ldots \nu_1)^4 \left| \varphi_0^{(2)} \right| < \delta^{-n} K^4 \left| \varphi_0^{(2)} \right|. \]
Thus to complete the proof we have only to show that \( \{ \tilde{\varphi}_n^{(1)} \} \) is a Cauchy sequence. To this end for \( n \in \mathbb{N} \) and \( p \in \mathbb{N} \), we set
\[
a_{n,p} = \nu_{n+p}\nu_{n+p-1}...\nu_{n+1}; \quad (3.53)
\]
\[
b_{n,p} = (\theta + 1)(1 - \delta^{-\lambda})^{-1} \sum_{s=n}^{n+p-1} \nu_{n+p}\nu_{n+p-1}...\nu_{s+2}\nu_{s+1}\delta^{-\lambda s}\tilde{\varphi}_s^{(2)}. \quad (3.54)
\]
Then the convergence of the product (3.38) yields
\[
a_{n,p} - 1 < \left( \prod_{k=n+1}^{\infty} \nu_k \right) - 1 \to 0, \quad n \to +\infty. \quad (3.55)
\]
On the other hand, (3.38) and (3.52) give
\[
|b_{n,p}| < (\theta + 1)(1 - \delta^{-\lambda})^{-1} K_0^7 \sum_{s=n}^{\infty} \delta^{-(1+\lambda)s} \to 0, \quad n \to +\infty. \quad (3.56)
\]
The estimates (3.12) and (3.13) yield respectively
\[
\tilde{\varphi}_{n+p}^{(1)} < a_{n,p}\tilde{\varphi}_n^{(1)}, \quad \tilde{\varphi}_{n+p}^{(1)} > a_{n,p}\tilde{\varphi}_n^{(1)} + b_{n,p}. \quad (3.57)
\]
Therefore
\[
(a_{n,p} - 1)\tilde{\varphi}_n^{(1)} + b_{n,p} < \tilde{\varphi}_{n+p}^{(1)} - \tilde{\varphi}_n^{(1)} < (a_{n,p} - 1)\tilde{\varphi}_n^{(1)}. \quad (3.58)
\]
Having in mind (3.2) and (3.36), one gets
\[
0 < \tilde{\varphi}_n^{(1)} = \delta^{\lambda n}\varphi_n^{(1)} < K. \quad (3.59)
\]
Now it suffices to apply the latter estimate together with (3.53) and (3.56) in (3.58) and conclude that \( \{ \tilde{\varphi}_n^{(1)} \} \) is a Cauchy sequence. Thus, for every \( \beta < \beta_* \), there exists \( \tilde{\varphi} = \tilde{\varphi}(\beta) > 0 \) such that \( \varphi_n^{(1)} \to \tilde{\varphi} \). Now we apply Lemma 2.1 and obtain the convergence to be proved.
**Remark 3.1** When proving the convergence of \( \{ \tilde{\varphi}_n^{(1)} \} \), the limit of this sequence has been estimated. Namely, we have obtained (see (3.59))
\[
\lim_{n \to \infty} \tilde{\varphi}_n^{(1)} \leq K = \varphi_0^{(1)} \prod_{n=1}^{\infty} \nu_n = \prod_{n=1}^{\infty} \frac{\tilde{\varphi}_0^{(1)}}{1 - (1 - \delta^{-\lambda})\varphi^{(1)}_{n-1}}. \quad (3.60)
\]
This bound is achieved for \( f_0(z) = C \exp(\alpha z) \) (in this case we may calculate \( g_n \) explicitly, see (2.34)). It is quite likely that this bound is achieved also in the general case, but to prove this conjecture we would need more sophisticated estimates than (3.13) or (3.16).
References
[1] V.N. Denisov, On Stabilization of solutions of the Cauchy problem for parabolic equations, Nonlinear Anal.: Theory, Methods, Appl., 30 (1997) 123–127
[2] I.A Ibragimov, Yu.V. Linnik, Independent and Stationary Sequences of Variables Random, Wolters–Noordhoff, Groningen, 1971
[3] L.Iliev, Laguerre Entire Functions, Bulgarian Academy of Sciences, Sofia, 1987
[4] S. Kamin (Kamenomostovskaya), On stabilization of solutions of the Cauchy problem for parabolic equation, Proceed. Royal Soc. Edinburgh, 76A (1977) 43–53
[5] Yu.V. Kozitsky, Hierarchical ferromagnetic vector spin model possessing the Lee–Yang property. Thermodynamic limit at the critical point and above, Journal of Statistical Physics, 87 (1997) 799–820
[6] Yu. Kozitsky, L. Wołowski, Laguerre entire functions and related locally convex spaces. Los Alamos Electronic Preprint CV/9812111, 1998
[7] B.J. Levin, Distribution of Zeros of Entire Functions. Amer. Math. Soc. 1964
[8] D. Luna, Fonctions différentiables invariantes sous l’opération d’un groupe réductif, Ann. Inst. Fourier, Grenoble, 26 (1976) 33-49.
[9] H. Weyl, The Classical Groups their Invariants and Representations, Princeton, 1938 | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
1940,
1
],
[
1940,
4540,
2
],
[
4540,
6060,
3
],
[
6060,
8246,
4
],
[
8246,
10452,
5
],
[
10452,
13180,
6
],
[
13180,
15457,
7
],
[
15457,
17581,
8
],
[
17581,
19883,
9
],
[
19883,
22428,
10
],
[
22428,
24463,
11
],
[
24463,
26794,
12
],
[
26794,
28391,
13
],
[
28391,
30382,
14
],
[
30382,
32429,
15
],
[
32429,
34900,
16
],
[
34900,
37172,
17
],
[
37172,
39522,
18
],
[
39522,
42223,
19
],
[
42223,
44173,
20
],
[
44173,
46220,
21
],
[
46220,
47911,
22
],
[
47911,
49819,
23
],
[
49819,
52159,
24
],
[
52159,
54611,
25
],
[
54611,
57604,
26
],
[
57604,
60122,
27
],
[
60122,
62148,
28
],
[
62148,
64019,
29
],
[
64019,
66650,
30
],
[
66650,
68799,
31
],
[
68799,
71147,
32
],
[
71147,
72335,
33
]
]
} |
2f5443b5a4c3791fe31b3b047855663c62cb5e96 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 10,
"total-fallback-pages": 0,
"total-input-tokens": 34324,
"total-output-tokens": 12590,
"fieldofstudy": [
"Biology",
"Medicine"
]
} | Antimicrobial resistance and genomic analysis of staphylococci isolated from livestock and farm attendants in Northern Ghana
Beverly Egyir¹*, Esther Dsani², Christian Owusu-Nyantakyi¹, Grebstad Rabbi Amuasi¹, Felicia Amoa Owusu¹, Emmanuel Allegye-Cudjoe³ and Kennedy Kwasi Addo¹
Abstract
Background: The emergence of antimicrobial resistant bacteria in food producing animals is of growing concern to food safety and health. Staphylococci are common inhabitants of skin and mucous membranes in humans and animals. Infections involving antibiotic resistant staphylococci are associated with increased morbidity and mortality, with notable economic consequences. Livestock farms may enable cross-species transfer of antibiotic resistant staphylococci. The aim of the study was to investigate antimicrobial resistance patterns of staphylococci isolated from livestock and farm attendants in Northern Ghana using phenotypic and genotypic methods. Antimicrobial susceptibility testing was performed on staphylococci recovered from livestock and farm attendants and isolates resistant to cefoxitin were investigated using whole genome sequencing.
Results: One hundred and fifty-two staphylococci comprising S. sciuri (80%; n = 121), S. simulans (5%; n = 8), S. epidermidis (4%; n = 6), S. chromogens (3%; n = 4), S. aureus (2%; n = 3), S. haemolyticus (1%; n = 2), S. xylosus (1%; n = 2), S. cohnii (1%; n = 2), S. condimenti (1%; n = 2), S. hominis (1%; n = 1) and S. arlettae (1%; n = 1) were identified. The isolates showed resistance to penicillin (89%; n = 135), clindamycin (67%; n = 102), cefoxitin (19%; n = 29), tetracycline (15%; n = 22) and erythromycin (11%; n = 16) but showed high susceptibility to gentamicin (96%; n = 146), sulphamethoxazole/trimethoprim (98%; n = 149) and rifampicin (99%; n = 151). All staphylococci were susceptible to linezolid and amikacin. Carriage of multiple resistance genes was common among the staphylococcal isolates. Genome sequencing of methicillin (cefoxitin) resistant staphylococci (MRS) isolates revealed majority of S. sciuri (93%, n = 27) carrying mecA1 (which encodes for beta-lactam resistance) and the sal(A) gene, responsible for resistance to lincosamide and streptogramin. Most of the MRS isolates were recovered from livestock.
Conclusion: The study provides insights into the genomic content of MRS from farm attendants and livestock in Ghana and highlights the importance of using whole-genome sequencing to investigate such opportunistic pathogens. The finding of multi-drug resistant staphylococci such as S. sciuri carrying multiple resistant genes is of public health concern as they could pose a challenge for treatment of life-threatening infections that they may cause.
Keywords: Staphylococci, Antimicrobial resistance, Multi-drug resistance, WGS, Ghana
Background
Staphylococci are the most common bacteria found on the skin and mucous membranes of mammals [1]. Bacteria of this genus are usually commensal organisms and can be divided into two groups based on their ability to produce the enzyme coagulase [2]. Pathogenic infections...
may result from colonization with staphylococci if primary skin barriers are compromised due to trauma [3]. Among the species producing coagulase, *Staphylococcus aureus* is of primary importance to human and animal health. *S. aureus* is a notable cause of mastitis in livestock and has been associated with bacteremia, skin and soft tissue infections in humans [4, 5].
The less pathogenic group of coagulase negative staphylococci (CoNS) have garnered interest in recent times due to their increasing role in the occurrence of opportunistic infections [6]. CoNS-related infections in humans have been associated with the presence of foreign bodies and immunosuppressive states of patients [7]. *Staphylococcus epidermidis* falls within the category of CoNS and is the most common cause of foreign body related blood stream infections in humans [8]. *S. epidermidis* and *S. chromogens* have been isolated in subclinical and clinical mastitis cases in cattle [9]. CoNS are known carriers of transferable genetic elements that contribute to the survival of some strains of *S. aureus* and are often cited as reservoirs of resistance genes [10].
The emergence of antimicrobial resistance (AMR) in staphylococci, though partly dependent on innate microbial characteristics, is mainly driven by antimicrobial use [11, 12]. *S. aureus* are known to adapt and gain resistance to nearly all antibiotics used to treat it. Concurrent resistance to non-β-lactam agents such as quinolones, tetracyclines, aminoglycosides, macrolides and lincosamides are increasingly reported among methicillin resistant strains of staphylococci, further diminishing the treatment options available for infected humans or animals [13]. Methicillin resistance is attributed to the production of a transpeptidase (PBP2a), encoded by the mecA gene within the staphylococcal cassette chromosome [14]. Methicillin resistant *S. aureus* (MRSA) infections often result in increased morbidity and an increase in health care associated costs [15].
Mounting evidence suggests that the development of resistance in commensal pathogens of livestock origin contribute to the persistence of carriage of these resistant organisms in humans. Antimicrobials are used routinely in livestock production and its misuse in livestock farming often leads to emergence of resistance due to selective pressure on microbes like staphylococci exposed to antibiotics [16]. Colonized livestock may spread resistant strains directly to humans or indirectly through the food chain [17]. The detection of MRSA in humans that have been linked to animals has heightened concerns of its ability to be transferred among species [18]. Livestock farmers, veterinarians, wool sorters, meat hygiene inspectors and people who frequently visit livestock farms have been found to be at increased risk for MRSA colonization [19].
The presence of multidrug resistant strains of staphylococci in livestock have implications for food safety and contribute to the global challenge of AMR [20]. Knowledge on carriage rates of resistant strains of CoNS in livestock is scarce in Ghana; such information is necessary to inform antimicrobial policies and improve integrated surveillance on antimicrobial resistance. Findings from antimicrobial susceptibility testing of bacteria species such as CoNS offer vital information for surveillance but are limited when it comes detection of clones, resistance and virulence of bacteria pathogens. Genomic sequencing on the other hand, provides massive information for characterizing bacteria species [21] including staphylococci. This study therefore sought to characterize staphylococci recovered from livestock and farm attendants in the Northern part of Ghana using phenotypic and genotypic methods.
**Results**
**Farm attendant characteristics**
Majority of the farm attendants were male (89%). The age of farm attendants ranged from 14 to 58 years. Daily participation in livestock rearing activities such as feeding, grazing and handling was reported by all 19 respondents. Most of the livestock attendants worked primarily on only one type of livestock (84%). Three attendants worked with more than one livestock type. Most of the farm attendants lived on the farm (83%) and had been working on the farm for at least eight years (78%).
**Nasal carriage of staphylococci**
Of the 311 nasal swabs collected from livestock and 19 samples collected from farm attendants, 152 staphylococcal isolates were recovered. Staphylococci were obtained in close to half of livestock samples (45%; *n* = 149) and in most farm attendant samples (58%; *n* = 11). Most of the isolates (98%; *n* = 149) were CoNS, with three isolates (2%) identified as *S. aureus*. Ten different CoNS species were confirmed, with *S. sciuri* being the most prevalent (80%; *n* = 121). Others include *S. simulans* (5%; *n* = 8), *S. epidermidis* (4%; *n* = 6), *S. chromogens* (3%; *n* = 4), *S. haemolyticus* (1%; *n* = 2), *S. xylosus* (1%; *n* = 2) *S. cohnii* (1%; *n* = 2), *S. condimenti* (1%; *n* = 2), *S. hominis* (1%; *n* = 1) and *S. arlettae* (1%; *n* = 1).
*S. sciuri* was found in nasal swabs from all livestock types in this study. *S. epidermidis* was isolated only from nasal swabs obtained from farm attendants. *S. haemolyticus* was isolated from human and sheep samples. *S. condimenti* was found only in pigs, whilst *S. hominis* and *S. arlettae* were isolated only in sheep. Six different species of staphylococci were found in samples from goats and consisted of *S. sciuri*, *S. simulans*, *S. aureus*, *S. xylosus*, *S. chromogens* and *S. cohnii* (Table 1).
Antimicrobial resistance in staphylococcal isolates
Isolates from farm attendants were mainly resistant to penicillin (100%; n = 11), tetracycline (55%; n = 6), cefoxitin (27%; n = 3), clindamycin (36%; n = 4), sulphamethoxazole/trimethoprim (27%; n = 3), erythromycin (18%; n = 2) and gentamycin (18%; n = 2). All staphylococcal isolates from farm attendants were susceptible to linezolid, amikacin and rifampicin. Isolates obtained from livestock were mainly resistant to penicillin (88%; n = 124), clindamycin (70%; n = 98), cefoxitin (18%; n = 26), tetracycline (11%; n = 16) and erythromycin (10%; n = 14) (Table 2). Among isolates from livestock, resistance to gentamicin and rifampicin was less prevalent (3%; n = 4 and 1%; n = 1). All cefoxitin resistant isolates (19%; n = 29) were susceptible to vancomycin.
The predominant isolates detected, S. sciuri were resistant to 6 out of 10 antimicrobials agents tested in all: penicillin (94%; n = 114), clindamycin (80%; n = 97), cefoxitin (22%; n = 27), tetracycline (8%; n = 10), erythromycin (8%; n = 10) and gentamicin (2%; n = 3). S. epidermidis isolates were resistant to seven out of 10 antimicrobials with a single isolate exhibiting resistance to six antibiotic agents. Half (50%; n = 3) of S. epidermidis isolates were resistant to sulphamethoxazole/trimethoprim. Although low numbers of S. xylosus isolates were identified, resistance was detected to five out of 10 antibiotics (penicillin, clindamycin, tetracycline, erythromycin and rifampicin). S. aureus isolates recovered were resistant to penicillin, tetracycline and erythromycin. S. chromogens and S. cohnii were susceptible to all tested antibiotic agents except penicillin (Table 3).
Of the 152 staphylococci isolated, 49 (32%) were MDR. Overall, MDR rates were higher in farm attendants (45%; n = 5) than in livestock (31%; n = 44).
Genomic analysis of cefoxitin resistant staphylococci
Whole-genome sequencing of the cefoxitin-resistant isolates revealed that all S. sciuri possessed mecA1 gene, while S. epidermidis and S. haemolyticus harbored mecA gene. Tetracycline resistance genes
| Parameter | Humans | Cattle | Sheep | Goat | Pig | Total |
|-----------|--------|--------|-------|------|-----|-------|
| No. of isolates | 11 | 19 | 71 | 32 | 19 | 152 |
| Staphylococcal species | | | | | | |
| S. epidermidis | 6 | - | - | - | - | 6 |
| S. haemolyticus | 1 | - | 1 | - | - | 2 |
| S. xylosus | 1 | - | - | - | - | 2 |
| S. sciuri | 3 | 18 | 65 | 21 | 14 | 121 |
| S. aureus | - | - | 2 | 3 | 3 | 8 |
| S. simulans | - | - | 1 | 1 | 2 | 4 |
| S. chromogens | - | 1 | 1 | 2 | - | 4 |
| S. cohnii | - | - | - | - | - | 2 |
| S. hominis | - | - | 1 | - | - | 1 |
| S. arlettae | - | - | 1 | - | - | 1 |
| S. condimenti | - | - | - | - | 2 | 2 |
Table 2: Antimicrobial resistance of staphylococci isolated from livestock and farm attendants, 2018
| Antimicrobial resistance of staphylococci isolated from livestock and farm attendants, 2018 |
|---------------------------------|---------------------------------|---------------------------------|---------------------------------|
| Antimicrobial agent | Livestock n = 141 (%) | Farm attendants n = 11 (%) | Total N = 152(%) |
|---------------------|---------------------|---------------------|---------------------|
| Penicillin | 124 (88) | 11 (100) | 135 (89) |
| Clindamycin | 98 (70) | 4 (36) | 102 (67) |
| Cefoxitin | 26 (18) | 3 (27) | 29 (19) |
| Tetracycline | 16 (11) | 6 (53) | 22 (15) |
| Erythromycin | 14 (10) | 2 (18) | 16 (11) |
| Gentamicin | 4 (3) | 2 (18) | 6 (4) |
| Rifampicin | 1 (1) | 0 (0) | 1 (1) |
| Sulphamethoxazole-Trimethoprim | 0 (0) | 3 (27) | 3 (2) |
| Amikacin | 0 (0) | 0 (0) | 0 (0) |
| Linezolid | 0 (0) | 0 (0) | 0 (0) |
Table 3 Pattern of antimicrobial resistance of staphylococcal isolates, 2018
| S. sciuri | 121 | Pen | Clin | Cef | Tet | Ery | Gen | Rif | STX- |
|----------|-----|-----|------|------|------|------|-----|------|------|
| S. epidermidis | 6 | 114 (94) | 97 (80) | 27 (22) | 10 (8) | 10 (8) | 3 (2) | - | - |
| S. haemolyticus | 2 | 6 (100) | 1 (17) | 1 (17) | 5 (83) | 2 (33) | 1 (17) | - | 3 (50) |
| S. xylosus | 2 | 2 (100) | 1 (50) | 1 (50) | 1 (50) | 1 (50) | - | - | - |
| S. simulans | 8 | 1 (12.5) | - | - | - | 3 (38) | - | - | - |
| S. chromogens | 4 | 3 (75) | - | - | - | - | - | - | - |
| S. cohnii | 2 | 1 (100) | - | - | - | - | - | - | - |
| S. hominis | 1 | 1 (100) | - | - | - | - | - | 1 (100) | - |
| S. arlettae | 1 | 1 (100) | 1 (100) | - | 1 (50) | - | - | - | - |
| S. condimenti | 2 | - | - | - | 1 (50) | - | - | - | - |
| S. aureus | 3 | 3 (100) | - | - | - | 2 (67) | 1 (33) | - | - |
| Total (N, %) | 152 | 135 (89) | 102 (67) | 29 (19) | 22 (15) | 16 (11) | 6 (4) | 1 (0.7) | 3 (2) |
Discussion
The findings of this study show that multidrug-resistant staphylococci are prevalent in livestock and farm attendants on the farms sampled. The detection of S. sciuri, S. aureus, S. xylosus, S. simulans, S. chromogens, S. cohnii, S. hominis, S. arlettae and S. condimenti are consistent with previous reports on prevalence of CoNS in livestock [22, 23]. S. sciuri was the most prevalent staphylococci identified in this study (80%) and was isolated in both livestock and farm attendants. Primarily considered a livestock-associated bacterium, S. sciuri can be found in large numbers in the farm environment [22]. Though the colonizing population may be low outside the farm environment, they are found to readily adapt and persist in health care settings and thus may pose a threat to human health [23]. S. sciuri has been associated with pneumonia and septicemic shock in Grasscutter (Thryonomys swinderianus) in Ghana [24]. This pathogen was detected in China as the causative organism for endocarditis [25] and in Thailand, as the agent in a food poisoning outbreak investigation [26].
S. aureus was detected in samples from three goats and none contained the mecA gene (MRSA). This is in sharp contrast with reports from other geographic areas [9]. Of note, the CoNS that were resistant to cefoxitin and also positive for mecA1 in this study originated from livestock. Previous studies in Ghana however, found MRSA among farm attendants and none from livestock [27]. MRSA may be more prevalent in intensive farming systems where antimicrobials are used in the production chain more frequently, and in hospital settings due to selective pressure of bacteria in these environments and their presence in colonized inpatients [28].
and *S. xylosus* were frequently detected in samples from farm attendants. This concurs with previous reports that identified *S. epidermidis* as the most frequently occurring CoNS found on skin and mucosae in humans [1]. *S. epidermidis* and *S. haemolyticus* have increasingly been associated with nosocomial infections and are described to be highly adaptable to medical devices hence the need to monitor carriage rates in humans [29].
The level of resistance of staphylococci to critically needed antimicrobial agents is a growing public health concern. The overall prevalence of MDR was 32%, with higher rates observed for farm attendants. The high rate of resistance to penicillin observed in this study is consistent with previous reports on staphylococci from both clinical and non-clinical samples in Ghana [27, 30–34] and elsewhere [35, 36] thus, was expected.
The proportion of isolates resistant to tetracycline was higher in isolates from farm attendants (55%) as compared to livestock (11%), and this is in concordance with the rates of tetracycline resistance in staphylococci. More than half of CoNS from livestock attendants (*S. epidermidis, S. haemolyticus*) were tetracycline resistant. Tetracycline resistance in all livestock in this study was lower (11%) than was reported in *S. aureus* isolates recovered from livestock (47%) in a previous study in Ghana [27] and from chicken droppings (74%) elsewhere [37]. This observation can be attributed to the frequency of its use in the various farming systems.
Tetracycline and its derivatives are often used as part of feed for growth promotion and prophylaxis in intensive poultry farming. Though its use in livestock is widespread, oral preparations are not common.
Resistance to sulphamethoxazole/trimethoprim (STX) was found in *S. epidermidis*, from three farm attendants. STX has been used in the treatment of infections caused by community-acquired *S. aureus*; resistance to this agent among methicillin resistance strains may point to a reduction in its efficacy due to exposure [38]. High susceptibility of isolates to vancomycin, linezolid, amikacin, rifampicin and gentamicin is crucial for the treatment of severe infections in humans. A notable example is the use of vancomycin for the treatment of MRSA infections [39].
Phylogenetic analysis of MRS isolates showed close genetic relatedness between isolates recovered from humans and livestock, suggesting that these pathogens may not be host-specific. The observation could also reflect possible transmission between the different hosts.
The *mec* variants (*mecA* and *mecA1*) found in the MRS have been linked to resistance to beta-lactam antibiotics in staphylococci [40]. Several studies have pointed to *mecA1* detected in *S. sciuri* as an evolutionary ancestor of the *mecA* gene found in MRSA [40–42]. *mecA1* gene is naturally adapted to *S. sciuri* resistance to beta-lactams due to changes in the promoter region of this gene have been reported [40, 43].
The high levels of resistance to clindamycin among the isolates can be linked to the sal(A) gene detected in majority of the S. sciuri (93%) isolates. sal(A) is located between two housekeeping genes of the core genome of S. sciuri subspecies; it encodes for resistance to lincosamide and streptogramin antibiotics [44].
The plasmids detected in this study harbored antibiotic resistance genes. Many resistance determinants are plasmid-mediated, and this has been demonstrated in previous studies on staphylococci [45]. Horizontal transfer of plasmids can occur among staphylococcal strains of different species although data on plasmid distribution in staphylococci are scarce [10, 46]. In this study, seven different plasmid sequences were detected based on the sequences of their rep genes. The most prevalent sequence was rep7a, which is similar to studies conducted on the sequences of their rep genes. The most dominant rep genes in S. aureus isolates [47].
Co-occurrence of rep7a plasmid with tet(K) gene was observed in three isolates. Similarly, the occurrence of rep7a plasmid with cat(pC221) was observed in one isolate. This is consistent with reports of strong association between this plasmid, tetracycline and chloramphenicol resistance [48, 49]. Tetracycline resistance genes: tet(K), (M) and (L) have been reported among staphylococci recovered from clinical and non-clinical samples in African countries including Ghana [27, 33, 35, 50] suggesting that these genes are widely disseminated in these regions.
The potential risks of transfer of plasmid-borne AMR genes from S. sciuri to other Staphylococcus species was previously reported by Li et al., [51] pointing to the need to routinely monitor AMR gene carriage on plasmids in coagulase negative staphylococci. The presence of AMR genes borne on plasmids in CoNS isolated supports the evidence that CoNS may serve as reservoirs for the spread of AMR [10]. Dissemination of plasmids carrying multiple resistance genes will substantially limit the efficacy of antibiotic agents and urgently warrants surveillance of staphylococci from animal and human sources. Previous studies have shown that plasmid sequence associated with rep16 and rep20 was prevalent in clinical S. aureus and S. haemolyticus isolates [52]. rep13, rep16, rep19, rep22 and rep20 have also been detected in S. aureus isolates from different geographic regions with rep16 carrying multiple resistance genes [53, 54]. To the best of our knowledge, the co-occurrence of erm(B), dfrK, aadD resistance genes and replicon plasmids rep16, rep22, repP767 in ST 226 S. epidermidis has not been reported from farm attendants in previous studies in Ghana. Interestingly, ST 226 S. epidermidis was detected in a blood sample of a neonate in Ghana and from hospital and community settings in China [55, 56]; on the other hand, ST30 S. haemolyticus found in this study, has also been detected in blood stream and catheter related infections from India, often showing vancomycin heteroresistance [57, 58] thus, confirming invasive characteristics of these CoNS clones.
**Conclusion**
The study provides insights into the genomic content of MRS from farm attendants and livestock in Ghana and therefore highlights the importance of using whole-genome sequencing to investigate such opportunistic pathogens. CoNS may serve as reservoirs for transmission of resistant genes to S. aureus at the farm level among livestock and farm attendants. The finding of multi-drug resistant CoNS including S. sciuri carrying multiple resistant genes is of public health concern as they could pose a challenge for treatment of life-threatening infections that they may cause.
**Materials and methods**
**Study sites and sample collection**
The Northern region is a major hub for livestock production in Ghana, consisting of numerous smallholder and pastoral farming systems [59]. Samples were collected in July 2018 from one multi-species livestock breeding station and four livestock farms in the Northern region of Ghana (Fig. 2). The Livestock breeding station was selected purposively due to its role in the livestock supply chain in the Northern region. The four farms were selected randomly from 2 districts in the region which were integrated with households in four communities. Nasal swabs were obtained from three hundred and eleven (311) livestock and nineteen (19) farm attendants. Livestock on selected farms were selected randomly within their pens or sheds making sure to collect samples from at least five pens on farms with more than five pens. On farms with very few pens (≤5) samples were collected from at least three pens.
All nasal swabs were placed in 10 ml of Mueller–Hinton broth (Oxoid Ltd., Basingstoke, UK), supplemented with 6.5% NaCl in sterile tubes and labeled. Samples were immediately transported on ice to the laboratory for testing. Data on demographic characteristics for each livestock attendant was collected using a semi-structured questionnaire.
**Identification of S. aureus and Coagulase Negative Staphylococci**
Pre-enrichment was carried out by incubating samples in Mueller–Hinton broth with 6.5% NaCl for 48 h at 37 °C. A volume of 10 µl of each sample was then plated on Mannitol salt agar and incubated for 48 h at 37 °C. Based on the colony morphology and ability to ferment
mannitol, presumptive colonies were streaked on 5% sheep blood agar (Oxoid Ltd., Basingstoke, UK), and incubated for 24 h at 37 °C. Identification of staphylococci was achieved by using the matrix-assisted laser desorption ionization–time of flight mass spectrometry (MALDI-TOF MS) instrument. Briefly, the procedure for MALDI-TOF MS involved spreading well isolated colonies from overnight cultures on a steel target plate. This film is then overlaid with 1 µl of formic acid and allowed to dry for 15 min. 1 µl of matrix preparation containing cyan-4-hydroxy-cinnamic acid in 50% acetonitrile with 2.5% trifluoroacetic acid was placed on each sample and left to dry for a further 15 min. MALDI-TOF MS was then conducted and ionization peaks generated were matched against the integrated reference library for speciation of the bacteria [60, 61].
Antimicrobial susceptibility testing of staphylococci
Antimicrobial susceptibility testing was performed using Kirby Bauer’s disk diffusion method with 10 antimicrobial agents: (cefoxitin (30 µg), amikacin (30 µg), penicillin (1 unit), rifampicin (5 µg), clindamycin (2 µg), erythromycin (15 µg), gentamycin (10 µg), sulphamethoxazole/trimethoprim (25 µg), tetracycline (30 µg), linezolid (10 µg). The measured diameters of the zones of inhibition were interpreted according to the European Committee on Antimicrobial Susceptibility Testing (EUCAST) guidelines [62]. The minimum inhibitory concentration of cefoxitin-resistant isolate was done using vancomycin using E-test strips (bioMerieux) and interpreted based on EUCAST guidelines. Multidrug resistance was defined as resistance to three or more antimicrobial agents [63].
Whole-genome sequencing and Analysis
Whole-genome sequencing was performed on all cefoxitin-resistant isolates using the illumina Miseq platform. DNA of freshly cultured isolates was extracted using Qiagen DNA MiniAmp kit following the manufacturer’s instructions. Extracted DNA was quantified using Qubit 4.0 Fluorometer assay kit (Thermo Fisher Scientific, MA), followed by library preparation with illumina DNA prep following the manufacturer’s instructions. The quality and concentration of fragmented DNA were assessed with the 2100 bioanalyzer system (Agilent) and qPCR (Kapa Sybr Fast qPCR kit) respectively. Libraries were then pooled and loaded on illumina 2 × 300 cycle cartridge for sequencing on Miseq platform (Illumina Inc., San Diego, CA).
Raw sequenced reads were quality filtered and trimmed using FASTQC (http://www.bioinformaticsb abraham.ac. uk/ projects/fastqc/) and Trimmomatic (http://www.usadellab.org/cms/index.php?page=trimmomatic) respectively with a minimum quality set at Q20 [64, 65]. Trimmed reads were
de-novo assembled with Unicycler V0.4.9 from which only contigs greater than 200 bp were used for further analysis.
Assembled files were uploaded to Resfinder (https://cge.cbs.dtu.dk/services/ResFinder/), a tool available on Center for Genomic Epidemiology platform to detect resistance genes present in the sequenced isolates using an identity threshold of 90% and a minimum length of 60%. Plasmids and mobile genetic elements were predicted using PlasmidFinder (https://cge.cbs.dtu.dk/services/PlasmidFinder/) and MGEfinder (https://cge.cbs.dtu.dk/services/MobileElementFinder/) respectively. The sequence types of the isolates were predicted using MLSTFinder (https://cge.cbs.dtu.dk/services/MLST/).
Assembled sequences were mapped to a reference genome (GenBank accession number LS483305.1) and a core maximum likelihood phylogenetic tree was constructed using CSI phylogeny tool on Center for Genomic Epidemiology (CGE). Analysis was performed with default parameters. The resultant tree was annotated in the Interactive Tree of Life (iTOL) [66].
Acknowledgements
The research team is thankful to farm attendants and farm owners of selected farms for their participation in the study.
Authors' contributions
BE was involved in the design of this study and supervision of all aspects of the study. BE, ED, CON, GRA, and FO were involved in sample and data collection, laboratory testing, interpretation of data and drafting of the manuscript. EAC and KKA contributed to the writing of the manuscript. All authors contributed to the writing of the manuscript and approved the final manuscript.
Funding
This study was supported by the University of Ghana Research Fund [URF/9/ILG-067/2015–2016] and The DELTAS Africa Initiative [Africa One – ASPIRE/DEI-15–008]. Africa One – ASPIRE is funded by a consortium of donors including the African Academy of Sciences (AAS), Alliance for Accelerating Excellence in Science in Africa (AESA), the New Partnership for Africa’s Development Planning and Coordinating (NEPAD) Agency, the Wellcome Trust [107753/A/15/Z] and the UK government. Sequencing of cefoxitin positive faecal samples and sequencing of cefoxitin negative faecal samples was supported by the Fleming fund/SEQAFRICA project.
Availability of data and materials
The data sets used during the current study are available from the corresponding author on reasonable request.
Declarations
Ethics approval and consent to participate
Ethical clearance for this study was obtained from the institutional review board (IRB) (FWA00001824) and Animal Care and Use Committee at Noguchi Memorial Institute for Medical Research (2016–01–3 N) for human and animal research activities respectively. All methods were performed in accordance with the relevant guidelines and regulations for field studies and research on animals. Informed consent to participate in the study was obtained from farm owners and farm attendants. In the case of farm attendants who were minors, informed consent was also obtained from legal guardians. Samples collected were coded, and any information obtained was used for the study and remains confidential.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Author details
1 Department of Bacteriology, Noguchi Memorial Institute for Medical Research, University of Ghana, Accra, Ghana. 2 Regional Veterinary Laboratory, Ho, Volta Region, Ghana. 3 Central Veterinary Laboratory, Pong-Tamale, Northern Region, Ghana.
Received: 2 August 2021 Accepted: 1 July 2022
Published online: 21 July 2022
References
1. Otto M. Staphylococcus colonization of the skin and antimicrobial peptides. Expert Review of Dermatology. 2010;5:183–95.
2. Winn W, Allen S, Janda W, Koneman E, Procop G, Schreckenberger P, et al. Isolation of Pathogenic Gram-Negative Bacteria from Urinary Tract Infected Patients [Internet]. 2006 [cited 2022 Mar 15]. Available from: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1922007/
3. Cunha MLRS, Calsolari RA. Toxicity of Staphylococcus aureus and coagulase-negative staphylococci: epidemiological and molecular aspects. Microbiol Insights. 2008;1:MBI–S796.
4. Tong SYC, Davis JS, Eichenberger E, Holland TL, Fowler VG. Staphylococcus aureus infections: Epidemiology, pathophysiology, clinical manifestations, and management. Clin Microbiol Rev. 2015;28(3):603–61.
5. Flu C. Live associations and Coagulase-negative Staphylococcus aureus. Clin Microbiol Infect. 2012;18:735–44.
6. Heilmann C, Ziebuhr W, Becker K. Are coagulase-negative staphylococci virulent? Clin Microbiol Infect. 2019;25:1071–80.
7. Von Eiff C, Arciola CR, Montanaro L, Becker K, Campoccia D. Emerging Staphylococcus aureus species as new pathogens in implant infections. 2006.
8. Sievert DM, Ricks P, Edwards JR, Schneider A, Patel J, Srinivasan A, et al. Antimicrobial-Resistant Pathogens Associated with Healthcare-Associated Infections Summary of Data Reported to the National Healthcare Safety Network at the Centers for Disease Control and Prevention, 2009–2010. Infection Control & Hospital Epidemiology. 2013;34(1):1–14. Available from: https://www.cambridge.org/core/core/product/identifier/501959417000131921?type=journal_article.
9. Klimešová M, Wanja I, Nejeschlebová L, Horáček J, Ponižil A, Vondrušková E. Occurrence of Staphylococcus aureus in cattle, sheep, goat, and pig rearing in the Czech Republic. Acta Vet Brno. 2017;86(1):3–10.
10. Otto M. Coagulase-negative staphylococci as reservoirs of genes facilitating MRSA infection: Staphylococcal commensal species such as Staphylococcus aureus epidermids are being recognized as important sources of genes promoting MRSA colonization and virulence. BioEssays. 2013;35(1):4–11.
11. Founou RC, Founou LL, Essack SY. Clinical and economic impact of antibiotic resistance in developing countries: A systematic review and meta-analysis, vol. 12. PLoS ONE: Public Library of Science; 2017.
12. WHO. Global Strategy for Containment of Antimicrobial Resistance. 2001.
13. Gilani M, Usman J, Latif M, Munir T, Gill MM, Anjum R. Methicillin resistant coagulase negative Staphylococcus from colonizer to a pathogen. 2016.
14. Stryjewski ME, Corey GR. Methicillin-resistant staphylococcus aureus: An evolving pathogen. Clin Infect Dis. 2014;58(suppl_1):S10–9.
15. Goetchebeur M, Landry PA, Han D, Vicente C. Methicillin-resistant Staphylococcus aureus: A public health issue with economic consequences. 2006.
16. Catry B, Laevens H, Devriese LA, Opsomer G, de Kruif A. Antimicrobial resistance in livestock. 2003.
as Causes of Human Infection and Colonization in Germany. PLoS ONE. 2013;8(2):e55040.
18. Cömblé F, Argudín MA, Vanderhaeghen W, Hermans K, Haesebrouck F, Butaye P. Transmission dynamics of methicillin-resistant Staphylococcus aureus in pigs. Front Microbiol. 2013;4:57.
19. Morgan M. Methicillin-resistant Staphylococcus aureus and animals: Zoonosis or humanosis? J Antimicrob Chemother. 2008;62:1181–7.
20. Kadazi J, Smith TC, Thapalya D. Staphylococcus aureus and Staphylococcal Food-Borne Disease: An Ongoing Challenge in Public Health, vol. 2014. BioMed Research International: Hindawi Publishing Corporation; 2014.
21. WHO. GLASS Whole-genome sequencing for surveillance of antimicrobial resistance Global Antimicrobial Resistance and Use Surveillance System (GLASS). 2020.
22. Piessens V, van Coillie E, Verbeist B, Supré K, Braem G, van Nuffel A, et al. Distribution of coagulase-negative Staphylococcus species from milk and environment of dairy cows differs between herds. J Dairy Sci. 2011;94(6):2933–44.
23. Dąkic I, Morrison D, Vuković M, Szewczyk EM. Staphylococcus haemolyticus An emerging threat in the twilight of the antibiotics age. Microbiology. 2006;14:5.
24. Enyetornye B, Kwamena Ab R, Kodua E, Sop Foka EI, Narh Ahia K, Habibur R, et al. Whole genome Sequencing for food-borne outbreaks in Thailand. 2021 [cited 2022 Feb 12]. Available from: https://www.ncbi.nlm.nih.gov/nuccore/CP070060.1/.
25. Hu X, Zheng B, Jiang H, Kang Y, Cao Q, Ning H, et al. Draft genome sequence of Staphylococcus sciuri subspp. sciuri strain 28, isolated from human skin. Genome Announc. 2015;3(4):e00714-15.
26. Buahpong R, Joyinda Y, Rodpan A, Yornrat S, Pomprnt T, Ampoot W, et al. Whole genome Sequencing for food-borne outbreaks in . 2021. Available from: http://www.biomedcentral.com/1471-2180/12/104.
27. Egyir B, Hadjirin NF, Gupta S, Owusu F, Agbodzi B, Adogla-Bessa T, et al. Characterization of methicillin-resistant Staphylococcus sciuri isolates from industrially raised pigs, cattle and broiler chickens. J Antimicrob Chemother. 2014;69(1):2928–34.
28. Gómez-Sanz E, Haro-Moreno JM, Jansen SD, Roda-Garcia JJ, López-Pérez M. The Resistome and Mobilome of Multidrug-Resistant Staphylococcus sciuri C29865 Unveil a Transferable Trimethoprim Resistance Gene. Designated dfrE, Spread Unnoticed. 2021. Available from: https://journals.asm.org/journal/msystems.
29. Couto I, Wu SW, Tomas A, de Lencastre H. Development of methicillin resistance in clinical isolates of Staphylococcus sciuri by transcriptional activation of the mecA homologue native to the species. J Bacteriol. 2011;193(18):5645–53.
30. Czekaj T, Ciszewski M, Szewczyk EM. Staphylococcus aureus USA300. Journal of Global Antimicrobial Resistance. 2015;3(1):26–30.
31. Egyir B, Oteng AA, Owusu E, Newman MJ, Addo KK, Larsen AR. Characterization of metmethicillin-resistant Staphylococcus aureus isolates from livestock and farm attendants in Ghana. J Clin Microbiol. 2005;43(4):2782–5.
32. Egyir B, Guardabassi L, Sørum M, Nielsen SS, Kolekang A, Frimpong E, et al. Molecular epidemiology and antimicrobial susceptibility of clinical and food samples in Algeria. BMC Res Notes. 2018;11(1):663.
33. Dakić I, Morrison D, Vuković D, Savić B, Shittu A, Ježek P, et al. Isolation and molecular characterization of Staphylococcus sciuri in the hospital environment. J Clin Microbiol. 2005;43(6):2933–44.
34. Egyir B, Guardabassi L, Nielsen SS, Larsen AJ, Ali A, Khan MA, Rizwan M, et al. Molecular epidemiology of clinical and carrier strains of methicillin resistant Staphylococcus aureus (MRSA) in the hospital settings of north India. Ann Clin Microbiol Antimicrob. 2006;14:5.
35. Czekaj T, Crzewski M, Szewczyk EM. Staphylococcus haemolyticus An emerging threat in the twilight of the antibiotics age. Microbiology. 2015;161:2061–8.
36. Egyir B, Oteng AA, Owusu E, Newman MJ, Addo KK, Larsen AR. Characterization of staphylococcus aureus from human immunodeficiency virus (HIV) patients in Accra, Ghana. J Infect Dev Ctries. 2010;4(5):453–6.
37. Egyir B, Guardabassi L, Esson J, Nielsen SS, Newman MJ, Addo KK, et al. Insights into nasal carriage of Staphylococcus aureus in an urban and a rural community in Ghana. PLoS ONE. 2014;9(2):e89716.
38. Egyir B, Guardabassi L, Monecke S, Addo KK, Newman MJ, Larsen AR. Methicillin-resistant Staphylococcus aureus strains from Ghana include USA300. Journal of Global Antimicrobial Resistance. 2015;3(1):26–30.
39. Egyir B, Guardabassi L, Nielsen SS, Larsen AJ, Addo KK, Newman MJ, et al. Prevalence of nasal carriage and diversity of Staphylococcus aureus among inpatients and hospital staff at Korle Bu Teaching Hospital. Ghana Journal of Global Antimicrobial Resistance. 2013;3(4):189–93.
40. Rolo J, Worning P, Boye Nielsen J, Sobral R, Bowden R, Bouchami O, et al. Novel sequence types among staphylococcus haemolyticus isolated from neonatal blood samples. Microbiol Resour Announc. 2021;10(3):e00710–21.
41. Nemeghaire S, Vanderhaeghen W, Angeles Argudín M, Haesebrouck F, Butaye P. Characterization of methicillin-resistant Staphylococcus sciuri isolates from poultry farms in. 2010. Available from: https://www.researchgate.net/publication/284028206.
42. Wool JB, Smith DB, Baker EH, Brecher SM, Gupta K. Has the emergence of community-associated methicillin-resistant Staphylococcus aureus increased trimethoprim-sulfamethoxazole use and resistance? A 10-year time series analysis. Antimicrob Agents Chemother. 2012;56(1):5655–60.
43. Monophor P. Vancomycin hydrochloride for injection. Tokyo: USP, Fresenius Kabi Canada Inc.; 2017. Control. (204448).
44. Butaye P. Transmission dynamics of methicillin-resistant Staphylococcus sciuri. 2014. Available from: https://www.researchgate.net/publication/284028206.
45. Olayinka B, Bala Lis H, Olojey B, Onalopajo LA. Multidrug resistant Staphylococcus aureus isolates from poultry farms in Zaria, Nigeria. Antimicrobial resistance profile and enterotoxigenicity of S. aureus isolated from dry fish View project Mercy Aboh View project Multidrug resistant Staphylococcus aureus isolates from poultry farms in. 2010. Available from: https://www.researchgate.net/publication/284028206.
46. Morgan M. Methicillin-resistant Staphylococcus aureus and animals: Zoonosis or humanosis? J Antimicrob Chemother. 2008;62:1181–7.
47. Rolo J, Worning P, Boye Nielsen J, Sobral R, Bowden R, Bouchami O, et al. Evidence for the evolutionary steps leading to mecA-mediated B-lactam resistance in staphylococci. PLoS Genet. 2017;13(4):e1006674.
48. Piessens V, van Coillie E, Verbeist B, Supré K, Braem G, van Nuffel A, et al. Distribution of coagulase-negative Staphylococcus species from milk and environment of dairy cows differs between herds. J Dairy Sci. 2011;94(6):2933–44.
59. DAI. DFID Market Development (MADE) in Northern Ghana Programme [Internet]. 2014. Available from: www.dai.com.
60. Wolters M, Rohde H, Maier T, Belmar-Campos C, Franke G, Scherpe S, et al. MALDI-TOF MS fingerprinting allows for discrimination of major methicillin-resistant Staphylococcus aureus lineages. Int J Med Microbiol. 2011;301(1):64–8.
61. Christner M, Rohde H, Wolters M, Sobottka I, Wegscheider K, Aepfelbacher M. Rapid Identification of Bacteria from Positive Blood Culture Bottles by Use of Matrix-Assisted Laser Desorption-Ionization Time of Flight Mass Spectrometry Fingerprinting. J Clin Microbiol. 2010;48(5):1584–91.
62. European Committee on Antimicrobial Susceptibility Testing. Breakpoint tables for interpretation of MICs and zone diameters. 2019.
63. Magiorakos AP, Srinivasan A, Carey RB, Carmeli Y, Falagas ME, Giske CG, et al. Multidrug-resistant, extensively drug-resistant and pandrug-resistant bacteria: An international expert proposal for interim standard definitions for acquired resistance. Clin Microbiol Infect. 2012;18(3):268–81.
64. Bolger AM, Lohse M, Usadel B. Trimmomatic: A flexible trimmer for Illumina sequence data. 2014;30(15):2114–20.
65. Andrews S. FastQC: a quality control tool for high throughput sequence data. 2010 [cited 2022 Mar 20]. Available from: https://www.bioinformatics.babraham.ac.uk/projects/fastqc/.
66. Letunic I, Bork P. Interactive Tree of Life (iTOL) v4: Recent updates and new developments. Nucleic Acids Res. 2019;47(W1):W256–9.
**Publisher’s Note**
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3110,
1
],
[
3110,
8741,
2
],
[
8741,
12488,
3
],
[
12488,
15274,
4
],
[
15274,
18281,
5
],
[
18281,
23626,
6
],
[
23626,
26342,
7
],
[
26342,
32899,
8
],
[
32899,
39665,
9
],
[
39665,
41315,
10
]
]
} |
0af46c8eeaf69416b2858ce3b805100b9ae4d0f8 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 18,
"total-fallback-pages": 0,
"total-input-tokens": 57798,
"total-output-tokens": 22487,
"fieldofstudy": [
"Biology",
"Medicine"
]
} | The Calcium-Sensing Receptor and the Reproductive System
Isabella Ellinger*
Pathophysiology of the Placenta, Department of Pathophysiology and Allergy Research, Center for Pathophysiology, Infectiology and Immunology, Medical University Vienna, Vienna, Austria
Active placental transport of maternal serum calcium ($\text{Ca}^{2+}$) to the offspring is pivotal for proper development of the fetal skeleton as well as various organ systems. Moreover, extracellular $\text{Ca}^{2+}$ levels impact on distinct processes in mammalian reproduction. The calcium-sensing receptor (CaSR) translates changes in extracellular $\text{Ca}^{2+}$-concentrations into cellular reactions. This review summarizes current knowledge on the expression of CaSR and its putative functions in reproductive organs. CaSR was detected in placental cells mediating materno-fetal $\text{Ca}^{2+}$-transport such as the murine intraplacental yolk sac (IPYS) and the human syncytiotrophoblast. As shown in casr knock-out mice, ablation of CaSR downregulates transplacental $\text{Ca}^{2+}$-transport. Receptor expression was reported in human and rat ovarian surface epithelial (ROSE) cells, where CaSR activation stimulates cell proliferation. In follicles of various species a role of CaSR activation in oocyte maturation was suggested. Based on studies in avian follicles, the activation of CaSR expressed in granulosa cells may support the survival of follicles after their selection. CaSR in rat and equine sperms was functionally linked to sperm motility and sperm capacitation. Implantation involves complex interactions between the blastocyst and the uterine epithelium. During early pregnancy, CaSR expression at the implantation site as well as in decidual cells indicates that CaSR is important for blastocyst implantation and decidualization in the rat uterus. Localization of CaSR in human extravillous cytotrophoblasts suggests a role of CaSR in placentation. Overall, evidence for functional involvement of CaSR in physiologic mammalian reproductive processes exists. Moreover, several studies reported altered expression of CaSR in cells of reproductive tissues under pathologic conditions. However, in many tissues we still lack knowledge on physiological ligands activating CaSR, CaSR-linked G-proteins, activated intracellular signaling pathway, and functional relevance of CaSR activation. Clearly, more work is required in the future to decode the complex physiologic and pathophysiologic relationship of CaSR and the mammalian reproductive system.
Keywords: calcium-sensing receptor, reproduction, testes, ovaries, uterus, placenta
Abbreviations: AC, adenylyl cyclase; cAMP, cyclic adenosine monophosphate; EGFR, epidermal growth factor receptor; Gd$^{3+}$, Gadolinium; GV, germinal vesicle; LH, luteinizing hormone; MAPK, mitogen-activated protein kinase; Mg$^{2+}$, Magnesium; PI-3K, phosphoinositide 3-kinase; PLC, phospholipase C; PKC, protein kinase C; CaSR, Calcium-sensing receptor; phos, phosphatase; PTH, Parathyroid hormone; PTHrP, Parathyroid hormone-related protein; PT, parathyroid; PY, tyrosine phosphorylation.
**INTRODUCTION**
Calcium (Ca\(^{2+}\)) is indispensable in the context of mammalian reproduction (Baczyk et al., 2011; Correa et al., 2015; Kornbluth and Fissore, 2015). Firstly, Ca\(^{2+}\) contributes to crucial developmental processes such as skeletal formation and mineralization (Riccardi et al., 2013; Kovacs, 2014, 2015), lung (Riccardi et al., 2013) and kidney development (Gilbert et al., 2011) or formation and maturation of neuronal circuits and long-term memory (Leclerc et al., 2011). Therefore, Ca\(^{2+}\) must be supplied in sufficient quantities to the growing offspring, which is accomplished by active Ca\(^{2+}\)-transport from maternal to fetal or neonate blood circulation across placental and mammary tissue, respectively (Olaussen et al., 2012; Kovacs, 2014, 2015, 2016).
Secondly, Ca\(^{2+}\) is the most universal second messenger. It is modulated downstream of numerous receptors and can activate diverse cytoplasmic signaling proteins (Berridge et al., 2000). Not surprisingly, therefore, Ca\(^{2+}\) signaling pathways also play crucial roles in early reproductive events like gamete formation and maturation in the male and female gonads, and fertilization as well as pre- and peri-implantation development in the female reproductive tract (Kashir et al., 2013; Armant, 2015).
Both, extracellular and intracellular Ca\(^{2+}\)-linked processes require a tightly regulated extracellular calcium (Ca\(^{2+}\)) concentration. Mammals have therefore developed a carefully balanced Ca\(^{2+}\) homeostatic system, which is based on Ca\(^{2+}\)-sensors. The calcium-sensing receptor (CaSR), is the master regulator of Ca\(^{2+}\) concentration (Brown, 2013; Tyler Miller, 2013; Alfadda et al., 2014). CaSR controls secretion of a regulatory hormone, parathyroid hormone (PTH), that in turn impacts on Ca\(^{2+}\) via cells in the target tissues kidney, intestine, and bone (Brown, 2013).
CaSR is additionally expressed in other adult tissues, including the central and peripheral nervous system (Ruat and Traiffort, 2013; Jones and Smith, 2016), the cardio-vascular system (Smajilovic et al., 2011; Schepelmann et al., 2016), the lung (Riccardi et al., 2013), the pancreas (Squires et al., 2014), the epidermis (Tu and Bikle, 2013), or the intestine (Macleod, 2013). There, the function of CaSR is not related to control of Ca\(^{2+}\)-homeostasis. Instead, CaSR modulates functions such as proliferation and differentiation, apoptosis and chemotaxis, ion channel activity, or hormone secretion, to name a few.
The outstanding role of Ca\(^{2+}\) in reproduction together with CaSR expression in reproductive organs implicates a role of CaSR in reproductive processes. This review first introduces CaSR and its functional versatility. It then gives a survey on organs and processes required for reproduction, and summarizes the still sparse information on expression, localization, and function of CaSR in gametes, gonads, uterus, and placenta in health and disease (summarized in Table 1). Finally, it indicates research demand in these areas. Expression and function of CaSR in mammary epithelial cells is not addressed in this article as this has been reviewed recently (Kovacs, 2016). Likewise, the role of CaSR in proper development of the skeleton (Riccardi et al., 2013; Kovacs, 2014), the lung (Riccardi et al., 2013; Brennan et al., 2016) and the brain (Liu et al., 2013) is not considered in this article.
**THE CALCIUM SENSING RECEPTOR, CaSR, AND ITS FUNCTIONAL VERSATILITY**
CaSR is a member of the class C of the G protein-coupled receptors and is present in all vertebrate classes. The fully glycosylated monomer has a molecular mass of 160 kDa and consists of a large N-terminal glycosylated extracellular domain, a seven transmembrane domain and an intracellular C-terminal domain. The extracellular domain contains a bi-lobed Venus-flytrap-like domain. The functional receptor is a dimer, where the Venus-flytrap-like domains of two monomers are linked via covalent as well as non-covalent interactions. Ca\(^{2+}\)-binding in the cleft between the two lobes of each Venus-flytrap-like domain causes a rotation of one monomer relative to the other, which finally allows for G proteins to interact with the cytoplasmic side of the CaSR (Zhang et al., 2015).
CaSR is, however, promiscuous in ligand binding; it can be stimulated by other divalent (Mg\(^{2+}\)) and tervalent (Gd\(^{3+}\)) inorganic cations, as well as organic polycations (e.g., neomycin, spermine). Moreover, it is modulated by various physiological stimuli including extracellular pH, L-aromatic amino acids, and ionic strength. Different ligand binding sites can stabilize distinct conformational changes, which results in “ligand-biased signaling.” As a consequence, CaSR was shown to interact with the heterotrimeric G proteins G\(_{q/11}\), Gi\(_{o/16}\), G\(_{12/13}\), and G\(_s\) and is able to target all major intracellular signaling pathways. CaSR-mediated activation of G\(_{q/11}\) results in stimulation of phospholipase C (PLC), Ca\(^{2+}\) mobilization from intracellular stores, and activation of protein kinase C (PKC) isoforms. CaSR-coupling to Gi\(_{o/16}\) can inhibit adenylyl cyclase (AC). On the other hand, it can activate mitogen-activated protein kinases (MAPK) such as ERK1/2 and JNK. This can lead to transactivation of the epidermal growth factor receptor (EGFR). Activation of G\(_{12/13}\) modulates several pathways. This can lead to migration via rho-mediated actin polymerization and membrane ruffling or induce cell differentiation. It can also target tyrosine kinases, protein phosphatases, or activate certain AC isoforms. CaSR-coupling to G\(_s\) also activates AGs. Furthermore, CaSR activation can stimulate PLA, phosphatidylinositol 3-kinase (PI-3K) and PI-4K. Overall, major consequences of CaSR activation in cells are Ca\(^{2+}\) mobilization, regulation of intracellular cAMP levels, activation of various protein kinases as well as activation of gene transcription factors. CaSR-mediated signaling, however, depends on the cell-type-specific expression of important components of the downstream signaling pathways (Conigrave and Ward, 2013).
An example for the cell-type specific function of CaSR is the contradictory role in cancer development, where it acts as either an oncogene (breast, prostate) or as a tumor suppressor gene (colon, parathyroid) (Brennan et al., 2013; Peterlik et al., 2013; Tennakoon et al., 2016). CaSR activation can also have diametrical consequences in normal and tumor cells as shown for mammary epithelial cells by activating different G-proteins (Mamillapalli et al., 2008). The multiple consequences of CaSR activation are illustrated by its variable impact on
### TABLE 1 | CaSR expression and putative functions in healthy reproductive tissues.
| Organ/Tissue | Species | mRNA | Anti-CaSR antibody | Protein WB | Protein IFM/IHC | Function related to CaSR | References |
|--------------|---------|------|--------------------|------------|-----------------|-------------------------|------------|
| **MALE REPRODUCTIVE SYSTEM** | | | | | | | |
| Rat Testis Epididymis | | | Rabbit anti-CaSR Acris (N-terminal domain) | | | | |
| | | | | | | | Mendoza et al., 2012 |
| | | | | | | | |
| Horse | | | Goat anti CaSR (F19) Santa Cruz (N-terminal domain) | Sperm 100 kDa + 77 kDa | Sperms | Sperm capacitation ↓ Sperm motility ↑ | Macías-García et al., 2016 |
| Human | | | Rabbit anti-CaSR Sigma (N-terminal domain) | | | | |
| | | | | | | | Feng et al., 2014 |
| **OVAR** | | | Polyclonal anti-CaSR Affinity Bioreagents | | | Pro-liferation ↑ Ca²⁺ ↑ IP3 ↑ | McNeil et al., 1998 |
| Human | Ovarian surface epithelial cell lines | | | | | | |
| | | | | | | | De Iuliis et al., 2006 |
| Horse | | | Rabbit anti-CaSR (O0117-15) US Biological (C-terminal) | | | Oocyte (GV, MI, MII state) | |
| | | | | | | | Liu et al., 2015 |
| Pig | Oocytes Granulosa cells of Cumuli oophori | | Goat anti-CaSR Santa Cruz | Granulosa cells, 120–130 kDa | Oocyte maturation↑ | | |
| Japanese Quail | | | Mouse anti-CaSR Abcam or NPS Pharmaceutical (Extracellular domain) | Granulosa explants 115–125 kDa +100–110 kDa | Granulosa cells of preovulatory follicles | Survival↑ (Decreased apoptosis) | De Iuliis et al., 2010 |
| **UTERUS** | | | Rabbit anti-CaSR Affinity Bioreagents | | | Implanting blastocyst | |
| Rat Uterine luminal epithelium Uterine stromal cells | | | | | | Decidua-lization | Xiao et al., 2005 |
| | | | | | | | Pistilli et al., 2012 |
| Rat | | | Anti-CaSR Affinity Bioreagents | | | Relaxation? | |
intracellular Ca$^{2+}$ concentration. CaSR can directly increase cytosolic Ca$^{2+}$ through PLC activation to open Ca$^{2+}$ channels. Alternatively, CaSR can trigger ERK/phospho-ERK pathways, thereby increasing transcription factor (e.g., CREB) activity, which stimulates expression of Ca$^{2+}$-channels with appropriate response elements. And finally, CaSR can increase K$^{+}$-channel activity, and as a consequence increase membrane potential and a Ca$^{2+}$-driving force. Many intracellular signaling pathways, in turn, are sensitive to cytosolic Ca$^{2+}$-rises, and as a consequence, cellular processes such as proliferation or migration can result from CaSR activation (Tennakoon et al., 2016).
Overall, CaSR has immense functional versatility by activating different signaling pathways in a ligand- and cell-type specific way. In the context of reproduction (see below), mainly activation of MAPK pathways (e.g., ERK1/2, p38, or JNK) has been investigated so far, probably because MAPK activation is of great importance in reproduction (Li et al., 2009; Almog and Naor, 2010; Fan et al., 2012; Nunes et al., 2015). However, CaSR can also induce other pathways such as the PI-3K/AKT pathway (Bilderback et al., 2002; Liao et al., 2006) in the reproductive system. Activation of diverse intracellular signaling routes should be considered in future studies addressing the function of CaSR in reproduction.
### CaSR AND THE MALE REPRODUCTIVE SYSTEM
#### Spermatogenesis
The mass production of the male gametes starts with puberty, when the hypothalamic-pituitary-gonadal axis is established, and is a continuous, life-long process. Spermatogenesis consists of three major phases (1) the proliferation of the stem cells (spermatogonia) resulting in spermatocytes, (2) two meiotic divisions that give rise to haploid spermatids, and (3) spermiogenesis, the differentiation into mature sperms (for details see Kornbluth and Fissore, 2015). Spermatogenesis occurs in the seminiferous tubulus of the testes and is supported by testicular non-germ line cells, such as Sertoli and Leydig cells, which nourish the sperms and/or produce factors required for proper spermatogenesis. Within the epididymis the sperms complete maturation. Secretory products of the male accessory sex glands (e.g., prostate gland) support the functionality of sperms. Once in the female tract, sperms undergo capacitation to increase motility (hyperactivation) and prepare for fertilization of the oocyte. Only capacitated sperms can bind to molecules in the egg's zona pellucida, which triggers the acrosome reaction. Enzymes released from the acrosome, a Golgi-derived sperm organelle, digest a way through the zona pellucida enabling the sperm to follow and to finally fertilize the egg (de Kretser, 2012). Ca$^{2+}$ is a major determinant of proliferation and differentiation of spermatogonia, sperm motility, capacitation, and acrosome reaction (Breitbart, 2002; Yoshida and Yoshida, 2011; Correia et al., 2015; Kornbluth and Fissore, 2015). In contrast to Ca$^{2+}$ channels, which are well studied in sperms (Correia et al., 2015), sparse information is available on the expression and function of CaSR in sperm or male reproductive tissues (see also Table 1).
CaSR Expression in Healthy Male Reproductive Tissue
In rats, CaSR mRNA expression appeared higher in testes compared to epididymis (Figure 1A). In testis, CaSR protein was found in Sertoli cells, spermatogonia, spermatocytes, and spermatids with highest expression level in spermatids (Figure 1B). Leydig cells and fibroblasts, in contrast, presented CaSR negative. Mature sperms in the epididymis also expressed CaSR, predominantly at the head domain. Epithelial epididymal cells exhibited staining at the apical pole. Since a calcimimetic drug (AMG 641) caused a moderate, but significant increase of motility of isolated rat sperms, a role of CaSR in sperm motility was suggested. A similar stimulatory effect on pig sperms mobility indicated expression of CaSR also in male gametes of this species (Mendoza et al., 2012).
In isolated equine sperms, CaSR protein was located predominantly in the head of the sperm, with lower expression seen along the tail. Proteins detected with an anti-CaSR antibody by western blotting had a molecular weight of 100 and 75 kDa (Macias-Garcia et al., 2016), which is smaller than that of fully glycosylated CaSR transiently expressed in HEK cells (160 kDa) (Pidasheva et al., 2006). The authors suggested involvement of CaSR in sperm capacitation as well as sperm mobility. Capacitation occurs when alterations in the extracellular milieu induce cAMP and activate PKA. The result is tyrosine phosphorylation (PY) of various proteins. Among factors impacting on PY is Ca$^{2+}$. In species such as stallion (González-Fernández et al., 2013), human and mice (Baker et al., 2004), Ca$^{2+}$ in the capacitation medium inhibits PY. Ca$^{2+}$-dependent PY inhibition in stallion sperm was reversed in the presence of a CaSR antagonist (NPS 2143), while a CaSR agonist (AC-265347) inhibited PY similarly to Ca$^{2+}$. The result suggested that CaSR reduces capacitation in stallion sperm. A modulatory role of the pH was observed. In addition, NPS 2143 caused a significant decrease in sperm motility indicating the CaSR is also involved in the regulation of equine sperm mobility (Macias-Garcia et al., 2016).
CaSR and Disorders of the Male Reproductive System
Diabetes, being an increasing problem worldwide\(^1\), can cause testicular damage and male infertility. A recent study demonstrated up-regulated CaSR in testicular tissues in streptozotocin-induced diabetic rats (Kong et al., 2016). The diabetic rats had significantly lower testes weights and serum levels of testosterone compared to healthy controls. A connection between CaSR activation and testicular damage was found. Specific activation of CaSR by Gd$^{3+}$ increased, while specific inhibition of CaSR by the antagonist NPS 2390 reduced testicular damage in the diabetic rats. Increased lipid peroxidation, decreased anti-oxidative capacity, increased apoptosis of germ cells, and activation of the mitochondrial apoptotic pathways were observed in testicular tissue of diabetic rats and the parameters were further aggravated by the administration of Gd$^{3+}$, and attenuated by NPS 2390. CaSR was found to be an activator of different MAPK pathways (ERK, p38, JNK). It was concluded that CaSR activation had a pro-apoptotic impact on germ cells in diabetic rats and overall participated in diabetes-induced testicular damage.
While CaSR expression in normal rat Leydig cells could not be shown (Mendoza et al., 2012), cultured Rice H-500 rat Leydig cell tumor express the receptor mRNA and protein (Sanders et al., 2000). H-500 cells are a transplantable model for humoral hypercalcemia of malignancy. Humoral hypercalcemia of malignancy is a syndrome seen in various types of cancers including prostate cancer, but also testicle or breast cancer. It arises from tumor-derived humoral factors which destroy normal calcium homeostasis (Chakravarti et al., 2009). Upon implantation into adult male rats, H-500 cells start proliferation and cause hypercalcemia by abundant release of the humoral factor parathyroid hormone-related protein (PTHrP). PTHrP release, proliferation, and protection of cells from apoptosis, are stimulated by Ca$^{2+}$ via CaSR. CaSR-induced proliferation depends on AKT and MAPK p38, but not on MAPK ERK1/2 (Tfelt-Hansen et al., 2004). CaSR also stimulates transcription of the PThrP gene, and release of PTHrP in H-500 cells by activating PKC as well as various MAPK pathways (ERK1/2, p38, JNK) (Tfelt-Hansen et al., 2003a). Partly, these effects are caused by transactivation of EGFR by CaSR (Tfelt-Hansen et al., 2005). In addition to PTHrP, Ca$^{2+}$ also up-regulates mRNA of the oncocite pituitary tumor transforming gene as well as vascular endothelial growth factor genes in H-500 cells, which leads to the robust proliferation and angiogenesis at the site of their implantation (Tfelt-Hansen et al., 2003b). Stimulation of PTHrP release initiates a vicious circle of hypercalcemia maintained by CaSR expression in Leydig cell tumors, which suggests CaSR as a potential therapeutic target for CaSR antagonists. Colloton and coworkers investigated the ability of cinacalcet, an allosteric modulator of CaSR, to attenuate hypercalcemia in mice bearing H-500 cells and indeed demonstrated that cinacalcet effectively reduced tumor-mediated hypercalcemia (Colloton et al., 2013).
In an immunohistochemical study, comparing human prostate cancer tissue sections in microarrays, CaSR expression was confirmed not only in primary prostate cancer tissue, but also in normal prostate tissue (Figure 1A). No significant difference in the CaSR expression level between these tissues was observed. However, a significant higher expression level of CaSR was found in the metastatic prostate cancer tissues obtained from bone (Feng et al., 2014). For breast cancer cells it was demonstrated that the elevated Ca$^{2+}$-release during bone remodeling represents a chemoattractant, which promotes migration of cancer cells to bone via activated CaSR (Saidak et al., 2009). CaSR mRNA and protein is also detected in the highly bone metastatic prostate cancer cell lines PC-3 and C4-2B, while comparatively lower expression of CaSR is found in non-skeletal metastatic, epithelial-derived prostate cell line LNCaP cells (Liao et al., 2006). Prostate cancer most commonly metastasizes to bone, preferring areas of high bone turnover. As a result of bone remodeling, Ca$^{2+}$ and growth factors are released. In PC-3 and C4-2B, but not LNCaP cells elevated Ca$^{2+}$ activated CaSR. Activation resulted in stabilization of cyclin D, promoted PI-3K/AKT/ mTOR signaling, and increased
---
\(^1\)http://www.who.int/mediacentre/factsheets/fs312/en/ (Accessed June 04, 2016).
FIGURE 1 | The cartoon depicts (A) major components of the human male reproductive system and (B) major steps in spermatogenesis. Organs/tissues/cells, which were shown to express CaSR are depicted in color. Red color, CaSR expression shown in human ± other mammalian species; blue color, CaSR expression shown in mammalian species other than human (for details on species and assumed function of CaSR see Text and Table 1).
metastatic potential (Liao et al., 2006). A few clinical studies supported the notion that CaSR promotes lethal prostate cancer. First, the CaSR Q1011E minor allele, which is common in populations with African ancestry, appeared to be associated with a less aggressive form of prostate cancer among African-American men (Schwartz et al., 2010). A second study assessed genetic variations across CaSR and lethal prostate cancer risk in Caucasian men. Common genetic variations in CaSR were found associated with both higher and lower risk for lethal prostate cancer. The association was stronger in patients with lower plasma levels of vitamin D (Shui et al., 2013). Third, in a study that correlated primary tumor CaSR expression with the risk for lethal prostate cancer, a higher CaSR tumor expression was associated with an approximately two-fold higher risk for lethal progression. This risk was independent of Gleason grade and pathological stage. Higher CaSR expression was significantly associated with lethal progression among cases with lower tumor vitamin D receptor expression but not among cases with high tumor vitamin D receptor expression (Ahearn et al., 2016).
**Research Demands**
Reports on CaSR expression in human male reproductive system are currently mainly related to cancer. For more detailed information on the role of CaSR in tumors, the reader is referred to other reviews (Singh et al., 2013; Mateo-Lozano et al., 2016; Tennakoon et al., 2016). The high CaSR expression in Leydig and prostate cell tumors asks for further evaluation of the prognostic usability of CaSR. As CaSR promotes bony metastasis of cancer, this raises the possibility of reducing the risk of such metastases with CaSR-based therapeutics.
Infertility is among the most serious social problems affecting advanced nations today. Infertility affects both men and women. A variety of known factors is associated with male infertility, but in 30–45%, the cause of the abnormal semen parameters is not identified (Jungwirth et al., 2012). In this context, knowledge of all molecules that impact on proper sperm development is of relevance. If CaSR would be demonstrated to significantly improve or reduce sperm quantity or quality, agonists or antagonists of the receptor, respectively, could serve for treatment. But currently, many open questions remain. The intracellular signaling pathways associated with the observed effect of CaSR on (rat, porcine, and equine) sperm motility and capacitation remain to be investigated. The predominant physiological ligands responsible for these effects are unknown. Of interest, Ca$^{2+}$ concentrations in the uterine fluid vary during estrous cycle in various species (Casslén and Nilsson, 1984; Alavi-Shoushtari et al., 2012; Alavi Shoushtari et al., 2014). Polyamines (spermine, spermidine, and putrescine), which are type I calciumimetics (Brown, 2010) are secreted by the prostate gland into semen. Whether polyamines, or other CaSR ligands in the semen could be sensed by CaSR expressed on sperms and have effects, is not known. It is unknown, whether CaSR under physiological conditions impacts on sperm cell apoptosis. Likewise, CaSR may modulate acrosome reaction or spermatic hyperactivation. The function of CaSR expressed in (rat) Sertoli cells and epididymal cells remains to be investigated. CaSR expression was not observed in healthy rat Leydig cells. However, there is functional evidence for a divalent cation (Ca$^{2+}$) receptor present on the surface of murine cells inducing Ca$^{2+}$ release from ryanodine receptor-gated intracellular Ca$^{2+}$ stores (Adebanjo et al., 1998). Since a raise of extracellular Ca$^{2+}$ can induce testosterone secretion of Leydig cells (Meikle et al., 1991), re-evaluation of CaSR expression in Leydig cells in mammalian species might be of interest when looking for new therapies to increase or reduce hormone secretion. The molecular size of CaSR protein detected in equine sperm is small compared to the mature glycosylated CaSR. The reason for this difference is currently unknown. It may relate to different glycosylation of CaSR or alternatively spliced CaSR in the tissue. In addition, a recent study indicated that the western blotting profiles in tissues depend on the anti-CaSR antibody used (Graca et al., 2016). Various anti-CaSR antibodies were used in the studies summarized in this review. They are listed in Table 1.
**CaSR IN OVARY AND OOCYTES**
**Ovaries and Oogenesis**
Only a small number of mature oocytes is released during the reproductive years of a woman. Ovulation occurs in cycles consisting of follicular phase, ovulation and luteal phase. The follicular phase is characterized by estrogen dominance, while in the luteal phase, progesterone is the dominant sex hormone. Due to the cyclic release of the steroids, the female body exhibits cyclicity, which is accompanied by structural and functional changes in the ovaries, oviducts, and the uterus. In most animals, this is called estrous cycle, while higher primates including human experience menstrual cycles. The reason of the changes occurring during female cyclicity is the dual function of the female reproductive tract. Under estrogen dominance, the body is prepared to receive the male gametes and enable fertilization, while under progesterone dominance the body is prepared for implantation and nourishment of the conceptus (for details see Findlay, 2012).
The ovarian surface is covered with a single layer of epithelial cells. Ovarian surface epithelial cells are responsible for the most malignant forms of ovarian carcinoma. In the ovarian cortex, ovarian follicles of various sizes and at different stages of development are located. The follicles are the functional units of the ovary. They contain a single oocyte and are surrounded by epithelial granulosa cells. Theca cells are closely associated with the follicles. Theca cells differentiate from the interfollicular stroma due to signals from growing follicles and produce the androgen substrate, which is required for estrogen biosynthesis in the granulosa cells. After ovulation, theca cells are transformed from androgen-producing to progesterone-producing cells, thereby becoming the pregnancy-maintaining cells of the corpus luteum. The polycystic ovary syndrome (PCOS) is characterized by hyperandrogenism, oligo- and/or anovulation, and polycystic ovarian morphology. PCOS is associated with insulin resistance, hyperinsulinemia and central obesity. Excessive proliferation of theca cells is often associated with PCOS; this is a major cause of infertility due to ovarian hyperandrogenism (Magoffin, 2005).
Oogenesis starts with the formation of primary oocytes during the fetal period in utero. Stem cells (oogonia) first proliferate and then enter the first meiotic division, which is halted in a prophase state of meiosis I until sexual maturity. This first meiotic arrest is characterized by a large nucleus called the germinal vesicle (GV see Figure 2B). The oocyte and the surrounding granulosa cells, together constituting the primordial follicles, have complex paracrine interactions during follicle growth and development. Oocyte maturation depends on secretory products of the surrounding cells (Findlay, 2012).
Oocyte maturation—defined as the period of progression from the first to the second meiotic arrest—starts with puberty, when during the follicular phase of each menstrual/estrous cycle, a pool of follicles is recruited. Hormonal signals stimulate the oocytes as well as their surrounding granulosa cells to grow and theca cells attach to the follicle. One dominant follicle continues growing. Increasing estrogen levels produced by the follicle's granulosa cells cause a pulsatile release of luteinizing hormone (LH) from the pituitary gland, which stimulates the release of the oocyte from the ovary (ovulation). Upon that stimulus, meiosis I continues and is terminated shortly before ovulation. Oocytes at metaphase I (MI) stage are defined as oocytes with no GV (intact nucleus) and no polar body (see Figure 2B). Granulosa cells and the oocyte cooperate and transmit signals involved in maintaining or releasing the meiotic arrest in the oocyte. The arrest in prophase I is mediated by increased CaSR protein expression in the MI stage as compared to the MII stage of oocyte (McNeil et al., 1998). Induced CaSR concentrations induced a release occurred. Expression of an interfering mutant CaSR inhibited the proliferative response to elevated extracellular Ca$^{2+}$ (McNeil et al. (1998)).
CaSR in Ovarian Surface Epithelial Cells
Expression of CaSR in the ovary was first described in human surface epithelial cells (Figure 2A and Table 1). Proteins detected by western blotting show a molecular weight of 120–140 kDa (McNeil et al., 1998). Increasing Ca$^{2+}$ concentrations induced a significant proliferative response in these cells, indicating that the cells can sense Ca$^{2+}$ concentrations in the surroundings. Induced proliferation of these cells due to high Ca$^{2+}$ concentrations may be of physiological relevance during the healing of the ruptured surface following each ovulation, when neighboring cells are locally exposed to ovarian follicular fluid. At least in pig ovarian follicular fluid, Ca$^{2+}$ concentrations of around 2.34 mmol/L have been measured (Schuetz and Anisowicz, 1974; CaSR is active above threshold Ca$^{2+}$ levels between 0.5 and 2 mmol/L (Conigrave and Ward, 2013). Upon treatment of human surface epithelial cells with the CaSR agonists Gd$^{3+}$, Ca$^{2+}$ as well as neomycin, intracellular Ca$^{2+}$ release occurred. The same observation was made in rat ovarian surface epithelial (ROSE) cells. There, inositol triphosphate production increased after stimulation with Gd$^{3+}$ and Ca$^{2+}$. Expression of an interfering mutant CaSR inhibited the proliferative response to elevated extracellular Ca$^{2+}$. CaSR agonists induced tyrosine phosphorylation, ERK activation and proliferation. Expression of interfering mutants for Ras, Raf, and MKK1 indicated that proliferation of ROSE cells in response to increased Ca$^{2+}$ involves cross-talk between CaSR and a tyrosine kinase-dependent Ras-Raf-MKK1-ERK signaling pathway. Interestingly, agonists of CaSR also increased the kinase activity of Src, which is a proto-oncogene (Hobson et al., 2000). This work was later extended by Bilderback et al. (2002), who demonstrated an additional ERK-independent, but PI-3K/AKT-dependent component in the proliferative response of ROSE cells. Activation of these pathways has also been observed upon stimulation of CaSR in prostate and Leydig cell lines (see Section CaSR and Disorders of the Male Reproductive System).
Ovarian surface epithelial cells are the cell type primarily responsible for malignant ovarian carcinoma, which is the most lethal female genital malignancy. McNeil et al. (1998) observed increased expression of CaSR mRNA in two ovarian tumor cell lines (BG-1 and CAOV-3). More evidence for a link between CaSR and ovarian cancer is given by the observation that the G allele of the CaSR rs17251221 polymorphism seems to protect against ovarian cancer (Yan et al., 2015). CaSR is considered as a molecule that can either promote or prevent tumor growth depending on the type of cancer (Tennakoon et al., 2016). The exact role of CaSR the development of ovarian cancer remains to be determined.
CaSR in Follicular Cells
CaSR is present at the surface of human oocytes and granulosa cells within the corona radiata (Figure 2B and Table 1). Western-blot analysis revealed a single 130 kDa protein in denuded oocytes and a protein doublet of 130/120 kDa in cumulus cells (Dell’Aquila et al., 2006). The expression and localization of CaSR protein in human oocytes at different maturation stages (GV, MI, and MII) was studied by immunofluorescence microscopy. Increased CaSR protein expression in the MI stage as compared...
FIGURE 2 | The cartoon depicts (A) major components of the human female reproductive system and (B) major steps in oogenesis. Organs/tissues/cells, which were shown to express CaSR are depicted in color. Red color, CaSR expression shown in human ± other mammalian species; blue color, CaSR expression shown in mammalian species other than human (for details on species and assumed function of CaSR see Text and Table 1).
to GV and MII oocytes (Figure 2B) suggested a role of CaSR in the process of meiotic maturation, which would correlate with the observed role of external Ca$^{2+}$ in mobilization of intracellular Ca$^{2+}$ during oocyte maturation, activation, and fertilization (review by Tosti, 2006).
CaSR mRNA and protein expression was also shown in equine follicles (Table 1). Again, western blot analysis revealed a single 130 kDa protein in denuded oocytes and a protein doublet of 130/120 kDa in cumulus cells (De Santis et al., 2009). When studied by confocal microscopy, CaSR was demonstrated at the plasma membrane and, more pronounced, within the cytoplasm of oocytes at all examined stages of meiosis (GV, MI, MII). Corona radiata cells exhibited strong plasma membrane labeling. CaSR was also detected in the transzonal cytoplasmic processes of corona radiata cells, which penetrate through the zona pellucida and contact the oocyte membrane. A role of CaSR in oocyte maturation was investigated. The CaSR agonist NPS R-467, which is an allosteric modulator of CaSR sensitizing the CaSR to Ca$^{2+}$ without activating it, in the absence of Ca$^{2+}$, had a stimulatory effect on oocyte maturation. Pre-incubation with the CaSR antagonist NPS 2390 attenuated the effect. Stimulation of maturation by CaSR agonist depended on the presence of external Ca$^{2+}$ (2.92 mM) and was not observed at suboptimal external Ca$^{2+}$ (0.5 mM). However, variations of Ca$^{2+}$ between 0.5 and 4 mM Ca$^{2+}$ in the absence of the agonist did not stimulate in vitro oocyte maturation. In oocytes treated with NPS R-467, CaSR immunostaining increased at the plasma membrane, while it was reduced in the cytosol. Finally, treatment of oocytes as well as cumulus cells with CaSR agonist resulted in an increased activity (phosphorylation) of MAPK (ERK) in these cells (De Santis et al., 2009). Activation of MAPK is necessary for gonadotropin-induced meiotic resumption of oocytes (Fan and Sun, 2004).
CaSR mRNA and protein is also present in porcine oocytes and cumulus cells (Table 1). In contrast to human and equine oocytes, a 160 kD protein was detected by western blotting. The effects of gonadotropins and EGF, two key factors involved in oocytes maturation (Conti et al., 2006; Uhm et al., 2010), on CaSR expression and localization in porcine oocytes were tested. CaSR expression was up-regulated in oocytes matured in gonadotropin-containing, but not EGF-containing medium. Cortical distribution of CaSR was enhanced with gonadotropins but not EGF. Porcine cumulus-oocyte-complexes exposed to CaSR agonist NPS R-568 in gonadotropin-containing medium showed increased maturation rate, while CaSR antagonist NPS 2390 to medium supplemented with gonadotropins significantly decreased oocyte maturation. MAPK (ERK) phosphorylation was increased during in vitro maturation as well as after NPS R-568 treatment. Treatment with NPS 2390 resulted in reduced levels of phosphorylated MAPK during oocyte maturation. It was concluded that CaSR participates in gonadotropin-induced oocyte nuclear maturation through MAPK signal transduction (Liu et al., 2015).
Apoptosis of granulosa cells is an important process in follicular atresia. The causal relationship between Ca$^{2+}$ and induction of apoptosis was investigated in cultured avian granulosa cell explants of Japanese quail (Coturnix japonica). Increasing extracellular Ca$^{2+}$ resulted in a biphasic response of the cells; an initial inhibitory effect on apoptosis was followed by a delayed phase of increased apoptosis. As the initial inhibitory effect of the Ca$^{2+}$ on apoptosis was mimicked by applying the CaSR agonists Mg$^{2+}$ and Gd$^{3+}$, an involvement of CaSR in inhibition of apoptosis was suggested (Mussche et al., 2000). In a follow up paper, the same group by immunocytochemistry confirmed expression of CaSR in granulosa cells of quail pre-ovulatory follicles as well as in the remnants of the granulosa layer after ovulation (Table 1). CaSR was not detected in the granulosa cells of smaller undifferentiated follicles. The presence of CaSR in follicles destined to ovulate was confirmed by western blotting showing a protein of 115-125 kDa. The rate of apoptosis of F1 granulosa explants (F1 being the largest preovulatory follicle) stimulated by either gonadotropin withdrawal alone or in combination with Ca$^{2+}$-ceramide was significantly decreased with a CaSR agonist (NPS R-568) as well as the ions Ca$^{2+}$ and Mg$^{2+}$. The authors suggested that activated CaSR may play a role in securing the survival of avian follicles after their selection (Diez-Fraile et al., 2010).
**Research Demands**
Disturbance in oocyte meiotic events can lead to subfertility or premature aging by reducing the functional ovarian reserve. Any molecular target that would allow for promoting or reducing oocyte maturation would therefore be of interest. Expression of CaSR in human, equine, and porcine oocyte has been shown. In analogy to sperms, the molecular weight of the detected CaSR protein in oocytes and granulosa cells differs between the species. Reasons for that are given in Section Research Demands (page 7). Current data support a role of CaSR in maturation (completion of first meiosis) of oocytes and a contribution of the MAPK ERK signaling pathway. However, the interplay of CaSR with other molecules that maintain oocytes in the meiotic arrest and those that initiate meiotic resumption (such as LH) (Celik et al., 2015) is currently not well explored.
The oocyte–somatic cells interaction is very important. Low quality of somatic cells and difficulties in the interaction between oocyte and granulosa cells can reduce the fertilization and implantation capacity of the oocyte/zygote, which again results in poor pregnancy outcome. The expression of CaSR in granulosa cells of various species was confirmed, but current data addressing the function of CaSR in these cells are still limited and point toward an anti-apoptotic function. Expression of CaSR in theca cells remains unexplored. PCOS is a common multifaceted metabolic disease in women of fertile age, which has a strong genetic component. Recent results provided evidence that CaSR Hin1I gene polymorphism represents a candidate for the genetic contribution to the development or the severity of insulin secretion in women with PCOS; So far, the exact molecular mechanism underlying this association is largely undetermined (Ranjzad et al., 2011). It remains to be demonstrated whether theca cells are also affected.
Finally, CaSR expression was observed in epithelial surface cells of ovaries, where it promotes a proliferative response. Up-regulation of the response in case of tumors need to be further explored before therapeutic use of antagonist can be considered.
**CaSR IN THE UTERUS**
**Uterus and Implantation**
During mammalian development, parts of the Müllerian ducts develop into the female uterus. The extent of duct-fusion is species-dependent, resulting in different shapes such as simplex uterus in humans and primates, or duplex uterus in rodents such as rats and mice. Irrespective of the shape, the function of the uterus is to enable implantation of the fertilized egg (zygote), to house the growing conceptus and to expulse the fetus during delivery (Spencer et al., 2012).
The uterus consists of a tripled-layered wall, composed of perimetrium, myometrium and endometrium. The endometrium is a mucosal layer which undergoes marked changes in thickness and structure during the estrous cycle in animals such as rats (Westwood, 2008), but most pronounced changes are seen during the menstrual cycle of humans/primates (Fazleabas and Strakova, 2002). The early embryo enters the uterus in the morula stage (12–16 cells). Then, transformation into the blastocyst occurs, which is comprised of a layer of trophectoderm cells that contacts the uterine epithelium and starts to form the placenta, and the inner cell mass that gives rise to the embryo. The blastocyst can implant after shedding the zona pellucida; in human, implantation occurs 9 days post coitum (p.c.), while in rats and mice it occurs 4–5 days p.c. The principle purpose of implantation is to enable a contact between maternal blood supply and the developing embryonic blood vessels. The mechanism of implantation of the conceptus is, however, species dependent. Based on the interaction between blastocyst and uterine cells it is classified as being interstitial (e.g., human, guinea pig), centric (e.g., rabbits, domestic animals), and eccentric (e.g., rats, mice) (Lee and DeMayo, 2004). During interstitial implantation the conceptus breaks through the surface epithel of the maternal uterus and invades the underlying stroma. Centric implantation means fusion of blastocyst with uterine epithelium without penetration and in eccentric implantation, the luminal epithelium invaginates and surrounds the blastocyst. Due to implantation, endometrial stromal cells undergo the decidual reaction and become decidual cells (Gellersen et al., 2007).
Successful implantation requires a delicate interplay of many molecules in a limited period of time (the window of implantation). If communication between the embryo and the endometrium fails, then implantation fails. This is an important cause of infertility. There are estimations that only 50–60% of all conceptions advance beyond 20 weeks of gestation and from the pregnancies that are lost, 75% represent a failure of implantation. Failed implantation is also a major limiting factor in assisted reproduction. To treat disorders such as infertility, which increases worldwide due to an increasing toxic environment, but also diseases such as obesity, it is important to understand the molecular mechanisms of implantation and placentation (Norwitz et al., 2001). Many factors including steroid hormones, cytokines, and growth factors, but also Ca$^{2+}$ play a role in the course of implantation (Ruan et al., 2014). Ca$^{2+}$ seems to promote the blastocyst-endometrium interaction (Thie and Denker, 2002).
Of interest, the Ca$^{2+}$ concentration in rat uterine secretion changes at the time of implantation (Nilsson and Ljung, 1985).
**Expression of CaSR in the Uterus**
Xiao et al. (2005) found CaSR mRNA expression in rat uterus (Figure 2A and Table 1). CaSR mRNA and protein appeared in the luminal epithelium on day 1 of pregnancy. Expression of CaSR was switched from the luminal epithelium to stromal cells on days 1–3 of pregnancy. Expression diminished on day 4, but was again induced by the implanting blastocyst. The results suggested that CaSR expression in the stromal cells in the receptive status of the uterus was induced by the implanting blastocysts, while in epithelial cells during day 1 through day 5, the expression of CaSR was regulated by some non-embryonic factors. An embryo transplantation model confirmed that CaSR expression in the uterus was induced by the implanting blastocysts. Artificial decidualization caused upregulation of CaSR expression in the decidualized cells. Furthermore, estrogen as well as progesterone induced the expression of CaSR protein in the uterus. The strong CaSR expression at the implantation site and decidual cells in rat uterus suggests that CaSR is of relevance for blastocyst implantation and decidualization (Xiao et al., 2005).
In addition to the endometrium, also the myometrium, the thick muscular coat of the uterus, has important functions during reproduction as it contributes to sperm and embryo transport, but also to implantation. Ca$^{2+}$ plays an important role for the uterine contractility (Aguilar and Mitchell, 2010). Based on the observation that uterine contractions can be inhibited by the CaSR ligands spermine and high concentrations of Mg$^{2+}$, it was speculated that CaSR was involved in the regulation of myometrial contractility (Pistilli et al., 2012). CaSR expression was confirmed in the estrogen-dominated rat uterus. Highest expression of CaSR was seen in the luminal epithelium, but it was also detected in longitudinal and circular muscle layers of the myometrium (Figure 2A and Table 1). Oxytocin-induced contraction of the rat uterus was not only inhibited by various CaSR agonists such as polyvalent cations and polyamines, but also by two synthetic positive allosteric CaSR modulators, (R)-calindol and (R)-cinacalcet. However, the positive allosteric modulation of CaSR did not show the appropriate stereoselectivity. (S)-cinacalcet, which is usually less potent than the (R)-enantiomer, inhibited contraction to the same extent. Furthermore, the negative allosteric modulator calhex 231 also caused concentration-dependent relaxation. Thus, the pharmacological profile of inhibition of contractility by CaSR ligands was not consistent with their effects being mediated through CaSR, but was rather consistent with promiscuous actions of the ligands. Later, the same authors investigated CaSR expression and function in the pregnant human myometrium. Despite bright staining in the human placenta, only sparse expression of CaSR receptors in pregnant human myometrium was observed (Figure 2A and Table 1). Exposure of human myometrial strips to CaSR receptor ligands showed that calindol and
cinacalcet, CaSR agonists, were ineffective as inhibitors of contractions, while the CaSR antagonist calhex 231 produced partial inhibition of contractility (Crankshaw et al., 2013). In summary, the role of CaSR in the rat myometrium remains unclear.
**Research Demand**
In assisted reproduction, implantation failure is the pregnancy rate-limiting step. The mechanisms underlying human embryo-endometrium signaling are not fully understood, but this is required to improve assisted reproduction outcomes. A detailed understanding of the implantation process is also crucial to develop effective interventions to prevent early pregnancy loss. The small number of studies currently addressing CaSR expression in the uterus demonstrated expression in rat endometrium, but more functional studies confirming the suggested role in implantation and decidualization are required, not only for the rat system, but also for humans and all other species, where assisted reproduction could be of interest. It is known that studies done in animal models do not always translate well to humans. Human in-vitro models of implantation (Weimar et al., 2013) may provide an alternative possibility to study human CaSR function during implantation and decidualization. Expression of CaSR in the myometrium was so far only investigated in rat and human. The function of CaSR in the myometrium remains unclear.
**PLACENTA**
**Placenta Formation and Function**
Placentas are unique and transient organs, which develop in female mammals during pregnancy at the interface of maternal and fetal circulation. The organ exhibits an amazing range of morphological variations across species (Benirschke et al., 2012).
Formation of a placenta is of great importance for the development of the embryo and starts very early in pregnancy. The first differentiation process gives rise to trophoblast cells. Trophoblasts initiate implantation of the embryo into the maternal endometrium by interaction with decidual cells of the maternal uterus. By proliferation, invasion and differentiation, trophoblast cells are the most important builders of the placenta. With progression of (human) placenta formation, two distinct populations of trophoblast cells, the villous and the extravillous trophoblast, which exhibit distinct functions, become evident. The expanding chorionic villi of the placenta, which mediate materno-fetal transport of nutrients are covered by a multinucleated layer of syncytiotrophoblast (STB). This cell layer is maintained by proliferation and fusion of the underlying villous cytotrophoblasts. Extravillous trophoblasts, in contrast, invade the uterus and interact with maternal cells. These cells are important for proper placentation.
The process of implantation of the conceptus is species dependent and can be either invasive as seen in humans, most primates, dog, cat, mouse, rat, or rabbit meaning that the conceptus will break through the surface epithelium of the maternal uterus and invades the underlying stroma or can be non-invasive (pig, sheep, cow, horse), integrating the uterine epithelium in the placenta. The depths of invasion as well as the degree of proximity between maternal and fetal circulation can vary largely among species. In humans and guinea pigs, the conceptus invades the stroma so deeply that the uterine surface epithelium is restored over it (interstitial implantation). Other species (dog, cat, rat), may invade the stroma only partially and project into the uterine lumen (eccentric implantation). This can result in a contact to other sites of the uterine lumen and additional placentation development (e.g., bidiscoid placenta in rhesus monkey, zonary placenta in dog and cat). While in some species the maternal tissue remains relatively intact (dog, cat), meaning that trophoblast cells contact maternal capillary endothelium, in other species, trophoblast cells also invade the maternal endothelium and ultimately bath in maternal blood (human, rabbit, rat, mouse). These types of placentas are classified as haemochorial, which means that all maternal tissue layers are removed and the chorion (i.e., the trophoblast) bathes directly in maternal blood. But even structures of murine and human placentas differ to some extent. Whereas, the term human placenta is monochorial, which means that one continuous trophoblast cell layer, the STB, separates maternal and fetal blood circulation, the murine placenta is trichorial. Moreover, in rodent placenta, but not in human, other primate, or ruminant placentas the primitive yolk sac, which in all species participates in nutrient exchange between the fetal and maternal circulations before the formation of the placenta, is incorporated into the placenta and turns into the intraplacental yolk sac (IPYS). The IPYS is positioned between fetal vessels and maternal blood spaces, well situated for exchange of substances between mother and fetus. It is a bilayered membrane, where smaller parietal or cuboidal cells on a thick basement membrane (Reichert’s membrane) overlie maternal blood spaces and vessels, while tall columnar cells on the visceral or endothelial side overly the fetal vessels. Between these layers is the sinus of Duval, which communicates with the yolk sac cavity and the uterine lumen (Metz et al., 1976).
To ensure optimal fetal development, the placenta fulfills a plethora of functions including gas exchange, nutrient transfer, hormone secretion, and immunological functions. Materno-fetal transfer of the ion Ca$^{2+}$ is indispensable for proper development including mineralization of fetal skeleton. About 30 g Ca$^{2+}$ are actively transported across the human placenta, predominantly during the last trimester of pregnancy. As fetal serum Ca$^{2+}$ concentrations are set at significant higher concentrations than maternal serum concentrations, trans-placental Ca$^{2+}$ transport occurs against an extracellular Ca$^{2+}$-concentration gradient. Placental transfer of Ca$^{2+}$ involves various proteins, including Ca$^{2+}$ channels, Ca$^{2+}$-ATPases and intracellular Ca$^{2+}$-binding proteins (Calbindin-D9k). Current knowledge on placental Ca$^{2+}$ transfer as well as regulation of maternal and fetal Ca$^{2+}$ homeostasis have been reviewed in several recent publications (Baczyk et al., 2011; Olausson et al., 2012; Kovacs, 2014, 2015, 2016).
Despite this active Ca$^{2+}$ transfer, the placental trophoblasts still uses Ca$^{2+}$ as a second messenger to activate diverse cellular functions such as differentiation or proliferation, or—in the case of extravillous trophoblasts—also invasion (Baczyk et al., 2011).
CaSR Expression and Function in Trophoblast and Yolk Sac Cells
An involvement of CaSR in regulation of murine placental Ca\(^{2+}\) transfer was confirmed by heterozygous or homozygous ablation of the CaSR gene in mice. Casr knock down reduced placental Ca\(^{2+}\) transfer. CaSR disruption may, directly or indirectly, downregulate PTHrP or influence the PTHrP effect on the placenta (Kovacs et al., 1998). PTHrP reaches the maternal circulation during pregnancy most likely from the placenta and breasts, as well as possibly from the uterus and fetal tissues. PTHrP significantly stimulates the placental Ca\(^{2+}\) transport via proteins involved in transport (Kovacs et al., 1996; Strid et al., 2002; Bond et al., 2008). A Nuf mice with an activating mutation of CaSR exists (Hough et al., 2004), but, placental Ca\(^{2+}\) transport has not been analyzed in this strain. In murine placenta, CaSR mRNA was detected by in situ hybridization in both types of IPYS cells, but not in the trophoblasts. By immunohistochemistry, using a monoclonal antibody directed against a region of the CaSR that has been deleted in the Casr-null mice, the CaSR was found to be expressed in both layers of the IPYS (Table 1). CaSR was also present in the surrounding labyrinth trophoblasts of wt placenta, but was absent in placentas obtained from Casr-null mice. Other molecules important for materno-fetal Ca\(^{2+}\)-transfer, including PTHrP, PTH/PTHrP receptor, calbindin-D9k, or Ca\(^{2+}\)-ATPase, were also higher expressed in the IPYS of the murine placenta compared to the trophoblasts. Overall, this suggests that IPYS is the important route of Ca\(^{2+}\) exchange between mother and fetus in the mouse (Kovacs et al., 2002).
Some evidence for involvement of human CaSR in transplacental Ca\(^{2+}\)-transfer has been obtained recently. Reduced expression of CaSR in placentas derived from women suffering from gestational diabetes mellitus compared with healthy placentas was found. This was associated with lower Ca\(^{2+}\) levels measured in cord blood of infants from women suffering from gestational diabetes mellitus supporting its role in placental Ca\(^{2+}\)-transfer (Papadopoulou et al., 2014). In humans, expression of CaSR was found in both villous and extravillous tissue of first trimester and term placentas (Table 1). In chorionic villi, CaSR was mainly detected at the apical membrane of the STB, which contacts maternal blood and at lower levels in cytotrophoblast cells (Figure 3). This location would be in line with the control of placental Ca\(^{2+}\) movement. The CaSR was also localized in extravillous trophoblast cells in close proximity to maternal blood vessels (Figure 3). It was speculated that CaSR senses maternal extracellular Ca\(^{2+}\) levels during the process of placentation and participates in regulation of placental development (Bradbury et al., 2002). Earlier, Bradbury and coworker had demonstrated that isolated human extravillous cytotrophoblasts expressed the full-length transcript of CaSR. A splice variant lacking exon 3 was also found, which encoded a truncated protein of 153 amino acids (compared with 1078 amino acids for the full length protein). Upon translation, this CaSR splice variant, however, would not be incorporated into the plasma membrane. The extravillous cytotrophoblasts responded to elevation of extracellular Ca\(^{2+}\), and also to extracellular Mg\(^{2+}\) with a bi-phasic elevation of intracellular Ca\(^{2+}\) (Bradbury et al., 1998).
Research Demand
CaSR modulates transplacental Ca\(^{2+}\) transfer, at least in the mouse. Some evidence also exists for a role in human transplacental Ca\(^{2+}\) transfer. In breast cells, CaSR is expressed in the basolateral membrane of the lactating alveolus and regulates PTHrP secretion. CaSR senses the availability of Ca\(^{2+}\) for milk production, and stimulates production of PTHrP when the Ca\(^{2+}\) supply is insufficient. CaSR also impacts on a Ca\(^{2+}\)-ATPase (PMCA2) to stimulate Ca\(^{2+}\) secretion into milk when the Ca\(^{2+}\) supply is adequate (Kovacs, 2016). In the murine placenta, CaSR impacts on PTHrP, but detailed information of CaSR function in the murine or human hemochorial placentas is lacking. Information on expression of CaSR in the epitheliochorial placentas of other species is lacking.
CaSR can regulate proliferation, differentiation or apoptosis, but neither in extravillous nor villous human trophoblasts this issue has been addressed so far. Expression of CaSR in extravillous trophoblasts suggests an important role in placentation. In this context, not only Ca\(^{2+}\), but also other CaSR ligands such as L-amino acids (Conigrave et al., 2000) may be modulators of placental tissue development in response to e.g., maternal Ca\(^{2+}\) concentration or maternal diet. Signaling pathways targeted by CaSR in the placenta are also unknown. A detailed understanding of the modulators of placentation is necessary before effective interventions can be considered.
Finally, it remains to be demonstrated whether CaSR is the only relevant Ca\(^{2+}\)-sensing protein of the placenta. In 1989, Juhlin and collaborators generated several monoclonal anti-parathyroid antibodies (E11, G11, B6) by immunization of mice with intact parathyroid glands. Two of these antibodies (G11 and B6) interfered with the Ca\(^{2+}\)-sensing mechanism of parathyroid cells (Juhlin et al., 1987). When monoclonal antibody E11 was applied in immunohistochemistry on placenta and uterus of the pregnant rat, positively stained rat placental cells were found at the end of pregnancy. Staining was confined exclusively to the columnar epithelial cells lining the sinuses of Duval, i.e., in the IPYS. In the uterus, positive staining of the epithelium lining the uterine lumen was obtained prior to and during implantation (days 5–6) (Bernadotte et al., 1989). When G11 and E11 were applied on sections of human placenta, both antibodies labeled the cytotrophoblast cells of anchoring and floating villi as well as cytotrophoblasts in the chorionic plate. The STB, however, was not stained. Isolated cytotrophoblasts were found to react with G11 and E11. In these cells, a temporary increase of Ca\(^{2+}\) upon elevation of external Mg\(^{2+}\) was observed, which was blocked by G11 antibodies. Raised extracellular Ca\(^{2+}\) inhibited release of PTHrP from the cells, and this inhibition was blocked by the G11 antibody (Hellman et al., 1992). E11 was also used in immunoelectron microscopical studies showing positive staining of cytotrophoblast cells of the human placenta, and trophoblast cells lining fetal blood vessels in the rat placenta (Bjerneroth et al., 1992). Both antibodies, however, detected a 500 kDa protein, which is much larger than CaSR (Juhlin et al., 1990). When the protein was then cloned from human placenta, it was found to belong to the LDL-receptor superfamily of glycoprotein and it was identified as gp330 (megalin, LRP2) (Lundgren et al., 1994; Hjälm et al., 1996).
In addition to expression in human parathyroid cells, kidney proximal tubule cells and placental cytotrophoblasts, the protein was also detected in other reproductive tissues such as epididymal epithelial cells and mammary epithelium. It was suggested to have Ca^{2+} sensing functions (Lundgren et al., 1997). Unfortunately, further investigations to clarify the role of this protein in Ca^{2+} sensing were not performed.
**SUMMARY AND OUTLOOK**
CaSR is expressed in many cells of male and female reproductive organs. Due to its functional diversity, CaSR could be involved in a variety of reproductive processes ranging from proliferation or maturation of germ cells to implantation of the zygote, and from placentation to transplacental transport processes. Apart from physiologic actions, current data also suggest a role of CaSR in diseases of reproductive organs or pregnancy. Currently, however, we know very little about CaSRs physiologic and pathophysiologic functions in reproduction. Exploration of CaSR function in the context of diseases of reproduction such as male and female infertility and early pregnancy loss, PCOS, or gestational diabetes mellitus as well as tumors of reproductive organs may add novel possibilities for diagnosis and treatment.
**AUTHOR CONTRIBUTIONS**
IE designed and wrote the article and meets all criteria for authorship.
**FUNDING**
The author is funded by the EU Marie Skłodowska Curie Action grant CaSR Biomedicine (675228).
REFERENCES
Adelanbo, O. A., Igetseme, J., Huang, C. L., and Zaidi, M. (1998). The effect of extracellularly applied divalent cations on cytosolic Ca\(^{2+}\) in murine Leydig cells: evidence for a Ca\(^{2+}\)-sensing receptor. J. Physiol. 513 (Pt 2), 399–410. doi: 10.1111/j.1469-7793.1998.tb969.x
Aguilar, H. N., and Mitchell, B. F. (2010). Physiological pathways and molecular mechanisms regulating uterine contractility. Hum. Reprod. Update. 16, 725–744. doi: 10.1093/humupd/dmq016
Ahearn, T. U., Tchrakian, N., Wilson, K. M., Li, R., Nuttall, E., and Kissling, S. D., et al. (2016). Calcium sensing receptor tumor expression and lethal prostate cancer progression. J. Clin. Endocrinol. Metab. 101, 2520–2527. doi: 10.1118/1555-9665.EPI-12-0670-T
Alavi-Shoushtari, S. M., Asri-Rezaie, S., Khaki, A., Belbasi, A., and Tahmasebian, H. (2010). Calcium and magnesium concentrations in uterine fluid and blood serum during the estrous cycle in the bovine. Vet. Res. Forum 3, 137–141.
Alavi Shoushtari, S. M., Asri Rezaie, S., Khaki, A., Belbasi, A., and Tahmasebian, H. (2014). Calcium and magnesium content of the uterine fluid and blood serum during the estrous cycle and pre-pubertal phase in water buffaloes. Vet. Res. Forum 5, 301–305.
Alfadda, T. I., Saleh, A. M., Houillier, P., and Geibel, J. P. (2014). Calcium-sensing receptor protein in human placenta (CaSR) in Reproduction. Biochem. Pharmacol. 80, 297–307. doi: 10.1016/j.bcp.2010.04.002
Brennan, E. M. (2013). Role of the calcium-sensing receptor in extracellular calcium homeostasis. Best Pract. Res. Clin. Endocrinol. Metab. 27, 333–343. doi: 10.1016/j.beem.2013.02.006
Brennan, S. C., Wilkinson, W. J., Tseng, H. E., Finney, B., Monk, B., Dibble, H., et al. (2016). The extracellular calcium-sensing receptor regulates human fetal lung development via CFTR. Sci. Rep. 6:21975. doi: 10.1038/srep21975
Brown, E. M. (2010). Clinical utility of calcimimetics targeting the extracellular calcium-sensing receptor (CaSR). Biochem. Pharmacol. 80, 297–307. doi: 10.1016/j.bcp.2010.04.002
Brown, E. M. (2013). Role of the calcium-sensing receptor in extracellular calcium homeostasis. Best Pract. Res. Clin. Endocrinol. Metab. 27, 333–343. doi: 10.1016/j.beem.2013.02.006
Casslén, B., and Nilsson, B. (1984). Human uterine fluid, examined in undiluted samples for osmolarity and the concentrations of inorganic ions, albumin, glucose, and urea. Am. J. Obstet. Gynecol. 150, 877–881. doi: 10.1016/0002-9378(84)90466-6
Celik, O., Celik, N., Gunog, S., Haberalk, E. T., and Aydin, S. (2015). Selective regulation of oocyte meiotic events enhances progress in fertility preservation methods. Biochem. Insights 8, 11–21. doi: 10.4137/BCI.S28596
Chakravarti, B., Dwivedi, S. K., Mithal, A., and Chattroopadhyay, N. (2009). Calcium-sensing receptor in cancer: good cop or bad cop? Endocrine 35, 271–284. doi: 10.1007/s12020-008-9131-5
Chen, H., Kui, C., and Chan, H. C. (2013). Ca(2+) mobilization in cumulus cells: role in oocyte maturation and acrosome reaction. Cell Calcium 53, 68–75. doi: 10.1016/j.ccaca.2012.11.007
Collopton, M., Shatzen, E., Wiemann, B., Starnes, C., Scully, S., Henley, C., et al. (2013). Cinacalcet attenuates hypercalcemia observed in mice bearing either Rice H-500 Leydig cell or C26-DCT colon tumors. Eur. J. Pharmacol. 712, 8–15. doi: 10.1016/j.ejphar.2013.04.013
Conigrave, A. D., Quinn, S. J., and Brown, E. M. (2000). L-amino acid sensing by the extracellular Ca(2+)-sensing receptor. Nat. Acad. Sci. USA. 97, 4814–4819. doi: 10.1073/pnas.97.9.4814
Conigrave, A. D., and Ward, D. T. (2013). Calcium-sensing receptor (CaSR): pharmacological properties and signaling pathways. Best Pract. Res. Clin. Endocrinol. Metab. 27, 315–331. doi: 10.1016/j.beem.2013.05.010
Coni, M., Hsieh, M., Park, J. Y., and Su, Y. Q. (2006). Role of the epididymal growth factor network in ovarian follicles. Mol. Endocrinol. 20, 715–723. doi: 10.1210/me.2005-0185
Correia, J., Michelangeli, F., and Publicover, S. (2015). Regulation and roles of Ca(2+)-stores in human sperm. Reproduction 150, R65–R76. doi: 10.1530/REP-15-0102
Crankshaw, D. J., Pistilli, M. J., O’Brien, Y. M., Sweeney, E. M., Dockery, P., Holloway, A. C., et al. (2013). The effects of extracellular calcium-sensing receptor ligands on the contractility of pregnant human myometrium in vitro. Reprod. Sci. 20, 882–890. doi: 10.1177/1933719112468949
de Kretser, D. (2012). Molecular Biology of the Male Reproductive System. Burlington, MA: Elsevier Science.
De Santis, T., Casavola, V., Reshkin, S. J., Guerra, L., Ambrosoni, B., Fiandanza, N., et al. (2009). The extracellular calcium-sensing receptor is expressed in the cumulus-oocyte complex in mammals and modulates oocyte meiotic maturation. Reproduction 138, 439–452. doi: 10.1530/REP-09-0078
Dell’Aquila, M. E., De Santis, T., Cho, Y. S., Reshkin, S. J., Caroli, A. M., Maritato, F., et al. (2006). Localization and quantitative expression of the calcium-sensing receptor protein in human oocytes. Fertil. Steril. 88(Suppl. 1), 1240–1247. doi: 10.1016/j.fertnstert.2005.11.033
Díez-Fraile, A., Muschhe, S., Vanden Berge, T., Espeel, M., Vandenabeele, P., and D’Herde, K. G. (2010). Expression of calcium-sensing receptor in quail granulosa explants: a key to survival during folliculogenesis. Anat. Rec. (Hoboken) 293, 899–899. doi: 10.1002/ar.21100
Fan, H. Y., Liu, Z., Mullany, L. K., and Richards, J. S. (2012). Consequences of RAS and MAPK activation in the ovary: the good, the bad and the ugly. Mol. Cell. Endocrinol. 356, 74–79. doi: 10.1016/j.mce.2011.12.005
Fan, H. Y., and Sun, Q. Y. (2004). Involvement of mitogen-activated protein kinase cascade during oocyte maturation and fertilization in mammals. Biol. Reprod. 70, 535–547. doi: 10.1095/biolreprod.103.022830
Fazleabas, A. T., and Strakova, Z. (2002). Endometrial function: cell specific changes in the uterine environment. Mol. Cell. Endocrinol. 186, 143–147. doi: 10.1016/S0303-7207(01)00655-4
Feng, J., Xu, X., Li, B., Brown, E., Farris, A. B., Sun, S. Y., et al. (2014). Prostate cancer metastatic to bone has higher expression of the calcium-sensing receptor...
explicants. *Ann. N.Y. Acad. Sci.* 926, 101–115. doi: 10.1111/j.1749-6632.2000.tb05653.x
Nilsson, B. O., and Ljung, L. (1985). X-ray micro analyses of cations (Na, K, Ca) and anions (S, P, CI) in uterine secretions during blastocyst implantation in the rat. *J. Exp. Zool.* 234, 415–421. doi: 10.1002/jez.4802340309
Norwitz, E. R., Schuchard, J. D., and Fisher, M. J. (2001). Implantation and the survival of early pregnancy. *N. Engl. J. Med.* 345, 1400–1408. doi: 10.1056/NEJMra000763
Nunes, C., Silva, J. V., Silva, V., Torgal, I., and Fardilha, M. (2015). Signalling pathways involved in oocyte growth, acquisition of competence and activation. *Hum. Fertil. (Camb.)* 18, 149–155. doi: 10.3109/14647273.2015.1006962
Olausson, H., Goldberg, G. R., Laskey, M. A., Schoenmakers, I., Jarjour, L. M., and Prentice, A. (2012). Calcium economy in human pregnancy and lactation. *Nutr. Res.* 25, 40–67. doi: 10.1016/j.nutres.2011.08.007
Papadopoulou, A., Gole, E., Moutafi, A., Sfikas, C., Oehrl, W., Samiotaki, M., et al. (2014). Calcium sensing receptor in pregnancies complicated by gestational diabetes mellitus. *Placenta* 35, 632–638. doi: 10.1016/j.placenta.2014.05.001
Peterlik, M., Kállay, E., and Cross, H. S. (2013). Calcium nutrition and extracellular calcium sensing: relevance for the pathogenesis of osteoporosis, cancer and cardiovascular diseases. *Nutrients* 5, 302–327. doi: 10.3390/nu50200302
Pidasheva, S., Grant, M., Canaff, L., Ercan, O., Kumar, U., and Hendy, G. N. (2006). Calcium-sensing receptor dimerizes in the endoplasmic reticulum: biochemical and biophysical characterization of CASR mutants retained intracellularly. *Hum. Mol. Genet.* 15, 2200–2209. doi: 10.1093/hmg/ddl145
Pistilli, M. J., Petrik, J. J., Holloway, A. C., and Crankshaw, D. J. (2012). Calcium-sensing receptor regulates calcium uptake in rat uterine smooth muscle. *Clin. Exp. Pharmacol. Physiol.* 39, 37–42. doi: 10.1111/j.1440-1681.2011.05631.x
Ranjad, F., Mahban, A., Shemirani, A. I., Mahmoudi, T., Vahedi, M., Nikzamir, X., et al. (2011). Influence of gene variants related to calcium homeostasis on prostate malignancy. *Mol. Reprod. Dev.* 84, 118–126. doi: 10.1002/mrd.22038
Saidak, Z., Boudot, C., Abdoune, R., Petit, L., Brazier, M., Mentaverri, R., et al. (2013). Calcium-sensing receptor induces messenger ribonucleic acid of the calcium-sensing receptor and beta-cell function. *Endocrinology* 154, 1211–1217. doi: 10.1210/en.2011-1023
Singh, N., Promkan, M., Liu, G., Varani, J., and Chakrabarty, S. (2013). Role of calcium sensing receptor (CaSR) in tumorigenesis. *Best Pract. Res. Clin. Endocrinol. Metab.* 27, 455–463. doi: 10.1016/j.beem.2013.04.001
Smajlovic, S., Yano, S., Jabbari, R., and Telt-Hansen, J. (2011). The calcium-sensing receptor and calcimimetics in blood pressure modulation. *Br. J. Pharmacol.* 164, 884–893. doi: 10.1111/j.1476-5381.2011.01317.x
Spencer, T. E., Dunlap, K. A., and Filant, J. (2012). Comparative developmental biology of the uterus: insights into mechanisms and developmental disruption. *Mol. Cell. Endocrinol.* 354, 34–53. doi: 10.1016/j.mce.2011.09.035
Squires, P. E., Jones, P. M., Younis, M. Y., and Hills, C. E. (2014). The calcium-sensing receptor and beta-cell function. *Vitam. Horm.* 95, 249–267. doi: 10.1016/B978-0-12-800174-5.00010-7
Strid, H., Care, A., Jansson, T., and Powell, T. (2002). Parathyroid hormone-related protein (38-94) amide stimulates ATP-dependent calcium transport in the Basal plasma membrane of the human syngestocytrophoblast. *J. Endocrinol.* 175, 517–524. doi: 10.1677/joe.0.1795157
Swann, K., and Lai, F. A. (2016). Egg activation at fertilization by a soluble sperm protein. *Physiol. Rev.* 96, 127–149. doi: 10.1152/physrev.00012.2015
Tennakoon, S., Aggarwal, A., and Kallay, E. (2016). The calcium-sensing receptor and the hallmarks of cancer. *Biochem. Biophys. Acta* 1863(6 Pt B), 1398–1407. doi: 10.1016/j.bbamrc.2015.11.017
Telt-Hansen, J., Chattopadhyay, N., Yano, S., Kanaparthi, D., Rooney, P., Schwarz, P., et al. (2004). Calcium-sensing receptor induces proliferation through p38 mitogen-activated protein kinase and phosphatidylinositol 3-kinase but not extracellularly regulated kinase in a model of humoral hypercalcemia of malignancy. *Endocrinology* 145, 1211–1217. doi: 10.1210/en.2003-0749
Telt-Hansen, J., MacLeod, R. J., Chattopadhyay, N., Yano, S., Quinn, S., Ren, X., et al. (2003a). Calcium-sensing receptor stimulates PTHrP release by pathways dependent on PKC, p38 MAPK, [NK], and ERK1/2 in H-500 cells. *Am. J. Physiol. Endocrinol. Metab.* 285, E329–E337. doi: 10.1152/apend.00489.2002
Telt-Hansen, J., Schwartz, P., Terverliger, E. F., Brown, E. M., and Chattopadhyay, N. (2003b). Calcium-sensing receptor induces messenger ribonucleic acid of human securin, pituitary tumor transforming gene, in rat testicular cancer. *Endocrinology* 144, 5188–5193. doi: 10.1210/en.2003-0520
Telt-Hansen, J., Yano, S., John Macleod, R., Smajlovic, S., Chattopadhyay, N., and Brown, E. M. (2005). High calcium activates the EGF receptor potentially through the calcium-sensing receptor in Leydig cancer cells. *Growth Factors* 23, 117–123. doi: 10.1080/08977190500126272
Thie, M., and Denker, H. W. (2002). *In vitro* studies on endometrial adhesiveness for trophoblast: cellular dynamics in uterine epithelial cells. *Cells Tissues Organs* 172, 237–252. doi: 10.1159/000066963
Tosti, E. (2006). Calcium ion currents mediating oocyte maturation events. *Reprod. Biol. Endocrinol.* 4:26. doi: 10.1186/1477-7827-4-26
Tu, C. L., and Bikle, D. D. (2013). Role of the calcium-sensing receptor in calcium regulation of epidermal differentiation and function. *Best Pract. Res. Clin. Endocrinol. Metab.* 27, 415–427. doi: 10.1016/j.beem.2013.03.002
Tyler Miller, R. (2013). Control of renal calcium, phosphate, electrolyte, and water excretion by the calcium-sensing receptor. *Best Pract. Res. Clin. Endocrinol. Metab.* 27, 345–358. doi: 10.1016/j.beem.2013.04.009
Uhm, S. J., Gupta, M. K., Yang, J. H., Chung, H. J., Min, T. S., and Lee, H. T. (2010). Epidermal growth factor can be used in lieu of follicle-stimulating hormone for nuclear maturation of porcine oocytes in vitro. *Theriogenology* 73, 1024–1036. doi: 10.1016/j.theriogenology.2009.11.029
Wang, C., and Machaty, Z. (2013). Calcium influx in mammalian eggs. *Reproduction* 145, R105–R108. doi: 10.1530/rep-12-0496
Weimar, C. H., Post Uittererw, E. D., Teeklenburg, G., Heijnen, C. J., and Macklon, N. S. (2013). *In vitro* model systems for the study of human embryo-endometrium interactions. *Reprod. Biomed. Online* 27, 461–476. doi: 10.1016/j.rbmo.2013.08.002
Westwood, F. R. (2008). The female rat reproductive cycle: a practical histological guide to staging. *Toxicol. Pathol.* 36, 375–384. doi: 10.1177/0192623308315665
Xiao, L. J., Yuan, J. X., Li, Y. C., Wang, R., Hu, Z. Y., and Liu, Y. X. (2005). Extracellular Ca$^{2+}$-sensing receptor expression and hormonal regulation in rat uterus during the peri-implantation period. *Reproduction* 129, 779–788. doi: 10.1530/rep.1.00621
Yan, S., Yuan, C., Yang, Q., Li, X., Yang, N., Liu, X., et al. (2015). A genetic polymorphism (rs17251221) in the calcium-sensing receptor is associated with ovarian cancer susceptibility. *Oncol. Rep.* 34, 2151–2155. doi: 10.3892/or.2015.4179
Yoshida, M., and Yoshida, K. (2011). Sperm chemotaxis and regulation of flagellar movement by Ca$^{2+}$. *Mol. Hum. Reprod.* 17, 457–465. doi: 10.1093/molehr/gar041
Zhang, C., Miller, C. L., Brown, E. M., and Yang, J. J. (2015). The calcium sensing receptor: from calcium sensing to signaling. *Sci. China Life Sci.* 58, 14–27. doi: 10.1007/s11427-014-4779-y
**Conflict of Interest Statement:** The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
*Copyright © 2016 Ellinger. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.* | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3123,
1
],
[
3123,
9879,
2
],
[
9879,
11720,
3
],
[
11720,
14973,
4
],
[
14973,
21671,
5
],
[
21671,
22096,
6
],
[
22096,
28760,
7
],
[
28760,
34068,
8
],
[
34068,
34489,
9
],
[
34489,
41306,
10
],
[
41306,
47779,
11
],
[
47779,
54431,
12
],
[
54431,
61478,
13
],
[
61478,
62955,
14
],
[
62955,
69102,
15
],
[
69102,
69102,
16
],
[
69102,
75753,
17
],
[
75753,
77459,
18
]
]
} |
95db3ba898d7a036c65f421db40a65e3acf49eea | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 7,
"total-fallback-pages": 0,
"total-input-tokens": 20782,
"total-output-tokens": 8121,
"fieldofstudy": [
"Biology",
"Medicine"
]
} | Quercetin liposomes protect against radiation-induced pulmonary injury in a murine model
HAO LIU\textsuperscript{1,2}, JIAN-XING XUE\textsuperscript{1}, XING LI\textsuperscript{1}, RUI AO\textsuperscript{2} and YOU LU\textsuperscript{1}
\textsuperscript{1}Department of Thoracic Oncology, Cancer Center and State Key Laboratory of Biotherapy, West China Hospital, West China Medical School, Sichuan University, Chengdu 610041; \textsuperscript{2}Department of Oncology, Sichuan Academy of Medical Sciences, Sichuan Provincial People’s Hospital, Chengdu, Sichuan 610041, P.R. China
Received January 20, 2013; Accepted May 17, 2013
DOI: 10.3892/ol.2013.1365
Abstract. In the present study, the hypothesis that quercetin liposomes are able to effectively protect against radiation-induced pulmonary injury in a murine model was tested. C57BL/6J mice receiving whole-thorax radiotherapy (16 Gy) were randomly divided into three groups: control, radiation therapy plus saline (RT+NS) and RT plus quercetin (RT+QU). At 1, 4, 8 and 24 weeks post-irradiation, lung injury was assessed by measuring oxidative damage and the extent of acute pneumonitis and late fibrosis. In the lung tissues from the RT+NS group, the malondialdehyde (MDA) levels were significantly elevated and superoxide dismutase (SOD) and glutathione peroxidase (GSH-PX) activities were significantly reduced; the total cell counts and inflammatory cell proportions in the bronchoalveolar lavage fluid (BALF), plasma tumor necrosis factor (TNF)-\(\alpha\) and transforming growth factor (TGF)-\(\beta\)1 concentrations and the hydroxyproline (HP) content were significantly increased. Quercetin liposome administration significantly reduced the MDA content and increased SOD and GSH-PX activities in the lung tissues, and reduced the total cell counts and inflammatory cell proportions in the BALF, plasma TNF-\(\alpha\) and TGF-\(\beta\)1 concentrations and the HP content in the lung tissues. A histological examination revealed suppression of the inflammatory response and reduced TGF-\(\beta\)1 expression and fibrosis scores. Radiation-induced oxidative damage ranged from pneumonitis to lung fibrosis. Quercetin liposomes were shown to protect against radiation-induced acute pneumonitis and late fibrosis, potentially by reducing oxidative damage.
Introduction
Radiation therapy (RT) is currently the cornerstone of the treatment of malignant thoracic diseases, including lung cancer, breast cancer, malignant lymphoma, esophageal cancer and thymoma. To ensure coverage of the tumor, the irradiation of normal tissues surrounding the tumor is unavoidable and may result in symptomatic injury (1). Radiation-induced pulmonary injuries (RIPIs), including radiation-induced pneumonitis and lung fibrosis, limit the therapeutic ratios of tumor treatment and reduce the quality of life in long-term survivors (1). Thus, effective prevention and control of RIPIs is extremely important in these patients.
The pathological process of RIPIs is complex, beginning with an acute inflammatory response that includes alveolar cell depletion and interstitial inflammation in the lung. Irreversible fibrosis, including fibroblast proliferation with collagen accumulation, occurs in the late stages of this process and eventually leads to the loss of normal lung structure (2). The biological effects of ionizing radiation begin with the direct generation of various reactive oxygen species (ROS), which cause oxidative damage to DNA, proteins and lipids, as well as the activation of transcription factors and signal transduction pathways (3). Oxidative damage to cellular components in the lung leads to cell damage and even cell death, and triggers inflammation that induces reparative processes and results in radiation-induced lung fibrosis (4). Thus, molecules with radical-scavenging properties show particular promise as radio-protectors (5).
Animal studies have shown that antioxidant therapy reduces the extent of radiation-induced lung damage: hydrogen therapy has been shown to reduce cell damage, improve the viability of ionizing A549 cells and attenuate irradiation-induced damage by reducing oxidative stress (6); a superoxide dismutase (SOD) mimetic has been demonstrated to increase the tolerance of ionizing radiation in the lungs of rats (7); and amifostine was shown to reduce radiation-induced damage by scavenging oxygen and oxygen free radicals (8).
Quercetin, or 3,3',4',5,7-pentahydroxyflavone, is categorized as a flavonol, one of the six subclasses of flavonoid compounds (9). The protective effects of flavonoids in biological systems are ascribed to their capacity for transferring electrons to free radicals, activating antioxidant enzymes and inhibiting oxidative stress (10). Quercetin has a superior antioxidant activity
Correspondence to: Professor You Lu, Department of Thoracic Oncology, Cancer Center and State Key Laboratory of Biotherapy, West China Hospital, West China School of Medicine, Sichuan University, 37 Guoxue Lane, Chengdu, Sichuan 610041, P.R. China
E-mail: [email protected]
Key words: radiation pneumonitis, quercetin, oxidative stress, liposome
due to the presence of the catechol group in the B ring and the OH group at position 3 on the AC ring. These structural features allow quercetin to donate hydrogen to scavenge free radicals and increase the stability of flavonoid radicals (11). Quercetin is known to possess marked antioxidative, anti-inflammatory and antibacterial capacities. Animal experiments have demonstrated its ability to scavenge oxygen free radicals, inhibit lipid oxidation and affect the glutathione redox status (12,13). Quercetin has been shown to improve the inflammatory status by reducing tumor necrosis factor (TNF-α) and inducible nitric oxide synthase production in obese Zucker rats (14). In vitro, quercetin inhibits keloid fibroblast proliferation, collagen production and keloid contraction by suppressing transforming growth factor (TGF)-β/Smad signaling (15). In vivo, quercetin has been shown to improve liver histology and reduce collagen content in rats with carbon tetrachloride-induced cirrhosis (16). We thus hypothesized that quercetin would be an ideal candidate for the amelioration of RIs.
At present, the routine treatment for acute radiation pneumonitis includes a combined regime of adrenal cortex hormones and antibiotics, but this treatment does not effectively prevent or cure radiation pneumonitis or fibrosis. The present study aimed to investigate the effect and potential mechanism of the action of quercetin liposomes on RIs in a murine model.
Materials and methods
Quercetin liposome preparation. Since quercetin naturally has poor water solubility, laboratory-prepared quercetin liposomes characterized by improved solubility and increased in vivo absorbability (State Key Laboratory of Biotherapy, West China Hospital, Sichuan University, Chengdu, Sichuan, China) were used.
The quercetin liposomes were prepared as described previously (17). Briefly, mixtures of lecithin/cholesterol/PEG 4000/quercetin in 13:4:1:6 weight ratios were dissolved in chloroform/methanol (3:1, v/v) and evaporated until dry under reduced pressure in a rotary evaporator. The dried lipid films were sonicated in 5% glucose solution in a homothermal container. The final products were concentrated, lyophilized under vacuum for 5 h and stored at -20°C. This end-product has good solubility and may be used directly or dissolved in saline intraperitoneally.
Animal model and experimental protocol. All animal procedures were approved by the Laboratory Animal Care Committee of Sichuan Province. Female C57BL mice (Experimental Animal Center of Sichuan University, Chengdu, Sichuan, China) aged 6-8 weeks, with approximate body weights of 18-20 g, were used in this study.
A total of 69 mice were randomly divided into three groups: a control group; an RT plus saline (RT+NS) group that received intraperitoneal injections of 200 μl saline 2 h prior to irradiation and on days 1-28 subsequent to RT; and an RT plus quercetin liposome (RT+QU) group that received intraperitoneal injections of 5 mg/kg quercetin liposome, based on a previous study (17), 2 h prior to irradiation and on days 1-28 subsequent to RT.
For the thoracic irradiation, the mice were anesthetized by the intraperitoneal administration of 10 ml/kg 3.5% chloral hydrate. A single dose of cobalt-60 γ radiation (GWXJ80; Nuclear Power Institute of China, Chengdu, China) was administered to the entire thorax (0.8953 Gy/min; source-skin distance, 80 cm) of each mouse. Organs above and below the thorax were shielded.
At 1, 4, 8 and 24 weeks post-RT, four or five mice in each group were sacrificed. Peripheral blood samples and bronchoalveolar lavage fluid (BALF) were obtained, the left lung was fixed in 4% paraformaldehyde and the right lung was cryopreserved at -80°C.
Malondialdehyde (MDA) content and SOD and glutathione peroxidase (GSH-PX) activities. Tissue from one lobe of each right lung was homogenized in 5% phosphate-buffered saline. The homogenate was then centrifuged at 800 x g for 10 min and the clear supernatant fluid was used. The MDA content and the SOD and GSH-PX activities in the lung were measured using respective kits (Nanjing Jiancheng Bioengineering Institute, Nanjing, China) according to the manufacturer's instructions.
BALF analysis. At 1, 4, 8 and 24 weeks post-irradiation, the mice were sacrificed, an open tracheotomy was performed and a small plastic tube was inserted into the trachea. BALF was extracted three times with 2 ml physiological saline. The BALF was centrifuged (400 x g, 15 min) and the cell pellet was suspended in 1 ml modified Hank's balanced salt solution. Total nucleated and differential cell counts were performed on cellular monolayers prepared by cytocentrifugation at 800 rpm for 10 min, followed by hematoxylin and eosin (HE) staining. The percentages of inflammatory cell types (including neutrophils and lymphocytes) that were present were assessed by differential counts of 400 cells.
TNF-α and TGF-β1 concentrations in plasma. The TGF-β1 and TNF-α contents of the plasma were measured by sandwich enzyme-linked immunosorbent assays (ABC-ELISA, R&D Systems, Minneapolis, MN, USA), according to the manufacturer's instructions.
Hydroxyproline (HP) assay. Collagen deposition was estimated by determining the total HP content of one lobe of each right lung using alkaline hydrolysis (Nanjing Jiancheng Bioengineering Institute). Briefly, the lung tissue in the test tube was weighed, 1 ml hydrolyzate was added and hydrolysis was performed in a boiling water bath for 20 min to regulate the pH (pH 6.0-6.8). The hydrolyzate was diluted by adding activated carbon, then the contents of the tube were mixed thoroughly and centrifuged at 3,500 rpm for 10 min and 1 ml supernatant was tested. Once the reagents had been added to the reaction mixture, the supernatant absorbance was measured at 550 nm.
Histology and immunocytochemistry. The left lungs were fixed by an intratracheal instillation of 4% paraformaldehyde, allowed to cure overnight, embedded in paraffin and cut into 5-μm thick sections. Certain sections were stained with HE and Masson's trichrome for the determination of collagen content. Pulmonary fibrosis was scored using the scale developed by Ashcroft et al (18). Briefly, entire fields of 15 sections were scanned and each field was graded visually on a scale ranging from 0 (normal) to 8 (total fibrotic obliteration of
the field). The mean of the scores obtained for all fields was used as the visual fibrosis score. The remaining sections were immunocytochemically stained with anti-TGF-β1 antibody (Santa Cruz Biotechnology, Inc., Santa Cruz, CA, USA) to detect active TGF-β1 expression. Five fields were randomly selected for each mouse and three mice from each group were examined; thus, a total of 15 sections were analyzed for each group. The number of cells showing active TGF-β1 expression within each field was counted under a light microscope at x400 magnification (CX41RF; Olympus; Tokyo, Japan).
Statistical analysis. Data are presented as the mean ± standard deviation. The statistical analysis was performed by a one-way analysis of variance, followed by Dunnet’s t-test. P<0.05 was considered to indicate a statistically significant difference.
Results
MDA content and SOD and GSH-PX activity in lung tissue. From 1 to 24 weeks post-RT, the MDA content of the lung tissues increased significantly (all P<0.01 vs. control group; Fig. 1). Quercetin liposome administration significantly reduced the MDA content (all P<0.05 vs. RT+NS group).
From 1 to 24 weeks post-RT, the SOD and GSH-PX activities in the lung tissue significantly decreased (all P<0.01 vs. control group; Fig. 1). Quercetin liposome administration significantly increased the MDA content (all P<0.05 vs. control group).
Total cell counts and proportions of inflammatory cells in BALF. Epithelial cells and macrophages were the main cell types identified in the BALF from rats in the control group and the presence of lymphocytes were rare (Fig. 2). At 4 and 8 weeks post-RT, the total cell counts of the BALF and the percentages of inflammatory cells were increased significantly (all P<0.01 vs. control group). In the RT+QU group, the total cell counts of the BALF and the percentages of inflammatory cells were significantly reduced (all P<0.05 vs. RT+NS group) at 4 and 8 weeks post-RT.
TNF-α and TGF-β1 concentrations in plasma. In the control group, the TNF-α concentrations in plasma was 135.1±33.6 pg/ml (Fig. 3). At 1, 4 and 8 weeks post-RT, the TNF-α concentrations increased significantly, resulting in concentrations of 273.4±32.2, 367.0±52.5 and 328.8±51.7 pg/ml, respectively (all P<0.01 vs. control group). In the RT+QU group, the TNF-α concentrations declined significantly, with results of 203.1±34.2, 264.7±45.4 and 228.0±47.3 pg/ml, respectively (all P<0.05 vs. RT+NS group).
In the control group, the TGF-β1 concentration in plasma was 4,207.2±732.1 pg/ml (Fig. 3). At 4, 8 and 24 weeks post-RT, the TGF-β1 concentrations increased significantly to 10,373.2±1,084.8, 14,650.6±1,632.6 and 12,265.5±740.7 pg/ml, respectively (all P<0.01 vs. control group). In the RT+QU group, the TGF-β1 concentrations declined significantly, with results of 7,100.8±1,009.4, 9,056.6±1,484.5 and 7,466.8±1,138.5 pg/ml, respectively (all P<0.01 vs. RT+NS group).
Histological changes in lung tissue. Subsequent to irradiation, two pathological phases of RIPIs were observed; an initial phase of acute and subacute pneumonitis (1-8 weeks), followed by late fibrosis (24 weeks; Figs. 4 and 5). In the pneumonitis phase, numerous inflammatory cells infiltrated the alveoli and alveolar walls and the lung interstitium was thickened, although
Minimal fibrosis was present on the alveolar walls, which were stained with Masson’s trichrome. In the late fibrosis stage, lung interstitium thickening and inflammatory cell infiltration were observed and the alveolar structure became disordered and collapsed. Notably, Masson’s trichrome staining revealed diffuse fibrous changes in the alveolar walls. The lung fibrosis score at 24 weeks post-irradiation was significantly higher (4.2±0.8) compared with the control group (0.6±0.55; P<0.01).
Figure 4. Photomicrographs of hematoxylin and eosin (HE)-stained lung sections from the control (CON), radiotherapy plus saline (RT+NS) and radiotherapy plus quercetin liposome (RT+QU) groups at various timepoints after irradiation. Magnification, x400.
Figure 5. (A) Masson's trichrome staining of lung tissue sections, with collagen fibers dyed blue. Magnification, x400. (B) Lung fibrosis scores at 24 weeks after irradiation. Con, control; RT, radiotherapy; NS, saline; Qu, quercetin liposome.
Figure 6. (A) Immunocytochemical staining with anti-transforming growth factor (TGF)-β1, with the cytoplasm of cells expressing TGF-β1 stained brown. Magnification, x400. (B) Number of stained cells was counted within each field. Values are expressed as the mean ± standard deviation (SD). *P<0.01, *P<0.05. Con, control; RT, radiotherapy; NS, saline; Qu, quercetin liposome.
However, the damage was clearly minor in the RT+QU group, with a lung fibrosis score of 2.6±1.1 at 24 weeks post-irradiation (P<0.05). The cells with active TGF-β1 expression infiltrated the lung tissue between 4 and 24 weeks post-irradiation (Fig. 6), although the degree of infiltration was significantly lower in the RT+QU group compared with the RT+NS group (all P<0.05 vs. RT+NS group).
**HP content in the lung tissue.** Fibrosis is characterized by collagen deposition, and the HP content in the lung tissues reflects the proportion of tissue with collagen fibers. The lung tissues in the control group contained 185.5±34.4 µg HP/g lung (Fig. 7). The HP content began to increase significantly in the first 8 weeks post-irradiation and peaked at 24 weeks (562.7±63.2 µg/g wet tissue; P<0.01). Quercetin liposome administration noticeably reduced the HP content of the lung tissue (446.0±64.1 µg/g lung at 24 weeks; P<0.05).
**Discussion**
The present findings of marked increases in MDA content and reductions in SOD and GSH-PX activities between 1 and 24 weeks after whole-lung irradiation demonstrated oxidative stress sustained from radiation-induced pneumonitis and lung fibrosis. Ionizing radiation causes DNA damage through direct and indirect mechanisms (19); sensitive molecules in cells are directly damaged and interactions between radiation and water molecules in cells lead to the production of ROS, including superoxide anion radicals, hydrogen peroxide and hydroxyl radicals. Hydroxyl radicals are responsible for an estimated 60-70% of all ionizing radiation-induced cell damage (3,19). The radiation-induced burst of ROS generation is transient, but radiation also damages critical biomolecules governing the metabolic production of ROS, including mitochondria and oxidoreductase enzymes. Oxidative stress also contributes to the biological effects of ionizing radiation long after exposure (20). Leach et al (21) reported that the transient generation of ROS occurs within minutes of cell exposure to ionizing radiation, damaging mitochondrial permeability and resulting in the constant enhancement of ROS generation. Previous studies have shown that oxidative damage is increased and antioxidative capacities are decreased in radiation-induced lung injury (6,22). The effective protection of antioxidants have also been shown to indirectly reflect the potential causative role of oxidative stress in the development of RIPIs (7).
The antioxidant activities of quercetin are attributed to numerous factors, including free radical scavenging, protection against lipid oxidation (23), up-regulation of antioxidant enzymes and ROS trapping by direct hydrogen ion donation (12). However, quercetin administration has been hampered by its extreme water insolubility. The encapsulation of quercetin in liposomes improves its water solubility, prolonging circulation times in the blood and accumulation times in the lung (17). Significantly, the use of liposomal quercetin was shown to reduce the injection dose compared with free quercetin (17). Hence, in the present study, intraperitoneal injections of quercetin liposome were administered prior to and following RT. A lower MDA content and higher SOD and GSH-PX activities were observed in the lung tissue in the RT+QU group compared with the RT+NS group, demonstrating that quercetin inhibited pulmonary oxidative damage.
Inflammation may be central in the initiation and establishment of RIPIs (2). Changes in cell populations in the BALF have often been considered to reflect inflammatory changes in the lung (24). As a pro-inflammatory cytokine, TNF-α is likely to be involved in the early phase of RIPIs. Hence, the proportions of inflammatory cells in the BALF and TNF-α concentrations in the plasma were measured to estimate the extent of the inflammatory response. It was observed that the quercetin liposome significantly decreased the total cell counts and the proportion of inflammatory cells in the BALF, and also reduced plasma TNF-α concentrations. A histological examination revealed the suppression of the inflammatory response in the RT+QU group. The anti-inflammatory effects of quercetin may be attributed to the interplay between oxidative stress and inflammation (23). ROS are involved not only in the occurrence of oxidative stress, but also in the promotion of inflammatory processes. ROS are key mediators of inflammatory reactions in atherosclerosis (25). They are able to activate transcription factors such as nuclear factor (NF)-κB and activator protein-1, which induce the production of cytokines such as TNF-α (26). Consequently, ROS scavenging not only prevents oxidative stress, but also mitigates inflammation. Quercetin has been reported to inhibit TNF-α production and gene expression via NF-κB modulation (27). In animal models of allergic airway inflammation and asthma, quercetin has been demonstrated to reduce inflammatory cell infiltration and inflammatory cytokine production (28).
Tissue fibrosis is the excessive accumulation of collagen. TGF-β1 is a key cytokine in the fibrotic process that activates myofibroblast progenitors and upregulates collagen protein synthesis (2). Hence, in the present study, the plasma TGF-β1 concentrations and HP content in the lung tissue were measured, and Masson's trichrome staining was used to estimate the extent of lung fibrosis. It was observed that quercetin liposomes significantly reduced the plasma TGF-β1 concentrations and HP content in the lung tissue. A histological examination revealed the suppression of TGF-β1 expression and collagen deposition in the lung. The lung fibrosis scores were significantly lower in the RT+QU group compared with the RT+NS group. The mechanism of quercetin's antifibrotic effects may also be associated in part with the reduction of oxidative stress (29). Oxidative stress is postulated to play an important role in the development of lung fibrosis.
role in a wide range of fibrotic diseases, including atherosclerosis, cardiac fibrosis and idiopathic lung fibrosis (30). ROS and lipid peroxidation products stimulate fibrogenic cytokines that act as chemoattractants, mitogens and differentiating agents for smooth muscle cells (25,31). TGF-β isoforms are secreted in a latent complex, and the release of TGF-β from this complex is called activation. The ROS-mediated oxidation of a methionine residue in the latent complex releases TGF-β from extracellular reservoirs (32). In vitro, quercetin has been shown to suppress TGF-β-induced collagen production in normal human lung fibroblasts (33). In biliary-obstructed rats, quercetin has been shown to maintain an antioxidant defense and reduce oxidative damage, ameliorating liver fibrosis (29).
In conclusion, oxidative stress in the lung leads to radiation-induced pneumonitis and lung fibrosis. The present study demonstrated that quercetin liposomes inhibit pulmonary oxidative stress, alleviating radiation-induced acute pneumonitis and late fibrosis. Thus, quercetin effectively protected lung tissue against RIPIs.
Acknowledgements
The present study was supported by the National Major Project of China (No.2011ZX09302-001-01), and the Natural Science Fund of China (No.81172131).
References
1. Stone HB, Coleman CN, Ansch MS and McBride WH: Effects of radiation on normal tissue: consequences and mechanisms. Lancet Oncol 4: 529-536, 2003.
2. Tsoutsou PG and Koukourakis MI: Radiation pneumonitis and fibrosis: mechanisms underlying its pathogenesis and implications for future research. Int J Radiat Oncol Biol Phys 66: 1281-1293, 2006.
3. Zhao W and Robbins ME: Inflammation and chronic oxidative stress in radiation-induced late normal tissue injury: therapeutic implications. Curr Med Chem 16: 130-143, 2009.
4. Graves PR, Siddiqui F, Ansch MS and Mowas B: Radiation pulmonary toxicity: from mechanisms to management. Semin Radiat Oncol 20: 201-207, 2010.
5. Karbowink M and Reiter RF: Antioxidative effects of melatonin in protection against cellular damage caused by ionizing radiation. Proc Soc Exp Biol Med 225: 9-22, 2000.
6. Terasaki Y, Ohsawa I, Terasaki M, et al: Hydrogen therapy attenuates irradiation-induced lung damage by reducing oxidative stress. Am J Physiol Lung Cell Mol Physiol 301: L415-L426, 2011.
7. Vujaskovic Z, Batincic-Haberle I, Rabbani ZN, et al: A small molecular weight catalytic metalloporphyrin antioxidant with superoxide dismutase (SOD) mimetic properties protects lungs from radiation-induced injury. Free Radic Biol Med 33: 857-863, 2002.
8. Koukourakis MI: Amifostine in clinical oncology: current use and future applications. Anticancer Drugs 13: 181-209, 2002.
9. Kelly GS: Quercetin. Monograph. Altern Med Rev 16: 172-194, 2011.
10. Heim KE, Tagliaferro AR and Bobilya DJ: Flavonoid antioxidants: chemistry, metabolism and structure-activity relationships. J Nutr Biochem 13: 572-584, 2002.
11. Heijnen CG, Haenen GR, Oostveen RM, Stalpers EM and Bast A: Protection of flavonoids against lipid peroxidation: the structure activity relationship revisited. Free Radic Res 36: 575-581, 2002.
12. Cai Q, Rahn RO and Zhang R: Dietary flavonoids, quercetin, luteolin and genistein, reduce oxidative DNA damage and lipid peroxidation and quench free radicals. Cancer Lett 119: 99-107, 1997.
13. Meyers KJ, Rudolf JL and Mitchell AE: Influence of dietary quercetin on glutathione redox status in mice. J Agric Food Chem 56: 830-836, 2008.
14. Rivera L, Morón R, Sánchez M, Zarzuelo A and Galisteo M: Quercetin ameliorates metabolic syndrome and improves the inflammatory status in obese Zucker rats. Obesity (Silver Spring) 16: 2081-2087, 2008.
15. Phan TT, Lim IJ, Chan SY, Tan EK, Lee ST and Longaker MT: Suppression of transforming growth factor beta/smad signaling in keloid-derived fibroblasts by quercetin: implications for the treatment of excessive scars. J Trauma 57: 1032-1037, 2004.
16. Pavanato A, Tuñón MJ, Sánchez-Campos S, et al: Effects of quercetin on liver damage in rats with carbon tetrachloride-induced cirrhosis. Dig Dis Sci 48: 824-829, 2003.
17. Yuan ZP, Chen LJ, Fan LY, et al: Liposomal quercetin efficiently suppresses growth of solid tumors in murine models. Clin Cancer Res 12: 3193-3199, 2006.
18. Ashcroft T, Simpson JM and Timbrell V: Simple method of estimating severity of pulmonary fibrosis on a numerical scale. J Clin Pathol 41: 467-470, 1988.
19. Ward JF: DNA damage produced by ionizing radiation in mammalian cells: identities, mechanisms of formation, and reparability. Prog Nucleic Acid Res Mol Biol 35: 95-125, 1988.
20. Spitz DR, Azzam EL, Li JJ and Gius D: Metabolic oxidation/reduction reactions and cellular responses to ionizing radiation: a unifying concept in stress response biology. Cancer Metastasis Rev 23: 311-322, 2004.
21. Leach JK, Van Tuyle G, Lin PS, Schmidt-Ullrich R and Mikkelson RB: Ionizing radiation-induced, mitochondria-dependent generation of reactive oxygen/nitrogen. Cancer Res 61: 3894-3901, 2001.
22. De AK, Rajan RR, Krishnamoorthy L, Bhatt MB and Singh BB: Oxidative stress in radiation-induced interstitial pneumonitis in the rat. Int J Radiat Biol 68: 405-409, 1995.
23. Boots AW, Haenen GR and Bast A: Health effects of quercetin: from antioxidant to nutraceutial. Eur J Pharmacol 585: 325-337, 2008.
24. Hong JH, Jung SM, Tsao TC, et al: Bronchoalveolar lavage and interstitial cell have different roles in radiation-induced lung injury. Int J Radiat Biol 79: 159-167, 2003.
25. Madamanchi NR, Hakim ZS and Range MS: Oxidative stress in atherogenesis and arterial thrombosis: the disconnect between cellular studies and clinical outcomes. J Thromb Haemost 3: 254-267, 2005.
26. Rahman I: Oxidative stress, transcription factors and chromatin remodelling in lung inflammation. Biochem Pharmacol 64: 935-942, 2002.
27. Nair MP, Mahajan S, Reynolds JL, et al: The flavonoid quercetin inhibits proinflammatory cytokine (tumor necrosis factor alpha) gene expression in normal peripheral blood mononuclear cells via modulation of the NF-kappa beta system. Clin Vaccine Immunol 13: 319-328, 2006.
28. Rogerio AP, Kanashiro A, Fontanari C, et al: Anti-inflammatory activity of quercetin and isorquercitin in experimental murine allergic asthma. Inflamm Res 56: 402-408, 2007.
29. Peres W, Tutón MJ, Collado PS, Herrmann S, Marroni N and González-Gallego J: The flavonoid quercetin ameliorates liver damage in rats with biliary obstruction. J Hepatol 33: 742-750, 2000.
30. Yarnold J and Brotons MC: Pathogenic mechanisms in radiation fibrosis. Radiolother Oncol 97: 149-161, 2010.
31. Poli G and Parola M: Oxidative damage and fibrogenesis. Free Radic Biol Med 22: 287-305, 1997.
32. Jobling MF, Mott JD, Finnegan MT, et al: Isoform-specific activation of latent transforming growth factor beta (LTGF-beta) by reactive oxygen species. Radiat Res 166: 839-848, 2006.
33. Nakamura T, Matsuhashi M, Hayashi Y, et al: Attenuation of transforming growth factor beta activity in liver fibroblasts by quercetin-induced heme oxygeasase-1. Am J Respir Cell Mol Biol 44: 614-620, 2011. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
5170,
1
],
[
5170,
11550,
2
],
[
11550,
14859,
3
],
[
14859,
15354,
4
],
[
15354,
16230,
5
],
[
16230,
22182,
6
],
[
22182,
29278,
7
]
]
} |
2511da90098f5beeeb2d64064b4d40b60e92f6ac | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 19,
"total-fallback-pages": 0,
"total-input-tokens": 80647,
"total-output-tokens": 27423,
"fieldofstudy": [
"Mathematics"
]
} | In personalized medicine, it is often desired to determine if all patients or only a subset of them benefit from a treatment. We consider estimation in two-stage adaptive designs that in stage 1 recruit patients from the full population. In stage 2, patient recruitment is restricted to the part of the population, which, based on stage 1 data, benefits from the experimental treatment. Existing estimators, which adjust for using stage 1 data for selecting the part of the population from which stage 2 patients are recruited, as well as for the confirmatory analysis after stage 2, do not consider time to event patient outcomes. In this work, for time to event data, we have derived a new asymptotically unbiased estimator for the log hazard ratio and a new interval estimator with good coverage probabilities and probabilities that the upper bounds are below the true values. The estimators are appropriate for several selection rules that are based on a single or multiple biomarkers, which can be categorical or continuous.
**KEYWORDS**
adaptive threshold design, enrichment designs, stratified medicine, subgroup analysis, survival data
---
**1 | INTRODUCTION**
Clinical trials in personalized medicine involve assessing whether a patient’s characteristic(s), known as biomarkers, can be used to determine their best care. A biomarker may influence the progression of disease without treatment (prognostic biomarker) or the size of the effect of a treatment (predictive biomarker). We focus on predictive biomarkers, where the effects of a new treatment in different subpopulations defined by biomarker values are assessed. Several efficient two-stage adaptive designs with an interim analysis to determine the part of the population (subpopulation) to benefit most from a new treatment have been proposed. The general framework of such designs is that patients are recruited from the full population in stage 1, with an interim analysis performed to determine the subpopulation where the new treatment is apparently beneficial. In stage 2, patients are recruited from this group. Confirmatory analysis then includes data from...
both stages. Appropriate analysis of two-stage adaptive trials needs to adjust for the bias arising from using stage 1 data for both subpopulation selection and the final analysis.
Time to event patient outcomes are considered in several clinical trials assessing predictive biomarkers.\(^7\)\(^{-10}\) For two-stage adaptive trials, methods for controlling type I error rate and/or increasing power have been developed.\(^2\)\(^,\)\(^3\)\(^,\)\(^7\) However, existing point estimators and confidence intervals that adjust for subpopulation selection do not consider time to event data.\(^4\)\(^,\)\(^6\)\(^,\)\(^11\) Li et al.\(^12\) quantify the bias of the naive estimator for time to event data but do not derive unbiased estimators. Thus, there is a need to develop point and interval estimators for time to event data in two-stage adaptive trials with subpopulation selection. This is the aim of this article. Using the asymptotic distribution of the log hazard ratio, we extend existing methods for normally distributed data to time to event patient outcomes. We also address the additional complexity associated with following in stage 2 the stage 1 patients without the event of interest at the interim analysis.
For normally distributed outcomes, estimators that adjust for subpopulation selection may be obtained in three ways. The first involves estimating and subtracting the bias of the naive estimator.\(^6\)\(^,\)\(^13\)\(^{-15}\) The second utilizes the empirical Bayes technique to obtain shrinkage estimators.\(^6\)\(^,\)\(^15\)\(^{-17}\) The third is based on the Rao-Blackwell theorem that the expected value of the unbiased stage 2 estimator conditional on the selected subpopulation and a sufficient statistic is the uniformly minimum variance conditional unbiased estimator (UMVCUE).\(^4\)\(^,\)\(^6\)\(^,\)\(^18\)\(^{-22}\) Kimani et al.\(^6\) compared the estimation approaches in the context of subpopulation selection, concluding that the UMVCUE was superior. As we expect the same conclusion if the three estimators are extended to time to event data, in this article, we have only extended the UMVCUE. To address the complexity associated with time to event data, we assume hypothesis testing similar to that proposed by Jenkins et al.\(^3\) and use the duality with hypothesis testing to construct confidence intervals with desired properties as proposed for non-time to event data by Magirr et al.\(^23\)
Previous research has considered biomarkers of various forms (a binary biomarker, a continuous biomarker, or multiple biomarkers) and different subpopulation selection rules. Our point and interval estimators are appropriate for different selection rules and biomarkers of many forms.
2 | SETTING AND NOTATION
2.1 | Partitioning the population and general concepts in selecting partitions
This section describes the partitioning of the full population \((F)\) and general approaches for specifying selection rules. Specific selection rules will be described in Section 2.3. Figure 1 summarizes the partitioning of \(F\). We first describe concepts common to all settings that we consider, indicated as general concepts in the figure. Assume that \(F\) consists of \(K \geq 2\) distinct partitions. For partition \(j (j = 1, \ldots, K)\), we denote the true prevalence of patients by \(p_j\) and hazard functions for the control and experimental groups by \(h_{Cj}(t)\) and \(h_{Ej}(t)\), respectively. Assuming proportional hazards within a partition, we denote the log hazard ratio (HR) for partition \(j (j = 1, \ldots, K)\) by \(\theta_j\), with \(\theta_j < 0\) indicating that the experimental treatment delays occurrence of the event in partition \(j\) and hence is superior to the control.
Let \(S \subseteq \{1, \ldots, K\}\) be the subset of indices corresponding to the partitions selected to continue to stage 2. The partitions are selected based on the stage 1 estimate for \((\theta_1, \ldots, \theta_K)^T\). At the end of the trial, for each \(j \in S\), the aim is to estimate \(\theta_j\). We will obtain log HR estimates in selected partitions separately, corresponding to a stratified model. Consequently, although the selection rules we consider in this paper are aimed at identifying predictive biomarkers, as shown in Figure 1, control group hazard functions in different partitions may be different so that the biomarker may also be prognostic. A disadvantage of this approach is that in some cases, such as when the biomarker is neither predictive nor prognostic, it would be better to obtain a single estimate using the data from all the partitions while assuming proportional hazards overall in \(F\) rather than separate estimates of effects assuming proportional hazards only within a partition. A model with partition membership as a categorical covariate and an interaction term for partition and treatment would enable an estimator of a combined effect. However, this model is not as general as the stratified model, imposing more restrictions on the hazard functions.
The expected relationship between biomarker and treatment effect informs the partitioning of \(F\) and the selection rule. Figure 1 gives an example of the two-stage adaptive threshold enrichment design.\(^5\)\(^,\)\(^24\) Here, it is assumed that a single continuous biomarker and the treatment effect are monotonically related with higher biomarker values associated with bigger treatment effects. Consequently \(K\) candidate threshold values \(c_1 > c_2 > \ldots > c_K\) are specified to subdivide \(F\) into \(K\)
### General concepts
#### Hazard function
| Partitions | Prevalence | Control | Experimental | Log hazard ratio |
|------------|------------|---------|--------------|-----------------|
| Partition 1 | $p_1$ | $h_{C_1}(t)$ | $h_{E_1}(t)$ | $\theta_1 = \ln \left( \frac{h_{E_1}(t)}{h_{C_1}(t)} \right)$ |
| Partition 2 | $p_2$ | $h_{C_2}(t)$ | $h_{E_2}(t)$ | $\theta_2 = \ln \left( \frac{h_{E_2}(t)}{h_{C_2}(t)} \right)$ |
| Partition $K$ | $p_K$ | $h_{C_K}(t)$ | $h_{E_K}(t)$ | $\theta_K = \ln \left( \frac{h_{E_K}(t)}{h_{C_K}(t)} \right)$ |
**FIGURE 1** Partitioning of the full population
distinct partitions. Setting $c_0 = \infty$, partition $j (j = 1, \ldots, K)$ consists of patients with biomarker values in $[c_j, c_{j-1}]$. As it is expected that $\theta_1 \leq \theta_2 \leq \cdots \leq \theta_K$, a selection rule is prespecified to test partitions in stage 2 with biomarker values above $c_s (s \in \{1, \ldots, K\})$.
Partitioning of $F$ and selection rules can be similarly given for biomarkers of other forms. Common cases are a single binary biomarker and multiple biomarkers. A single binary biomarker where the effect in one partition is expected to be bigger than in the complementary partition is a special case of the continuous biomarker with $K = 2$. For multiple biomarkers, we consider two scenarios. In the first, we assume biomarkers’ values can be combined into an aggregate score with a monotonic relationship with the treatment effect, with this score used to define partitions and a selection rule as for a single continuous biomarker. In the second scenario, the partitions consist of different combinations of biomarker level categories. A monotonic relationship between the biomarker values and treatment effects is not assumed and so a selection rule where partition $j (j = 1, \ldots, K)$ is considered for continuing to stage 2 based on the stage 1 estimate for $\theta_j$ only is specified. A single binary biomarker, where there is no knowledge of the partition that is more likely to benefit, can be considered a special case of the second scenario with $K = 2$.
### 2.2 Analysis times and notation of estimates for different subsets of trial data
Figure 2 shows the available data at different times in the trial. Each horizontal line that ends with a circle corresponds to a patient, with the line’s length being the patient’s survival time in the trial. The left hand end of each line corresponds to the calendar time a patient was recruited. Filled and non-filled circles correspond to an event having occurred and not, respectively.
The trial starts recruiting at some time $t_0$ and an interim analysis is performed at time $t_1$. In Sections 4 and 5, we will take $t_1$ to correspond to when a prespecified number of events is observed. Alternatives include $t_1$ being a prespecified date.
Stage 1 consists of the data that are used in the interim analysis, with the survival times being the lengths of continuous lines in Figure 2. As described below, we obtain estimates from these data based on the distribution of the score statistic. Estimates based on the distribution of the score statistic are similar to those from the Cox’s proportional hazards model. The choice of the model used to obtain estimates is discussed in Section 6. Let $S_{1j}$ and $V_{1j} (j = 1, \ldots, K)$ be the score statistic and Fisher information, respectively, obtained from analyzing partition $j$ stage 1 data at $t_1$. Based on
the score statistic theory, asymptotically $S_{1,j} \sim N(\theta_j V_{1,j}, V_{1,j})$. Note that the estimator $\hat{\theta}_{1,j}$ defined by $S_{1,j}/V_{1,j}$ is $N(\theta_j, \sigma^2_{1,j})$, where $\sigma^2_{1,j} = 1/V_{1,j}$ (for example, see chapter 3 of Whitehead$^{27}$ and chapter 13.4 of Jennison and Turnbull$^{28}$).
Based on the stage 1 observed value for the vector $(\hat{\theta}_{1,1}, \ldots, \hat{\theta}_{1,K})'$, the trial stops for futility or continues to stage 2 with $F$ or some part of $F$. Various selection rules are described in Section 2.3. Stage 2 patients are recruited only from the selected partitions. Recruitment and follow-up of stage 2 patients stops at calendar time $t_2$. In Sections 4 and 5, we take $t_2$ to correspond to when a prespecified number of events from stage 2 patients is observed but alternatives such as $t_2$ being a prespecified date can be used. In Figure 2, the survival times of stage 2 patients correspond to the lengths of the dotted lines.
At the interim analysis, some stage 1 patients will not have had the event of interest. As following these patients further gives estimators with smaller standard errors, we assume that they are followed up to time $\tilde{t}_1$. The choice of $\tilde{t}_1$ is described below. We refer to the data collected from stage 1 patients after the interim analysis as the incremental data.
For $j \in S$, let $S_{N,j}$ and $V_{N,j}$ denote the score statistic and Fisher information obtained from all patients recruited in partition $j$ with the survival times and status for stages 1 and 2 patients determined at times $\tilde{t}_1$ and $t_2$, respectively. Similar to above, $\hat{\theta}_{N,j}$ defined by $S_{N,j}/V_{N,j}$ is asymptotically $N(\theta_j, \sigma^2_{N,j})$, where $\sigma^2_{N,j} = 1/V_{N,j}$. In the next paragraph, we will describe a strategy for achieving approximate independence between data collected before and after the interim analysis. When independence can be assumed, score statistic theory has been extended to a setting with repeated analyses of data, such as analyzing all patients’ data at $t_1$ and $t_2$.$^{26,29}$ This gives $S_{N,j} - S_{1,j}$ independent of $S_{1,j}$ and asymptotically $N(\theta_j(V_{N,j} - V_{1,j}), V_{N,j} - V_{1,j})$. It follows that $\hat{\theta}_{2,j}$ defined as $(S_{N,j} - S_{1,j})/(V_{N,j} - V_{1,j})$ is $N(\theta_j, \sigma^2_{2,j})$, where $\sigma^2_{2,j} = 1/(V_{N,j} - V_{1,j})$. Note that
$$\hat{\theta}_{N,j} = \frac{\sigma^2_{1,j} \hat{\theta}_{1,j} + \sigma^2_{2,j} \hat{\theta}_{2,j}}{\sigma^2_{1,j} + \sigma^2_{2,j}}. \quad (1)$$
Estimators developed in Section 3 require $S_{N,j} - S_{1,j}$ to be independent of $S_{1,j}$ (the independent increment structure), where test statistics based on the data from before and after the interim analysis are independent. However, adaptation such as subpopulation selection may induce correlation. If, as we propose above, $t_i$ ($i = 1, 2$) depends on stage $i$ patients only, conditional on the selection made, stage 2 patients’ data are independent of $S_{1,j}$ and so any correlation between $S_{N,j} - S_{1,j}$ and $S_{1,j}$ is assumed to be induced by the stage 1 patients’ incremental data. Some authors ignore this correlation noting that the independent increment structure assumption holds approximately. We follow Jenkins et al.$^3$
who, in addition to setting \( t_1 \) and \( t_2 \) independent of each other, for example, as described above, suggest improving the independent increment structure assumption by fixing in advance the rule for how long the stage 1 patients without events of interest at \( t_1 \) are followed post stage 1. This ensures independence of Fisher information for stage 1, stage 2, and the incremental data. We suggest two rules for fixing the length of post stage 1 follow-up, and hence \( \tilde{t}_1 \). These rules are valid when \( t_1 \) and \( t_2 \) are determined as above, that is, independently, and they (\( t_1 \) and \( t_2 \)) are either prespecified dates, correspond to observation of prespecified numbers of events or are based on any other method for prespecifying duration of trials with time-to-event data.\textsuperscript{3,25} In the first, a fixed time between \( t_1 \) and \( \tilde{t}_1 \) is prespecified. This rule achieves approximate independence for whether or not stage 1 patients from the dropped partitions without events at \( t_1 \) are followed until \( \tilde{t}_1 \), though this should be specified before the trial and also, they should only be followed as part of the trial if they continue with the allocated treatments and adhere to the trial protocol. In the second rule, \( \tilde{t}_1 \) is the time when a prespecified number of events from stage 1 patients without events at \( t_1 \) is obtained. For the approximate independence to work well, this rule requires that the patients from dropped partitions are followed until \( \tilde{t}_1 \). Therefore, we only recommend this rule if it is plausible for the stage 1 patients from the dropped partitions to continue with the allocated treatments and adhere to the trial protocol. In Sections 4 and 5, we used the first rule. To assess the approximate independence assumption with this approach, we computed correlations between \( \tilde{\theta}_{1,j} \) and \( \tilde{\theta}_{2,j} \) for some scenarios in Section 5 (not presented) and obtained similarly small values as Tsiatis et al.\textsuperscript{29} Note that if \( t_1 \) and \( t_2 \) correspond to prefixed dates, it is valid to set \( \tilde{t}_1 = t_2 \).
In some cases, such as when \( t_2 \) corresponds to the time when a prespecified number of events from stage 2 patients is obtained and \( \tilde{t}_1 \) is a prefixed date, it is possible to have \( \tilde{t}_1 > t_2 \). In practice, this is undesirable since stage 2 patients’ follow-up information beyond \( t_2 \) is not included in data analysis. Therefore, in practice, \( \tilde{t}_1 \) should be fixed in such a way that \( \tilde{t}_1 > t_2 \) is very unlikely.
In this section, we have made the assumption that, for \( j (j = 1, \ldots, K) \), \( \hat{\theta}_{1,j} \sim N(\theta_j, \sigma_{1,j}^2) \) and for each \( j \in S \), \( \hat{\theta}_{N_j} \sim N(\theta_j, \sigma_{2,j}^2) \) and \( \hat{\theta}_{2,j} \sim N(\theta_j, \sigma_{2,j}^2) \). We emphasize that these distributional assumptions are conditional on the selection made. For example, while deriving unbiased estimators in Section 3.1, we will adjust for subpopulation selection by taking the expectation over the region of the decision made based on the interim analysis results. Also, since there is no overlap of patients among the partitions, estimates from different partitions are independent. For example, for \( j \neq j' \), \( \hat{\theta}_{1,j} \) is independent of each of \( \hat{\theta}_{1,j'}, \hat{\theta}_{N_{j'}}, \) and \( \hat{\theta}_{2,j'} \).
### 2.3 Selection rules
Estimators proposed in this article can be used to adjust for any subpopulation selection rule based only on the stage 1 observed value for the vector \((\hat{\theta}_{1,1}, \ldots, \hat{\theta}_{1,K})'\). In this section, we review selection rules suggested by various authors. The first is appropriate for the two-stage adaptive threshold enrichment design described in paragraph three of Section 2.1.\textsuperscript{6,7} Let \( r_s \) denote the subpopulation consisting of partitions 1 to \( s \) and let \( p_j' = \sum_{i=1}^{j} P_i (j = 1, \ldots, K) \). To maximize the number of partitions tested in stage 2, we continue with the largest subpopulation \( r_s \) (\( s = 1, \ldots, K \)) such that \( \sum_{i=1}^{j} P_i \hat{\theta}_{1,i}/p'_j \leq b \), where \( b \) is a prespecified value. Note that although \( \sum_{i=1}^{j} P_i \hat{\theta}_{1,i}/p'_j \) is not interpretable, it can give an indication of the treatment effects in the \( s \) partitions included. Figure 3A shows the decision regions for this rule when \( K = 2 \) and \( p_1 = p_2 \). The filled square is an example of a case where both partitions would continue to stage 2, while the filled circle is an example of a case where only partition 1 would continue.
The selection rule just described is appropriate when a monotonic relationship between the biomarker and the treatment effect is expected. However, as described in Section 2.1, sometimes it is not expected that the relationship is monotonic. In such a case, for a binary biomarker, a selection rule should enable the trial to continue to stage 2 with partition 1 (biomarker +ve), partition 2 (biomarker -ve) or both (\( F \)). As described in Section 2.1, this can be extended to \( K > 2 \). A common selection rule in this setting is to decide whether partition \( j (j = 1, \ldots, K) \) continues to stage 2 based on \( \hat{\theta}_{1,j} \) only.\textsuperscript{12} Thus, with a futility boundary, partitions with stage 1 estimates below \( b \) continue to stage 2. The decision regions for this rule when \( K = 2 \) are shown in Figure 3B.
We will demonstrate the estimators developed in Section 3 with the above two selection rules. Other selection rules\textsuperscript{4,5,12,34} are reviewed in the supplementary material. For all selection rules, for some values of \((\theta_1, \ldots, \theta_K)\), even when \( F \) is selected, the naive estimates are biased because of subpopulation selection. The new estimators in Section 3 correct for this bias since they condition on the selection rule, the selected partitions, and the observed data. The estimators also correct for bias appropriately when the selection rule does not reflect the true underlying relationship between biomarker and treatment effect.
FIGURE 3 Decision regions for two selection rules when $K = 2$. The continuous lines are the decision boundaries. The filled circle and square are two possible stage 1 results that lead to selecting partition 1 and $F$, respectively. The edges of the vertical dashed and dotted lines give the bounds for estimating $\theta_1$ that are denoted by $l_1$ (lower bound) and $w_1$ (upper bound). The edges of the horizontal dashed lines give the bounds for estimating $\theta_2$ and are denoted by $l_2$ (lower bound) and $w_2$ (upper bound). A, Adaptive threshold enrichment design. B, Selecting partitions independently.
2.4 Naive estimation
We will consider $\hat{\theta}_{Nj}$ given by expression (1), as the naive point estimator. Note that $\hat{\theta}_{Nj}$ is not simply the estimate based on all data available at the end of the trial because, as described in Section 2.2, it is based on the data where the independent increment is assumed. For the special case of $\bar{t}_1 = t_1$, the bias of $\hat{\theta}_{Nj}$ corresponds to the subpopulation selection bias. The difference in biases for $\hat{\theta}_{Nj}$ computed at $\bar{t}_1 = t_1$ and $\hat{\theta}_{Nj}$ computed at $\bar{t}_1 > t_1$ gives an indication of the bias attributable to the incremental data.
For the naive confidence interval, we assume that for each $j \in S$, the naive estimator $\hat{\theta}_{Nj} \sim N(\theta_j, \sigma^2_{Nj})$. Consequently, for each $j \in S$, the two sided naive confidence interval for $\theta_j$ that splits $\alpha$ equally among the $|S|$ selected partitions is
$$\hat{\theta}_{Nj} \pm Z_{\alpha/(2|S|)} \sigma_{Nj},$$
where $Z_{\alpha/(2|S|)} = \Phi^{-1}(1 - \alpha/(2|S|))$. This naive confidence interval addresses the issue of the independent increments as described in Section 2.2 and adjusts for multiple hypotheses but not the subpopulation selection.
3 BIAS ADJUSTED ESTIMATORS
3.1 New approximately conditionally unbiased point estimator
To adjust for the subpopulation selection, for each $j \in S$, we derive a UMVCUE for $\theta_j$. The UMVCUE is based on the Rao-Blackwell theorem, which was initially proposed in adaptive designs by Cohen and Sackrowitz\(^{18}\) and subsequently extended to several treatment and subpopulation selection rules.\(^{4,6,19-22,35,36}\)
Conditional on the selection made, for each $j \in S$, the estimator $\hat{\theta}_{2j}$ provides an unbiased estimator for $\theta_j$ by the Rao-Blackwell theorem, the UMVCUE is the expected value of this estimator given the sufficient and complete statistic. Here, the UMVCUE is conditional on the subpopulation selection rule used, the partitions selected to continue to stage 2 and the observed data. This is reflected in the UMVCUE for $\theta_j$ by its expression having terms for the lower and upper bounds for $\hat{\theta}_{1j}$ that are determined based on the selection rule, the selected partitions, and the observed stage 1 data. Since the lower and upper bounds depend on the stage 1 data, they are random variables which we denote by $L_j$ and $W_j$.\(^{18,32,35,36}\)
with observed values $l_j$ and $w_j$, respectively. Let $p'_j = \sum_{i=1}^j p_i$ $(j = 1, \ldots, K)$. For the adaptive threshold enrichment design selection rule in Section 2.3, when a subpopulation consisting of $s$ $(s = 1, \ldots, K)$ partitions is selected, for each $j \in \{1, \ldots, s\} = S$, $w_j = \left( p'_j b - \sum_{i=1}^{s} p_i \hat{\theta}_{1,i} \right) / p_j$ (the term $\sum_{i=1}^{s} p_i \hat{\theta}_{1,i}$ is set to zero when $s = 1$) and
$$l_j = \max \left\{ \frac{p'_{j+1} b - \sum_{i=j}^{s+1} p_i \hat{\theta}_{1,i}}{p_j}, \frac{p'_{j+2} b - \sum_{i=j}^{s+2} p_i \hat{\theta}_{1,i}}{p_j}, \ldots, \frac{p'_K b - \sum_{i=j}^{K} p_i \hat{\theta}_{1,i}}{p_j} \right\},$$
with $l_j$ set to be $-\infty$ if all partitions are selected. For the selection rule of continuing to stage 2 with any partition whose treatment effect is $\leq b$ (second rule in Section 2.3), for all $j \in S$, $l_j = -\infty$ and $w_j = b$. For $K = 2$, the points corresponding to the expressions for $l_j$ and $w_j$ are illustrated in Figure 3. For estimating $\theta_1$, $l_1$ and $w_1$ are the lower and upper edges of the vertical dashed and dotted lines that go through the stage 1 estimates, respectively. For estimating $\theta_2$, $l_2$ and $w_2$ are the right and left hand edges of the horizontal lines that go through the stage 1 estimates, respectively. The details of how the bounds for the adaptive threshold enrichment design selection rule and some other selection rules suggested in literature are derived are given in the supplementary material.
Let $Q_S$ denote the event of the observed data and $S$. Suppose that $|S| = s$ and that the $s$ selected partitions are indexed $1, \ldots, s$. Define $\hat{\theta}_{N_j} = (\sigma_{2j}/\sigma_{1j}) \hat{\theta}_{1,j} + (\sigma_{1j}/\sigma_{2j}) \hat{\theta}_{2,j}$, the vector $(\hat{\theta}_{N_1}, \hat{\theta}_{1,2}, \ldots, \hat{\theta}_{1,K}, \hat{\theta}_{2,2}, \ldots, \hat{\theta}_{2,s}, Q_S)$ is sufficient and complete for estimating $\theta_1$. Therefore, the UMVCUE for $\theta_1$ is the expression for $E(\hat{\theta}_{2,1}|\hat{\theta}_{N_1}, \hat{\theta}_{1,2}, \ldots, \hat{\theta}_{1,K}, \hat{\theta}_{2,2}, \ldots, \hat{\theta}_{2,s}, Q_S)$. The expression is obtained by deriving the conditional density $f_{Q_S}(\hat{\theta}_{2,1}|\hat{\theta}_{N_1}, \hat{\theta}_{1,2}, \ldots, \hat{\theta}_{1,K}, \hat{\theta}_{2,2}, \ldots, \hat{\theta}_{2,s})$ with $E(\hat{\theta}_{2,1}|\hat{\theta}_{N_1}, \hat{\theta}_{1,2}, \ldots, \hat{\theta}_{1,K}, \hat{\theta}_{2,2}, \ldots, \hat{\theta}_{2,s}, Q_S)$ obtained by deriving the expression for $\int \hat{\theta}_{2,1} f_{Q_S}(\hat{\theta}_{2,1}|\hat{\theta}_{N_1}, \hat{\theta}_{1,2}, \ldots, \hat{\theta}_{1,K}, \hat{\theta}_{2,2}, \ldots, \hat{\theta}_{2,s}) d\theta_{2,1}$. The UMVCUEs for the effects in the other selected partitions are obtained similarly. We show in the supplementary material that for each $j \in S$, the UMVCUE for $\theta_j$ is given by
$$\hat{\theta}_{U_j} = \hat{\theta}_{N_j} - \frac{\sigma_{2j}^2}{\sigma_{1j}^2} \frac{\phi(g(L_j)) - \phi(g(W_j))}{\sqrt{\sigma_{1j}^2 + \sigma_{2j}^2} \Phi(g(L_j)) - \Phi(g(W_j))},$$
where $g(x) = \sqrt{\frac{\sigma_{1j}^2 + \sigma_{2j}^2}{\sigma_{1j}^2}} (\hat{\theta}_{N_j} - x)$, and $\phi$ and $\Phi$ denote the density and distribution functions of a standard normal, respectively.
For the special case of $l_1 = t_1$, $\hat{\theta}_{U_j}$ is an asymptotic UMVCUE for $\theta_j$. However, when patients without events at $t_1$ are followed in stage 2, that is, $l_1 > t_1$, $\hat{\theta}_{U_j}$ is an approximate asymptotic UMVCUE for $\theta_j$ meaning in some scenarios it may have small biases because as described in Section 2.2, the independent structure which is assumed in the derivation of $\hat{\theta}_{U_j}$ is an approximate assumption. Like any estimator based on the asymptotic score statistic distribution(s), $\hat{\theta}_{U_j}$ may be biased because score statistic distributions, such as those summarized in the last paragraph of Section 2, are asymptotic distributions that assume the value of $\theta_j$ is close to zero, that is, a small effect size. These aspects will be explored further in a simulation study in Section 5.
### 3.2 A new method for constructing confidence intervals
In this section, we construct new simultaneous confidence intervals that are based on the duality between hypothesis testing and confidence intervals. To account for the stage 1 patients that are followed further in stage 2 because they did not have an event at the interim analysis, we propose hypothesis testing using the strategy suggested by Jenkins et al. They combine evidence from stages 1 and 2 using a $P$-value combination function and adjust for multiple hypotheses by the closure principle (CP). Let $H_j$ $(j = 1, \ldots, K)$ denote the elementary null hypothesis $\theta_j = 0$ and $H_I$ $(I \subseteq \{1, \ldots, K\})$ the intersection null hypothesis $\cap_{\theta_j \in I} H_j$, where for simplicity, for example, we write $H_{1,2}$ for $H_{\{1,2\}}$. We derive the expressions for the lower and upper bounds separately based on one-sided tests. For the lower bounds, the alternative hypothesis for $H_I$ $(I \subseteq \{1, \ldots, K\})$ is that for at least one $j \in I$, $\theta_j > 0$ and we denote the corresponding one-sided $P$-value for $H_I$ obtained using data from patients recruited in stage $k$ $(k = 1, 2)$ only by $p_{k,I}^+$. Note that $\theta_j > 0$ indicates that the experimental treatment is inferior in partition $j$ and that a lower bound below 0 is not sufficient to conclude that the experimental treatment is significantly beneficial. The $P$-value $p_{k,I}^+$ $(k = 1, 2)$ is obtained using stage $k$ patients only since the $P$-value
combination functions assume that \( p_{1j}^+ \) and \( p_{2j}^+ \) are independent. Therefore, \( p_{2j}^+ \) is computed by separately analysing the patients whose survival times correspond to the wholly dotted lines in Figure 2. For the selected partitions, while computing \( p_{1j}^+ \) using the stage 1 patients, so as to include the incremental data in hypothesis testing, following Jenkins et al, the survival time and status are determined at time \( \bar{t}_1 \). Consequently, the survival times for patients with events at the interim analysis correspond to the continuous lines in Figure 2, while the survival times for patients without events at the interim analysis correspond to the lines consisting of continuous and dashed segments. While computing \( p_{1j}^+ \), if the patients in the dropped partitions are followed after the interim analysis, as for the selected partitions, their survival times and status are determined at \( \bar{t}_1 \). However, if the patients in the dropped partitions are not followed after the interim analysis, their survival times and status are determined at \( t_1 \) in the computation of \( p_{1j}^+ \), so that their survival times correspond to the continuous line segments in Figure 2. We described in Section 2.2 how to decide whether to follow up to \( t_1 \) stage 1 patients from dropped partitions. For stage \( k (k = 1, 2) \) patients, since there is no overlap in the data used to obtain \( p_{k}^+ \) and the data used to compute \( p_{k,i}^+ \) (\( i \neq i' \)), we recommend the Šidak adjusted \( P \)-value given by \( p_{k,j}^+ = 1 - (1 - \min_{i \neq i'} p_{k,i}^+)^{|I|} \) because its type I error rate is exact. Using the weighted inverse normal method\(^{38} \) to combine the evidence from the two stages, the combined \( P \)-value \( C(p_{1j}^+, p_{2j}^+) = 1 - \Phi(\omega_1 \Phi^{-1}(1 - p_{1j}^+) + \omega_2 \Phi^{-1}(1 - p_{2j}^+)) \), where \( \omega_1 \) and \( \omega_2 \) are prespecified weights such that \( \omega_1^2 + \omega_2^2 = 1 \). We take \( \omega_k (k = 1, 2) \) to be the square root of the proportion of the prespecified total number of events from stage \( k \) patients. To control the type I error rate by the CP, it is concluded that \( \theta_j > 0 (j = 1, \ldots, K) \) if all hypotheses \( H_j (I \subseteq (1, \ldots, K), \text{with } j \in I \) are rejected or equivalently if the adjusted \( P \)-value \( \max_I C(p_{1j}^+, p_{2j}^+) \leq \alpha/2 \), with \( j \in I \). To allow for the dropped partitions, the stage 2 \( P \)-value \( p_{2j}^+ \) is obtained using the test for \( H_{I \cap S} \), with \( p_{2j}^+ \) set to be 1 if \( I \cap S = \emptyset \).
Stage 1 pairwise \( P \)-values \( p_{1j}^+ (j = 1, \ldots, K) \) that are required in the expression for the Šidak adjusted \( P \)-value, \( p_{1j}^+ \), can be obtained using statistics similar to those in Section 2.2. Let \( \tilde{S}_{1,j} \) and \( \tilde{V}_{1,j} (j = 1, \ldots, K) \) denote the score statistic and Fisher information for partition \( j \) stage 1 patients with survival time and status evaluated at \( \bar{t}_1 \) if partition \( j \) patients without events at \( t_1 \) are followed in stage 2 until \( \bar{t}_1 \) and at \( t_1 \) if partition \( j \) patients without events at \( t_1 \) are not followed in stage 2. Defining \( \tilde{\theta}_{1j} = \tilde{S}_{1,j}/\tilde{V}_{1,j} \) and \( \tilde{\sigma}_{1j}^2 = \tilde{V}_{1,j}^{-1}p_{1j}^+ = 1 - \Phi(\tilde{\theta}_{1j}/\tilde{\sigma}_{1j}) \). Similarly, for each \( j \in S \), stage 2 pairwise \( P \)-value \( p_{2j}^+ \) that is required in the expression for the Šidak adjusted \( P \)-value, \( p_{2j}^+ \), is computed using the score statistic and Fisher information obtained by separately analyzing the patients corresponding to the dotted lines in Figure 2.
Magirr et al\(^{23} \) developed simultaneous confidence intervals following two-stage adaptive clinical trials with treatment selection that are based on the duality between confidence intervals and hypothesis testing. They assume a hypothesis testing approach that is similar to that we have proposed above. Following their work, we give simultaneous confidence intervals following two-stage adaptive clinical trials with subpopulation selection that are compatible with the above testing procedure. Magirr et al describe the theory of how to obtain a confidence region with the correct coverage and subsequently how to extract simultaneous confidence intervals. We do not repeat the theory and only focus on giving the expressions for the confidence intervals in our setting. We give the expressions assuming that the Šidak adjustment is used for the intersection hypotheses. The expressions are functions of the \( P \)-values for the generalized null hypotheses. Let \( H_I(\theta^*) \) denote the generalized null hypothesis \( \theta_j = \theta_j^* \) and for \( I \subseteq (1, \ldots, K) \), we write \( H_I(\theta^*) \) for the generalized intersection hypothesis \( \cap_{i \in I} H_i(\theta_i^*) \). For an observed stage \( k (k = 1, 2) \) dataset \( x_k \), the generalized \( P \)-value for \( H_I \) is \( p_{k,j}(\theta^*, x_k) \) and is computed as \( \text{Prob}(X_k \geq x_k; \theta^*) \), where \( \theta^* = (\theta_1^*, \ldots, \theta_k^*) \). The combined \( P \)-value for \( H_I(\theta^*) \) is \( C(p_{1j}^+(\theta^*, x_1), p_{2j}^+(\theta^*, x_2)) = 1 - \Phi(\omega_1 \Phi^{-1}(1 - p_{1,j}^+(\theta^*, x_1)) + \omega_2 \Phi^{-1}(1 - p_{2,j}^+(\theta^*, x_2))) \). The Šidak adjusted generalized \( P \)-value, \( p_{k,j}(\theta^*, x_k) (k = 1, 2) \), is given by \( 1 - (1 - \min_{i \neq i'} p_{k,i}(\theta^*, x_k))^{||I|} \), where \( p_{k,i}(\theta^*, x_k) \) is the generalized pairwise \( P \)-value. As an example, \( p_{1j}(\theta^*, x_1) (j = 1, \ldots, K) \) is given by \( 1 - \Phi((\tilde{\theta}_{1j} - \theta_j^*)/\tilde{\sigma}_{1j}) \).
Let \( p_{M}^+ \) be the maximum stage 1 \( P \)-value for all the intersection hypotheses \( H_l (I \subseteq (1, \ldots, K) \setminus S) \). For example if \( K = 4 \) and \( S = \{1, 2\} \), \( p_{M}^+ = \max[p_{134}^+, p_{13}^+ + p_{14}^+ + p_{34}^+] \). If all partitions are selected to continue to stage 2 so that \( \{1, \ldots, K\} \setminus S = \emptyset \), \( p_{M}^+ \) is set equal to 0. If at the end of stage 2 it is concluded that \( \theta_j > 0 \) for all \( j \in S \), then for each \( j \in S \), the lower bound for the effect in partition \( j \) is given by
\[
\theta_{j,S} = \max \left( 0, \sup \left\{ v : C(\max[p_{M}^+, 1 - (1 - p_{1j}(v, x_1))^2], 1 - (1 - p_{2j}^+(v, x_2)))^{||I|} \leq \alpha/2 \right\} \right).
\]
Note that \( p_{k,j}^+(v, x_k) (k = 1, 2) \) is a generalized pairwise \( P \)-value for \( H_j \) and so it is computationally quick to find the root.
If at the end of the trial, for some \( j \in S \), it is not concluded that \( \theta_j > 0 \), the expression for the lower bound of the effect in a partition depends on the outcome of the hypothesis testing. For \( j \in S \) where it is concluded that \( \theta_j > 0 \), the lower
bound for \( \theta_j \) is
\[
\theta_{j,L} = 0. \tag{5}
\]
For \( H_I(I \subseteq \{1, \ldots, K\}) \), based on stage \( k (k = 1, 2) \) patients’ data, we define \( p_{k,j} \), \( j = 1, \ldots, K \) as the probability of \( \theta_j \) being greater than or equal to \( \theta_j \) for \( k \) patients. The upper bound for the effect in partition estimates and the adjusted \( P \)-values can be obtained from expression (5), where \( \theta_j \) is a \( K \times 1 \) vector whose \( j \)th entry is \( \theta_j \) and the other entries are zero. For \( I \subseteq \{1, \ldots, K\} \) with \( j \in I \), we define \( \theta_{j,L} = \infty \) if \( C(p_{1,j}^+, p_{2,j}^+) < \alpha/2 \) and \( \theta_{j,U} = \sup \{ v : C(p_{2,j}^+, p_{2,j}^+) \leq \alpha/2 \} \) otherwise. For \( j \in S \) where it is not concluded that \( \theta_j > 0 \), the lower bound for \( \theta_j \) is
\[
\theta_{j,L} = \min_{I \subseteq \{1, \ldots, K\}} \{ \theta_{j,L} \}. \tag{6}
\]
Note that in this case where at the end of the trial, for some \( j \in S \), it is not concluded that \( \theta_j > 0 \), the confidence intervals for the effects in the partitions where it is concluded that the log HRs are greater than 0 are not informative. This is because from expression (5), the lower bounds for those partitions are fixed to be 0 regardless of the values of the point estimates and the adjusted \( P \)-values. This is a drawback of the method.\(^\text{23}\) We emphasize that the lower bounds obtained using expression (6) are informative and those obtained using expression (4) would be expected to be informative most of the time. So non-informative lower bounds are mostly obtained when more than one partition is selected to continue to stage 2 and it is concluded that the log HR in at least one partition is not greater than 0 (the lower bounds in such partitions are informative) and it is concluded that the log HR in at least one partition is greater than 0 (the lower bounds for such partitions are set to be 0 and hence non-informative).
To derive the upper bounds, the alternative hypothesis for \( H_I(I \subseteq \{1, \ldots, K\}) \) is that for at least one \( j \in I \), \( \theta_j < 0 \). Note that, when the upper bound is less than 0, then the experimental treatment is significantly better. Let \( \delta_{j} = -\theta_j \) and \( \delta_{k,j} = -\hat{\theta}_{k,j} \), the stage 1 “conventional” and generalized \( P \)-values in this case are \( p_{1,j} = \Phi(\hat{\theta}_{1,j}/\hat{\sigma}_{1,j}) = 1 - \Phi(\hat{\delta}_{1,j}/\hat{\sigma}_{1,j}) \) and \( p_{2,j} = \Phi((\hat{\theta}_{1,j} - \hat{\theta}_j)/\hat{\sigma}_{1,j}) = 1 - \Phi((\hat{\delta}_{1,j} - \hat{\delta}_j)/\hat{\sigma}_{1,j}) \), respectively. Note that \( p_{2,j} \) is the \( P \)-value for the hypothesis test \( \theta_j = 0 \) against \( \theta_j < 0 \) as well as the hypothesis test \( \delta_j = 0 \) against \( \delta_j > 0 \), where \( \hat{\delta}_j = -\hat{\theta}_j \). Therefore, as we do in Sections 4 and 5, the upper bound for the effect in partition \( j \), \( \theta_{j,U} \), can be obtained as follows. Change the signs of the point estimates, for example, changing \( \hat{\theta}_{1,j} \) to \(-\hat{\theta}_{1,j}\), and then obtain the lower bound, \( \delta_{j,L} \), for \( \delta_j = -\theta_j \) as described for \( \theta_j \) above. The upper bound for the effect in partition \( j \) is \( \theta_{j,U} = -\delta_{j,L} \). As with the lower bounds, the upper bounds can be non-informative.
# 4 | Example
To illustrate how to compute the various estimates, we construct a two-stage enrichment trial using data from a single-stage trial that compared intravenous methotrexate (C-MTX) and high-dose methotrexate (HDMTX) in the treatment of T-cell acute lymphoblastic leukemia (T-ALL) in children.\(^\text{10}\) The numbers of patients allocated to C-MTX and HDMTX were 519 and 512, respectively. Based on the clinical features, the patients were categorized as low risk (LRI), intermediate risk (IRI), and high risk (HRI). The analysis included assessing separate effects in 109 LRI, 707 IRI, and 215 HRII patients and so we take the risk level as the biomarker. So as not to have too few events in each stage of the constructed example, we use disease free survival (DFS). The conclusion from the trial was that C-MTX is superior to HDMTX. The observed advantage of C-MTX over HDMTX increased with risk level and was statistically significant for intermediate and high risk levels. Although the aim of the trial was to assess which of C-MTX and HDMTX is superior, for the constructed example, we take HDMTX and C-MTX to be the control and experimental treatment, respectively. Also, because of the few LRI patients and events from them, for the constructed example, we combine LRI and IRI patients into one category. Therefore, we have two partitions, one consisting of the HRI patients and the other consisting of the LRI and IRI (LRI/IRI) patients.
We take the futility boundary \( b = 0 \). Based on the observed monotonic relationship between treatment effect and risk level on the initial categorization (LRI, IRI, and HRI), the adaptive threshold enrichment design could be used. For this design, based on Figure 1, partitions 1 and 2 correspond to HRI and LRI/IRI patients, respectively. If for this design we use the first selection rule in Section 2.3, we need to specify the prevalences of the partitions, which we have assumed to be known. In this illustrative example, we use the observed prevalences in the entire trial (\( p_1 = 0.2 \) and \( p_2 = 0.8 \)). Since we do not pool estimates from multiple partitions, the estimates remain valid for any set of prevalences. However, if better guesses of the prevalences are available, for example, from historical data, they could be used as they influence the
probability of selecting the desired partitions. The selection rule of continuing with any
partition whose stage 1 estimate is \( \leq b \) can also be used with this example. We will
demonstrate how to compute estimates based on both selection rules.
Patients were recruited in 2720 days, the last follow-up was 3644 days after recruitment started, and there were 122
events. We assume that the interim analysis was conducted after 60 events (21 in partition 1 and 39 in partition 2), which
corresponds to 2176 days after recruitment started and when 80% of the patients (stage 1 patients) had been recruited.
The number of events from the 20% of the patients who were recruited after the interim analysis (stage 2 patients) is
31 (13 in partition 1 and 18 in partition 2). The number of events from stage 1 patients who did not have events at the
interim analysis was 31 (11 in partition 1 and 20 in partition 2). The last follow-up of stage 2 patients was 3644 days from
when the trial first recruited. We assume that it was prespecified that the follow-up of stage 2 patients will stop after
31 events were observed from them and that this happened 3644 days from when recruitment started. This assumption
enables us to describe how \( t_i \) that is different from \( t_2 \) can be prespecified, and the consequences of this. We assume that
it was prespecified that stage 1 patients without events at the interim analysis will be followed for 3.5 years after the
interim analysis, which corresponds to 3455 days from when recruitment started. This resulted in not including in the
final analysis one DFS event from stage 1 patients who did not have events at \( t_1 \). Note that \( t_1, t_1, \) and \( t_2 \) correspond to
calendar dates 2176, 3455, and 3644 days from the date of first enrolment, respectively.
Details of formatting the data and the R\(^{39}\) code used to analyze them are provided in the supplementary material.
The estimates are summarized in Table 1. The stage 1 estimates in partitions 1 and 2 are \( \hat{\theta}_{1,1} = -0.904 \) and \( \hat{\theta}_{1,2} = -0.419 \),
respectively. For the adaptive threshold enrichment design selection rule, since \( (p_1 \hat{\theta}_{1,1} + p_2 \hat{\theta}_{1,2}) < -0.516 < b = 0 \), both
partitions \( (F) \) are selected to continue to stage 2. The naive estimates for partitions 1 and 2 are \( \hat{\theta}_{N,1} = -0.746 \) and \( \hat{\theta}_{N,2} = -0.362 \), respectively. Since \( F \) is selected, from Section 3.1, \( l_1 = l_2 = -\infty \), \( w_1 = \left( \sum_{i=1}^{2} p_i \hat{\theta}_{1,i} \right) / p_1 = (b - p_2 \hat{\theta}_{1,2}) / p_1 = (0 - [0.8 \times -0.419]) / 0.2 = 1.676 \). Similarly, \( w_2 = (b - p_1 \hat{\theta}_{1,1}) / p_2 = 0.226 \). For example, for partition 1, substituting \( \hat{\theta}_{N,1}, \sigma_{1,i}^2, \sigma_{2,i}^2, L_1 \) and \( W_1 \) in Equation (3) with \( \hat{\theta}_{N,1} = -0.746, \sigma_{1,1}^2 = 0.191, \sigma_{2,1}^2 = 0.167, l_1 = -\infty \), and \( w_1 = 1.676 \), respectively, the
UMVUCUE for the effect in partition 1 is \( \hat{\theta}_{U,1} = -0.737 \). Similarly, the UMVUCUE for the effect in partition 2 is \( \hat{\theta}_{U,2} = -0.359 \). The
UMVUCUEs are closer to zero than the corresponding naive estimates. With the selection rule of continuing with any
partition whose stage 1 estimate \( \leq b (= 0) \), \( F \) is selected since \( \hat{\theta}_{1,1} = -0.902 < 0 \) and \( \hat{\theta}_{1,2} = -0.419 < 0 \). From Section 3.1, \( l_1 = l_2 = -\infty \) and \( w_1 = w_2 = b = 0 \). All the other quantities to substitute in Equation (3) are the same as for the adaptive
threshold rule. The UMVUCUEs for the rule of continuing with any partition whose the observed stage 1 effect is \( \leq 0 \)
(independently selecting partitions) are closer to zero (\( \hat{\theta}_{U,1} = -0.631 \) and \( \hat{\theta}_{U,2} = -0.335 \)) than the corresponding naive
estimates and the UMVUCUEs for the adaptive threshold design. This indicates that the naive estimates may have bigger biases when a partition is selected independent of the observed effects in the other partitions compared to when partitions are
selected using the adaptive threshold design selection rule.
The naive and duality confidence intervals are conditional on the number of partitions selected and not the selection
rule used to select the partitions. Hence, since \( F \) was selected with the above two selection rules, the naive and duality
confidence intervals are the same for the two selection rules. For the naive confidence interval, for \( \alpha = 0.05 \), \( z_{\alpha/2} \)
in expression (2) is \( z_{0.05/2} = 2.241 \). The values for \( \hat{\theta}_{N} \) and \( \sigma_{N} (j = 1, 2) \) are given in Table 1. Consequently, the naive
confidence intervals for the effects in partitions 1 and 2 are \( (-1.415, -0.077) \) and \( (-0.876, 0.153) \), respectively. For the
duality confidence intervals, we take the weights \( \omega_1 = \sqrt{0.75} \) and \( \omega_2 = \sqrt{0.25} \). These are approximately proportional to
the number of events from stages 1 and 2 patients, which is optimal in combining stages 1 and 2 evidence.\(^{38}\) This assumes that, in advance, we could tell how many events will be observed from patients recruited in each stage. In practice, it may
not be possible to specify optimal weights. Since there are two partitions, the null hypotheses tested are \( H_1 (\theta_1 = 0), H_2 (\theta_2 = 0) \), and \( H_{1,2} (\theta_1 = \theta_2 = 0) \). For the lower bound, the alternative hypothesis for \( H_j (j = 1, 2) \) is \( \theta_j > 0 \), while the alternative
| TABLE 1 | Summary of the estimates from the constructed example |
| --- | --- |
| Stage 1a | All dataa |
| Increment* | UMVCUE (\( \hat{\theta}_{U} \))a |
| Confidence intervals | | |
| \( \hat{\theta}_{1,1} (\sigma_{1,i}^2) \) | \( \hat{\theta}_{N,1} (\sigma_{N,i}^2) \) | \( \hat{\theta}_{1,2} (\sigma_{1,i}^2) \) | ATb | INDc | Naive | Duality |
| Partition 1 | \(-0.902 (0.191)\) | \(-0.746 (0.089)\) | \(-0.609 (0.167)\) | \(-0.737 (0.631)\) | \(-1.415, -0.077)\) | \(-1.499, 0.000)\) |
| Partition 2 | \(-0.419 (0.103)\) | \(-0.362 (0.053)\) | \(-0.301 (0.108)\) | \(-0.359 (0.335)\) | \(-0.876, 0.153)\) | \(-0.911, 0.093)\) |
---
*a* \( j = 1 \) for partition 1 and \( j = 2 \) for partition 2.
*b* AT = Adaptive threshold design.
*c* IND = Independently selecting partitions.
hypothesis for $H_{[1,2]}$ is $\theta_1 > 0$ or $\theta_2 > 0$. The stagewise and the combined $P$-values are given in the supplementary material (Figure S2). The adjusted $P$-values for partitions 1 and 2 are both equal to 0.998 so that we do not conclude the effects are greater than 0. Therefore, to get the lower bounds of the effects in both partitions, we use expression (6) giving the lower bounds for the effects in partitions 1 and 2 as $-1.499$ and $-0.911$, respectively. For the upper bound, the alternative hypothesis for $H_j (j = 1, 2)$ is $\theta_j < 0$, while the alternative hypothesis for $H_{[1,2]}$ is $\theta_1 < 0$ or $\theta_2 < 0$. The stagewise and the combined $P$-values are given in the supplementary material (Figure S3). The adjusted $P$-values for partitions 1 and 2 are 0.0179 and 0.0601, respectively, so that the conclusion is that the log HR in partition 1 is less than 0, while we do not conclude that the log HR in partition 2 is less than 0. Hence, the confidence interval for the effect in partition 1 is not informative with upper bound fixed to be 0 by expression (5). When the duality confidence interval upper bound is not informative, in Section 6, we propose using the naive upper bound to make a decision on the treatment effect. For the upper bound for the effect in partition 2, we use expression (6) and the last paragraph in Section 3.2 to obtain 0.093.
To assess the impact of a bigger trial and to demonstrate how to use expression (4) to compute duality confidence intervals' limits, we combined the above data with a bootstrap sample with the same number of patients. The proportion of events at the interim analysis is the same. The results are in the supplementary material (Table S2 and Section 5.3). The bias corrections for some of the naive estimates are smaller. This may be attributed to more precise stage 1 estimates, which may indicate the treatment effects are less than 0 and hence less correction for the futility rule. Also, the log HRs in both partitions are concluded to be less than 0 and so the duality confidence intervals for the effects in the two partitions are informative.
5 | SIMULATION STUDY
5.1 | The simulation study setting
For data generation, we assumed the Weibull distribution with the hazard function for death for treatment $i$ ($i = C, E$) in partition $j$ ($j = 1, \ldots, K$) parameterized as
$$h_j(t) = \lambda_j \gamma_j t^{\gamma_j - 1},$$
where $t$ is time (in days for the simulation study), and $\lambda_j$ and $\gamma_j$ are the scale and shape parameters, respectively. In all simulation scenarios, we considered the case of $\gamma_j = \gamma$. For two scenarios where the HRs in partitions are the same, but in one scenario the biomarker is prognostic while in the other the biomarker is not prognostic, the properties of the new estimators are expected to be the same. Therefore, in all simulation scenarios, we only considered the case of a biomarker that is predictive but not prognostic taking the scale parameter for the control group in all partitions to be $\lambda_C = \lambda_C$. In most simulations, we will take $\gamma = 0.5$ but in order to assess the effect of the shape parameter, we will compare some results for $\gamma = 0.5$ with the cases of $\gamma = 1$ (exponential distribution) and $\gamma = 1.5$.
The log HR in partition $j$ ($j = 1, \ldots, K$) is given by $\theta_j = \ln \left( \frac{\lambda_E}{\lambda_C} \right)$. In most simulations, we considered four partitions of equal prevalences (quartiles) and three configurations for $(\theta_1, \theta_2, \theta_3, \theta_4)'$, which are $(0.0198, 0.0198, 0.0198, 0.0198)', (-0.2231, -0.0953, 0.3364, 0.4055)',$ and $(-0.4055, -0.2231, -0.0953, 0)'$. Log HRs equal to $-0.4055$, $-0.2231$, $-0.0953$, 0, 0.0198, 0.3364, and 0.4055 correspond to HRs equal to 0.6667, 0.80, 0.9091, 1, 1.02, 1.4, and 1.5, respectively. In all simulations, we set the futility boundary $b = 0$.
Sample sizes in the simulations are selected such that a power of approximately 80% would be obtained in a single-stage one-year trial with a HR of 0.8. This corresponds to a setting typical of many oncology trials. The hazard function parameters and the required number of deaths and patients are given in Table 2. For the control arm, we set the scale parameters so that the median survival time is 400 days, with the scale parameters for the experimental arm chosen so that $\lambda_E/\lambda_C = 0.8$. For 80% power, the required number of deaths is 630 in all scenarios, while the required numbers of patients are 2060, 2600, and 3300 for $\gamma = 0.5$, $\gamma = 1.0$, and $\gamma = 1.5$, respectively. Informed by these sample sizes for one-year single-stage trials, we considered two-stage trials with an interim analysis after 300 deaths and with stage 2 patients followed until 300 deaths are observed from them. For $\gamma = 0.5$, $\gamma = 1$, and $\gamma = 1.5$, we assumed, respectively, 2200, 2800, and 3400 patients can be recruited uniformly over two years.
We will assess the properties of the various estimators for the case where stage 1 patients without events at $t_1$ are not followed in stage 2, that is, $t_2 = t_1$, and for the case where they are followed in stage 2 up to time $t_1 > t_1$, which corresponds
Simulation results for the adaptive threshold enrichment design
For both estimator is underestimating the true effect size. We first describe the biases and RMSEs for the naive estimator \( \hat{\theta} \). A positive bias indicates that the estimator is overestimating the true effect size while a negative bias indicates that the estimator is underestimating the true effect size. We first describe the biases and RMSEs for the naive estimator \( \hat{\theta}_N \). For both \( \hat{\theta}_N \) and \( \hat{\theta}_N \), \( \hat{\theta}_N \) can be positively or negatively biased. The biases for \( \hat{\theta}_N \) are smaller when \( \hat{\theta}_N > \theta_1 \) than when \( \hat{\theta}_1 = \theta_1 \). Hence, the incremental data induce negative bias when subpopulation selection bias is positive and the
| True log hazard ratios | Ideal selection | Distribution | Partitions selected |
|-----------------------------|-----------------|--------------|--------------------|
| (Configuration 1) | Stop | \( \gamma = 0.5 \) | \( 1, 2, 3, and 4 \) | \( 1, 2, and 3 \) | \( 1 \) | \( 2 \) | \( 3 \) | \( 4 \) |
| \( \theta_1 = \theta_2 = \theta_3 = \theta_4 = 0.0198 \) | \( \gamma = 0.5 \) | 0.4329 | 0.0875 | 0.0764 | 0.0812 | 0.3219 |
| \( \gamma = 1.0 \) | 0.4306 | 0.0866 | 0.0752 | 0.0841 | 0.3235 |
| \( \gamma = 1.5 \) | 0.4308 | 0.0872 | 0.0766 | 0.0834 | 0.3220 |
The scenarios we have described in this section cover a subset of the simulations undertaken. Other scenarios are considered in the last paragraph of Section 5.2 and in Section 5.3. For each scenario, we simulated 100,000 trials. For each simulated trial, for each selected partition, we computed two naive estimates corresponding to \( \hat{\theta}_1 = \theta_1 \) and \( \hat{\theta}_1 > \theta_1 \) and similarly two UMVCUE estimates. We also computed the naive confidence interval and the duality confidence interval.
5.2 Simulation results for the adaptive threshold enrichment design
We first consider the case of selecting partitions to continue to stage 2 using the adaptive threshold enrichment design selection rule described in Section 2.3. Table 3 shows the simulated probabilities of selecting different partitions under different settings. The probabilities for \( \gamma = 0.5 \), \( \gamma = 1.0 \), and \( \gamma = 1.5 \) are similar. For the first two configurations, the probabilities of making the ideal decisions (shown in bold in Table 3) are relatively small (32% and 34%, respectively). The naive estimators have more bias when the ideal decision is not made and so the naive estimators would be expected to have large biases when the probability of making the ideal decision is small.
Table 4 shows the simulated biases and root mean square errors (RMSEs) of the point estimators for \( \gamma = 0.5 \). Columns labeled \( \hat{\theta}_1 = \theta_1 \) correspond to when stage 1 patients without events at the interim analysis are not followed after \( \theta_1 \), while columns labeled \( \hat{\theta}_1 > \theta_1 \) correspond to when stage 1 patients without events at the interim analysis are followed until \( \theta_1 \). A positive bias indicates that the estimator is overestimating the true effect size while a negative bias indicates that the estimator is underestimating the true effect size. We first describe the biases and RMSEs for the naive estimator \( \hat{\theta}_N \). For both \( \hat{\theta}_N \) and \( \hat{\theta}_N \), \( \hat{\theta}_N \) can be positively or negatively biased. The biases for \( \hat{\theta}_N \) are smaller when \( \hat{\theta}_N > \theta_1 \) than when \( \hat{\theta}_N = \theta_1 \). Hence, the incremental data induce negative bias when subpopulation selection bias is positive and the
| True log hazard ratios | Ideal selection | Distribution | Partitions selected |
|-----------------------------|-----------------|--------------|--------------------|
| (Configuration 2) | | \( \gamma = 0.5 \) | \( 1, 2, 3, and 4 \) | \( 1, 2, and 3 \) | \( 1 \) | \( 2 \) | \( 3 \) | \( 4 \) |
| \( \theta_1 = 0.4055; \theta_2 = -0.0953; \) | \( \gamma = 0.5 \) | 0.9395 | 0.0323 | 0.0146 | 0.0065 | 0.0070 |
| \( \theta_2 = -0.2231; \theta_4 = 0.0000 \) | \( \gamma = 1.0 \) | 0.9389 | 0.0332 | 0.0140 | 0.0068 | 0.0070 |
| (Configuration 3) | \( \gamma = 1.5 \) | 0.9386 | 0.0334 | 0.0144 | 0.0065 | 0.0071 |
TABLE 2 Sample sizes for 1-year single-stage trials
| Shape parameter \( \gamma \) | Control \( \lambda_C \) | Median days \( \lambda_E \) | Experimental Median days | Required deaths | Required patients |
|------------------------------|------------------------|---------------------------|--------------------------|----------------|------------------|
| 0.5 | \( \ln(2)/20 \) | 400 | \( \ln(2)/25 \) | 625 | 630 | 2060 |
| 1.0 | \( \ln(2)/20^2 \) | 400 | \( \ln(2)/500 \) | 500 | 630 | 2600 |
| 1.5 | \( \ln(2)/20^3 \) | 400 | \( \ln(2)/10^4 \) | 465 | 630 | 3300 |
incremental data induce positive bias when subpopulation selection bias is negative. In all cases, the RMSEs for \( \hat{\theta}_N \) when \( t_1 > t_1 \) are smaller than when \( t_1 = t_1 \). Thus, the naive estimator has better properties when patients without events of interest at the interim analysis are followed further in stage 2. Next, for \( t_1 > t_1 \), we compare the naive estimator \( \hat{\theta}_N \) to the UMVCUE (\( \hat{\theta}_U \)). Estimator \( \hat{\theta}_U \) evaluated when \( t_1 > t_1 \) is slightly biased in some cases but its biases are smaller than those for \( \hat{\theta}_N \) evaluated when \( t_1 > t_1 \), and the differences are big in some cases. Still focusing on when \( t_1 > t_1 \), the RMSEs for \( \hat{\theta}_U \) and \( \hat{\theta}_N \) are close, sometimes with negligible difference so that when \( t_1 > t_1 \), we consider \( \hat{\theta}_U \) to be a better estimator than \( \hat{\theta}_N \) since the two estimators have close RMSEs but the former has smaller biases. The summary so far is that we consider the UMVCUE (\( \hat{\theta}_U \)) when \( t_1 > t_1 \) to be better than the naive estimator (\( \hat{\theta}_N \)) both when \( t_1 > t_1 \) and \( t_1 = t_1 \). Finally, we compare \( \hat{\theta}_U \) when \( t_1 > t_1 \) and when \( t_1 = t_1 \). For \( t_1 = t_1 \), \( \hat{\theta}_U \) is mean unbiased. This is expected since by derivation, when \( t_1 = t_1 \), \( \hat{\theta}_U \) is an asymptotic UMVCUE. Although \( \hat{\theta}_U \) when \( t_1 = t_1 \) is mean unbiased, it has bigger RMSEs than \( \hat{\theta}_U \) when \( t_1 > t_1 \). We consider \( \hat{\theta}_U \) when \( t_1 > t_1 \) to be better than when \( t_1 = t_1 \), since in the former, \( \hat{\theta}_U \) is only slightly biased but has smaller RMSEs. The results for the first row in Table 4 for Scenario 1 (\( \theta_1 = \theta_2 = \theta_3 = \theta_4 = 0.0198 \)), the first two rows for Scenario 2 (\( \theta_1 = -0.2231, \theta_2 = -0.0953, \theta_3 = 0.3365, \theta_4 = 0.4055 \)), and the first row for Scenario 3 (\( \theta_1 = -0.4055, \theta_2 = -0.2231, \theta_3 = -0.0953, \theta_4 = 0 \)) are complemented by Figure 4A-D, respectively. We note that, even in the cases in Table 4 where \( \hat{\theta}_U \) for \( t_1 > t_1 \) seems to have noticeably more bias than when \( t_1 = t_1 \), the median 50% estimates and the maximum values for \( \hat{\theta}_U \) when \( t_1 > t_1 \) are closer to the true value. Hence, the conclusion from Figure 4A-D is the same as that made from Table 4. Thus the summary from Table 4 and Figure 4 is that, for an adaptive trial with subpopulation selection, it is better to follow stage 1 patients without events of interest at the interim analysis up to a prespecified time \( t_1 > t_1 \) in stage 2 and estimate the effects in partitions using the approximate asymptotic UMVCUE. Additionally, we note that for both \( \hat{\theta}_N \) and \( \hat{\theta}_U \), the estimators have smaller RMSEs when \( t_1 > t_1 \) than when \( t_1 = t_1 \). This feature would be expected in all scenarios since for \( t_1 > t_1 \), \( \hat{\theta}_N \) and \( \hat{\theta}_U \) contain additional information collected from stage 1 patients without events of interest at the interim analysis, which asymptotically are approximately an independent increment.
Table 5 summarizes the simultaneous properties for the confidence intervals of the effects in the selected partitions for \( a = 0.05 \). In most scenarios, the naive confidence regions have at least the desired 95% coverage probability. However, there are also several scenarios where they do not. Moreover, the “type I error” rate (non-coverage at upper end, which is defined as the probability that at least one upper bound is less than the true value) seems to be more severe than the violations of general coverage. Consequently, in general, the naive confidence intervals do not have the desired properties. For the duality confidence regions, in all scenarios, as desired, the coverage probabilities for the confidence regions are at least 95%. The confidence regions are not symmetric but the probabilities that at least one upper bound is less than the true value are below the desired 2.5%. However, these probabilities tend to be very small compared to the target 2.5%. This is partly due to the non-informative upper bounds. Hence, although the simultaneous duality confidence intervals have the desired coverage probabilities and type I error rates, they may be non-informative.
Results for other scenarios (\( \gamma = 1, \gamma = 1.5 \), slower recruitment rate, more events from stage 1 patients without events at \( t_1 \), fewer events in a trial and conducting subpopulation earlier in the trial) are given in the supplementary material (Section 7, Tables S4 to S17, and Figures S5 to S11). In all scenarios, we recommend having \( t_1 > t_1 \) and obtaining point estimates using \( \hat{\theta}_U \). Furthermore, we consider the duality confidence regions to have at least the nominal coverage probabilities and the probabilities that at least one upper bound is less than the true value to be less than the target 2.5% but usually very small, which is partly explained by non-informative confidence intervals.
### 5.3 Simulation results for a different selection rule
To assess the characteristics of the various estimators when a different selection rule is used, we performed simulations for the case of continuing with any partition whose stage 1 log hazard ratio estimate is \( \leq 0 \). This corresponds to the second selection rule in Section 2.3, with \( b = 0 \). The other aspects of the simulations are the same as those used to obtain the results in Table 4. The results for the point estimators for the three configurations of \( (\theta_1, \theta_2, \theta_3, \theta_4) \), which are (0.0198, 0.0198, 0.0198, 0.0198)\(^{\top}\), (-0.2231, -0.0953, 0.3364, 0.4055)\(^{\top}\) and (-0.4055, -0.2231, -0.0953, 0)\(^{\top}\) are given in the supplementary material in Tables S18 to S20, respectively. The biases of the naive point estimator \( \hat{\theta}_N \) are positive in all cases. This is because a partition is selected if it has a positive effect. In several scenarios, biases are larger than in the case of the adaptive threshold enrichment design (Results in Section 5.2). When \( t_1 > t_1 \), the UMVCUE \( \hat{\theta}_U \) is slightly biased
**Table 4** Simulated biases and root mean squared errors of the estimators for the log hazard ratios (γ = 0.5)
| Selected partitions (S) | Partition | Simulated bias $\hat{\theta}_{N_j}$ | Root mean squared error $\hat{\theta}_{U_j}$ |
|-------------------------|-----------|---------------------------------------|----------------------------------------------|
| | $\hat{\theta}_1 > t_1$ | $\hat{\theta}_1 = t_1$ | $\hat{\theta}_1 > t_1$ | $\hat{\theta}_1 = t_1$ | $\hat{\theta}_1 > t_1$ | $\hat{\theta}_1 = t_1$ | $\hat{\theta}_1 > t_1$ | $\hat{\theta}_1 = t_1$ |
| All | 1 | 0.0423 | 0.0537 | 0.0142 | 0.0012 | 0.1469 | 0.1653 | 0.1514 | 0.1845 |
| | 2 | 0.0406 | 0.0518 | 0.0126 | $-0.0006$ | 0.1466 | 0.1655 | 0.1513 | 0.1856 |
| | 3 | 0.0422 | 0.0531 | 0.0145 | 0.0012 | 0.1472 | 0.1654 | 0.1516 | 0.1846 |
| | 4 | 0.0419 | 0.0529 | 0.0142 | 0.0010 | 0.1472 | 0.1655 | 0.1515 | 0.1846 |
| 1, 2, and 3 | 1 | 0.0235 | 0.0289 | 0.0101 | 0.0050 | 0.1322 | 0.1455 | 0.1501 | 0.1939 |
| | 2 | 0.0192 | 0.0237 | 0.0039 | $-0.0048$ | 0.1324 | 0.1450 | 0.1508 | 0.1947 |
| | 3 | 0.0221 | 0.0277 | 0.0075 | 0.0013 | 0.1314 | 0.1442 | 0.1502 | 0.1945 |
| 1 and 2 | 1 | 0.0235 | 0.0274 | 0.0074 | 0.0015 | 0.1181 | 0.1268 | 0.1339 | 0.1595 |
| | 2 | 0.0237 | 0.0278 | 0.0079 | 0.0022 | 0.1182 | 0.1266 | 0.1338 | 0.1584 |
| 1 | 1 | 0.0214 | 0.0241 | 0.0028 | $-0.0008$ | 0.0927 | 0.0969 | 0.1043 | 0.1141 |
| 1 and 2 | 1 | $-0.0098$ | $-0.0114$ | $-0.0017$ | 0.1392 | 0.1532 | 0.1552 | 0.1948 |
| | 2 | $-0.0107$ | $-0.0123$ | $-0.0030$ | 0.1276 | 0.1389 | 0.1401 | 0.1712 |
| 1 | 1 | $-0.0128$ | $-0.0138$ | $-0.0008$ | 0.0942 | 0.0983 | 0.1059 | 0.1149 |
| 1 and 2 | 1 | $-0.0671$ | $-0.0805$ | $-0.0245$ | $-0.0014$ | 0.1498 | 0.1658 | 0.1573 | 0.2004 |
| | 2 | $-0.0624$ | $-0.0769$ | $-0.0221$ | 0.1454 | 0.1619 | 0.1519 | 0.1928 |
| | 3 | $-0.0574$ | $-0.0678$ | $-0.0189$ | 0.1396 | 0.1551 | 0.1468 | 0.1860 |
| 1 and 2 | 1 | $-0.0652$ | $-0.0769$ | $-0.0190$ | 0.1348 | 0.1488 | 0.1363 | 0.1613 |
| | 2 | $-0.0611$ | $-0.0730$ | $-0.0167$ | 0.1291 | 0.1414 | 0.1306 | 0.1532 |
| 1 | 1 | $-0.0471$ | $-0.0523$ | $-0.0109$ | $-0.0046$ | 0.1001 | 0.1044 | 0.1007 | 0.1067 |
True log hazard ratios: $\theta_1 = \theta_2 = \theta_3 = \theta_4 = 0.0198$
True log hazard ratios: $\theta_1 = -0.2231$, $\theta_2 = -0.0953$, $\theta_3 = 0.3365$, $\theta_4 = 0.4055$
True log hazard ratios: $\theta_1 = -0.4055$, $\theta_2 = -0.2231$, $\theta_3 = -0.0953$, $\theta_4 = 0$
FIGURE 4 Boxplots for estimates in partition 1 (panels A, B, and D) and partition 2 (panel C) when the full population is selected to continue to stage 2 for Weibull distribution ($\gamma = 0.5$). The horizontal dashed and dotted line corresponds to the true log hazard ratio
in some cases but has smaller RMSE than when $\tilde{t}_1 = t_1$. Hence we recommend having $\tilde{t}_1 > t_1$ and using $\hat{\theta}_{Uj}$ to obtain estimates.
We expect the magnitudes of the biases for the point estimators for most selection rules that have a futility element to fall between the biases for the selection rule used in this section and the adaptive threshold selection rule considered in Section 5.2. This is because the selection rule in this section selects a partition based on the stage 1 observed effect in that partition only, while the adaptive threshold design considers stage 1 observed effects in all partitions and also assumes a relationship between the treatment effect and the biomarker value. Consequently, for most selection rules, we expect having $\tilde{t}_1 > t_1$ and using estimator $\hat{\theta}_{Uj}$ as the best way of obtaining point estimates.
The simultaneous properties of the naive and the duality confidence intervals are summarized in the supplementary material (Table S21). For the two scenarios where the values for $(\theta_1, \theta_2, \theta_3, \theta_4)'$ are $(0.0198, 0.0198, 0.0198, 0.0198)'$ and $(-0.4055, -0.2231, -0.0953, 0)'$, unlike the naive confidence regions, the duality confidence regions have at least 95% coverage and the probabilities that at least one upper bound is less than the true value are less than 2.5%. For the other
TABLE 5 Coverage probability and type I error rate (Weibull distribution, \(\gamma = 0.5\))
| True log hazard ratios | Selected partitions (S) | Coverage (Type I error rate)\(^a\) |
|------------------------|-------------------------|----------------------------------|
| \(\theta_1 = \theta_2 = \theta_3 = \theta_4 = 0.0198\) | All | 94.8 (4.5) |
| | 1, 2, and 3 | 96.1 (3.0) |
| | 1 and 2 | 96.0 (3.1) |
| | 1 | 96.3 (2.9) |
| \(\theta_1 = -0.2231, \theta_2 = -0.0953, \theta_3 = 0.3365, \theta_4 = 0.4055\) | All | 93.0 (6.6) |
| 1, 2, and 3 | 96.0 (3.1) |
| 1 and 2 | 96.3 (1.4) |
| 1 | 96.1 (1.5) |
| \(\theta_1 = -0.4055, \theta_2 = -0.2231, \theta_3 = -0.0953, \theta_4 = 0\) | All | 93.3 (0.3) |
| 1, 2, and 3 | 93.8 (0.7) |
| 1 and 2 | 94.0 (0.9) |
\(^a\) Type I error is the probability that at least one upper bound is less than the true value.
Based on the selection rule used in this section, we also performed simulations to assess the properties of the estimators for the case of bigger treatment effects. The simulated probabilities for \(S = \{1, 2, 3, 4\}\) and \(S = \{1, 2\}\) are 49.8% and 50.1%, respectively. The point estimation results are presented in the supplementary material (Table S22 and Figure S12). Even in scenarios where the selection bias is negligible, the point estimators are slightly negatively biased when the true hazard ratio is < 0.4. We describe the consequence of this finding in Section 6. We attribute the bias to the fact that the asymptotic distributions in Section 2.2 are based on the approximation of Taylor’s expansion of the likelihood function, and the accuracy improves as the effect size gets closer to zero.\(^{27}\) We have also assessed the properties of the confidence intervals for a scenario with big treatment effects and where the probability of having noninformative bounds with the duality confidence intervals is small (results in supplementary material Table S23). For both the naive confidence intervals and the duality confidence intervals, the probabilities that at least one upper bound is below the true value are smaller than 2.5%. As with point estimates, we attribute this to the underestimation of the treatment effects so that consequently the upper bounds are underestimated.
We have used the Rao-Blackwell theorem to derive a point estimator that adjusts for any subpopulation selection rule that is based on stage 1 estimates only in two-stage adaptive trials with time to event data. It is an asymptotic UMVCUE if the patients without events at stage 1 are not followed further in stage 2, while it is an approximate asymptotic UMVCUE if they are followed further in stage 2. When the stage 2 follow up length for stage 1 patients without events is specified before the trial, based on our simulation, the approximate asymptotic UMVCUE performed best. Unlike the case of normally distributed outcomes, compared with the naive estimator, this estimator did not have markedly higher RMSE and in some simulation scenarios, it outperformed the naive estimator in terms of RMSE. With time to event data, it is difficult to explore all factors that influence the properties of the various estimators. However, in our simulations, we considered several factors that may be encountered in real clinical trials and hence we expect the recommendation that the approximate UMVCUE is the best estimator to hold in most settings.
We have also described a new method for constructing simultaneous confidence intervals based on the duality between hypothesis testing and confidence intervals. In simulations, unlike the naive confidence intervals, the confidence regions corresponding to the new confidence intervals had at least the nominal coverage probability and also the probabilities that at least one lower bound was below the true value were acceptable. However, for example, as in the results in Table 1, the new confidence intervals can be non-informative. Focusing on the upper bounds, the non-informative confidence intervals are obtained in partitions where the treatment is concluded effective whenever in at least one selected partition, the treatment is not concluded effective. The probability of this happening depends on aspects such as the true treatment effects in partitions, the interim analysis sample size (events), the overall sample size (events), the selection rule, and the number of partitions. In the simulations, there was a high probability of this happening since most scenarios consisted of partitions where the new treatment is not effective and the futility rule only required stage 1 estimates to indicate the new treatment is as good as the control. More research to develop methods that do not give non-informative confidence intervals, such as extending existing work, is required.
We have assumed that there is no endpoint change between stages 1 and 2, such as using an early endpoint to make subpopulation selection in stage 1. This is appropriate in disease conditions such as pancreatic cancer where survival times are short and hence there is no practical advantage of considering an early endpoint in stage 1 and conditions such as uveal melanoma where an early endpoint does not exist. Increasingly, however, whenever practically feasible, adaptive clinical trials with time to event endpoints as the primary outcome(s) use time to some earlier event or different endpoints that are observed earlier than the primary outcome(s) to make adaptations in stage 1. The UMVCUE developed in this article can be extended by combining the techniques presented here and the techniques that consider using an early endpoint to make an adaptation. For the confidence intervals, the expressions for the new confidence intervals when there is change of endpoint are exactly the same as those in this article since they apply to any selection rule and hence no additional methodology is required. The coverage probabilities are, however, likely to be larger than those in this article since following Kimani et al., we expect the coverage probability to be closest to the nominal coverage if the same endpoint is used for subpopulation selection and estimation.
We have based the methodology on the score statistic. This has the advantage of producing estimates that align with the commonly used log rank test. However, since the asymptotic distribution of the score statistic holds best when the log hazard ratio is close to zero, we observed from the simulation study that for the cases where the true hazard ratio is < 0.4, the proposed approximate UMVCUE underestimates the treatment effect slightly. In real trials, this will have little impact since it is unlikely that the true hazard ratio is as small as 0.4. For example, for the stem cell therapies where relatively big treatment effects are observed, a simple online search of “stem cell therapies hazard ratios” did not identify a publication where the hazard ratio was less than 0.5. Furthermore, if the observed hazard ratio is smaller than 0.4, although possibly biased, the clinical decision that one treatment is superior would be unchanged if the expression for the proposed approximate UMVCUE is used to compute an estimate. An alternative to using the score statistic is to determine the asymptotic distribution of the log hazard ratio from the Cox's proportional hazards model using techniques described by several authors. This would be expected to give similar results to those based on score statistics in most realistic trials where the treatment effects are not expected to be very big. However, in the instance with a very big treatment effect, the hazard ratio estimate based on the Cox's model may be smaller than the one that is based on the score statistic. Also, the Cox model has the advantage of being able to incorporate covariates. Similarly, the upper bounds based on the score statistic distribution were observed to be conservative, which as with approximate UMVCUE will have little impact on trials. Using the Cox model to obtain the duality confidence intervals is straightforward because the stagewise P-values are obtained from stages 1 and 2 patients separately.
Since from our simulation study and previous work, the naive point estimator can have substantial bias, we recommend using the approximate UMVCUE. The expression for the UMVCUE given by (3) is straightforward to implement. Also, the naive confidence intervals do not have the desired properties. Hence, we recommend the confidence intervals obtained by using the bounds of the simultaneous duality confidence intervals that we have developed when they are informative, and using the naive confidence intervals bounds when the bounds of the simultaneous duality confidence intervals are not informative. For example, using the results in Table 1, the confidence interval for the effect in partition 1 would be (−1.499, −0.077). It is straightforward to obtain the naive confidence intervals using expression (2). While demonstrating how to compute the duality confidence intervals in Section 4, we have written R functions to solve expressions (4) and (6) that can be used with any number of partitions. The code that includes the R functions is available in the supplementary material and we have also provided the key estimates to input in the functions to enable reproducing the worked example results.
ACKNOWLEDGEMENTS
UK Medical Research Council (grant number MR/N028309/1) funded this work. The data used in the example are from work that was supported by the National Institutes of Health (NIH/NCI2U10CA180899-06). The contents of the paper are solely the responsibility of the authors and do not necessarily represent the official views of the NIH. We are also grateful to two reviewers for comments that improved the paper.
ORCID
Peter K. Kimani https://orcid.org/0000-0001-8200-3173
REFERENCES
1. Ballman KV. Biomarker: predictive or prognostic? J Clin Oncol. 2015;33:3968-3971.
2. Brannath W, Zuber E, Branson M, et al. Confirmatory adaptive designs with Bayesian decision tools for a targeted therapy in oncology. Stat Med. 2009;28:1445-1463.
3. Jenkins M, Stone A, Jennison C. An adaptive seamless phase II/III design for oncology trials with subpopulation selection using correlated survival endpoints. Pharm Stat. 2011;10:347-356.
4. Kimani PK, Todd S, Stallard N. Estimation after subpopulation selection in adaptive seamless trials. Stat Med. 2015;34:2581-2601.
5. Kunzmann K, Benner L, Kieser M. Point estimation in adaptive enrichment designs. Stat Med. 2017;36(25):3935-3947.
6. Kimani PK, Todd S, Renfro LA, Stallard N. Point estimation following two-stage adaptive threshold enrichment clinical trials. Stat Med. 2018;37:3179-3196.
7. Renfro LA, Coughlin CM, Grothey AM, Sargent DJ. Adaptive randomized phase II design for biomarker threshold selection and independent evaluation. Clin Clin Trials. 2014;3(1):3.
8. Joshi A, Zhang J, Fang L. Statistical design for a confirmatory trial with a continuous predictive biomarker: a case study. Contemp Clin Trials. 2017;63:19-29.
9. Grothey A, Strosberg JR, Renfro LA, et al. A randomized, double-blind, placebo-controlled phase II study of the efficacy and safety of monotherapy ontxizumab (MORA0-004) plus best supportive care in patients with chemotherapy refractory metastatic colorectal cancer. Clin Cancer Res. 2018;24(2):316-325.
10. Winter SS, Dunsmore KP, Devidas M, et al. Improved survival for children and young adults with T-lineage acute lymphoblastic leukemia: results from the children's oncology group AALL0434 methotrexate randomization. J Clin Oncol. 2018;36(29):3104-3115.
11. Rosenblum M. Confidence intervals for the selected population in randomized trials that adapt the population enrolled. Biom J. 2013;55(3):322-340.
12. Li W, Chen C, Lia X, Beckmanb RA. Estimation of treatment effect in two-stage confirmatory oncology trials of personalized medicines. Stat Med. 2017;36:1843-1861.
13. Whitehead J. On the bias of maximum likelihood estimation following a sequential test. Biometrika. 1986;73(3):573-581.
14. Stallard N, Todd S. Point estimates and confidence regions for sequential trials involving selection. J Stat Plann Infer. 2005;135:402-419.
15. Brückner M, Titman A, Jaki T. Estimation in multi-arm two-stage trials with treatment selection and time-to-event endpoint. Stat Med. 2017;36:3137-3153.
16. Hwang JT. Empirical Bayes estimation for the means of the selected populations. Indian J Stat Ser A. 1993;55:285-311.
17. Carreras M, Brannath W. Shrinkage estimation in two-stage adaptive designs with mid-trial treatment selection. Stat Med. 2013;32(10):1677-1690.
18. Cohen A, Sackrowitz HB. Two stage conditionally unbiased estimators of the selected mean. Stat Probab Lett. 1989;8:273-278.
19. Bowden J, Glimm E. Unbiased estimation of selected treatment means in two-stage trials. Biom J. 2008;50(4):515-527.
20. Robertson DS, Prevost AT, Bowden J. Accounting for selection and correlation in the analysis of two-stage genome-wide association studies. Biostatistics. 2016;17(4):634-649.
21. Kimani PK, Todd S, Stallard N. Conditionally unbiased estimation in phase II/III clinical trials with early stopping for futility. Stat Med. 2013;32(17):2893-2910.
22. Stallard N, Kimani PK. Uniformly minimum variance conditionally unbiased estimation in multi-arm multi-stage clinical trials. *Biometrika*. 2018;105:495-501.
23. Magirr D, Jaki T, Posch M, Klinglmueller F. Simultaneous confidence intervals that are compatible with closed testing in adaptive designs. *Biometrika*. 2013;100:985-996.
24. Simon N, Simon R. Adaptive enrichment designs for clinical trials. *Biostatistics*. 2013;14(4):613-625.
25. Jörgens S, Wassmer G, König F, Posch M. Nested combination tests with a time-to-event endpoint using a short-term endpoint for design adaptations. *Pharm Stat*. 2019;18:329-350.
26. Jennison C, Turnbull BW. Group-sequential analysis incorporating covariate information. *J Am Stat Assoc*. 1997;92:1330-1341.
27. Whitehead J. *The Design and Analysis of Sequential Clinical Trials*. 2nd ed. Chichester, UK: John Wiley & Sons Ltd; 1997.
28. Jennison C, Turnbull BW. *Group Sequential Methods with Applications to Clinical Trials*. 1st ed. Boca Raton, FL: Chapman & Hall/CRC; 2000.
29. Tsiatis AA, Boucher H, Kim K. Sequential methods for parametric survival models. *Biometrika*. 1995;82:165-173.
30. Tsiatis AA. The asymptotic joint distribution of the efficient scores test for the proportional hazards model calculated over time. *Biometrika*. 1981;68:311-315.
31. Wassmer G. Planning and analyzing adaptive group sequential survival trials. *Biom J*. 2006;48:714-729.
32. Wassmer G, Dragalin V. Designing issues in confirmatory adaptive population enrichment trials. *J Biopharm Stat*. 2015;25:651-669.
33. Bauer P, Posch M. Modification of the sample size and the schedule of interim analyses in survival trials based on data inspections (Letter to the editor). *Stat Med*. 2004;23:1333-1335.
34. Spießens B, Debois M. Adjusted significance levels for subgroup analyses in clinical trials. *Contemp Clin Trials*. 2010;31:647-656.
35. Bowden J, Glimm E. Conditionally unbiased and near unbiased estimation of the selected treatment mean for multistage drop-the-losers trials. *Biom J*. 2014;56(2):332-349.
36. Robertson DS, Prevost AT, Bowden J. Unbiased estimation in seamless phase II/III trials with unequal treatment effect variances and hypothesis-driven selection rules. *Stat Med*. 2016;35(22):3907-3922.
37. Marcus R, Peritz E, Gabriel KR. On closed testing procedures with special reference to ordered analysis of variance. *Biometrika*. 1976;63:655-660.
38. Lehmacher W, Wassmer G. Adaptive sample size calculations in group sequential trials. *Biometrics*. 1999;55:1286-1290.
39. R Development Core Team. *R: A Language and Environment for Statistical Computing*. Vienna, Austria: R Foundation for Statistical Computing; 2010.
40. Collett D. *Modelling Survival Data in Medical Research*. 2nd ed. Boca Raton, FL: Chapman & Hall/CRC; 2003.
41. Brannath W, Schmidt S. A new class of powerful and informative simultaneous confidence intervals. *Stat Med*. 2014;33:3365-3386.
42. Whitehead J. One-stage and two-stage designs for phase II clinical trials with survival endpoints. *Stat Med*. 2014;33:3830-3843.
43. Stallard N. Group-sequential methods for adaptive seamless phase II/III clinical trials. *J Biopharm Stat*. 2011;21(4):787-801.
44. Stallard N, Kunz C, Todd S, Parsons NR, Friede T. Flexible selection of a single treatment incorporating short-term endpoint information in a phase II/III clinical trial. *Stat Med*. 2015;34(23):3104-3115.
45. Kimani PK, Todd S, Stallard N. A comparison of methods for constructing confidence intervals after phase II/III clinical trials. *Biom J*. 2014;56(1):107-128.
46. Gu M, Ying Z. Group sequential methods for survival data using partial score processes with covariate adjustment. *Stat Sin*. 1995;5:793-804.
47. Scharfstein DO, Tsiatis AA, Robins JM. Semiparametric efficiency and its implication on the design and analysis of group-sequential studies. *J Am Stat Assoc*. 1997;92:1342-1350.
48. Chiu Y-D, Koenig F, Posch M, Jaki T. Design and estimation in clinical trials with subpopulation selection. *Stat Med*. 2018;37:4335-4352.
**SUPPORTING INFORMATION**
Additional supporting information may be found online in the Supporting Information section at the end of this article.
**How to cite this article:** Kimani PK, Todd S, Renfro LA, et al. Point and interval estimation in two-stage adaptive designs with time to event data and biomarker-driven subpopulation selection. *Statistics in Medicine*. 2020;39:2568–2586. https://doi.org/10.1002/sim.8557 | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2142,
1
],
[
2142,
7705,
2
],
[
7705,
11190,
3
],
[
11190,
14554,
4
],
[
14554,
20915,
5
],
[
20915,
24004,
6
],
[
24004,
29795,
7
],
[
29795,
36903,
8
],
[
36903,
42762,
9
],
[
42762,
49183,
10
],
[
49183,
54483,
11
],
[
54483,
59793,
12
],
[
59793,
66238,
13
],
[
66238,
69286,
14
],
[
69286,
70968,
15
],
[
70968,
73431,
16
],
[
73431,
79337,
17
],
[
79337,
84405,
18
],
[
84405,
88874,
19
]
]
} |
0e6310c2062672e11815210dbe0aa4d1d99b0b64 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 12,
"total-fallback-pages": 0,
"total-input-tokens": 48592,
"total-output-tokens": 17194,
"fieldofstudy": [
"Physics"
]
} | Optical non-linearities and spontaneous translational symmetry breaking in driven-dissipative moiré exciton-polaritons
A. Camacho-Guardian\(^1\) and N. R. Cooper\(^2,3\)
\(^1\)Departamento de Física Química, Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, Ciudad de México C.P. 01000, Mexico
\(^2\)T.C.M. Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
\(^3\)Department of Physics and Astronomy, University of Florence, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy
(Dated: October 26, 2022)
Moiré lattices formed from semiconductor bilayers host tightly localised excitons that can simultaneously couple strongly to light and possess large electric dipole moments. This facilitates the realization of new forms of polaritons that are very strongly interacting and that have been predicted to lead to strong optical non-linearities controlled by multi-photon resonances. Here, we investigate the role of the non-local component of the exciton-exciton (dipolar) interactions on the optical response of these strongly-interacting moiré exciton-polaritons under conditions of strong optical driving. We find that the non-local interactions can strongly influence the steady-state properties leading to multi-stabilities with spontaneously broken translational symmetry and pronounced distortions of the multi-photon resonances. We develop a self-consistent approach to describe the steady-state solution of moiré excitons coupled to a cavity field, treating the long-range interaction between the excitons and the photon field at the semi-classical level.
I. INTRODUCTION
In van der Waals bilayers, the moiré superlattice resulting from lattice mismatch or relative twist angle has emerged as a productive means to realize complex quantum many-body phases [1]. The quantum confinement provided by the moiré landscape has unfolded many opportunities towards the controlled realization of strongly correlated electronic phases such as Wigner crystals [2], Mott insulators [3], superconductivity [4, 5] and more [6–11]. In semiconductor bilayers, moiré materials have unveiled a new class of excitations [12–16]: moiré excitons. Moiré excitons possess properties that make them ideal to explore strongly interacting phases of bosonic matter in uncharted territory, which include prospects for high-temperature and long-lived Bose-Einstein condensates [17, 18], the superfluid-Mott transition [19], excitonic insulators [20], and supersolidity [21].
When combined with an optical cavity, the underlying nature of moiré excitons leads to novel forms of exciton-polaritons and presents new opportunities to engineer hybrid quantum states of light and matter with no equivalent in conventional polaritons. The strong confinement of excitons to the moiré sites yields distinctive moiré-induced polaritons [22], novel forms of quantum emitters [23–25], and promises a new generation of polaritons with tuneable features [26, 27]. The moiré superlattice activates a rich interplay between the tight confinement of the excitons, the light-matter coupling, and the strong exciton-exciton interactions.
Moiré polaritons are particularly interesting as the underlying excitons can inherit properties of both spatially direct and indirect excitons, which can provide them with valuable features such as sizeable light-matter coupling [12, 28] and strong exciton-exciton interactions [22]. Recent experimental [22] and theoretical studies [25] have demonstrated that moiré polaritons feature optical properties with large non-linearities very different from conventional polaritons in semiconductors. Theoretically, it has been shown that the tight confinement of the excitons to the moiré sites leads to pronounced multi-photon resonances governed by the underlying discrete excitonic energy spectrum [25], arising as a consequence of the quasi zero-dimensional character of the excitons and their strong local interactions. This is predicted to permit lasing based on single- and multi-photon processes induced by the moiré lattice.
In addition to the strong on-site exciton-exciton interactions, the indirect character of the moiré excitons leads to non-local interactions. While for moiré lattices the on-site interaction is expected to dominate over the
non-local interactions, the precise role of the non-local interactions remains relatively unexplored. The role of non-local interactions on out-of-equilibrium polaritons is further motivated by theoretical predictions and breakthrough experiments where non-local interactions are a key element to stabilizing states with spontaneously broken translational symmetry which can lead to complex many-body phases such as supersolids [29–32], and which have been already been observed in dipolar quantum gases [33–35]. The dipole-dipole interaction between excitons beyond the local interaction has very recently suggested the existence of supersolid phases of moiré excitons [21], and instigates the study of the interplay between these phases and polariton physics.
Here, motivated by this open question, we study the many-body optical properties of a van der Waals heterostructure bilayer, focusing on the effects of the non-local exciton-exciton interactions arising from their dipolar character. We show that non-local interactions can strongly modify the optical response of the system and demonstrate the emergence of steady states with broken translational symmetry. In addition, the presence of non-local interactions influences the multi-photon resonance conditions leading to a rich phase-diagram with strongly hysteretic features.
The outline of the paper is as follows. In Section II, we detail the model we study – a tight binding model of excitons coupled to cavity photons – and the methods we employ to determine its properties. Here, we introduce three coloured excitonic sites which we treat independently at the mean-field level, we also discuss the mean-field and semi-classical treatment for the cavity photons. In Section III we turn our attention to the study of hardcore excitons, and we reveal the emergence of steady states with broken translational symmetry that can be accessed through several hysteresis mechanisms. The interplay between the on-site and non-local interactions is unraveled in Section IV where we analyze the effects of the dipolar interactions have on the multi-photon resonances. Finally, in Section V we discuss the experimental consequences and outlook based on our results.
II. MODEL AND METHODS
We consider moiré excitons in a van der Waals heterostructure bilayer coupled to a microcavity in the presence of a coherent drive of photons. The moiré landscape leads to flat mini bands that arise from the tight localization of the excitons to the moiré sites. Hence, we describe the excitons via a tight binding Hamiltonian given by
\[ \hat{H}_X = \sum_i \omega_X \hat{x}_i^\dagger \hat{a}_i + \frac{U_X}{2} \sum_i \hat{x}_i^\dagger \hat{x}_i \hat{a}_i \hat{a}_i^\dagger + \sum_{i \neq j} V_{ij} \hat{x}_i^\dagger \hat{x}_j \hat{x}_j \hat{x}_i, \]
(1)
here \( \hat{x}_i^\dagger \) creates an exciton with energy \( \omega_X \) in the site \( i \), with \( N_x \) sites arranged on a triangular lattice. (We set \( \hbar = 1 \) throughout.) We neglect the hopping of excitons between local sites – i.e. the bandwidth of the lowest energy exciton band in the moiré lattice. For a wide range of parameters this can be small compared to the transport via the cavity mode. The on-site exciton-exciton interaction is denoted by \( U_X \), while \( V_{ij} \) corresponds to the interaction between an exciton in site \( i \) and an exciton in site \( j \). In general, the moiré potential supports multiple localised exciton states [14, 27]. Here we restrict our study to the lowest excitonic state and assume that the energy separation between the first and second bands remains larger than any other typical energy of the system.
The bilayer is embedded in a high-finesse microcavity with the ideal dispersion of the cavity photons described by
\[ \hat{H}_l = \sum_{\mathbf{k}} \omega_c(\mathbf{k}) \hat{a}^\dagger_{\mathbf{k}} \hat{a}_\mathbf{k}. \]
(2)
Here the free dispersion of photon is \( \omega_c(\mathbf{k}) = \omega_c + |\mathbf{k}|^2/(2m_c) \), where \( m_c \) is the cavity photon mass. The operator \( \hat{a}^\dagger_{\mathbf{k}} \) creates a cavity photon with in-plane momentum \( \mathbf{k} \). The coupling between excitons and cavity photons is given by the usual light-matter Hamiltonian
\[ \hat{H}_{1-m} = \sum_{\mathbf{k}} \Omega \left( \hat{a}^\dagger_{\mathbf{k}} \hat{x}_\mathbf{k} + \hat{x}^\dagger_{\mathbf{k}} \hat{a}_\mathbf{k} \right), \]
(3)
where \( \hat{x}^\dagger_{\mathbf{k}} \) creates an exciton with in-plane momentum \( \mathbf{k} \).
The strength of the light-matter coupling, denoted by the Rabi frequency \( \Omega \), is assumed much smaller than the typical energy of the excitons, so the light-matter Hamiltonian is written under the rotating wave approximation. (For typical systems \( \Omega \) is a several meV while \( \omega_X \) is on the order of 1 eV.) We, however, consider the regime of strong light-matter coupling such that the Rabi coupling is much larger than the cavity losses \( \gamma_c \), and light couples efficiently to the excitons.
To make further progress we shall restrict the light-matter coupling to the \( \mathbf{k} = 0 \) cavity mode [25]. Thus, we simplify the light and light-matter terms of the Hamiltonian as
\[ \hat{H}_1 + \hat{H}_{1-m} = \omega_c \hat{a}^\dagger \hat{a} + \frac{1}{\sqrt{N_x}} \sum_i \Omega \left( \hat{a}^\dagger \hat{x}_i + \hat{x}^\dagger \hat{a}_i \right), \]
(4)
where \( \hat{a} \) now refers to the \( \mathbf{k} = 0 \) cavity mode. This approximation assumes a spatially uniform coupling between the cavity photons and excitons occupying different sites in the moiré superlattice. This assumption is justified for two reasons. Firstly, due to the ultra-light mass of the cavity mode, the cavity photons decouple from the excitons when the kinetic energy of the photon becomes of the order of the Rabi coupling \( k^2/2m_c = \Omega \). This means that excitons only couple to cavity modes with wavelengths that are larger than a length scale \( \lambda = 2\pi/k \), which is typically very large, covering hundreds of moiré sites. This large lengthscale justifies
a mean-field treatment of the cavity-mediated exciton-exciton coupling. Secondly, we consider situations in which the cavity mode is pumped uniformly. Specifically, we consider an external coherent injection of photons via
\[ \hat{H}_{\text{drive}} = (F \hat{a}^\dagger e^{-i \omega_{\text{p}} t} + F^* \hat{a} e^{i \omega_{\text{p}} t}), \]
where \( F \) and \( \omega_{\text{p}} \) are the strength and the frequency of the driving term respectively. As will be discussed below, we will employ a mean-field approach for the cavity photons, where excitons couple only to the \( \mathbf{k} = 0 \) cavity mode. We describe the system in the rotating frame of this light field, using \( \hat{a} = \hat{a} e^{i \omega_{\text{p}} t} \) and \( \hat{x}_k = \hat{x}_k e^{i \omega_{\text{p}} t} \), for simplicity we drop the \( \sim \)’s in the following. The rotating frame introduces the pump energy detuning from the exciton and cavity detuning defined as \( \Delta \omega_X = \omega_p - \omega_X \) and \( \Delta \omega_c = \omega_p - \omega_c \), respectively.
We mention that the ability to create arbitrary number of excitons is limited by the intrinsic nature of the excitons, where its non-bosonic nature leads to saturation effects. Although this remains as an open question \cite{36, 37}, such effects can be accounted to a first approximation through an anharmonic light-matter coupling term \cite{38–40}. This term, however, only quantitatively modifies the optical properties for small exciton numbers \cite{25}.
We allow the system to be lossy, and study the density operator of the system, \( \hat{\rho} \), via the Gorini–Kossakowski–Sudarshan–Lindblad master equation \cite{41}
\[ \frac{d\hat{\rho}}{dt} = -i[\hat{H}, \hat{\rho}] + \mathcal{D}[\hat{\rho}] = \mathcal{L}[\hat{\rho}], \]
where the total Hamiltonian is given by \( \hat{H} = \hat{H}_X + \hat{H}_I + \hat{H}_{\text{loc}} + \hat{H}_{\text{drive}} \). The dissipative character of the system is accounted for by the operator
\[ \mathcal{D}[\hat{\rho}] = \frac{\gamma_c}{2} \left[ 2 \hat{a} \hat{a}^\dagger \hat{\rho} - \{\hat{\rho}, \hat{a}^\dagger \hat{a}\} \right] + \sum_x \frac{\gamma_x}{2} \left[ 2 \hat{x}_x \hat{x}_x^\dagger \hat{\rho} - \{\hat{\rho}, \hat{x}_x^\dagger \hat{x}_x\} \right], \]
where \( \gamma_x \) and \( \gamma_c \) are the damping rate of the excitons and photons respectively.
The spatial stacking of the monolayers leads to a moiré periodicity that confines the excitons into a triangular lattice. To allow spatial ordering of the excitons we introduce a 3-site supercell as illustrated in Fig. 1. We only consider the three sites within a larger unit cell, denoted in the figure (and referred to below) by three different colours: red, green, and blue. By treating these three sites independently, our present study extends beyond Ref. \cite{25} to explicitly permit states with broken translational symmetry. We will show that this can arise as a consequence of the non-local interaction \( V_{nn} \).
We employ a mean-field approximation to decouple the dipolar interactions in Eq. \( \ref{eq:hamiltonian} \). We define a supercell as illustrated in Fig. 1, treating the occupations of all sites of the same colour to be the same. We thus replace \( \hat{x}_i \rightarrow \hat{x}_\alpha \) where \( \alpha \in \{\text{R,G,B}\} \) labels the three distinct sites within the supercell. The Hamiltonian for each colour is then
\[ \hat{H}_{X,\alpha} = \left( \omega_X + V_{\text{d}a} n_\alpha + V_{\text{od}} \sum_{\beta \neq \alpha} n_\beta \right) \hat{\hat{x}}^\dagger_\alpha \hat{x}_\alpha + \frac{U_X}{2} \hat{x}_\alpha^\dagger \hat{x}_\alpha^\dagger \hat{x}_\alpha \hat{x}_\alpha + \frac{U_{X\text{d}}}{4} \hat{\hat{x}}^\dagger_\alpha \hat{\hat{x}}^\dagger_\alpha \hat{x}_\alpha \hat{x}_\alpha, \]
this local Hamiltonian treats the local terms in Eq. \( \ref{eq:hamiltonian} \) exactly, but takes the long-range dipolar interaction at the mean-field level, with the expectation values of the exciton number for the three different sites, \( n_\beta \), to be determined self-consistently. Here, \( V_{\text{d}a} = 2.124 \times V_{nn} \) and \( V_{\text{od}} = 4.455 \times V_{nn} \) give the mean-field dipole-dipole interaction between the site \( \alpha \) in the supercell and all of the different sites with same and different colour respectively, see further details in the Appendix A and Ref. \cite{42}. Here, \( V_{nn} = d^2/a_M^3 \) is the dipole-dipole interaction between excitons in nearest neighbour sites, where \( a_M \) is the moiré period of the superlattice and \( d \) is the dipole moment of the hybrid exciton due to its interlayer charge separation.
On the other hand, the light-matter coupling is insensitive to our artificial distinction of sites, that is, cavity photons couple equally to excitons regardless of the colour of the site they occupy. The light-matter coupling for a given colour simply reads as
\[ \hat{H}_{1-m,\alpha} = \frac{\Omega}{\sqrt{N_s}} \left( \hat{\hat{a}}^\dagger \hat{x}_\alpha + \hat{\hat{a}} \hat{x}_\alpha^\dagger \right). \]
To make further progress, we take a semi-classical approach for the cavity photons, where we replace the cavity field by its expectation value \( \langle \hat{a} \rangle = \sqrt{N_s} \psi_a \). In this case, the steady-state solution for the photon amplitude \( \psi_a \) is given by
\[ \psi_a = \frac{1}{\Delta_{\text{c}}} \left( f + \frac{\Omega}{3} \sum_{\alpha = \text{R,G,B}} \langle \hat{x}_\alpha \rangle \right), \]
where \( f = F/\sqrt{N_s} \). The last term inside of the brackets accounts for the possible different expectation value of sites with different colour. Here, \( \Delta_{\text{c}} = \Delta \omega_{\text{c}} + i \gamma_{\text{c}}/2 \).
These approximations permit us to define three Hamiltonians for differently colours \( \alpha \),
\[ \hat{H}_{\text{loc},\alpha} = \hat{H}_{X,\alpha} + \hat{H}_{1-m,\alpha}, \]
with \( \alpha, \beta \in \{\text{R,G,B}\} \), that are local. The coloured Hamiltonians are coupled through the exciton-exciton interactions and the light-matter coupling. The exciton-exciton interaction couples sites with different and same colours via the terms \( V_{\text{d}a} \) and \( V_{\text{od}} \), in Eq. \( \ref{eq:hamiltonian} \) treated at the mean-field level. This mean-field approximation can be understood intuitively: it introduces a self-consistent on-site energy that can vary for the three different colours and thus, can energetically favour the breaking of the translational symmetry. That is, the imbalanced-population steady-state solutions are a consequence of an emergent
colour-dependent on-site energy arising from the non-local interactions. We emphasize that since our starting Hamiltonian has the full translational symmetry of the triangular lattice, the emergence of collective phases with a reduced translational symmetry through interactions is an example of spontaneously broken symmetry [43]. Thus there is a residual (discrete) degeneracy of the ground state associated with the different ways in which these broken symmetry states can be placed on the triangular lattice. Which of the broken-symmetry states appears in the numerics is, as usual, determined by the initial seed. On the other hand, the light-matter coupling introduces a long-range mediated tunneling, where an exciton in a given site can convert to a cavity photon, which can decay into an exciton in any other moiré site. Thus, the long-range photon-mediated hopping couples sites with the same and different colours. This leads to a coupling between the coloured local Hamiltonians. That is, we assume that the cavity field retains the spatially uniform coupling to the excitons in the presence of non-local interactions and that the cavity field maintains population only in the $k = 0$ mode[25].
Our approach leads to a set of three coupled master equations, for the sites of each different colour
$$\frac{d\hat{\rho}_\alpha}{dt} = \mathcal{L}_\alpha[\hat{\rho}_\alpha]$$
\[= -\frac{i}{2} [\hat{H}_{\text{loc},\alpha}, \hat{\rho}_\alpha] + \frac{\gamma_\alpha}{2} \left( 2\hat{x}_\alpha \hat{\rho}_\alpha \hat{x}_\alpha^\dagger - \{\hat{x}_\alpha^\dagger \hat{x}_\alpha, \hat{\rho}_\alpha\} \right),\]
To obtain the steady-state properties we employ exact diagonalization of each of these three equations. They are coupled since, via Eqn.(10), the expectation values of the photon amplitude $\psi_\alpha$ and the exciton number $\langle x_\alpha^\dagger x_\beta \rangle$ must be obtained self-consistently. The numerical scheme is detailed in the Appendix B.
The long-range interaction between the excitons stems from their indirect nature that leads to a dipole-dipole interaction that scales with separation $r$ as $1/r^3$. Due to the large moiré periodicity, the on-site interaction $U_X$ is largely dominant with respect to $V_{nn}$. While the on-site interaction can be made of the order of some tens meV [22], the interaction between first neighbours is estimated $V_{nn} \sim 0.1 - 1$ meV [21], thus, for typical experiments one expects $V_{nn}/U_X \approx 10^{-1} - 10^{-2}$, which enables the study of the imprints of the non-local interactions over a wide range of parameters. We expect our approximation to be valid when the non-local interaction remains smaller compared to the on-site interaction $V_a/U_X \ll 1$ and $V_{aa}/U_X \ll 1$. We consider two cases, first, we consider hard-core excitons which are prevented from double occupation. Then, we study the interplay between multi-photon resonances and non-local interactions.
### III. HARD-CORE EXCITONS
For clarity, we start our study in the limit of hard-core excitons which explicitly forbids multiple occupa-
tion, this case will allow us to understand the effects of the long-range interaction disentangled from the on-site interaction.
For hard-core excitons $U_X \to \infty$ non-linearities arise from the impossibility to create multiple excitons per site and from the non-local interactions. First, we explore steady-state solutions with equal population on the three sites. We start by considering an initial seed for our self-consistent scheme that is population balanced ($n_R = n_G = n_B$), see Appendix B. In this case, we find a pair of solutions corresponding to low- and high-density hysteresis branches. The former corresponds to varying $f/V_{nn}$ from below while the latter arises from $f/V_{nn}$ being tuned from above. These solutions are illustrated in Fig. 2 for $\Omega/V_{nn} = 0.5$, while fixing the losses $\gamma_x/V_{nn} = \gamma_c/V_{nn} = 0.1$ and cavity and exciton detunings of $\Delta \omega_c/V_{nn} = -1$ and $\Delta \omega_X/V_{nn} = 0.9$, respectively.
The behaviour just described appears qualitatively similar to that found in Ref. [25], where it was shown that strong on-site interactions and the inherent nature of moiré exciton-polaritons can give rise to new physical phenomena absent in conventional polaritons [22, 25]. Fig. 2 illustrates that the transition from a low-density regime ($f/V_{nn} \lesssim 0.05$) to a regime dominated by the driving ($f/V_{nn} \gtrsim 0.3$) is separated by an intermediate regime where exciton-exciton interactions lead to an apparent bistability.
Intriguingly, as we now show, in this regime we find that the presence of non-local interactions can lead to additional steady-state solutions, turning the bistability into a multi-stability with four steady-states: the two solutions in Eq. 2 and two additional solutions with spatial ordering of the excitons, which we will now discuss. These solutions are illustrated in Fig. 3 for the same values of the parameters as in Fig. 2.
The ranges of values of the drive corresponding to states with broken translational symmetry are shaded in pink. In these regimes the different sites (labelled by
different colours) have unbalanced populations.
The photon amplitude in Eq. 10, which couples collectively to the sites with different colours, can also be used as a witness of this set of solutions with broken translational symmetry for the excitons. This is illustrated in Fig. 4 where we show the photon number $n_p = |\psi|^2$ for the various hysteresis branches discussed above. Since for excitons the low to high density transition occurs for different values of $f$, the photon number also exhibits this strong hysteresis dependence. Figure 4(b) shows the photon number for the same parameters as Figs. 2-3. Here, the black lines correspond to the photon densities when the excitons are uniformly distributed in the moiré lattice, that is, the population-balanced low- and high-density branches shown in Fig. 2. The red lines illustrate the photon densities of steady-state solutions for which the exciton occupations exhibit broken translational symmetry as in Fig. 3(a)-(b). The pink area corresponds to the regime where a steady state can be found with broken translational symmetry.
FIG. 3. Exciton number per site. (a) Steady-state solutions with $n_B = n_C > n_R$, i.e. one site of low density. (b) Steady-state solutions exhibiting a regime with $n_R > n_B = n_G$, i.e. one site of high density. The pink area illustrates the regime with unbalanced populations. Color code follows the lattice colouring. Parameters are the same as for Fig. 2.
Besides, additional solutions arise where only one coloured site suddenly jumps into a high-density phase at expenses of two moiré sites less populated. These solutions are illustrated in Fig. 3(b) where the red sites prevail in a high-density phases with much larger population than the blue and green exciton sites, here $n_R \neq n_B = n_G$. These steady-state solutions are accessed with a seed where the initial self-consistent parameters for the blue and green sites are set to zero while for the red sites the high-density hysteresis branch is followed, see details in Appendix B. We have explored different self-consistent schemes, allowing for fully population-imbalanced metastable states with $n_R \neq n_B, n_B \neq n_G$, and $n_R \neq n_G$, but our calculations show that these do not appear over the wide range of parameters that we have explored. We speculate that the absence of these solutions arises from the fact that each site can transit either to a low- or high-density phase, this binary characterisation of the population of the sites yields to only four kinds of different solutions shown in Fig. 2 and Fig. 3.
The size of the pink area is determined by the ratio between the light-matter coupling and the strength of the non-local interactions. To illustrate this point we show in Fig. 4 the shrinking of these solutions when $\Omega/V_{nn}$ is increased, from $\Omega/V_{nn} = 0.35$ to 0.5. The pink region clearly decreases for larger values of $\Omega/V_{nn}$. This illustrates that the solutions with broken translational symmetry are suppressed as for large $\Omega/V_{nn}$, and disappear for $\Omega/V_{nn} > 0.65$. The broadening of the excitonic lines leads to smoothing of the interaction effects, in turn, the large moiré periodicity which gives a small $V_{nn}$ imposes narrow excitonic lines. Experimentally, small broadening of the exciton linewidths have been reported in moiré setups, which can be of the order of 0.1meV [13].
Thus we have shown that non-local interactions allow for steady-state solutions with spontaneously broken translational symmetry, that is, with unbalanced population in terms of the exciton colour. Numerically, we
access states with broken translational symmetry by ini-
itializing our self-consisting approach with seeds that ex-
plicitly break this symmetry, see further details in the
Appendix B. We stress that although the ability to access
states with broken translational symmetry depends on
the initial seed, the existence of such steady-states hinges
on the non-local interactions and as these states are ab-
sent when $\Omega/V_{nn} \gg 1$. This dependence on the initial
seed is a feature commonly shared for any broken sym-
metry phenomenon, where the initial seed is used only
to select which of the various broken symmetry states is
realized. For example, in typical self-consistent schemes
for equilibrium Bose-Hubbard-like models, the detection
of states with broken translational symmetry requires an
initial ansatz that explicitly breaks this symmetry; then,
the self-consistent approach can drive the solution into
equilibrium states that may preserve the broken transla-
tional symmetry.
Our ansatz is based on the uses of a supercell contain-
ing three kinds of moiré sites, thus, the solutions follow
the restriction imposed by that ansatz. Solutions with
different spatial structures, not allowed by our ansatz,
could emerge through the use of other supercells. We
have also studied another simple two-site supercell which
allows for striped density order. We find that striped
solutions can also be appeared, but that these are less
stable than the structures that we present here. In par-
ticular, the striped phases do not appear for the set of
parameters discussed in Figs. 1-3. We cannot rule out
that other more complex spatial structures, which are
possible only in larger supercells, could be more stable
than those we present for the 3-site cell. Also, we expect
that disorder could play a significant role in determin-
ing the nature of the stable states. For clarity of our
presentation, we leave the comprehensive study of more
complex broken symmetry phases and disorder to future
investigations.
IV. MULTI-PHOTON RESONANCES AND
NON-LOCAL INTERACTIONS
Now, we turn our attention to the study of the inter-
play between the on-site interactions and the non-local
interactions. Thus, we relax the hard-core constraint and
allow for multiple occupation. In absence of non-local
interactions, that is, for $V_{nn} = 0$, the phase-diagram is
governed by the multi-photon resonance condition
$$N\omega_p = N\omega_X + \frac{U_X}{2}N(N-1), \quad (13)$$
which leads to the condition
$$\frac{2\Delta\omega_X}{U_X} = (N-1). \quad (14)$$
Physically this can be understood in terms of an ener-
geic condition dictating that $N$ exciton resonances are
promoted whenever the energy of $N$ non-interacting pho-
tons matches the energy of $N$ interacting excitons [25]. In
the presence of non-local interactions, we expect a shift of
this energetic condition: treating $V_{nn}$ at the mean-field
level, the interaction between adjacent excitons simply
displaces the on-site energy
$$\omega'_X = \omega_X + \left(V_d n_\alpha + V_{od} \sum_{\beta \neq \alpha} n_\beta\right),$$
thus, physically, one anticipates that for a site with a
given colour $\alpha$, the resonance is displaced to
$$N\omega_p = N\left(\omega_X + V_d n_\alpha + V_{od} \sum_{\beta \neq \alpha} n_\beta\right) + \frac{U_X}{2}N(N-1). \quad (15)$$
In this case, the multi-photon resonance (14) depends on
$n_\beta$ and is not longer necessarily an integer. One should
note that in contrast to the Bose-Hubbard model in equi-
librium where the occupation number per site of the in-
sulating phase is pinned to integer values, for driven-
dissipative systems the discrete lobular pattern deter-
mined by the multi-photon resonance condition is a rem-
nant of the discreteness of the equilibrium Hubbard en-
ergy spectrum. However, the occupation number is no
longer strictly an integer. That is, while the modulation
of the phase diagram for $V_{nn} = 0$ follows very closely the
discrete equation in Eq. 13, the exact value of the exciton
number slightly above the low-to-high density transition is
not necessarily an integer.
From our earlier analysis on the effects of the non-local
interactions we also anticipate the emergence of multi-
stabilities. Note that, although the cavity field and $V_{nn}$
are treated at the mean-field level, we still perform a full
quantum calculation for the driven excitons on a single
site.
We begin by discussing the case of large ratio $\Omega/V_{nn}$,
which as explained above, tends to inhibit solutions with
spatial ordering. We take $\Omega/U_X = 0.65$ which corre-
sponds to $\Omega/V_{nn} = 1.42$, finally, we consider $V_{od}/U_X = \frac{54x}{70}$
0.1. In Fig. 5 we show the solutions found for a finite on-site interaction. We turn our attention first to population-balanced solutions obtained with initial seeds that do not break translational symmetry \((n_R = n_B = n_{Q_2})\) and find two solutions corresponding to the low-density and high-density hysteresis branches.
Figure 5(a) corresponds to the phase-diagram following the low-density branch, that is, \(f/U_X\) being tuned from below. In this case, the phase-diagram shows sharp cusp-like features at detunings closely governed by the bare multi-photon resonance in Eqs. 13, 14. Figure 5(a) corresponds to the case where the low to high density transition is promoted from below, that is, it corresponds to \(n_\beta \approx 0\) in Eq. 15, and therefore the cusp-like features are barely shifted away from the resonance condition Eq. 13. The non-local interaction does introduce some blurring of the cusps, but the locations remain closely tied to Eq. 14.
On the high-density hysteresis branch, on the other hand, the transition is crossed from above. In this case, the exciton number of the adjacent sites is relatively large \(n_\beta \neq 0\), hence, the multi-photon resonances in Eq. 15 acquire large energy shifts away from Eq. 14 and visibly distort the phase-diagram. The deviations of the multi-photon resonances and the profound hysteresis contrast with the case in Ref. [25] where the high-density hysteresis branch respects the position of the multi-photon resonances. Therefore, one of the measurable consequences of the non-local interactions are shifts and broadenings of the lobular pattern. In the regime where the non-local interactions are further suppressed with respect to the on-site interactions, for instance \(V_{od}/U_X \approx 0.05\) one obtains a phase-diagram that closely follows the bare and discrete multi-photon resonances [25], as shown explicitly in Fig. 10 of Appendix C. Importantly, by means of the twist angle, one can therefore, enhance or suppress the effects of the non-local interactions on the optical response of the system [21].
We also find that the non-local interactions lead to more metastable states, even within the space of population-balanced solutions. This multistability is somewhat reminiscent of the multistability seen in Fig. 3 and Fig. 5 and consists of steady state solutions with modified multi-photon resonance patterns. However we emphasise that it differs from the cases presented in Section III in that the populations remain balanced. A set of four metastable solutions can be accessed through different hysteresis schemes which retain balanced populations, see Appendix C.
For finite \(U_X\) one can also obtain states with broken translational symmetry, such solutions require, however, smaller values of \(\Omega/V_{nn}\). In Fig. 6 we show, for \(\Omega/V_{nn} = 0.45\) solutions with unbalanced populations where red coloured exciton sites jump to a high density state with blue and green excitons smoothly increasing their density. One recognizes the similarities between Fig. 6 and the hard-core limit presented in Fig. 3(b) as both correspond to the same hysteresis protocol which give the same qualitative behaviour. Experimentally, the branches in Fig. 5 can be accessed through changing the direction of the drive \(f\), as commonly experimentally realized to detect bi-stabilities in conventional polaritons [40, 41, 44]. In general the states with complex hysteresis protocols are more challenging to access, as which of the states of differently broken translational symmetry will appear depends on how the translational symmetry breaking is seeded — by preparation or through underlying disorder.
V. EXPERIMENTAL PERSPECTIVES AND CONCLUSIONS
We have shown that non-local interactions \(V_{nn}\) have significant qualitative effects on the non-linear optical response of exciton-polaritons in moiré materials. In addition to the unique moiré-induced non-linearities arising of the strong on-site interactions [22, 25], the non-local interactions reveal new features including steady states with broken translational symmetry, multi-stabilities, and deviations from the on-site multi-photon resonance conditions. To study these features, we developed a self-consistent master equation based on a supercell containing three sites for excitons. These were treated independently at the mean-field level, allowing for the derivation of three coupled local master equations, which were solved self-consistently.
The predicted effects of the non-local interactions are readily measurable in experiment. They lead to a hys-
teretic dependence of the multi-photon resonance condition, wherein the form and position of the lobular pattern is determined by the direction of the drive (Fig. 9). Furthermore, a multi-valued hysteretic behaviour is found as a consequence of a spatial ordering of the excitons in the moiré sites. The form of these steady states could be experimentally detected by spatially resolving the positions of the excitons [45], but their existence is also apparent in measurements of the multi-stable hysteretic states of the cavity field [40, 44] (see Fig. 4).
Moiré systems are versatile platforms that allow for the control and manipulation of the excitonic properties over a wide range of parameters, for instance, by twisting the relative angle between the layers or by inserting an insulating layer between them to control the moiré superlattice properties and the features and degree of hybridisation of the excitons [46]. Our study encourages further studies to understand the behaviour of moiré excitons in different contexts. For instance, an intriguing avenue is to understand the interplay between multiple excitonic states, the strong exciton interactions, and the light-matter coupling. Another possibility is the study of non-local terms can be treated at the mean-field level, such that we take
\[ \sum_{i} V_{ij} \hat{n}_i \hat{n}_j \approx \frac{1}{a_M^3} \left( n_a + n_b + n_c \right)^3 \]
that is, we take \( \langle \hat{n}_i - \langle n_i \rangle \rangle \approx 0 \). Only the last term in (A1) will be relevant to the effective mean-field dynamics of the site \( i \).
As illustrated in Fig. 7 we introduce three exciton sites that colour the moiré lattice. Thus, we define a larger supercell of three sites (labelled by \( \alpha = R, G, B \)) and denote the position of that supercell by the index \( I \) such that the site index \( i \rightarrow (I, \alpha) \). In our mean-field ansatz the occupations of sites of the same colour \( \alpha \) within all supercells are equivalent \( \langle \hat{n}_{I,\alpha} \rangle = n_\alpha \). Any given site interacts with sites of the same and different colours. In Fig. 7 we illustrate the non-local dipole-dipole interaction between a green site and (a) other green sites distanced by \( r_{n,m}^{gg} = |n\mathbf{a}_1 + m\mathbf{a}_2| \), from the original green site, (b) blue sites distanced by \( r_{n,m}^{gb} = |n\mathbf{a}_1 + m\mathbf{a}_2 + (\mathbf{a}_1 + \mathbf{a}_2)/3 \), where \( n, m \in \mathbb{Z} \). Here \( a_1 = a_M(\sqrt{3}, 0) \) and \( a_2 = a_M(3/2, \sqrt{3}/2) \) being \( a_M \) the moiré lattice constant. The red sites (not shown) are separated by \( r_{n,m}^{gr} = |n\mathbf{a}_1 + m\mathbf{a}_2 - (\mathbf{a}_1 + \mathbf{a}_2)/3 | \).
In detail, the interaction between a site \( I \) with colour \( \alpha \) and sites with the same colour is given by
\[ \sum_{J \neq I} V_{I,\alpha}(J, \alpha) \hat{n}_{I,\alpha}(J, \alpha) \hat{n}_{I,\alpha} = \frac{a_M^3}{|n_1 + n_2|^3} \sum_{n,m} V_{nn} n_\alpha \hat{n}_{I,\alpha} \hat{n}_{I,\alpha} \approx n_\alpha \hat{n}_{I,\alpha} V_{nn} \times 2.12, \]
where the sum in the second line is restricted to exclude \( (n, m) = (0, 0) \). Here, \( V_{nn} = d^2/a_M^3 \).
Similarly, the interaction between the site in supercell \( I \) with colour \( \alpha \) and all sites with a different colour \( \beta \neq \alpha \) is
\[ \sum_{J} V_{I,\alpha}(J, \beta) \hat{n}_{I,\alpha}(J, \beta) \hat{n}_{I,\alpha} \approx n_\alpha \hat{n}_{I,\alpha} V_{nn} \sum_{n,m} a_M^3 |n_1 + n_2 + \alpha_1 + \alpha_2/3|^3 \approx n_\beta \hat{n}_{I,\alpha} V_{nn} \times 4.455, \]
where the sign \( \pm \) determines the colour of the sites. In Fig. 7 the sign \( \pm \) determines the coupling of the green sites to the blue (+) red (−) sites respectively, both sums give the same factor of 4.455; these sums are evaluated numerically and agree with the known results from Ref. [42].
VI. ACKNOWLEDGMENTS
We thank Atac Imamoglu for the careful reading of the manuscript and valuable comments. This work was partially supported by EPSRC Grant Nos. EP/P009565/1, EP/P034616/1 and by a Simons Investigator Award. ACG acknowledges grant No. IN108620 from DGAPA (UNAM).
Appendix A: Dipolar interactions
We start discussing our approach for the non-local exciton-exciton interactions. Here, we assume that the non-local terms can be treated at the mean-field level, thus we have
\[ \sum_{i} \frac{V_{ij}}{2} \hat{n}_i \hat{\phi}_j + \sum_{i} \frac{V_{ij}}{2} \langle \hat{\phi}_i \rangle \langle \hat{\phi}_j \rangle + \sum_{i \neq j} V_{ij} \hat{n}_i \hat{n}_j, \]
that is, we take \( \langle \hat{n}_i - \langle n_i \rangle \rangle \langle \hat{n}_j - \langle n_j \rangle \rangle \approx 0 \). Only the last term in (A1) will be relevant to the effective mean-field dynamics of the site \( i \).
Then, for the site $\alpha$ within any supercell we can define a local Hamiltonian that includes the non-local exciton-exciton interactions at the mean-field level,
$$
V_d n_\alpha + V_{od} \sum_{\beta \neq \alpha} n_\beta \hat{n}_{(I,\alpha)}
$$
with $V_d = 2.124 \times V_{nn}$ and $V_{od} = 4.455 \times V_{nn}$ as denoted in the main text. There, the number operator is written $\hat{n}_{(I,\alpha)} = \hat{x}_{\alpha}^\dagger \hat{x}_\alpha$, dropping the label $I$ of the supercell, since the mean-field self-consistency equation is the same for all supercells.
Appendix B: Self-consistent scheme
We now provide the details of our self-consistent approach which is based on an iterative exact diagonalization of the three Lindblad operators $\mathcal{L}_\alpha$ for $\alpha = R,G$ and $B$ that are coupled through the cavity field $\psi_\alpha$ and the long-range interaction term of the dipole-dipole interactions. The self-consistent approach consists of iteratively obtaining the exciton coherences $\langle \hat{x}_\alpha \rangle = x_\alpha$ and the populations $n_\alpha$.
The iterative scheme is obtained as follows and illustrated in Fig. 8 for a particular hysteresis branch.
1. For a given $\Delta\omega_X$ we start from a large $f_0$ where the steady-state is single valued. Thus, we start from a random set of parameters $(x_0^0(f_0), n_0^0(f_0))$. Here, the super-index denotes the step of the iteration which we now discuss.
2. We calculate $\mathcal{L}_\alpha(x_0^0(f_0), n_0^0(f_0))$ and calculate the expectation values of the operators $\hat{x}_\alpha$ and $\hat{n}_\alpha$ which define the seed for the next iteration $(x_{1,\alpha}^*(f_0), n_{1,\alpha}^*(f_0))$, which interpolates $x_\alpha^0(f_0) = \langle \hat{x}_\alpha \rangle = \langle \hat{x}_\alpha \rangle - \eta(\langle \hat{x}_\alpha \rangle - x_0^0(f_0))$, where $\eta$ is adjusted to speed numerical convergence. Note that the sub-index has remained unchanged.
3. We then iterate $\mathcal{L}_\alpha(x_{i,\alpha}^*(f_0), n_{i,\alpha}^*(f_0))$ using the parameters $(x_{i-1,\alpha}^0(f_0), n_{i-1,\alpha}^0(f_0))$. We iterate up to $i = N_{\text{max}} = 1800$ or when max(error$_R$,error$_G$,error$_B$) $< 10^{-8}$ where error$_\alpha = |n_{i-1,\alpha} - n_{i,\alpha}|$. The final state is denoted by $(x_{N_{\text{iter}},\alpha}^0(f_0), n_{N_{\text{iter}},\alpha}^0(f_0))$, where $N_{\text{iter}}$ is either $N_{\text{max}}$ or the number of iteration steps required to converge. Steps 2-3 are used for all of our numerics.
4. After convergence is achieved for $f_0$, we then decrease $f_0$ by an amount of $\Delta f > 0$, we define $f_1 = f_0 - \Delta f$. The initial seed $(x_0^0(f_1), n_0^0(f_1))$ is no longer random and is taken as detailed below:
- Full hysteresis:
$$
x_0^0(f_1) = x_{N_{\text{iter}},\alpha}^0(f_0),
n_0^0(f_1) = n_{N_{\text{iter}},\alpha}^0(f_0),
$$
for $\alpha \in \{R,G,B\}$ That is, all of the results obtained for $f_0$ are preserved. This protocol is used for Fig. 9(c) and the high-density hysteresis branch in Fig. 2.
- Two excitons hysteresis: We retain only two solutions, that is, we take for instance
$$
x_0^0(f_1) = x_{N_{\text{iter}},\alpha}^0(f_0),
n_0^0(f_1) = n_{N_{\text{iter}},\alpha}^0(f_0),
x_0^0(f_1) = 0,
n_0^0(f_1) = 0,
$$
for $\alpha \in \{R, G\}$. We use this scheme in Fig. 3(a) and Fig. 9(c).
- Single exciton hysteresis. We retain only one solution, while the remaining needed parameters are set to zero. For instance, one of these branches corresponds to
$$
x_0^0(f_1) = x_{N_{\text{iter}},\alpha}^0(f_0),
n_0^0(f_1) = n_{N_{\text{iter}},\alpha}^0(f_0),
x_0^0(f_1) = 0,
n_0^0(f_1) = 0,
$$
we use this procedure of Fig. 9(b) and Fig. 3(b). The procedure for this branch is illustrated in Fig. 8.
- Lower branch: None of the solutions are kept, that is,
$$
(x_0^0(f_1), n_0^0(f_1)) = (0, 0),
$$
for $\alpha \in \{R,G,B\}$. This is the scheme followed for the lower branch in Fig. 2 and Fig. 9(a).
5. We repeat step 2. Again, the arbitrary initial seed is only used to follow each hysteresis branch.
The convergence of our numerics is illustrated in Figs. 2, 3, 4 and Fig. 6 where error bars have been added and correspond to $|n_{N_{\text{iter}},\alpha}(f) - n_{N_{\text{iter}}-1}(f)|$. The barely visible error bars confirm that our results are fully converged. For Sec. III, the Hilbert space of the excitons is naturally restricted to having at most one exciton per site. For finite on-site interactions we introduce a cut-off and restrict to ten excitons per site. The validity of this truncation depends on the strength of the drive and the exciton detuning that determine the exciton number. For the spanned parameters we restrict to exciton occupations much smaller than our cut-off and have indeed verified that our results do not change for larger sizes. Restricting to relatively small occupation number is also motivated by the experimental limitations to create arbitrary numbers of excitons per site through effects such as saturation, population of higher bands, or even experimental damage of the samples due to the high intensity of the laser.
The different hysteresis schemes permit multistabilities. As mentioned in the main text, the low- and high-density hysteresis branches in Fig. 5 are accompanied by two additional branches that can be accessed via the mechanisms discussed in the Appendix B. These solutions are illustrated in Fig. 9.
The steady states in Figs. 9 do not break translational symmetry, however, the stark difference between the phase-diagrams strongly depend on the initial seed of our numerics. Figure. 9(b) corresponds to the high-density hysteresis branch for a single coloured exciton.
Figure. 9(c) corresponds to the hysteresis where two coloured excitons are recursively iterated. In addition, the deformation of the multi-photon resonances becomes more visible.
Finally, in Fig. 10 we set a much smaller value of the non-local interactions $V_{od}/U_X$ to demonstrate that the local multi-photon resonances of Eq. 14 are recovered in this limit.
Appendix C: Hysteresis schemes
[1] E. Y. Andrei, D. K. Efetov, P. Jarillo-Herrero, A. H. MacDonald, K. F. Mak, T. Senthil, E. Tutuc, A. Yazdani, and A. F. Young, Nature Reviews Materials 6, 201 (2021).
[2] L. Zhang, Z. Zhang, F. Wu, D. Wang, R. Gogna, S. Hou, K. Watanabe, T. Taniguchi, K. Uklarni, T. Kuo, S. R. Forrest, and H. Deng, Nature Communications 11, 5888 (2020).
[3] E. C. Regan, D. Wang, C. Jin, M. I. Bakti Utama, B. Gao, X. Wei, S. Zhao, W. Zhao, Z. Zhang, K. Yumigeta, M. Blei, J. D. Carlsström, K. Watanabe, T. Taniguchi, S. Tongay, A. Zettl, and F. Wang, Nature (London) 579, 359 (2020), arXiv:1910.09047 [cond-mat.mes-hall].
[4] L. Balents, C. R. Dean, D. K. Efetov, and A. F. Young, Nature Physics 16, 725 (2020).
[5] S. Kezilebieke, V. Vaño, M. N. Huda, M. Aapro, S. C. Ganguli, P. Liljeroth, and J. L. Lado, Nano Letters 22, 328 (2022), PMID: 34978831, https://doi.org/10.1021/acs.nanolett.1c03856.
[6] Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Nature (London) 556, 43 (2018), arXiv:1803.02342 [cond-mat.mes-hall].
[7] M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, Science 363, 1059 (2019), arXiv:1808.07865 [cond-mat.mes-hall].
[8] M. Serlin, C. L. Tschirhart, H. Polshyn, Y. Zhang, J. Zhu, K. Watanabe, T. Taniguchi, L. Balents, and A. F. Young, Science 367, 900 (2020), arXiv:1907.00261 [cond-mat.str-el].
[9] Y. Shimazaki, I. Schwartz, K. Watanabe, T. Taniguchi, M. Kroner, and A. Imamoglu, Nature 580, 472 (2020).
[10] Y. Tang, L. Li, T. Li, Y. Xu, S. Liu, K. Barmak, K. Watanabe, T. Taniguchi, A. H. MacDonald, J. Shan, and K. F. Mak, Nature (London) 579, 353 (2020).
[11] X. Huang, T. Wang, S. Miao, C. Wang, Z. Li, Z. Lian, T. Taniguchi, K. Watanabe, S. Okamoto, D. Xiao, S.-F. Shi, and Y.-T. Cui, Nature Physics 17, 715 (2021).
[12] E. M. Alexeev, D. A. Ruiz-Tijerina, M. Danovich, M. J. Hamer, D. J. Terry, P. K. Nayak, S. Ahn, S. Pak, J. Lee, J. I. Sohn, M. R. Molas, M. Koperski, K. Watanabe, T. Taniguchi, K. S. Novoselov, R. V. Gorbachev, H. S. Shin, V. I. Fal’ko, and A. I. Tartakovskii, Nature 567, 81 (2019).
[13] C. Jin, E. C. Regan, A. Yan, M. Iqbal Bakti Utama, D. Wang, S. Zhao, Y. Qin, S. Yang, Z. Zheng, S. Shi, K. Watanabe, T. Taniguchi, S. Tongay, A. Zettl, and F. Wang, Nature (London) 567, 76 (2019), arXiv:1812.09815 [cond-mat.mes-hall].
[14] K. Tran, G. Moody, F. Wu, X. Lu, J. Choi, K. Kim, A. Rai, D. A. Sanchez, J. Quan, A. Singh, J. Embley, A. Zepeda, M. Campbell, T. Autry, T. Taniguchi, K. Watanabe, N. L., S. K. Banerjee, K. L. Silverman, S. Kim, E. Tutuc, L. Yang, A. H. MacDonald, and X. Li, Nature (London) 567, 71 (2019), arXiv:1807.03771 [cond-mat.mes-hall].
[15] K. L. Seyler, P. Rivera, H. Yu, N. P. Wilson, E. L. Ray, D. G. Mandrus, J. Yan, W. Yao, and X. Xu, Nature (London) 567, 66 (2019), arXiv:1809.04562 [cond-mat.mes-hall].
[16] E. Liu, E. Barré, J. van Baren, M. Wilson, T. Taniguchi, K. Watanabe, Y.-t. Cui, N. M. Gabor, T. F. Heinz, Y.-c. Chang, and C. H. Liu, Nature 594, 46 (2021).
[17] C. Lagoin and F. M. C. Dubin, Phys. Rev. B 103, L041406 (2021).
[18] B. Remez and N. R. Cooper, arXiv e-prints , arXiv:2110.07628 (2021), arXiv:2110.07628 [cond-mat.mes-hall].
[19] N. Göttling, F. Lohof, and C. Gies, arXiv e-prints , arXiv:2201.10877 (2022), arXiv:2201.10877 [cond-mat.mtrl-sci].
FIG. 9. Exciton number per site for steady states with balanced colour population. (a) Low-density branch. (b) One exciton hysteresis protocol, (c) Two exciton hysteresis protocol and (d) full hysteresis scheme as explained above.
FIG. 10. Exciton number per site for steady states with balanced colour population. Here we illustrate the (a) low-density and (b) full hysteresis for $V_{od}/U_X = 0.05$ and remaining same parameters as in Fig. 9.
[20] Z. Zhang, E. C. Regan, D. Wang, W. Zhao, S. Wang, M. Sayyad, K. Yumigeta, K. Watanabe, T. Taniguchi, S. Tongay, M. Crommie, A. Zettl, M. P. Zaletel, and F. Wang, arXiv e-prints, arXiv:2108.07131 (2021), arXiv:2108.07131 [cond-mat.mes-hall].
[21] A. Julku, arXiv e-prints, arXiv:2205.01812 (2022), arXiv:2205.01812 [cond-mat.mes-hall].
[22] L. Zhang, F. Wu, S. Hou, Z. Zhang, Y.-H. Chou, K. Watanabe, T. Taniguchi, S. R. Forrest, and H. Deng, Nature 591, 61 (2021).
[23] H. Yu, G.-B. Liu, J. Tang, X. Xu, and W. Yao, Science Advances 3 (2017), 10.1126/sciadv.1701696, https://advances.sciencemag.org/content/3/11/e1701696.full.pdf.
[24] H. Baek, M. Brotons-Gisbert, Z. X. Koong, A. Campbell, M. Rambach, K. Watanabe, T. Taniguchi, and B. D. Gerardot, Science Advances 6 (2020), 10.1126/sciadv.aba8526.
[25] A. Camacho-Guardian and N. R. Cooper, arXiv e-prints, arXiv:2108.06177 (2021), arXiv:2108.06177 [cond-mat.mes-hall].
[26] H. Yu and W. Yao, Science Bulletin 65, 1555 (2020).
[27] J. M. Fitzgerald, J. J. P. Thompson, and E. Malic, arXiv e-prints, arXiv:2201.08437 (2022), arXiv:2201.08437 [cond-mat.mes-hall].
[28] D. A. Ruiz-Tijerina and V. I. Fal’ko, Phys. Rev. B 99, 125424 (2019).
[29] A. van Otterlo and K.-H. Wagenblast, Phys. Rev. Lett. 72, 3598 (1994).
[30] G. G. Batrouni, R. T. Scalettar, G. T. Zimanyi, and A. P. Kampf, Phys. Rev. Lett. 74, 2527 (1995).
[31] R. T. Scalettar, G. G. Batrouni, A. P. Kampf, and G. T. Zimanyi, Phys. Rev. B 51, 8467 (1995).
[32] K. Góral, L. Santos, and M. Lewenstein, Phys. Rev. Lett. 88, 170406 (2002).
[33] L. Tanzi, S. M. Roccozzi, E. Lucioni, F. Fanà, A. Fioretti, C. Gabbannini, G. Modugno, A. Recati, and S. Stringari, Nature 574, 382 (2019).
[34] M. A. Norcia, C. Politi, L. Klaus, E. Poli, M. Sohmen, M. J. Mark, R. N. Bisset, L. Santos, and F. Ferlaino, Nature 596, 357 (2021).
[35] L. Tanzi, J. G. Maloberti, G. Biasioni, A. Fioretti, C. Gabbannini, and G. Modugno, Science 371, 1162 (2021), https://www.science.org/doi/pdf/10.1126/science.aba4309.
[36] I. Carusotto and C. Ciuti, Rev. Mod. Phys. 85, 299 (2013).
[37] M. Combescot, M. A. Dupertuis, and O. Betbeder-Matibet, Europhysics Letters (EPL) 79, 17001 (2007).
[38] J. Levinsen, G. Li, and M. M. Parish, Phys. Rev. Research 1, 033120 (2019).
[39] C. Ciuti, P. Schwendimann, B. Deveaud, and A. Quattropani, Phys. Rev. B 62, R4825 (2000).
[40] S. Schmitt-Rink, D. S. Chemla, and D. A. B. Miller, Phys. Rev. B 32, 6601 (1985).
[41] A. Baas, J. P. Karr, H. Eleuch, and E. Giacobino, Phys. Rev. A 69, 023809 (2004).
[42] L. Carusotto and C. Ciuti, Rev. Mod. Phys. 85, 299 (2013).
[43] P. Lambin and P. Senet, International Journal of Quantum Chemistry 46, 101 (1993), https://onlinelibrary.wiley.com/doi/pdf/10.1002/qua.560460110.
[44] A. Altland and B. D. Simons, Condensed matter field theory (Cambridge University Press, 2010).
[45] T. K. Paraúso, M. Wouters, Y. Léger, F. Morier-Genoud, and B. Deveaud-Plédran, Nature Materials 9, 655 (2010).
[46] C. Lagoin, S. Suffit, K. Baldwin, L. Pfeiffer, and F. Dubin, Nature Physics 18, 149 (2022).
[47] Y. Jiang, S. Chen, W. Zheng, B. Zheng, and A. Pan, Light: Science & Applications 10, 72 (2021).
[48] M. Sidler, P. Back, O. Cotlet, A. Srivastava, T. Fink, M. Kroner, E. Demler, and A. Imamoglu, Nature Physics 13, 255 (2017).
[49] A. Julku, M. A. Bastarrachea-Magnani, A. Camacho-Guardian, and G. M. Bruun, Phys. Rev. B 104, L161301 (2021).
[50] L. B. Tan, O. Cotlet, A. Bergschneider, R. Schmidt, P. Back, Y. Shimazaki, M. Kroner, and A. m. c. Imamoglu, Phys. Rev. X 10, 021011 (2020).
[51] R. P. A. Emmanuele, M. Sich, O. Kyrrienko, V. Shahnazaryan, F. Withers, A. Catanzaro, P. M. Walker, F. A. Benimetiskiy, M. S. Skolnick, A. I. Tartakovskii, I. A. Sheplykh, and D. N. Krizhanovskii, Nature Communications...
[51] M. A. Bastarrachea-Magnani, A. Camacho-Guardian, and G. M. Bruun, Phys. Rev. Lett. 126, 127405 (2021).
[52] A. Camacho-Guardian and N. R. Cooper, In preparation.
[53] N. Cooper and C.-G. A., Apollo Repository (2022), doi.org/10.17863/CAM.89893. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4348,
1
],
[
4348,
10475,
2
],
[
10475,
17103,
3
],
[
17103,
22727,
4
],
[
22727,
26371,
5
],
[
26371,
31330,
6
],
[
31330,
35950,
7
],
[
35950,
40782,
8
],
[
40782,
45931,
9
],
[
45931,
50242,
10
],
[
50242,
54498,
11
],
[
54498,
54747,
12
]
]
} |
9a6183a42925ebb48b73807d681e79a583fd736a | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 7,
"total-fallback-pages": 0,
"total-input-tokens": 23133,
"total-output-tokens": 5769,
"fieldofstudy": [
"Materials Science"
]
} | Advances in tool grinding and development of end mills for machining of fibre reinforced plastics
Eckart Uhlmann a, Nikolas Schröer a*
*Institute for Machine Tools and Factory Management, Technische Universität Berlin, Berlin, Germany
Abstract
The extensive use of lightweight construction materials in the aerospace industry poses a great challenge for tool manufacturers. Materials like carbon fibre reinforced plastics (CFRP) are difficult to machine and therefore put high demands on cutting tools in terms of the cutting material as well as the macro- and microscopic design. In this paper two approaches for the improvement of CFRP milling processes are presented. One approach involves the optimization of the flute grinding process for cemented carbide milling tools by the use of innovative grinding wheel specifications and their influence on cutting-relevant tool features. The other approach deals with the development of ceramic end mills for CFRP machining. Investigations about the influence of different process- and tool-related parameters on the work result and process parameters are presented.
Keywords: tool grinding; ceramic; cemented carbide; CFRP; milling
1. Introduction
The ongoing awareness for sustainability issues in the industrial sector is resulting in optimization and advancements of existing technological systems in multiple fields to more resource preserving solutions. A usual approach, especially for dynamic systems, is to seek for a lower component weight. Besides constructive measures, further weight savings can usually be reached by the use of innovative materials, which have comparable or even better mechanical properties than conventional materials and at the same time have a lower density. A good example for the substitution of established materials could be observed in the aerospace industry for the last decades and is still ongoing [1]. Huge parts of modern airplanes consist of innovative lightweight materials like carbon reinforced plastics (CFRP) and aluminum alloys. Recently, the automotive industry has also put great efforts in the substitution of car body parts from steel to CFRP in order to compensate the battery induced weight gain of hybrid or fully electric power trains [2]. Thus, but also because of the increasing use of CFRPs in the wind energy, sports and molding compound sector, a rising demand for fibre reinforced plastics (FRP) is expected in the next years [3].
Since the part quality is insufficient in most cases after the primary shaping manufacturing processes of FRPs, the machining of inner and outer contours is often necessary in order to meet the high dimensional and surface qualities especially for the aerospace industry [4,5]. The superior properties of CFRPs put high demands on machining processes like milling and drilling as their two phase composite structure consisting of fibre and matrix material with diverse attributes goes along with an inhomogeneous and anisotropic configuration. High-tensile, brittle carbon fibres, which are embedded in a temperature sensitive synthetic matrix with high failure strain result in predominant abrasive wear during the machining process [6,7].
The superior properties of CFRPs on the other side pose a great challenge for tool manufacturers. As the characteristics of CFRP materials can vary widely due to different compositions of e.g. fibre types, diameters, lengths and
orientations as well as the synthetic matrix specification, they show also a diverse behavior during machining. Therefore it is often necessary to develop application related cutting tools in order to meet the different requirements that come along with variable workpiece properties. Hence, during machining of CFRPs versatile machining errors like delamination, fraying, fibre fracture, burr formation and burn can be observed. Currently polycrystalline diamond (PCD) and diamond coated cemented carbide tools are widely used [8,9].
There are some specific requirements regarding the tool design and the cutting material that should be met by all used tools. In terms of the tool design, it was investigated, that sharp cutting edges with a low cutting edge radius and chipping are necessary in order to realize a cutting of the fibres and prevent machining errors [10,11]. Another important tool feature with influence on the cutting process is the surface quality of the rake face. It was observed, that the surface quality can influence the adhesion tendency and the coating process significantly [12,13]. Regarding the cutting material a certain resistance against abrasive wear is essential to ensure an economical application of cutting tools. In recent research activities at the Institute for Machine Tools and Factory Management (IWF) different approaches were pursued in order to improve the machining behavior of CFRP cutting tools. In the following, two of them will be described in detail.
As the tool grinding process has a verifiable influence on the machining behavior of cutting tools [14] several investigations on the optimization of the flute grinding process of end mills were conducted. Therefore grinding tests with innovative grinding wheel specifications were carried out and the work result was evaluated in terms of cutting tool relevant parameters. Furthermore results from the development and use of ceramic end mills for CFRP machining are shown. Investigations about the influence of different process- and tool-related parameters on the milling work result and process parameters are presented.
2. Optimization of the flute grinding process
Tool grinding as the essential manufacturing process in the generation of the cutting edge geometry of end mills plays an important role because it influences the machining behavior of the milling tool notably. It involves all grinding operations for the generation of shapes and functional surfaces on a cutting tool. For one-piece end mills it can be applied that despite the great variety of tool geometries basically three grinding operations are necessary: flute, peripheral and face grinding. Within these operations the flute grinding process (Fig. 1) itself has a major function because in comparison it possesses a high material removal $V_w$ that goes along with a high main time and also has the dominating influence on the cutting edge generation [14,15]. Due to economical reasons flute grinding processes are generally performed in creep feed grinding mode.
Cemented carbide is extensively used in the cutting tool industry and requires the application of superabrasive grinding wheels because of its brittle hard material properties. In many cases resin bonded grinding wheels are used, although the material removal rate $Q'_w$ is limited, good surface and cutting edge qualities can be achieved [14,16]. In the last years new hybrid bond specifications were developed, which show a high potential for productivity and quality enhancements during flute grinding. Thus, grinding tests were performed with different grinding wheel specifications in terms of the bond and are analyzed regarding grinding forces, surface quality in the flute and cutting edge quality.
2.1. Experimental setup
The grinding tests were carried out on a 5-axis tool grinding machine WU 305micro by Alfred H. Schütte GmbH, Cologne. Equipped with 3 translational and 2 rotational linear drives, the grinding forces were evaluated by the analysis of the electric current from the machine control. The surface quality of the flute was analyzed with the tactile stylus instrument nanoscan 855 from Hommel Etamic GmbH, Schwenningen.
For each grinding test three flutes were ground in a round cemented carbide blank in order to neglect grinding-in effects. To determine the work result easily the helix angle was set to $\lambda = 0^\circ$ with a lead angle of $\lambda_p = 2.5^\circ$. After the third flute a material removal of $V_w = 1700 \text{ mm}^3$ was reached and the work result and process relevant parameters were analyzed. Important properties of the used grinding wheels and cemented carbide blanks are shown in Table 1 and Table 2.
Cutting speed \( v_f = 15 \text{ m/s} \)
Process parameter:
- Up grinding
- Material removal \( V_w = 1700 \text{ mm}^3 \)
2.2. Results
In Figure 2 the specific normal force \( F'_{\text{n}} \) and the cutting force ratio \( \mu \) for the tested grinding wheel specifications are plotted as a function of the feed rate \( v_f \) during flute grinding. Concerning the specific normal force \( F'_{\text{n}} \), a nearly linear increasing correlation with the feed rate \( v_f \) can be observed for all grinding wheel specifications. Only the resin bond grinding wheel shows a diverse behavior. With this grinding wheel, higher feed rates \( v_f > 30 \text{ mm/min} \) were not realized due to overloading of the bond, which could be identified by burning marks on the grinding wheel. The fact that a lowering of the grinding force ratio \( \mu \) in combination with the nonlinear rise of the specific grinding force \( F'_{\text{n}} \), can be observed at a feed rate of \( v_f = 30 \text{ mm/min} \), supports this assumption. With higher temperatures the grit retention force of the bond is lowered and whole grain breakouts are induced which leads to a less effective grinding process.
In comparison to the resin bond grinding wheel the other grinding wheel specifications were capable of higher feed rates \( v_f \) and accordingly material removal rates \( Q'_{\text{w}} \) without an indication of a less effective grinding process through a lower cutting force ratio \( \mu \). Comparing the specific normal forces \( F'_n \) for all process points to each other, it can be noticed that the vitrified bond grinding wheel induces the highest grinding forces and the hybrid bond grinding wheel with a metallic/vitrified bond the second highest. The other hybrid bond grinding wheel on metallic/resin basis generates the lowest specific grinding force \( F'_n \) for all analyzed process parameters. As all tested grinding wheels are identical except for the bond and also were dressed under the same conditions, the measured differences can be primarily led back to different mechanical and thermal properties of the bond. It can be assumed that the Young’s modulus in particular can act as an indicator for the grinding forces under constant boundary conditions.
In terms of the work result the surface quality of the workpiece was analyzed at two different positions for each ground flute. The positions are shown in Figure 3 and were chosen because on the one hand they are representing the rake face quality and on the other hand they show the surface quality in the ground of the flute. Figure 3 shows that the feed rate \( v_f \) has a diverging influence on the ten point height roughness \( R_z \). While the different grinding wheel specifications show nearly the same result for each tested feed rate in the ground of the flute, the ten point height roughness \( R_z \) is also not varying much between the tested feed rates \( v_f \). This behaviour can be explained by the high velocity ratios \( q \) that occur during creep feed grinding of cemented carbide. Due to the fact, that the speed ratio varies from \( q = 90,000 - 10,000 \) for the tested feed rates from \( v_f = 10 - 90 \text{ mm/min} \), it can be assumed that the maximal surface quality is already reached at speed ratio of \( q < 10,000 \) and cannot be further increased by a lowering of the feed rate.
In contrast to these results the surface quality of the rake face shows a significant tendency for a higher ten point height roughness \( R_z \) with increasing feed rates \( v_f \) for all tested grinding wheels and are in general one decimal lower. The material removal ratio varies along the active grinding wheel width \( b_{\text{eff}} \) according to Huebert [14] and therefore is lower at the edge of the grinding wheel. It can be assumed that also an increasing wear at the grinding wheel edge caused by higher loads with rising feed rates can be responsible for this behaviour. In combination with the different geometric-kinematic contact conditions at the rake face which are more similar to a face grinding process as to a peripheral grinding process, these differences can be explained.
specific grit retention force. Higher bonding friction can go along with a lower workpiece roughness. A potential difference in the wear mechanisms of the grinding wheels will be investigated in further research activities.
3. Development and use of ceramic end mills for CFRP machining
Cutting materials for CFRP machining have to meet high requirements in terms of abrasive wear resistance as the two phase composite structure of CFRPs consisting of fibre and matrix material with diverse attributes goes mainly along with this wear mechanism. Hence, PCD and diamond coated cemented carbide tools are widely used, as they have shown appropriate performance in CFRP milling and drilling operations [4]. While PCD cutting tools are very costly and also restricted in terms of feasible cutting tool geometries, diamond coated tools have the disadvantage that they cannot be resharpened, which can result in a low economic efficiency. As innovative ceramic cutting materials can possess a high hardness and adequate fracture toughness at the same time, they have the potential to be used as cutting material for CFRP machining as well. In order to improve the productivity and quality of CFRP milling processes, the potential of an innovative ceramic material, silicium infiltrated silicon carbide, which was developed primarily for this purpose, was analyzed in a research project at the IWF. A holistic approach of the project was realized, from the analysis and development of the cutting material, to the cutting geometry development, the analysis of the manufacturing processes and the cutting performance during milling. Due to the fact that ceramics generally have brittle hard material properties and therefore also show similar chip formation mechanisms as cemented carbides, many findings concerning the influence of the grinding parameters on e.g. the cutting edge formation at cemented carbide tools were transferred and applied during grinding of the ceramic end mills.
As part of the described technological investigations the influence of different tool geometry features on the milling forces were analyzed and presented in the following. Based on these investigations the machining behavior of ceramic and cemented carbide end mills are then compared.
3.1. Tool geometry development
The milling tests were performed on a 3-axis milling machine tool 10V HSC by Mikromat GmbH, Dresden. The milling forces were recorded with a 3 component force measurement system type 9257A from Kistler Instrumente AG, Winterthur, Switzerland.
Based on a tool geometry which was evaluated in preliminary investigations, different geometry features of the end mill were varied. The tool diameter was constant d = 8 mm for all tested geometries while the other relevant tool geometry parameters helix angle λ, number of teeth z, depth of flute t, as well as the rake γ and clearance angle α were varied. Table 3 gives an overview of the varied geometry features.
Table 3. Varied tool geometry parameters.
| Tool No. | No. of teeth z | Depth of flute $t_n$ | Helix angle $\lambda$ | Rake angle $\gamma$ | Clearance angle $\alpha$ |
|----------|----------------|----------------------|-----------------------|---------------------|------------------------|
| 1 | 6 | 0.8 mm | 20° | 5° | 10° |
| 2 | 8 | 0.8 mm | 20° | 5° | 10° |
| 3 | 6 | 1 mm | 20° | 5° | 10° |
| 4 | 6 | 1.2 mm | 20° | 5° | 10° |
| 5 | 6 | 1.4 mm | 20° | 5° | 10° |
| 6 | 6 | 1 mm | 10° | 5° | 10° |
| 7 | 6 | 1 mm | 30° | 5° | 10° |
| 8 | 6 | 1 mm | 20° | 5° | 5° |
| 9 | 6 | 1 mm | 20° | 5° | 15° |
| 10 | 6 | 1 mm | 10° | 5° | 5° |
| 11 | 6 | 1 mm | 10° | 10° | 5° |
| 12 | 6 | 1 mm | 20° | 10° | 5° |
| Opt. | 6 | 1.4 mm | 20° | 5° | 15° |
In Figure 4 the feed force $F_f$ during peripheral milling is shown for the thirteen tested tool geometries. For each geometry two identical end mills were brought into the milling process and the milling forces after a tool life travel path of $L_c = 3.5$ m were evaluated. Regarding the feed force a clear correlation between the number of teeth $z$ as well as the clearance angle $\alpha$ can be seen. It can be seen that the optimized tool geometry shows the lowest feed force in comparison. In addition to the analysis of the milling forces, the work result and the wear behavior were also taken into account to develop an optimized tool geometry.
3.2. Comparative analysis of the machining behavior of ceramic end mills
For the evaluation of the wear behavior of cutting tools usually the maximal width of flank wear land $V_B_{\text{max}}$ is used. For CFRP materials which tend to delamination and fraying, the workpiece edge quality can also be assessed as wear criterion. In order to classify the developed ceramic end mills in comparison with other types of tools, comparative technological investigations were carried out. Besides the ceramic end mill, a cemented carbide tool with the same geometry was used and the workpiece quality was evaluated after the same tool life travel path. The results of these technological investigations are presented in Figure 5. It can be seen that both tools cause solely fraying at the workpiece and that the ceramic tool generates better workpiece qualities after the same tool life travel path. These effects can be led back to the cutting edge condition during milling.
Workpiece quality with ceramic tool
Workpiece quality with cemented carbide tool
Hence, SEM photographs of both tools have been evaluated additionally. The results can be seen in Figure 6. While abrasive flank wear seems to appear at both tools, the surface structure for the cutting materials are significantly different. It can be assumed that the microgeometrical cutting edge parameters like chipping and radius are in correlation with the observed differences concerning the workpiece quality. Due to the brittleness of ceramic materials they have a higher potential for cutting edge chipping and breakouts, although no breakouts could be observed during these tests. A more detailed investigation of these influences on the workpiece quality will be performed in future research activities.
Additionally the milling forces were analyzed and shown in Figure 7. It can be seen that higher forces concerning the transverse, feed and passive force occur at the cemented carbide tool. As they have the same tool geometry, were ground under the same conditions and tested with the same process parameters during milling these differences can be related back to the diverging microstructure of the cutting edges, different friction conditions between the tool and the workpiece as well as differences in the thermal conductivity of the cutting materials.
Fig. 6. SEM pictures of the cutting edges for a) ceramic tool and b) cemented carbide tool.
4. Summary and Outlook
Within the presented paper, technological investigations for the improvement of CFRP milling processes are shown. Therefore different approaches were conducted. One approach deals with the use of innovative grinding wheel specifications during flute grinding of end mills and their influence on milling relevant parameters. It was shown that different bonding systems result in varying grinding forces during flute grinding and thus can have an impact on the shape and dimensional accuracy of the ground tool. Furthermore it was demonstrated that a change of feed speed $v_f$ during flute grinding has diverging impacts on the surface quality depending on the face that is examined. It was identified, that the influence of grinding process parameters on the surface quality of the rake face is significant. As the properties of the rake face are essential for the cutting mechanisms this should be taken into account by tool manufacturers. Upcoming research works will consider graded grinding tools for flute grinding processes in order to respect the complex non-constant contact conditions during grinding of helical flutes. Thereby further improvements of quality and productivity in tool grinding are targeted.
The other approach respectively research field which is pursued by the IWF is about the development of ceramic end mills and the analysis of their behavior during milling of CFRP. By the presented results it can be assumed that the developed milling tools have a high potential as an economic alternative for conventional CFRP milling tools like coated cemented carbide end mills.
Acknowledgements
The authors would like to thank the German Research Foundation (DFG) for the support. Parts of the presented research work were undertaken within the project DFG UH 100/162-1. Furthermore, the authors would like to thank the German Federal Ministry for Economic Affairs and Energy (BMWi) which supported the other parts of the presented work within the Central Innovation Programme for SME’s (ZIM).
References
[1] Breuer U. Herausforderungen an die CFK-Forschung aus Sicht der Verkehrsflugzeug-Entwicklung und Fertigung. 10. Nationalsymposium SAMPE Deutschland e.V.; 2005.
[2] Kleinhans C. Entwicklung: Der Markt für Karosserieleichtbau wächst weltweit - mit China als Hauptmarkt. Verfügbar unter: Automobil Industrie (58) 2013; 11/12:60-2.
[3] Kraus T, Kühnel M. Der globale CFK-Markt 2014. AVK Industrievereinigung Verstärkte Kunststoffe, Composites Marktbericht 2014.
[4] Neitzel M, Mitschang P, Breuer U. Handbuch Verbundwerkstoffe. 2. aktualisierte und erweiterte Auflage. Munich: Hanser; 2014.
[5] Campbell FC, et al. Post-Processing and Assembly. In: ASM Handbook, Vol. 21 Composites, Materials Park: ASM International; 2001.
[6] Sakuma K, Seto M, Taniguchi M, Yokoo Y. Tool Wear in Cutting Carbon-Fiber-Reinforced Plastics: The Effect of Physical Properties of Tool Materials. Bull JSME (245) 1985; 26:2781-2788.
[7] Wang X, Kwon PY, Starkevaitis C, Kim D. Lantrip J. Tool Wear of Coated Drills in Drilling CFRP. J Manuf Processes (1) 2012;15:127-135.
[8] Lantrip J. New Tools Needed. Cutt Tool Eng (8) 2008;60:72-84.
[9] Spur G, Wunsch UE. Turning of Fiber-Reinforced Plastics. Manuf Rev (2) 1988;1:124-129.
[10] Hartmann D. Delamination an Bauteilkanten beim Umrissfräsen kohlenstofffaserverstärkter Kunststoffe. In: Hintze W, et al., editors. Wissen schafft Innovation. Hamburg; 2012
[11] Rumenhöller S. Werkstofforientierte Prozeßauslegung für das Fräsen kohlenstofffaserverstärkter Kunststoffe. In: Eversheim W, et al., editors. Berichte aus der Produktionstechnik. Aachen: Shaker; 1996.
[12] Fuller KNG, Tabor D. The effect of surface roughness on the adhesion of elastic solids. Proc R Soc Lond 1975;345:327-342.
[13] Hütt T. Charakterisierung und Auslegung der Grenzschicht PVD-beschichteter Schneidkeramiken. In: Uhlmann E, editor. Berichte aus dem Produktionstechnischen Zentrum Berlin. Stuttgart: Fraunhofer IBF; 2010.
[14] Hübert C. Schleifen von Hartmetall- und Vollkeramik-Schaftfräsern. In: Uhlmann E, editor. Berichte aus dem Produktionstechnischen Zentrum Berlin. Stuttgart: Fraunhofer IBF; 2012.
[15] Uhlmann E, Hübert C. Tool Grinding of End Mill Cutting Tools Made from High Performance Ceramics and Cemented Carbides. CIRP Annals 2011;60:359-362.
[16] von Brevern P. Untersuchungen zum Tiefschleifen von Hartmetall unter besonderer Berücksichtigung von Schleifölkühlung. In: Fortschrittberichte VDI, Reihe 2, Nr. 401. Düsseldorf: VDI; 1996. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3423,
1
],
[
3423,
8136,
2
],
[
8136,
12357,
3
],
[
12357,
15321,
4
],
[
15321,
19789,
5
],
[
19789,
22063,
6
],
[
22063,
24952,
7
]
]
} |
f603a0884c63af320355befd815ce7d94c373496 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 5,
"total-fallback-pages": 0,
"total-input-tokens": 17303,
"total-output-tokens": 5144,
"fieldofstudy": [
"Physics"
]
} | Understanding the Plasmonics of Nanostructured Atomic Force Microscopy Tips
A. Sanders, R.W. Bowman, L. Zhang, V. Turek, D.O. Sigle, A. Lombardi, L. Weller, and J.J. Baumberg
Nanophotonics Centre, Department of Physics, Cavendish Laboratory, Cambridge, CB3 0HE
(Dated: July 25, 2016)
Structured metallic tips are increasingly important for optical spectroscopies such as tip-enhanced Raman spectroscopy (TERS), with plasmonic resonances frequently cited as a mechanism for electric field enhancement. We probe the local optical response of sharp and spherical-tipped atomic force microscopy (AFM) tips using a scanning hyperspectral imaging technique to identify plasmonic behaviour. Localised surface plasmon resonances which radiatively couple with far-field light are found only for spherical AFM tips, with little response for sharp AFM tips, in agreement with numerical simulations of the near-field response. The precise tip geometry is thus crucial for plasmon-enhanced spectroscopies, and the typical sharp cones are not preferred.
Within the last decade nano-optics has benefited from the advent of metallic tip-based near-field enhancement techniques such as TERS and scanning near-field microscopy (SNOM), leading to successes in single molecule detection and spatial mapping of chemical species. Despite their high spatial resolution and scanning capabilities, there remains confusion about the plasmonic response of metallic tips. Tip systems built on AFM probes can exhibit electric field enhancements close to 100 at the apex (Raman enhancements up to $10^8$), due to a combination of plasmonic localisation and a non-resonant lightning rod effect. The factors determining a tip’s ability to enhance the near-field include the experimental excitation/collection geometry, tip sharpness, surface metal morphology, and constituent material.
Despite large measured near-field enhancements, the standard sharp AFM tip geometry does not support radiative plasmons. The extended (∼20 µm) size and single curved metal-dielectric interface of an AFM tip supports only weakly confined localised surface plasmons (LSPs) and propagating surface plasmon polaritons (SPPs), which may be localised by adiabatic nanofocussing. Lack of a dipole moment means that neither LSPs or SPPs strongly couple with radiative light in the same manner as multipolar plasmons in subwavelength nanoparticles. For this reason, the tip near-field is often excited with evanescent waves or via nanofabricated gratings to access the optically-dark SPPs, with resonant scattering of evanescent waves, resonances in the TERS background and depolarised scattering images providing evidence for localised plasmon excitation. For Au tips such plasmon resonances are typically found between 600–800 nm.
Improvements in enhancement are often found in roughened tips with grains acting as individual nano-antennae for more confined LSPs, however this approach lacks reproducibility. In recent years controlled nanostructuring of the tip apex with a distinct subwavelength-size metallic feature has been explored in order to engineer and tune a plasmonic optical antenna precisely at the apex and better incorporate more localised multipolar plasmons. Etching, focussed-ion-beam machining, selective deposition, nanoparticle pickup, nanostructure grafting and electrochemical deposition have all been successfully used to nanostructure optical antenna tips. Scattering resonances in the visible-NIR spectrum have been directly measured on a subset of these while other reports use improvements in the field enhancement as a measurement of antenna quality.
The simplest geometry for a tip apex is a spherical nanoparticle (NP), giving LSPs similar to those in an
isolated spherical metallic nanoparticle. In this paper we demonstrate an effective method for characterising the radiative plasmon modes of a tip and clearly show the benefits of utilising spherically nanostructured tips as near-field enhancers.
The optical properties of AFM tips are studied using a custom-built confocal microscope with a supercontinuum laser source for dark-field scattering spectroscopy (Fig. 1). Both illumination and collection share the optical axis of a 0.8 NA IR objective. Supercontinuum laser light is filtered into a ring and incident on a tip at 0.6–0.8 NA while light scattered by the tip is confocally collected from the central laser focus using an iris to restrict the collection NA below 0.6. Broadband polarising beamsplitters are used to simultaneously measure spectra which are linearly polarised both along the tip axis (axial) and perpendicular to the tip axis (transverse).
A scanning hyperspectral imaging technique is applied to determine the local optical response at the tip apex. Tips are raster scanned under the laser spot and the dark field scattering from the confocal sampling volume measured at each point, forming a hyperspectral data cube. Images are formed at each wavelength contained in the cube, with each image pixel digitised into 1044 wavelengths between 400–1200 nm. Measured spectra are normalised to a spectrum of flat metal of the same material to show only structural effects. Image slices at individual wavelengths or wavelength bands are then readily constructed to display localised spectral features. Fast image acquisition is made possible by the high brightness supercontinuum laser source (100 $\mu$W.$\mu$m$^{-2}$) and cooled benchtop spectrometers, enabling 10 ms integration times (5 mins per image). Within plasmonics, this approach to hyperspectral imaging has been used to identify distributed plasmon modes in aggregated AuNP colloids [30] and to image SPPs [31] but has yet to be applied to tips. By using this technique, radiative plasmons can be spatially identified with a resolution around 250 nm.
To investigate the radiative plasmonic properties of nanostructured tips, hyperspectral images are taken of both standard (sharp) and spherical-tipped Au AFM tips. Spherical tips are either 300 nm diameter, 50 nm Au-coated NanoTools B150 AFM probes or electrochemically-deposited AuNP-on-Pt AFM probes, fabricated in-house [29] (shown in Fig. 2). Fabricated tips are pre-treated where possible prior to use with ambient air plasma and/or piranha solution to remove organic surface residue and, in some cases, smooth out surface roughness.
Comparisons between spherical- and sharp-tipped Au probes using hyperspectral image slices (Fig. 3) shows that spherical tips exhibit a characteristic red (600–700 nm) scatter, separated from the bulk tip. No similar localised scattering is seen in the visible spectrum with sharp Au tips, which have a ten-fold weaker optical response and appear similar to non-plasmonic Pt tips. This delocalised apex scatter can also be directly seen in dark-field microscopy images (Fig. 1b). The AuNP-on-Pt
structure behaves very similarly to the Au-coated spherical tip (which has diamond-like-carbon inside), likely because the 50 nm coating thickness is greater than the skin depth. As we show below, differences in plasmon resonances arise due to the Au-Pt and Au-Au neck boundaries.
Integrating spectra around each tip better shows the 600–700 nm scattering resonance from spherical Au tips (Fig. 3c), which are reliably present in all spherical-tipped AFM probes, both vacuum-processed and electrochemically deposited. We attribute these to localised surface plasmon excitation, while electron microscopy confirms this resonance correlates only with spherical Au tip shapes. The response of sharp Au tips shows no similar plasmonic features, while the slow rise in scattering towards the NIR is consistent with lightning rod scattering.
Broadband tuneable SERS measurements confirm that the optical scattering resonance seen in spherical Au tips is indeed caused by radiative plasmon excitation. The trapped plasmon fields enhance optical processes on the surface such as surface-enhanced Raman scattering (SERS) and here we use the SERS background as a reporter of the plasmonic near-field strength. SERS background spectra are integrated across a range of excitation wavelengths between 500 and 700 nm, spaced 10 nm apart, to extract any scattering resonances. The resulting spectrum (Fig. 3) shows a distinct peak around the spherical Au tip scattering resonance, while no such resonance is seen for sharp Au tips. Further confirmation stems from direct observation of plasmon coupling between spherical tips, as has been previously reported.
Plasmon resonances in spherical AuNP tips correspond to radiative antenna-like modes, similar to those in plasmonic nanoparticles, that efficiently couple far-field light into strong collective free electron oscillations without the need for SPP momentum matching. As with nanoparticles, the signature of these plasmons is an optical resonance indicating their large dipole moment (Fig. 3d). Since spherical metallic tips possess a neck behind the tip, they can support NP plasmonics. Sharp tips do not have this back surface, hence cannot support radiative plasmon resonances, although the single metal-dielectric surface supports launching of evanescent SPPs and a strong lightning rod component.
Simulated near-field spectra (using the boundary element method) around the apex of 300 nm spherical Au and AuNP-on-Pt tips with 120 nm neck diameters ($d_{\text{neck}} = 0.4 d_{\text{sphere}}$) are shown in Fig. 4a. Tips are simulated with a length of 1.88 μm to avoid truncation artefacts which are commonly seen in tip simulations and erroneously suggest plasmonic performance even in sharp tips. Strong modes appear along the tip axis for all spherical tips between 550–700 nm, as in experiments with peak wavelengths that match our hyperspectral results. Near-field maps corresponding to the main resonance in each tip (Fig. 4b,c) show dipole-like resonances with the neck spatially splitting the underside of each mode, mixing it with quadrupolar modes and shifting it towards the blue.
In order to directly compare the plasmonic behaviour of spherical and sharp Au tips independent of lightning rod contributions, the neck width is incrementally increased. This allows us to study structures which smoothly transition from a nanoparticle attached to the apex of a sharp Au tip, into a rounded tip geometry, without the apex radius ever changing. The field enhancement and peak positions extracted from this morphology transition (Fig. 4d) show resonances insensitive to the neck width until $d_{\text{neck}} > 0.8 d_{\text{sphere}}$, explaining the
robustness of observed spherical tip plasmons between different tip morphologies. However a steady decrease in the field enhancement is observed once \( d_{\text{neck}} > 0.4d_{\text{sphere}} \), decreasing faster once \( d_{\text{neck}} > 0.8d_{\text{sphere}} \). This supports the claim that sharp tips cannot sustain antenna-like plasmons and that the majority of enhancement is from lightning rod effects. We note that the lateral spatial localisation of the field approaches \( 0.3d_{\text{sphere}} \) independent of this neck diameter.
These results demonstrate the importance of considering which plasmons might exist in a particular experiment and nanostructure geometry, and that it is vital to characterise nanostructures prior to their application. Apex nanostructuring can controllably introduce radiative plasmons into the tip geometry, lifting the evanescent illumination restriction of sharp tips and permitting use of a wider range of microscope configurations. While the lightning rod effect will always contribute to the field enhancement and favour sharp tips, exploiting resonant plasmonic enhancement in a carefully optimised spherical tip can further improve the near-field enhancement. The spherical tip geometry and materials shown here are optimised for use with the typically-used 633 nm laser wavelengths.
Demonstrated interactions between spherical tip plasmons also suggests coupling with an image charge in a planar surface is possible and could be used in nanometric tip-surface gaps to further localise the field on resonance with near infrared lasers. Exploiting radiative tip plasmons in this manner bridges the gap between SERS and conventional TERS, forming a spatially-mappable version of the highly successful nanoparticle-on-mirror geometry. These systems repeatedly produce Raman enhancements of up to \( 10^6 \) with nanometric mode volumes, much like tips, and demonstrate that plasmonic gaps can exhibit comparably large field enhancements without relying only on the lightning rod effect.
Secondly, without prior knowledge of the tip-system spectral response it is difficult to properly interpret any measurements, such as TERS spectra. Improved tip characterisation is crucial to understanding vari-
ations in TERS spectra. Standard, wide-field microscopy/spectroscopy is not a particularly effective tool for optically characterising tips. Instead, confocal hyperspectral imaging provides a viable method for mapping the local scattering response while broadband tuneable SERS offers a unique way of optically characterising the near-field. Incorporating these techniques into existing microscopes is relatively simple and will greatly improve the reliability of tip-based near-field microscopy.
**ACKNOWLEDGMENTS**
The authors thank EPSRC grants EP/G060649/1 and EP/L027151/1, and ERC grant LINASS 320503 for funding and NanoTools for their services providing Au-coated spherical AFM tips. RWB thanks Queens’ College and the Royal Commission for the Exhibition of 1851 for financial support.
---
[1] R. Zhang, Y. Zhang, Z. Dong, S. Jiang, C. Zhang, L. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Luo, et al., Nature **498**, 82 (2013).
[2] B. Pettinger, P. Schambach, C. J. Villagómez, and N. Scott, Annual review of physical chemistry **63**, 379 (2012).
[3] W. Zhang, X. Cui, and O. J. Martin, Journal of Raman Spectroscopy **40**, 1338 (2009).
[4] M. I. Stockman, Physical review letters **93**, 137404 (2004).
[5] D. Pile and D. K. Gramotnev, Applied Physics Letters **89**, 041111 (2006).
[6] S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, The Journal of Physical Chemistry Letters **1**, 3427 (2016).
[7] J. S. Lee, S. Han, J. Shirdel, S. Koo, D. Sadiq, C. Lienau, and N. Park, Optics express **19**, 12342 (2011).
[8] S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, The Journal of Physical Chemistry Letters **3**, 945 (2012).
[9] N. C. Lindquist, J. Jose, S. Cherukulapuruth, X. Chen, T. W. Johnson, and S.-H. Oh, Laser & Photonics Reviews **7**, 453 (2013).
[10] H. F. Hamann, A. Gallagher, and D. J. Nesbitt, Applied Physics Letters **73**, 1469 (1998).
[11] C. Neacsu, G. Steudle, and M. Raschke, Applied Physics B **80**, 295 (2005).
[12] D. Mehtani, N. Lee, R. Hartschuh, A. Kisliuk, M. Foster, A. Sokolov, F. Cajko, and I. Tsukerman, Journal of Applied Physics A: Pure and Applied Optics **8**, S183 (2006).
[13] C. A. Barrios, A. V. Malkovskiy, A. M. Kisliuk, A. P. Sokolov, and M. D. Foster, The Journal of Physical Chemistry C **113**, 8158 (2009).
[14] B. Pettinger, K. F. Domke, D. Zhang, R. Schuster, and G. Ertl, Physical Review B **76**, 113409 (2007).
[15] B. Pettinger, K. F. Domke, D. Zhang, G. Picardi, and R. Schuster, Surface Science **603**, 1335 (2009).
[16] T. Mino, Y. Saito, and P. Verma, ACS nano **8**, 10187 (2014).
[17] N. Hayazawa, Y. Inouye, Z. Sekkat, and S. Kawata, Chemical Physics Letters **335**, 369 (2001).
[18] E. Bailo and V. Deckert, Chemical Society Reviews **37**, 921 (2008).
[19] N. Hayazawa, T.-a. Yano, and S. Kawata, Journal of Raman Spectroscopy **43**, 1177 (2012).
[20] T. Umakoshi, T.-a. Yano, Y. Saito, and P. Verma, Applied Physics Express **5**, 052001 (2012).
[21] S. Khairtsev, G. Hoffmann, A. Fishman, and M. K. Salakhov, Journal of Physics D: Applied Physics **46**, 145501 (2013).
[22] P. Uebel, S. T. Buehrschild, M. A. Schmidt, and P. S. J. Russell, Applied Physics Letters **103**, 021101.
[23] A. Weber-Bargioni, A. Schwartzberg, M. Schmidt, B. Harteneck, D. Ogletree, P. Schuck, and S. Cabrini, Nanotechnology 21, 065306 (2010).
[24] M. Fleischer, A. Weber-Bargioni, M. V. P. Altoro, A. M. Schwartzberg, P. J. Schuck, S. Cabrini, and D. P. Kern, ACS nano 5, 2570 (2011).
[25] I. Maouli, A. Taguchi, Y. Saito, S. Kawata, and P. Verma, Applied Physics Express 8, 032401 (2015).
[26] Y. Zou, P. Steinvurzel, T. Yang, and K. B. Crozier, Applied Physics Letters 94, 171107 (2009).
[27] A. I. Denisyuk, M. A. Tinskaya, M. I. Petrov, A. V. Shelaev, and P. S. Dorozhkin, Journal of nanoscience and nanotechnology 12, 8651 (2012).
[28] F. Huth, A. Chuvilin, M. Schnell, I. Amenabar, R. Krutokhvozov, S. Lopatin, and R. Hillenbrand, Nano letters 13, 1065 (2013).
[29] A. Sanders, L. Zhang, R. W. Bowman, L. O. Herrmann, and J. J. Baumberg, Particle & Particle Systems Characterization 32, 182 (2015).
[30] L. Herrmann, V. Valev, J. Aizpurua, and J. J. Baumberg, Optics express 21, 32377 (2013).
[31] M. Bashevoy, F. Jonsson, Y. Chen, and N. Zheludev, Optics Express 15, 11313 (2007).
[32] M. I. Stockman, Optics express 19, 22029 (2011).
[33] C. Huber, A. Trügler, U. Hohenester, Y. Prior, and W. Kautek, Physical Chemistry Chemical Physics 16, 2289 (2014).
[34] A. Lombardi, A. Demetriadou, L. Weller, P. Andrae, F. Benz, R. Chikkaraddy, J. Aizpurua, and J. J. Baumberg, ACS Photonics 3, 471 (2016).
[35] J. T. Hugall and J. J. Baumberg, Physical Review Letters (2015).
[36] K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, Nature 491, 574 (2012).
[37] J. Mertens, A. L. Eiden, D. O. Sigle, F. Huang, A. Lombardo, Z. Sun, R. S. Sundaram, A. Colli, C. Tserkezis, J. Aizpurua, et al., Nano letters 13, 5033 (2013).
[38] R. W. Taylor, F. Benz, D. O. Sigle, R. W. Bowman, P. Bao, J. S. Roth, G. R. Heath, S. D. Evans, and J. J. Baumberg, Scientific reports 4 (2014). | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3740,
1
],
[
3740,
6862,
2
],
[
6862,
10567,
3
],
[
10567,
16000,
4
],
[
16000,
17905,
5
]
]
} |
027f94fdad6432e9e6b8cc040acb001b75b197bd | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 19,
"total-fallback-pages": 0,
"total-input-tokens": 60282,
"total-output-tokens": 12987,
"fieldofstudy": [
"Economics"
]
} | Increasing Interstate Integration in the Agro-Industrial Complex of the EAEU Countries
Anatoly Altukhov¹, Alexander Semin²
Abstract:
The article presents the analysis of the integration processes that are taking place in the Eurasian Economic Union (EAEU), the unified agro-food policy developed by the participating countries, as well as strategic measures and mechanisms for further interstate integration in the field of agro-industrial production.
The article pays special attention to the issues of receiving the real economic (positive) impact from the integration through mechanisms promoting a coordinated agrarian policy.
The authors substantiate the significance of the cluster approach when creating cross-border units as one of the most effective methods of sustainable development of agricultural production in rural areas of the EAEC countries. The article proves the viability of creating joint ventures by agricultural producers and determines their basic characteristics.
Working on the paper, the authors applied traditional methods of research: dialectical (from general to particular), abstract logical, monographic ones, the method of comparative analysis, and expert assessments.
The research findings can be used by the government agencies that work in the field of agro-industrial production and implement targeted complex programs for the development of agriculture and regulation of markets of agricultural products, raw materials and food, as well as social development of rural areas.
The material presented in the article may be of interest to managers and experts of the agro-industrial complex, scientists, postgraduate students and students exploring the development of international relations and foreign trade.
Keywords: Agricultural raw materials, competitiveness, Eurasian Economic Union, food, integration, international trade.
JEL code: F02, F15, F53, Q17.
¹ Russian Academy of Sciences, All-Russian Research Institute of Agricultural Economics.
² Russian Academy of Sciences, Ural State Economic University, email: [email protected]
1. Introduction
The modern economy is experiencing the impact of globalization which increases competition in global markets. In such context, integration has acquired significance as a special mechanism that unites companies in their struggle for survival and market leadership. Another specific feature of the world economy is a rapid transnationalization which is interstate integration. Transnational corporations (TNCs) have become a sort of organizational embodiment of international relations that pursue the goal of private capital consolidation.
At present, the national production growth has become more dependent on the stability of the world economy, the development of international trade, intensification of global economic relations resulting from economies integration and the formation of TNCs. One of the main distinctive features of the current stage of the global integration development is increasing trans-border cooperation, which, for example, is rapidly expanding in the European Union and is emerging in the Eurasian Economic Union (hereinafter – the EAEU member states, the Union).
Due to historical, cultural and geographical proximity, the EAEU member states have the conditions necessary for the development of integrative cooperation in the agrarian sector of the economy and can achieve a common synergetic effect that ensures the dynamic development of their agrarian sector of the economy through effective use of the united agrarian potential. Subject matter of the study is agro-industrial production and international trade in food and agricultural raw materials by EAEU member states. Scope of the study is economic relations linked with the development of integrative cooperation between the EAEU countries in the agro-food sector of the economy. Goal of the study is to develop scientifically valid strategic measures and mechanisms for further deepening and facilitating interstate integration in the EAEU.
The main objectives of the study include:
- analysis of integration processes in the agrarian and agro-food spheres of the Eurasian Economic Union;
- assessment of the integration potential and competitive advantages of the EAEU member states;
- development of forms, methods and mechanisms for promoting interstate integration, increasing the investment attractiveness of agro-industrial production and its main component – agriculture, which requires modernization and innovative development.
The authors justified conceptual provisions related to measures and mechanisms that expand and deepen interstate integration of the Eurasian Economic Union. The paper determines the conditions that ensure the synergetic effect arising during the convergence of economic systems through horizontally and vertically integrated interstate
formations. The authors identified the most promising directions of agro-industrial production that increase the investment attractiveness of business entities.
2. Literature review and current state of research
Many researchers of the agrarian sector of economy focused on issues related to increasing competitiveness, developing integration processes, financial recovery and state support for agricultural production, improving the agricultural policy of the EAEU member states, for instance, Altukhov (2017), Ushachev et al. (2016), Maslova et al. (2018), Semin et al. (2018) and other scientists and experts working in this very specific sector.
The focus on these issues is not accidental. Issues concerning effective cooperation of the EAEU member states, alignment of the economies of the partner countries are still actively explored by many leading scientists of our time. For instance, Medvedeva, and Prokhorenko (2018), who study the problems of the development of agricultural exports by the EAEU member states, note that export of products with high added value should be diversified. Other authors identify the main factors hampering the export development and formulate some directions for promoting agricultural products and food of the EAEU member states to the food markets of third countries.
Borkhunov and Avdeev (2018) conducted a comparative analysis of the parity correlation of prices for agricultural and industrial products for the EAEU member states. The most favorable situation was registered in the republics of Kazakhstan and Belarus, which contributes to the economic development of agricultural producers.
Maslova et al. (2018) focused on the factor analysis of the competitiveness of agro-food products in the EAEU member states. They estimated the competitiveness according to the price factor as the basic one. Unfortunately, they do not consider factors related to modernization of agricultural production or intellectual property use. Experts studying the development of integration processes in the agrarian sector of the economy Rakhmanov and Ivoylova (2017) consider the creation and operation of agro-industrial clusters to be the most important direction in the EAEU development. The researchers identified several constraining factors, among them: poor development of organizational structures and management methods, bad transport and logistics, lack of a Eurasian strategy for entering new foreign markets for agricultural products and foods. Implementation of such a strategic approach will require introduction of large-scale innovations.
The effectiveness of formed interstate clusters is also confirmed by studies conducted by Nechaev et al. (2017). They note that many countries around the world have used clusters. For instance, there are more than 2,100 clusters in the EU countries. Of this total, the agro-industrial complex makes up for 11%. Taking into account the fact that grain production is of geopolitical significance and ensures the food securi-
ty of the EAEU states, the researchers suggested creating an interstate grain cluster of Russia and Kazakhstan within the framework of integrative cooperation. This approach opens up new promising areas for corporate interaction since these countries as large grain producers are largely cover their own needs in this product (Russia – 153.7%, Kazakhstan – 137.8%). The authors claim that creating a cross-border cluster is a necessary and viable measure. In our opinion, the creation of such a cluster is an effective way of solving problems of grain surplus in the Russian Federation and the Republic of Kazakhstan.
Also, it is worth mentioning the research papers of Semin et al. (2016) who assess the effectiveness of interaction between the economies of the EAEC states in the food trade. These researchers analyze the dynamics of foreign trade with third countries and inter trade in food and agricultural raw materials, seeing trade operations as the main criteria that describe the cooperation of the EAEU partner states. The researchers came to the conclusion that this integrative cooperation enabled to increase inter trade and to reduce imports of food products and agricultural raw materials. These scientists pay special attention to the issues of parallel import and protection of intellectual property rights in the foreign trade of the EAEU partner states. Differentiating counterfeit and original agricultural products and food imports remains an urgent problem for all five countries, members of the EAEU (Armenia, Belarus, Kazakhstan, Kyrgyzstan, and Russia).
Studies show that the EAEU member states currently do not pay enough attention to various opinions aired by international scientists on the environmental and social responsibility of developing the agro-industrial production. This can be seen both at the level of the created union of states, and the scale of its interaction with other countries of the world (Crosson and Brubaker, 2016; Thompson, 2017).
In the modern economy, when Russian scientists propose measures aimed at ensuring food sovereignty, international researchers (Mathe, 2013; Sekhampu, 2013) claim that agro-industrial production should be considered not only regarding its economic efficiency, but also in terms of social responsibility. The latter implies that business entities should apply agribusiness models with low human impact on the environment (Anfinogentova et al., 2017; Aranchiy et al., 2017; Prado et al., 2014; Mathe, 2013; Sekhampu, 2013; Vertakova and Plotnikov, 2017; Burkaltseva et al., 2017; Kovalenko et al., 2016).
At the same time, most studies of the agro-industrial complex do not thoroughly consider the specific features of agricultural production (Koshkarev and Boldyrev, 2016; Marwa et al., 2017). Due to its specifics, capital is invested not only in objects created by human labor, but also in natural objects, which is obviously associated with greater risks and a longer payback period of the invested funds (Danylenko et al., 2017).
The agrarian sector implies non-standard working hours, and employees have to interact with living creatures, take into account the seasonal nature of work, and pay great attention to the key component of production – the land, as well as to work in the open air.
There are no studies exploring investment processes that take place in agriculture, including the subsidized territories of the EAEU countries, and their potential is not considered. Researchers have not attempted to work out a set of strategic directions and priorities for the development of the EAEU member states in the context of new challenges of the external environment. Therefore, this article focuses on the abovementioned issues.
Carrying out the research, the authors applied such general scientific methods as analysis, synthesis, logical evaluation, monographic, economic-statistical, and abstract-logical methods, as well as authors' original observations. They also studied the unity of qualitative and quantitative criteria that can give the most thorough assessment of the economic phenomenon, event and subject, and next conducted studies in line with the objectives of this research.
3. Proposed methods and approaches to achieving the objectives set
The following research methods can be used to determine the factors impeding the development of forms, methods and mechanisms that enhance the effectiveness of integrative cooperation, investment attractiveness of agro-industrial production and its competitiveness in the EAEU member states: monographic (used to specify and expand the core content of processes of integrative cooperation between partner states, identify specifics of agricultural development under international economic sanctions, assess the forms, methods and mechanisms for promoting interstate integration that can increase the investment attractiveness of the agro-industrial production, especially its main element – agriculture which requires modernization and innovative development); economic-statistical (used to analyze integration processes in the agrarian and agro-food sectors of the Eurasian Economic Union, to assess the integration potential and competitive advantages of the EAEC member states); sociological (used to conduct a survey among heads of agricultural enterprises attracting investments and developing foreign trade cooperation); economic and mathematical (used to analyze the possibilities for developing foreign trade cooperation of the EAEU member states, to determine comparative advantages in the export of food and agricultural products).
4. Results
Having analyzed the integration processes in the agrarian sector of the economy of the Union, the authors proved that these countries receive real economic benefits from integrative cooperation by achieving the set goals, finding mutually beneficial ways of cooperation between their agrarian economies, building a mutually benefi-
cials export-oriented strategy through interaction in the sectors and sub-sectors of the agro-industrial complex that are of economic interest for these countries.
The provisions of the EAEU Agreement of May 29, 2014 imply the transition to a coordinated common, or ideally, to a unified agro-industrial policy of the EAEU member states by means of a gradual synchronization of the system of measures for state regulation aimed at the development of the agro-industrial complex. The Agreement states that reaching the objectives of the coordinated agro-industrial policy means using mechanisms of interstate cooperation in the agrarian and agro-food spheres, international trade, as well as developing technical and human potential, information support and other areas of integrative cooperation (Treaty on the Eurasian Economic Union, 2014).
The integrative potential and competitive advantages in the agrarian sector of the economy of each country and the Union as a whole can be more fully utilized only if they avoid mutual competition in specialized niches. On the one hand, this also implies that it is possible to facilitate interstate integration boosting innovative development of promising sectors of the agro-industrial complex, to ensure the growth of inter trade in agro-industrial products in the Union market and to substitute imports from the third countries.
On the other hand, this enables to take advantage of the efficient territorial and sectoral division of labor in the Union’s agro-industrial production, which is of crucial importance for increasing the production of food, agricultural products, and raw materials, as well as attracting new resources for expanding trade between the EAEU member states and exports to third countries (Altukhov, 2017; Ivanova and Seregin, 2016).
By present, the EAEU member states have already significantly increased the volume of food and agricultural raw materials exports within the framework of integrative cooperation (Table 1).
The volume of export in the inter trade of the EAEU member states in food and agricultural raw materials increased by 18.7% in 2017 as compared to the results of 2015 and amounted to USD 8,173.8 mln. Kyrgyzstan demonstrated the highest growth rate for this indicator – this integration partner exported through inter trade 2.6 more products (Table 1).
The analysis of exports by groups of goods depending on their destination also indicates an increase in exports for each group. For instance, the export of investment goods increased by 34.9% compared to January-December of 2016. The exports of intermediate goods grew by 28.9%, and consumer goods – by 22.2%.
Table 1. Export and Import of Food and Agricultural Raw Materials in the Inter Trade of the EAEU Member States, USD mln (2015-2017)
| EAEU states | Export (2017) | Export (2016) | Export (2015) | as % (2017 over 2015) | Import (2017) | Import (2016) | Import (2015) | as % (2017 over 2015) |
|-------------|--------------|--------------|--------------|-----------------------|--------------|--------------|--------------|-----------------------|
| Armenia | 319.7 | 258.4 | 167.9 | 190.4 | 275.2 | 215.3 | 215.3 | 127.8 |
| Belarus | 4362.2 | 3819.5 | 3855.1 | 113.2 | 1089.0 | 925.0 | 936.2 | 116.3 |
| Kazakhstan | 452.1 | 444.6 | 418.8 | 107.9 | 1597.3 | 1387.8 | 1460.8 | 109.3 |
| Kyrgyzstan | 146.2 | 109.2 | 56.0 | by 2.6 times | 481.4 | 370.4 | 397.4 | 121.1 |
| Russia | 2893.6 | 2486.1 | 2391.1 | 121.0 | 4481.7 | 3877.6 | 3627.3 | 123.6 |
| For the EAEU| 8173.8 | 7117.8 | 6888.9 | 118.7 | 7924.6 | 6776.1 | 6637.0 | 119.4 |
Source: Compiled using Eurasian Economic Commission, 2018.
Integration processes in the agro-industrial complex over the economic space of the Eurasian Economic Union should pursue the goal of implementing the relevant provisions of its Agreement and the Concept of Agreed (Coordinated) Agro-Industrial Policy of Member States in key sectors of the agro-industrial complex, creating a good competitive environment and ensuring the effective development of the unified agrarian market.
The activities of the Union facilitated creating additional macroeconomic conditions for the sustainable development of its agribusiness sectors through:
- devising a regulatory legal system of measures, including the Concept of Agreed (Coordinated) Agro-Industrial Policy of the EAEU Member States, as well as the Decree "On the methodology for estimating consolidated forecast balance of demand and supply of the EAEU member states for agricultural products, foods, flax fiber, cotton fiber and wool", which allowed to apply efficient mechanisms for regulating and monitoring the development of agro-industrial complex and rural areas at the interstate level;
- improving the system of state support measures in compliance with the principles formulated in Annex No. 29 "Protocol on state support to agriculture" of the Treaty on the Eurasian Economic Union of the Republic of Belarus, the Republic of Kazakhstan and the Russian Federation (Section 25 "Agro-industrial complex");
- ensuring equal access of domestic producers to the single agrarian market, main training fair competition between its economic entities, unifying the requirements to the products turnover (Appendix No. 19, "Protocol on general principles and rules of competition"), protecting economic interests of producers in the domestic and external markets, establishing uniform requirements and rules for veterinary and phytosanitary certification (Annex No. 9 "Protocol on technical regulation within the Eurasian Economic Union", Annex No. 12 "Protocol on the application
Increasing Interstate Integration in the Agro-Industrial Complex of the EAEU Countries
760
of sanitary, veterinary and quarantine phytosanitary measures”); - expanding the borders of the Union, and, consequently, using wider opportunities for the export potential of the agricultural sectors of its countries (Annex No. 6 "Protocol on unified customs and tariff regulation", Annex No. 7 "Protocol on measures of non-tariff regulation for third countries").
A key condition for stable economic growth of the EAEU member states is creating and developing an effective economic system and an adequate institutional environment, a range of growing and competitive domestic transnational companies acting as their basis. In this regard, for example, it will be viable to use the experience of developing integration processes accumulated by the Euro-regions in the European Union (Eurasian Economic Commission, 2014; Aleknevičiene et al., 2018; Gorb et al., 2017).
When creating cross-border units, it is feasible to use the cluster approach as one of the most effective methods of socio-economic development and a way to increase the competitiveness of national agribusinesses and interstate integration groups. For example, cross-border units can be used to develop joint projects in agribusiness: production and marketing of agricultural products; establishing joint ventures for production, storage and processing of agricultural products, agricultural machinery, etc.; creating logistics centers; developing innovative technologies; building export infrastructure.
To implement priority joint projects in cross-border regions, the following conditions should be met:
- concluding interstate agreements on the creation of cross-border regions, as well as building the necessary regulatory framework for cross-border and interstate cooperation of the EAEU member states;
- creating agencies and devising a joint strategy for the development of cross-border territories which should outline the main areas of cooperation for each cross-border region;
- developing and approving priority projects by the government agencies of the cross-border region that should be implemented on a competitive basis;
- devising a system of funding through joint funds, attracting private investment and grants;
- creating systems for monitoring and information support.
As a rule, in the EAEU member states, agricultural producers create joint ventures (JVs) on a voluntary basis and mutual agreement of the parties, except entities with partial or full state participation. The JV members do not have any economic privileges compared to other legal associations. There are two main legal forms in the Eurasian economic space. The first one is when contracting parties invest into joint physical capital or joint infrastructure to promote their products to the market (Semin et al., 2018).
The second form of association, unlike the first one, does not deal with physical capital of companies, but only aims at consolidating funds and coordinating the activities of the entities of participating countries in the promotion of goods in the world market. The second form of association is better applicable to such a typical commodity as grain.
Medium and large producers of agricultural products seek for ways to expand or diversify production as they reach full utilization of existing production capacities or saturate the market with their products. While they consider the first task as technical and most often solve it applying proven technological solutions, the second one implies finding and applying fundamentally new ideas, which requires significant financial resources that exceed the volume of free own resources for launching new product lines (Benesova et al., 2017; Gorb et al., 2016).
Creating agrarian clusters should be mentioned as one of the most important aspects of improving the effectiveness of integrative cooperation. The EAEU has great potential for building such structures, which can be explained by long-standing production and technological links in all branches of the agro-industrial complex. At the same time, when developing cluster initiatives and creating agrarian clusters, it is advisable to use the project approach accounting for the comparative advantages of the Union countries, primarily geographical, natural-resource and transport-logistic ones. Special attention should be paid to the quality of agricultural products determined by attracting investments, using advanced technological solutions, and developing logistics, as well as spotting weak sides which is done through value chain analysis.
The Union cannot objectively expand or deepen integration without modern transport and logistics infrastructure that allow creating new industries, labor mobility, and increase transit traffic over the Union's territory through the system of international transport corridors. For example, the main advantage of transit corridors over the territory of Kazakhstan is that transport connection between Europe and China via Kazakhstan is much faster in comparison with the sea route (by 35 days), as well as is shorter by a thousand kilometers if compared with transit through the Russian territory. The development of the Eurasian commodity distribution network of agricultural products, raw materials and foods will allow a 3-5% increase in the volume of trade in the agrarian sector of the economy between the member states, and a 13-17% reduction in average wholesale purchasing prices of agricultural products by reducing the number of intermediaries (Ushachev et al., 2016).
Flexible tariff policy for transportation of agro-food products will facilitate the development of inter trade in the Union. This aspect must be considered when preparing joint interstate programs for export development.
Thus, to improve the trade and export infrastructure of the Union, it is necessary:
Increasing Interstate Integration in the Agro-Industrial Complex of the EAEU Countries
762
- to assess the condition of the main facilities of the Union's trade and export infrastructure, to assess its compliance with modern requirements and, taking this into account, to make a list of the most important infrastructure facilities that need to be put into operation, regarding their integration into the Silk Road Economic Belt;
- to unify the common tariff policy aimed at developing unimpeded inter trade, export and transit of goods, as well as to ensure the agreement of standards in the transport sector, convergence of transport and transit tariffs;
- to carry out a coordinated investment policy for realizing the transit potential, to modernize the border infrastructure and modern logistics centers.
To develop inter-state integration of the EAEU, it seems viable to encourage the creation of logistic schemes that enable to reduce transaction costs, transportation and storage costs for the whole distribution chain, and to enhance the interaction of economic entities. In addition, it is necessary to unify and converge economic conditions to eliminate the excessive interference of state bodies in the activities of economic entities, to abolish or eliminate unreasonable administrative barriers, to develop a unified system of state support and to provide equal competition conditions for all agricultural producers (Avdonin, 2018).
Building the commodity distribution network of agricultural products, raw materials and foods within the EAEU member states will enable to implement complex measures for the delivery of agricultural products, raw materials and food, to create interstate exchange trading structures, risk insurance, bank lending and guarantees for the convergence of uniform laws and regulations, creating a single information space and unified electronic technologies to support transactions, and thereby promoting the overall food security of the Union.
As economic systems are becoming closer interlinked, it will become necessary to create horizontally and vertically integrated interstate unions. They should be export-oriented and import-substituting and facilitate competitive specialized production, scientific and innovative potential, and promoting products to the Union's market and the market of third countries. For example, it is possible to create intergovernmental entities specializing in the production of certain types of food products and agricultural raw materials: between Russia and Kazakhstan – wheat, sunflower oil, cattle meat and poultry; between Belarus and Russia – rye, buckwheat, pork and sugar made from sugar beet; between Belarus, Russia and Kyrgyzstan – dairy products; between Kazakhstan and Armenia – vegetables and fruits. In addition, Belarus, Armenia and Russia have a scientific and technological potential to produce almost the entire range of baby food.
In recent years, there have been a number of significant changes in Russia's trade policy, firstly, the integration association of the EAEU was extended with two new partners: Armenia and Kyrgyzstan have become the Union's full members; secondly, it refers to the introduction of the embargo on the import of food from the USA and the EU; thirdly, the policy of import substitution is being implemented. To assess the
impact of these factors on the development of foreign trade cooperation of the EAEU member states, we carried out special mathematical calculations of the index of comparative advantage using the Balassa index (Balassa, 1965).
The index is calculated by the formula:
$$RCA = \frac{(X_{ij} / X_{it})}{(X_{nj} / X_{nt})} = \frac{(X_{ij} / X_{nj})}{(X_{it} / X_{nt})},$$
(1)
where:
- $X$ is export,
- $i$ is the country under study,
- $j$ is the commodity (or the industry),
- $t$ is a set of commodities (or industries) and $n$ is a country.
Applying the Balassa index, it is possible to obtain indices describing the comparative export advantages of a commodity (industry). If the index has a value greater than 1, then the country under study has a proven comparative advantage for the export of a commodity, which in turn demonstrates its competitiveness (Bludova, 2016; Bondarev, 2016; Mariev et al., 2014). In the last three years (2015-2017), the EAEU states showed an increase in the export of food products and agricultural raw materials (by 7.1% to the base year of 2015), timber and pulp-and-paper products (by 22.4%), as well as textile, textile goods and footwear (by 29.3%).
Among the EAEU member states, Russia has comparative advantage in the export of such a major commodity group as food products and agricultural raw materials. Estimates suggest that the index of comparative advantage for this group has been steady for several years and is over 1 (in 2017 it was 1.027). It should be noted that Russia also has an index exceeding 1 in the export group "Machinery, equipment and vehicles". The Republic of Belarus demonstrated a large volume of export to third countries (according to the results of 2017). For instance, the Balassa index of comparative advantage for textile, textile goods and footwear is 7.989; chemicals – 3.625; machinery, equipment and vehicles – 2.264. Belarus lags Russia regarding foods and agricultural raw materials, with the index estimating only 0.576. Kazakhstan also is slowly increasing the export component for this indicator, with the Balassa index decreasing by 0.019 in 2017 as compared to 2016 and estimating 0.835 (Table 2).
Table 2. Estimation of the export from Russia, the Republic of Kazakhstan and the Republic of Belarus to "third countries" for a major commodity group using the index of comparative advantage (the Balassa index – RCA)
| Export for a major commodity group | 2014 | 2015 | 2016 | 2017 |
|-----------------------------------|------|------|------|------|
| **Russia** | | | | |
| Foods and agricultural raw materials | 1.015 | 1.008 | 1.016 | 1.027 |
| **Kazakhstan** | | | | |
| Foods and agricultural raw materials | 0.929 | 0.935 | 0.944 | 0.835 |
| **Belarus** | | | | |
| Foods and agricultural raw materials | 0.913 | 0.711 | 0.515 | 0.576 |
Source: Compiled and calculated by the authors using Eurasian Economic Commission, 2018.
As for relatively new partners in the union – Armenia and Kyrgyzstan, the conducted studies show that the obtained indices of comparative advantage for foods and agricultural raw materials (3.54 and 1.40, respectively) convincingly demonstrate the potential for further development of agro-industrial production in these EAEU member states. The share of Armenia and Kyrgyzstan's exports of foods and agricultural raw materials to third countries as of the end of 2017 to the total volume of this major export group of the EAEU member states estimated only 1.99% (with exported products worth USD 410.2 mln). Russia's export of this major commodity group for the same period amounted to USD 17,812.0 mln.
The Union has significant agrarian potential and is capable of attracting investment, creating and managing joint innovative projects aimed at the development of dairy and beef cattle breeding, vegetable and fruit farming, viticulture, modernization and construction of new food factories and feed mills, construction of fruit and vegetable stores, establishment of wholesale distribution centers, selection-genetic and breeding-seed centers, development of new veterinary vaccines and crop protection chemicals (Forecast of scientific and technological development of the agro-industrial complex of the Russian Federation for the period up to 2030: main provisions, 2016).
A number of investment projects are to be implemented, which will improve the processing of dairy raw materials and increase the competitiveness of the final product. Talking about promising directions of innovative development regarding milk and dairy products over the territory of the EAEU, one should mention investment projects that would enable to increase the production of high-quality dairy raw materials.
To increase the export of meat and meat products, it is necessary to develop further cooperation and specialization of the countries, using their strong points in the production of particular types of meat and meat products. For example, as for their specialization, Belarus focuses on the export of beef and poultry, Kazakhstan – beef, Russia – poultry and pork, Armenia and Kyrgyzstan – mutton. It is also crucial to create a unified meat products positioning system for the Union and their promotion to the markets of third countries (Tashbaev and Abdiev, 2016; Shpak and Bashko, 2016; Gorb et al., 2017).
The Union has not developed a single mechanism for supporting the production of fruits and products produced from these, despite the similarity of certain measures aimed at reducing the cost of material and financial resources, stimulating investment in the creation of new orchards. To promote the EAEU cooperation ties in the fruit production and processing, it is advisable to develop and implement a mutual program for improving this production that should be based on unified mechanisms for supporting producers. At the same time, the model of interstate unions in fruit production and products of its processing is created on the basis of certain factors: natural conditions for successful cultivation of fruits and berries; long experience and skills in growing various types of fruits and berries, the largest share of perennial plantations being occupied by fruits and berries.
Interstate cooperation in the field of fruit production and processing can be effective in the following directions:
- increasing production and improving the quality of fruits, products of its processing, expanding the range of competitive fruit products;
- increasing the load of farms specializing in the cultivation of different types and varieties of fruits, increasing the production capacity of fruit processing enterprises the infrastructure of post-harvest processing;
- building effective schemes for establishment and specialization of fruit farming, preparing and implementing the unified program for its development;
- coordinating scientific activities, joint research in the field of fruit farming and processing;
- fulfilling the export potential of fruit farming by the EAEU member states in the markets of third countries through joint marketing infrastructure.
Promising investment projects for the development of sugar beet production and sugar obtained from it in the Union include increasing the variety assortment of sugar beet seeds, modernization of planting, processing and harvesting of sugar beets, and development of high-quality equipment for sugar plants.
To further develop the export potential of the fat and oil industry, it is necessary to apply the model of innovative development, as well as new forms of public-private partnership on the basis of technological platforms (Altukhov, 2017; Baklakov and Alekseev, 2015; Popova et al., 2018).
Technical and technological modernization of agriculture is a key element in improving the competitiveness of agrarian products of the EAEU member states. To solve this incredibly challenging task, it is viable to create a structure and management system that would ensure monitoring of the technical condition of agro-production that the countries belonging to the integrative union have. Other relevant measures include forecasting, organizing and controlling processes of recovery and development of technical capacity.
The created organizational and economic mechanism should be open to innovations, allow the modernization and development of tractor and agricultural machinery, ensure the interconnection between government agencies, science, financial institutions and organizations that produce agricultural machinery and equipment on the territory of the Union, as well as agricultural entities – the core of this mechanism (Polukhin, 2014a; 2014b).
At present, the EAEU member states see Russia as a country with a significant market capacity for agricultural machinery, spare parts and agro-technical services. Unfortunately, Russia has not recovered its technical potential in the agrarian sector of the economy yet and has not used its competitive advantage in the development of domestic agricultural machinery. Considering the created model range and market niches covered by machinery demonstrate that Russian mechanical engineering cannot meet all the needs. This explains the importance of investments in the development of models that allow filling the import-dependent niches of the market (Polukhin, 2018).
Belarus occupies key positions in the agricultural machinery market, being its supplier to foreign markets, and keeps its market fairly closed. Kazakhstan represents an undeveloped market niche in the agricultural machinery market. Armenia and Kyrgyzstan can form market niches; however, they should carry out technical modernization by renovating run-down equipment.
On the one hand, when creating and managing joint ventures for the production of agricultural machinery, it is fairly important to assess the technical facilities of agriculture from the perspective of the state, agricultural producers, machinery producers and suppliers. On the other hand, only by assessing the availability of machinery, quantitative and price indicators of the agricultural machinery market, one can draw objective conclusions about development trends and make an informed management decision concerning technical modernization of agriculture.
However, when we assess technological infrastructure from the perspective of machinery producers, we can see that in this case the emphasis is placed on the evaluation of the level of production competitiveness, resource intensity, energy intensity, and costs. Moreover, it is important to assess the synergetic effect from using production capacities of the EAEU producers and the degree of protectionism in the market.
5. Discussion
In contrast to the papers studied and the findings of other authors (Bondarev, 2016; Glotova and Osinina, 2016; Drobot et al., 2017; Zayats, 2014; Ratushnyak, 2018; Rakhmanov and Ivoilova, 2017; Sarkisov, 2009), this article aims to analyze the integration processes occurring in the Eurasian Economic Union, the developed unified agro-food policy of the member states, as well as strategic measures and mechanisms for further intergovernmental integration in the field of agro-industrial production. In this research special attention was paid to the issues related to achieving really economic (synergetic) benefit from integration through the mechanisms ensuring coordinated agrarian policy of the EAEU member states.
The authors identified factors that reduce the effectiveness of integrative cooperation. First, until now the states have not worked out a single agrarian policy and the concept of collective food security. Second, national schemes of the territorial-sectoral division of labor in agro-industrial production have not been proposed. Third, the approved draft of the export policy for foods and agricultural raw materials has a number of gaps and should be revised. Fourth, regulatory documents aimed at the implementation of goods turnover procedures on the EAEU territory should be simplified by means of digital technologies. Fifth, the states should consistently move to a unified methodology for providing state support to agricultural producers.
The most significant research results in comparison with other studies include the identification of comparative advantages in the export of foods and agricultural raw materials of the EAEU member states that function in the context of increasing competition, embargoes, economic sanctions and import substitution policies.
The authors justify the need for using the cluster approach when organizing trans-border unions and see it as one of the most effective methods for sustainable development of agricultural production in rural areas of the EAEU countries. The paper considers the viability of establishing joint ventures by agricultural producers, as well as their basic characteristics. The authors propose ways of creating and developing transport and logistics infrastructure which would facilitate the implementation of interstate programs for export development within the framework of a flexible tariff policy.
There are some issues that require further study: for instance, challenges of forming a single market of organic products, and application of digital technologies in the agrarian sector of the economy of the EAEU member states.
6. Conclusion
Having studied the economic relations in the field of integrative cooperation development between the EAEC countries in the agro-food sector of the economy, the authors obtained the following results.
They justified the necessity and relevance of more effective and deep integrative cooperation of the EAEU member states in the agrarian and agro-industrial sectors of the economy. At the same time, it is noted that a coordinated strategy for developing integration units should imply the rational use of all types of resources and intellectual potential, ensuring the introduction of innovations in agricultural production, sustainable development of rural areas, and increasing the states' share in the international division of labor.
It was shown that the development of interstate integration in the agrarian sector of the Union's economy should be gradual. When starting work on a unified agrarian policy, the EAEU member states should pay special attention to ensuring the harmonious development of the agro-food market and the market of the production means.
The countries should focus on the creation of trade and logistics associations promoting foods and agricultural raw materials, which would accelerate and facilitate trade turnover in the agrarian sector of the economy, increase the goods competitiveness in the Union and external agro-food markets through efficient marketing and logistics support.
The paper proposes specific forms, methods and mechanisms that can attract and intensify the inflow of investment and financial resources into agro-industrial production. The authors determine promising directions for attracting investments aimed at the creation of new high-tech markets within the Union. These are linked with the production of high-tech types of crop and livestock goods, creation of new varieties and hybrids of crops, development of antiviral drugs for livestock and crop protection products, food biotechnology systems and synthetic biology.
The research theoretically substantiates and experimentally confirms the effective forms, methods and mechanisms that promote interstate integrative cooperation and the inflow of investment and financial resources into the agro-industrial production of the EAEU member states. The findings can be used by the management and experts of the agro-industrial complex at various levels when preparing programs of agricultural development and regulation of markets of agricultural products, raw materials and food, as well as social development of rural areas.
The material presented in this article can be used by managers and experts of government agencies in the agro-industrial complex when developing, adjusting and improving agro-food policy, as well as by scientists, post-graduate students and students exploring the issues of the world economy and international relations.
Acknowledgement:
The article was prepared with the financial support of the Russian Foundation for Basic Research within the scientific project No. 17-02-00327.
References:
Alekneviciene, A., Stareviciute, B., Alekneviciute, E. 2018. Evaluation of the efficiency of European Union farms: a risk-adjusted return approach. Agricultural Economics, 64, 241-255.
Altukhov, A.I. 2017. Territorial and sectoral division of labor in agro-industrial production as the basis for inter-state integration in the agrarian sector of the economy of the Eurasian economic union. Agro-Food Policy of Russia, 10(70), 2-10.
Anfinogentova, A.A., Dudin, M.N., Lyasnikov, N.V., Protsenko, O.D. 2017. A technique for assessing the quality of the activities of enterprises of the agro-industrial complex on the basis of an ecologically responsible approach. The Economy of the Region, 13(2), 579-590.
Aranchiy, V., Makhmudov, H., Yasnolob, I., Radionova, Ya. 2017. The developing of conceptual foundation of the process of organizing innovation activities at agro-industrial enterprise based on outsourcing and the program business process model and notation. Economic Annals-XXI, 165(5-6), 84-89.
Avdonin, A. 2018. What should be done to accelerate the integration of the Eurasian Economic Union. Available at: https://www.sonar2050.org/publications/ekonomicheskie-itogi-eaes-integracii-20152017-gg-i-perspektivy-20182020-gg/.
Baklakov, P.A., Alekseev, S.I. 2015. The system of bans and restrictions in the foreign goods trade of the Eurasian Economic Union member states. Moscow, Russian Customs Academy.
Balassa, B. 1965. Trade liberalisation and revealed comparative advantage. The Manchester School of Economic and Social Studies, 33, 99-123.
Benesova, I., Maitah, M., Smutka, L., Tomsik, K., Ishchukova, N. 2017. Perspectives of the Russian agricultural exports in terms of comparative advantage. Agricultural Economics, 63(7), 318-330.
Bludova, S.N. 2016. Evaluation of the dynamics of comparative advantages in the external trade of the EAEU countries. Bulletin of the North Caucasus Humanitarian Institute, 1(17), 30-34.
Bondarev, I.I. 2016. EAEU: comparative advantages for Russia and the member states. Problems and Prospects of Economy and Management: materials of the 5th International Scientific Conference. St. Petersburg, 53-57. Available at: https://moluch.ru/conf/econ/archive/219/11486/.
Borkhunov, N., Avdeev, M. 2018. Price parity in the agro-industrial complex of Russia and the EAEU member states. Agro-Industrial Complex: Economy, Management, 3, 60-68.
Burkaltseva, D.D., Sivash, O.S., Boychenko, O.V., Savchenko, L.V., T.N. Bugaeva, T.N., Zotova, S.A. 2017. Realization of Investment Processes in the Agricultural Sector of the Digital Economy. European research Studies Journal, 20(4B), 366-379.
Crosson, P.R., Brubaker, S. 2016. Resource and Environmental Effects of U.S. Agriculture. New York, Routledge.
Danylenko, A., Satyr, L., Shust, O. 2017. Price parity in the agricultural sector as a guarantee of the national food security. Economic Annals-XXI, 164(3-4), 61-64.
Drobot, E.V., Abrosimova, A.S., Savitskaya, K.S. 2017. The influence of sanctions on the formation of the Eurasian Economic Union. Economic Relations, 7(1), 55-64.
Increasing Interstate Integration in the Agro-Industrial Complex of the EAEU Countries
Eurasian Economic Commission. 2014. Analysis of strategies for integrative cooperation (models for the implementation of the integration potential) of the world's best-known integration associations. Moscow.
Eurasian Economic Commission. 2018. Analytical materials. Available at: http://www.eurasiancommission.org/ru/act/analytics/Pages/default.aspx.
Forecast of scientific and technological development of the agro-industrial complex of the Russian Federation for the period up to 2030: Main provisions. 2016. Available at: https://issek.hse.ru/data/2016/05/25/1131427693/Основные%20направления%20Прогноза%20АПК.pdf.
Glotova, I.N., Osinina, A.Yu. 2016. Agro-insurance in the EAEU states as an element of the single agrarian market: common points. Economics of Agricultural and Processing Enterprises, 11, 66-70.
Gorb, O., Yasnolob, I., Dedukhno, A., Kaliuzhna, Yu. 2017. The formation of the management system of ecological, social, and economic development of rural territories using the experience in European Union. Journal of Environmental Management and Tourism, 8(3), 516-528.
Gorb, O.O., Yasnolob, I.O., Protsiuk, N.Y. 2016. Organizational-economic mechanism of management of food industry enterprises competitiveness. Annals of Agrarian Science, 14(3), 191-195.
Ivanova, V.N., Seregin, S.N. 2016. Intertrade of the EAEU member states with countries of free trade zones and their export potential. Economics of Agricultural and Processing Enterprises, 1, 27-31.
Koshkarev, I.A., Boldyrev, A.V. 2016. Planning and state regulation as tools for eliminating disproportionality in agriculture development. Economics of Agricultural and Processing Enterprises, 1, 32-38.
Kovalenko, E.G., Yakimova, Y.O., Avtaykina V.E. and Zaytseva, O.O. 2016. Problems and Mechanisms of Sustainable Development of Rural Areas (at the example of the Republic of Mordovia). European Research Studies Journal, 19(3) Part A, 110-122.
Mariew, O.S., Naberezhneva, E.P., Tatarkin, A.I. 2014. The main optimization directions for the sectoral structure of Russia's foreign trade through the assessment of comparative advantages. Humanitarian and Social Sciences, 5, 22-40.
Marwa, T., Bashir, A., Azwardi, M., Adam, M., Thamrin, H.M.K. 2017. Market Integration of Agricultural Products. International Journal of Economics & Business Administration, 5(2), 69-82.
Maslova, V., Zaruk, N., Avdeev, M. 2018. Factor analysis of the competitiveness of agro-food products in the EAEU member states. Agro-industrial Complex: Economics, Management, 4, 75-85.
Mathe, K.M. 2013. Agricultural Growth and Food Security: Problems and Challenges International. Journal of Research in Commerce, Economic & Management, 7(3), 131-137.
Medvedeva, N., Prokhorenko, O. 2018. Increasing export of agricultural products as an important direction of agrarian policy of the EAEU member states. Agro-industrial Complex: Economics, Management, 2, 74-81.
Nechaev, V.I., Mikhaylushkin, P.V., Slepneva, T.N. 2017. New approaches to advanced grain processing by forming an interstate cluster (Russia-Kazakhstan). Economics of Agricultural and Processing Enterprises, 9, 52-55.
Polukhin, A.A. 2014a. Organizational and economic mechanism of technical modernization of agriculture. Doctoral Thesis. Moscow.
Polukhin, A.A. 2014b. Problems of technical and engineering modernization of agriculture of Russia in conditions of the WTO membership and the Eurasian Economic Union. Bulletin of Orel State Agrarian University, 50(5), 12-18.
Polukhin, A. 2018. Economic evaluation of the export potential of Russian agricultural machine engineering. Agro-industrial Complex: Economics, Management, 2, 15-21.
Popova, L., Dosova, A., Litvinova, T., Rogachev, A. 2018. Mechanism of public-private partnership for developing infrastructure support of the Russian market of agricultural machinery. Agro-Industrial Complex: Economics, Management, 3, 37-44.
Prado, J.R., Segers, G., Voelker, T., Carson, D., Dobert, R., Phillips, J. 2014. Genetically Engineered Crops: From Idea to Product. Annual Review of Plant Biology, 65, 769-790.
Rakhmanov, A., Ivoiylova, I. 2017. Clustering of the agro-industrial complex as the crucial element in the development of Eurasian integration in the agrarian sphere. Agro-Industrial Complex: Economics, Management, 10, 74-81.
Ratushnyak, E.S. 2018. Modern measures for protecting the internal market of the EAEU. Scientific Review: Theory and Practice, 4, 20-21.
Sarkisov, V.B. 2009. State support priorities for parties of foreign trade in the conditions of economic instability. Bulletin of the Institute of Friendship of Peoples of the Caucasus. Economic Theory and National Economy Management, 2(10), 104-108.
Sekhampu, T.J. 2013. Determinants of the Food Security Status of Households Receiving Government Grants in Kwakwatsi, South Africa. Mediterranean Journal of Social Sciences, 4(1), 147-153.
Semin, A., Kibirov, A., Rassukhanov, U. 2018. Problems and Main Mechanisms to Increase Investment Attractiveness of Agricultural Production. European Research Studies Journal, 21(2), 378-400.
Semin, A.N., Kovalev, V.E., Falchenko, O.D. 2016. Interaction of the EAEU economies in the trade in food products: Problems of integration within the intellectual property market. Economics of Agricultural and Processing Enterprises, 8, 10-17.
Shpak, A.P., Bashko, A.Yu. 2016. Import substitution in the agro-industrial complex of the Republic of Belarus. Economics of Agricultural and Processing Enterprises, 1, 23-26.
Tashbaev, A.M., Abdiev, M.Zh. 2016. Analysis and evaluation of the development of the food and processing industry in the Kyrgyz Republic. Economics of Agricultural and Processing Enterprises, 4, 65-68.
Thompson, P.B. 2017. The Spirit of the Soil: Agriculture and Environmental Ethics. London, Routledge.
Treaty on the Eurasian Economic Union. 2014. Available at: https://www.alta.ru/tamdoc/14bn0044/.
Ushachev, I.G., Tarasov, V.I., Ivoylova, I.V., Osinina, A.Yu., Chikanova, Yu.A. 2016. Assessment of the role of food commodity distribution network of the EAEU for eastern and western partners. Agro-Industrial Complex: Economics, Management, 10, 4-12.
Vertakova, Yu., Plotnikov, V. 2017. Problems of sustainable development worldwide and public policies for green economy. Economic Annals-XXI, 166(7-8), 4-10.
Zayats, A. 2014. "Politics was put ahead of the economy". What are the benefits of the Eurasian Union? Available at: https://news.tut.by/politics/401129.html?crnd=4001. | 2025-03-06T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2092,
1
],
[
2092,
4877,
2
],
[
4877,
7893,
3
],
[
7893,
10915,
4
],
[
10915,
13841,
5
],
[
13841,
16502,
6
],
[
16502,
19910,
7
],
[
19910,
22788,
8
],
[
22788,
25831,
9
],
[
25831,
29182,
10
],
[
29182,
31368,
11
],
[
31368,
34023,
12
],
[
34023,
37001,
13
],
[
37001,
39986,
14
],
[
39986,
42843,
15
],
[
42843,
45666,
16
],
[
45666,
48759,
17
],
[
48759,
51984,
18
],
[
51984,
55337,
19
]
]
} |
0f46d3cd271a5d5b83368fbf6f246f3c1c7a16d7 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 25940,
"total-output-tokens": 9422,
"fieldofstudy": [
"Medicine",
"Physics"
]
} | Cardiac dose reduction during tangential breast irradiation using deep inspiration breath hold: a dose comparison study based on deformable image registration
Ji Hyeon Joo¹, Su Ssan Kim¹*, Seung Do Ahn¹, Jungwon Kwak¹, Chiyoung Jeong¹, Sei-Hyun Ahn², Byung-Ho Son² and Jong Won Lee²
Abstract
Background: Radiation therapy (RT) for a left-sided breast cancer often involves some incidental exposure of the heart and increase in the rate of major coronary events. One method to reduce the dose to the heart during a tangential breast irradiation is the deep inspiration breath hold (DIBH) technique. Our department adopted DIBH for selected left breast cancer patients with a maximum cardiac distance ≥ 10 mm. We evaluated the effect of the DIBH on cardiac dose compared to normal free breathing (FB). The secondary objective of our present study was to use modeled risk estimates to quantify the risk of coronary events after RT with DIBH.
Methods and materials: Thirty-two patients who underwent RT with DIBH at our hospital were retrospectively analyzed. For each patient, two computed tomography (CT) scans were acquired, FB-CT and DIBH-CT. Using a deformable image registration tool, the target volume was deformed from DIBH-CT to FB-CT, and conventional tangential treatment planning was performed, focusing on the equality of target coverage between the two plans. Doses to the heart, left anterior descending (LAD) artery, and ipsilateral lung were assessed.
Results: By using DIBH, the average mean heart dose was reduced from 724.1 cGy to 279.3 (p < 0.001). The relative heart volume irradiated with 10 Gy–50 Gy was consistently reduced. The mean dose to the LAD coronary artery was reduced from 4079.1 cGy to 2368.9 cGy (p < 0.001). The ipsilateral lung volume receiving 20 Gy or more and 40 Gy or more was reduced by 2.2 % in both cases. Estimated risks of coronary events at 10 years were 4.03 and 2.55 % for RT with FB and DIBH, respectively (p < 0.001).
Conclusions: The use of DIBH during RT of the left-sided breast considerably reduces the doses delivered to the heart and LAD artery with similar target coverage. For the current study patients, the probability of major coronary events was reduced with DIBH.
Keywords: Breast radiotherapy, Deep inspiration breath hold, Heart dose, Cardiac toxicity, Deformable image registration
Background
Postoperative radiotherapy (RT) for breast cancer patients has been widely used since it was proven to reduce the risk of local recurrence and improve long-term survival [1, 2]. However, the absolute benefit of RT on long-term overall mortality is less than its benefit on breast cancer-related mortality. The excess mortality in these patients is mainly due to heart disease and lung cancer [1].
RT for left-sided breast cancer often involves some incidental exposure of the heart and ipsilateral lung to radiation. Exposure of the heart to radiation is related to increased rates of coronary events and cardiac mortality [3]. In tangential RT of left-sided breast, part of the anterior heart, including the left anterior descending artery (LAD), usually receives a non-negligible dose. It is not clear whether this results in myocardial damage or coronary artery damage, or both. Generally, the mean cardiac dose causes a proportional increase in the rate of major coronary events per gray. Darby et al. [3] have reported that the rates of major coronary events increased by 7.4 % per gray.
In recent years, considerable effort has been exerted to identify techniques that reduce the dose to the heart in patients receiving postoperative RT for breast cancer. One method involves respiratory gating using the deep inspiration breath hold (DIBH) technique. During deep inspiration, the heart moves posteriorly and inferiorly due to lung expansion and diaphragmatic movements. Thus, the distance between the chest wall and heart is maximized at or near the deep inspiration. Treatment delivery only at deep inspiration reduces the area of the heart that receives a high dose. Exposure of the ipsilateral lung to irradiation is not consistent with DIBH but the relative volume of the irradiated lung usually decreases. Several groups have reported a reduction in the heart and lung dose using DIBH in both dose planning and clinical studies [4, 5].
Our department adopted DIBH in selected left breast cancer patients with a maximum cardiac distance of $\geq 10$ mm. Every patient who was treated using DIBH in our department underwent additional computed tomography (CT) with normal breathing (free-breathing CT [FB-CT]) in the same treatment position. We conducted our current CT planning study using two CT sets (DIBH-CT and FB-CT) in the same patient. When comparing the dose to organs at risk, it is essential that the target coverage is as equal as possible. The female breast is usually defined by an external surface structure. Generally, it can extend from mid-axillary line to mid-sternum, and from the second anterior rib to the sixth anterior rib. Because the shape varies depending on the position, it is not reliable to compare target coverage when the position of patient is different. During full inspiration, the shape of the breast tissue changes as the chest wall inflates and moves anterocranially. Thus, we used a deformable image registration tool to achieve the most consistent dose coverage.
Darby et al. [3] have previously conducted a population-based case–control study that suggested a reliable prediction model of major coronary events based on individual cardiac risk factors and the irradiated cardiac volume. Based on this model, we tried in our present study to predict the absolute risk reduction in women who were treated using RT after breast cancer surgery.
Methods
Patients
This analysis was conducted in accordance with the regulations of the Asan Medical Center Institutional Review Board (2015–0855). Between 2012 and 2015, 32 patients who were referred for adjuvant RT after left breast cancer surgery, including a breast-conserving operation or mastectomy, were treated using the DIBH technique at our institution. Patients were not consecutively included. After FB-CT, physicians decided whether to use DIBH. Principally, patients with a maximum cardiac distance $\geq 10$ mm in a CT simulation, and with a good performance who could reproduce a breath-holding status were included. The mean age of the patients in our current study was 48 years (range, 25–77 years) and they also had to be able to hold their breath. All patients were treated using respiratory gating. Patient and treatment characteristics are summarized in Table 1.
Respiratory gating
The Varian Real-time Position Management respiratory gating system (version 1.7.5; Palo Alto, CA) was used for respiratory gating. An infrared reflecting marker was placed on the patient, normally over the xiphoid process, and its position was marked on the patients’ skin so that it could be reproduced during the treatment period. The anteroposterior motion of the marker due to chest wall movement was detected by a camera. Before CT simulation and delivery of the first treatment, patients were trained how to breathe. No form of audio or visual guide was used but the operator told the patient when to take a deep inspiration and when to release their breath. The gating window was individually set to the maximum inspiration $\pm 5$ mm. All respiration cycle curves were observed during whole treatment time by 2 experienced therapists and a physician. As the beam delivery was stopped by instant changes of the graph, the actual gating window was much smaller.
The continuous cine-image was further checked using an electronic portal image device (7.5 frames/s). Normally, a single tangential field took about 10 to 15 s. The CT slice thickness was 5 mm and the image acquisition
was conducted in helical mode. Image acquisition commenced when the breathing amplitude marker reached the gating window. The scanning time was approximately 20 s and most patients managed to complete the scan during one respiration cycle.
Delineation of the target and organs at risk
Contouring of the target volumes and organs at risk was performed in accordance with the guidelines published by the Radiation Therapy Oncology Group (RTOG) and the Danish Breast Cancer Cooperative Group (DBCG) [6, 7]. For breast-conserving operations, the clinical target volume (CTV) included all residual mammary tissues and was bordered by the clavicular head cranially, 20 mm inferiorly to the breast fold caudally, the midsternal line medially, and the mid-axillary line laterally. For mastectomies, the caudal margin was defined based on palpation of the contralateral breast.
Mammary tissue is usually visible on CT slices but there can be considerable inter- or intra-observer variability. Sometimes also, defining mammary tissues is confusing even for experienced radiation oncologists if, for example, the patient has very small breasts with loose breast tissues. To account for these uncertainties and ensure objectivity in our analysis, deformable image registration was used for the CTV. Using a contouring deformable registration tool (Mirada RTx Advanced ver. 1.62), the CTVs were deformed from DIBH-CT to FB-CT. Registered target volumes were checked by an experienced radiation oncologist. After deformable image registration, the planning target volume (PTV) was made separately in FB-CT and DIBH-CT, for beam generation and plan evaluation. The PTV was generated using a 5 mm margin from CTV, limited to the midline, and shrunk 5 mm from the skin. The PTV was not deformed because deformation of slit-like shaped PTV made it fragmented or distorted.
The ipsilateral lung was contoured using an automatic contouring tool. The heart was contoured in accordance with RTOG 1106 organs at risk atlases. Along with the pericardial sac, the superior aspect began at the level of the inferior aspect of the pulmonary artery passing the midline and extended inferiorly to the apex of the heart [8]. The LAD coronary artery was delineated in the anterior interventricular groove from its initiation down to the apex of the heart.
Treatment planning
Two opposing 6 MV tangential conformal fields with a multileaf collimator were used. The prescription dose was 50 Gy in 2 Gy fractions. A minimum of 95 % of the target volume was to be covered by the 95 % isodose line (V95 ≥ 95 %). The tumor bed boost was usually delivered using a 3D-conformal plan, at 10 Gy in 2 Gy fractions, but this was excluded from our current analysis. In our institution, internal mammary node (IMN) irradiation is only considered in cases with a clinically suspected or pathologically proven metastasis. IMN irradiation was not done in any of the analyzed patients in this study. All treatment planning was performed by an experienced radiation technologist. The field-in-field technique and wedges were used to avoid hotspots exceeding 110 %. The dose to normal organs was kept as low as possible without compromising the target volume dose. For each patient, only minor differences between the two plans, with respect to target coverage, field-in-field, wedges, beam energy, and geometry, were accepted.
| Table 1 Patient, tumor, and treatment characteristics |
|-----------------------------------------------|
| Characteristics | N = 32 (%) |
| Median age at treatment (years) | 48 (25–77) |
| Cigarette smoking | |
| Yes | 1 (3) |
| No | 31 (97) |
| Cardiopulmonary comorbidities | |
| None | 19 (59) |
| Hypertension | 7 (22) |
| Hyperlipidemia | 2 (6) |
| Diabetes mellitus | 4 (3) |
| Breast cancer stage | |
| I | 9 (28) |
| II | 9 (28) |
| III | 14 (44) |
| Tumor stage | |
| T1 | 14 (44) |
| T2 | 11 (34) |
| T3 | 7 (22) |
| Nodal stage | |
| 0 | 11 (34) |
| 1 | 9 (28) |
| 2 | 2 (6) |
| 3 | 10 (31) |
| Breast conservation | |
| Yes | 20 (63) |
| No | 12 (37) |
| Systemic therapy | |
| Neoadjuvant chemotherapy | 15 (47) |
| Adjuvant chemotherapy | 13 (41) |
| Adjuvant trastuzumab | 11 (34) |
| Adjuvant endocrine therapy | 9 (28) |
| None | 0 (0) |
Individual cardiac risk estimation
To estimate each individual's risk of major coronary events (myocardial infarction or coronary death), the Framingham Coronary Heart Disease Risk Score [9] and the assumption of Darby et al. (3) were used. The risk assessment tool from the Framingham Heart Study predicts the chance of myocardial infarction or coronary death in the next 10 years. It was chosen because RT-induced heart disease develops after a long period and the Darby model is based upon major coronary events. According to the Darby model, the excess risk of major coronary events is linearly dependent on the mean heart dose at a rate of 16.3 % during years 0–4 and 15.5 % during years 5–9 following breast RT. To estimate the risk at 10 years, we used the more conservative estimate of 15.5 % per gray because this likely approximates the excess relative risk during years 0–9 [10]. To group our current study patients according to their baseline risk, American Heart Association (AHA) risk groups were used. Patients were classified into high-risk, at-risk, or optimal-risk groups according to their risk factors [11].
Statistical analysis
Dose–volume histograms were extracted and compared for each of the DIBH and FB plans. For the heart, the $V_{10Gy} - V_{50Gy}$ as well as the mean heart dose ($D_{mean}$) and maximum heart dose ($D_{max}$), were measured. For the left lung, the $V_{20Gy}$, $V_{40Gy}$, and $D_{mean}$ were determined. For the LAD, the $D_{max}$ and $D_{mean}$ were determined. Paired t-tests were used for statistical analysis of the differences with SPSS statistical software version 21.0. Data were considered statistically significant at $p < 0.05$.
Results
Deformable image registration
In most of the current study cases, the anatomical correlation was excellent, and additional adjustment was not needed. The equality of target coverage was checked by measuring the shortest distance between the beam margin and long thoracic vein in digitally reconstructed radiographs (no significant difference). One example each of DIBH-CT and FB-CT is shown in Fig. 1. In the axial CT image, the deformed CTV is anatomically well correlated, as shown by its relation to the sternum and the long thoracic vein. The posterior–inferior cardiac displacement and decreased heart distance in the tangential field is shown in the sagittal section and digitally reconstructed radiograph (Fig. 2).
Cardiac dose
The main results of the comparisons of the mean values of the dose metrics for the DIBH and FB plans are listed in Table 2. In the DIBH plans, 2 of the 32 hearts were outside the beam portal, whereas all hearts were included in the beam portal in the FB plans. The average maximal heart distance decreased from 2.1 cm (FB: range 1.2–3.9 cm) to 0.7 cm (DIBH: range, 0–1.6 cm) ($p < 0.001$). The average mean heart dose was also reduced, from 724.1 cGy (FB: range, 310.5–1405.3 cGy) to 279.3 cGy (DIBH: range 116.5–521.0 cGy) ($p < 0.001$). The relative heart volume irradiated with 10 Gy–50 Gy was consistently reduced by DIBH. The $V_{10}$, $V_{20}$, $V_{30}$, $V_{40}$ and $V_{50}$ values for FB vs. DIBH were 14.6 vs. 4.0 % (-73 %), 12.3 vs. 2.7 % (-78 %), 10.7 vs. 2.0 % (-82 %), 8.7 vs. 1.3 % (-85 %), and 2.5 vs. 0.2 % (-91 %), respectively. The relative reductions in cardiac doses were similar between the low- and high-dose regions. The maximum heart dose was 5114.0 cGy with FB and 4947.4 cGy with DIBH ($p = 0.191$). In 26 patients (81 %), the $V_{40}$ value was larger than 5 % when using the FB technique compared with 0 % (i.e. none of the patients) when using DIBH.
For the LAD coronary artery, the $D_{mean}$ was significantly reduced from 4079.1 cGy (range 568.3–5359.3 cGy) to 2368.9 cGy (range, 370.0–4415.0 cGy) using DIBH ($p < 0.001$). The maximum LAD artery dose was 5058.6 cGy (range, 4389.8–5604.6 cGy) with FB and 4720.9 cGy (1505.9–5610.9 cGy) with DIBH ($p = 0.010$). Due to its anatomical position, the LAD coronary artery is often within the high-dose region. In 9 and 7 of the FB and DIBH plans, respectively, the maximum LAD artery dose was higher than 5000 cGy.
The baseline and estimated coronary event risks were evaluable in all 32 study patients. About one-third of the patients had cardiopulmonary comorbidities (Table 1). From the plan comparisons, the estimated risks of coronary events at 10 years in all patients were 4.03 % (range, 1.48–21.74 %) and 2.55 % (range, 1.18–13.79 %) for RT with FB and DIBH, respectively ($p < 0.001$). The median 10-year relative risk reduction was 32 % (range, 16.15–83.28 %) with the DIBH technique, and the absolute risk reduction was 1.48 % (range, 0.25–7.95 %). The AHA risk grouping was high risk, at risk, and optimal risk in 4 (13 %), 16 (50 %), and 12 (37 %) patients, respectively. The 10-year estimated risks using FB vs. DIBH were 5.08 vs. 3.44 % in the high-risk, 4.97 vs. 3.07 % in the at-risk, and 2.41 vs. 1.55 % in the optimal-risk groups (Fig. 3).
Pulmonary dose
The distance of the lung included in the beam portal increased when using the DIBH technique. The average central lung depth was 2.6 cm with FB and 2.9 cm with DIBH ($p = 0.014$). However, the average mean pulmonary dose was reduced with DIBH, from 1018.4 cGy (range 488.9–1516.8 cGy) to 943.7 cGy (range 505.1–1386 cGy) ($p = 0.001$). Similarly, for the average ipsilateral lung
volume receiving 20 Gy or more, the $V_{20}$ was reduced from 18.9% (range 8.3–30.9%) to 16.7% (range 9.2–24.7%) ($p<0.001$). The $V_{40}$ was also reduced from 14.1% (range 5.8–23.8%) to 11.9% (range 6.3–19.2) with DIBH ($p<0.001$). Although the lung depth in the beam portal was increased, all pulmonary dose parameters improved when using DIBH, due to lung expansion. Similar to the heart, the relative reduction in the exposed lung volume was similar between the low and high doses.
**Discussion**
Assuming that the same dose coverage has been achieved, the heart and lung dose parameters were significantly reduced in the present study patients by using respiratory gating. The average heart distance in the tangential field was reduced from 2.1 cm to 0.7 cm, and the mean cardiac dose was reduced from 724 cGy to 279 cGy (-61%). The reduction in the mean cardiac dose was similar to that of earlier studies but the absolute cardiac dose and range of dose reduction was higher.
in our current study. Swanson et al. [12] reported a mean heart dose reduction of 4.2 Gy with FB vs. 2.5 Gy (-40 %) with DIBH. All other heart parameters evaluated favored the delivery of DIBH over FB plans. Vikstrom et al. [5] showed an average mean dose of 3.7 Gy with FB for the heart and 1.7 Gy (-54 %) with DIBH. Stranzl et al. [13] reported a mean heart dose reduction of 2.3 Gy with FB vs. 1.3 Gy (-56 %) with DIBH. DIBH also shows benefit when combined to modern technique RT. In a study by Hayden et al. [14], DIBH resulted in a significant reduction in radiation dose to the heart and LAD compared with an FB, utilizing tangential intensity modulated RT (IMRT) plans with simultaneous integral boost. Nissen et al. [4] found that the mean heart dose reduced from 5.2 Gy to 2.7 Gy (-48 %) with a DIBH and IMRT plan. As the prescribed dose in all studies, including our current report, was 50 Gy/25 fx, there are two possible explanations for the discrepancy. First, not all left breast cancer patients were treated using DIBH at our center. We specifically included selected women with a maximum cardiac distance ≥ 10 mm in CT simulation. Second, due to the smaller lung volume of Asian women compared with Caucasians, the distance between the left ventricle and chest wall might be shorter [15, 16]. This is supported by the higher D_max of the heart in the DIBH plan (25–27 Gy vs. 49 Gy) and the lower proportion
| Table 2 Comparisons of dose metrics | DIBH | FB | p-value |
|-------------------------------------|------|----|---------|
| **Heart** | | | |
| D_{mean} (cGy) | 279.3| 99.7| |
| D_{max} (cGy) | 4947.4| 810.6| 0.191 |
| V_{10} (%) | 4.0 | 2.2 | |
| V_{20} (%) | 2.7 | 1.8 | |
| V_{30} (%) | 2.0 | 1.5 | |
| V_{40} (%) | 1.3 | 1.2 | |
| V_{50} (%) | 0.2 | 0.4 | |
| MHD (cm) | 0.7 | 0.4 | |
| **Lung** | | | |
| D_{mean} (cGy) | 943.7| 223.2| 0.008 |
| V_{20} (%) | 16.7 | 4.4 | |
| V_{40} (%) | 11.9 | 3.6 | |
| V_{50} (%) | 2.9 | 0.6 | |
| CLD (cm) | 2.9 | 0.6 | |
| **LAD** | | | |
| D_{mean} (cGy) | 2368.9| 1162.1| 0.000 |
| D_{max} (cGy) | 4720.9| 911.8 | 0.044 |
DIBH deep inspiration breath hold, FB free breathing, SD standard deviation
of patients (59 vs. 6%) in our current series whose heart was completely outside the fields. Thus, we suggest that DIBH is particularly helpful for patients with a long maximal heart distance and small lung volume, such as Asian women.
With DIBH, we found that the relative reductions in cardiac doses were similar between low- and high-dose regions. For postoperative RT of breast cancer, the aspect that is most responsible for ischemic heart disease, for example, the mean dose or maximum dose of the heart or LAD artery, is still debated [17, 18]. In addition, the part of the heart anatomy most affected by radiation is still inconclusive. In a study by Correa et al. [19], a statistically significant higher prevalence of cardiac stress test abnormalities was seen among left-side irradiated patients vs. those of the right side (8 vs. 59%). Moreover, most left-sided abnormalities in that study (70%) were in the LAD artery territory. Mark et al. [20] found that RT causes volume-dependent perfusion defects in approximately 40% of patients within 2 years of RT. The perfusion defects were significantly associated with the left ventricular volume included within the RT field. With these results, the target of the deleterious radiation in breast cancer treatment is thus the coronary artery. In a study by Nilsson et al. [21], a direct link between the RT field and location of coronary artery stenosis was observed. However, microvascular (fibrotic) damage is also possible after a longer latency period [22].
Although the mechanism is unclear, the relationship between the mean cardiac dose and cardiac disease risk is well established. Furthermore, the LAD artery dose closely correlates with the mean cardiac dose [23]. Thus, estimation of the risk of the radiation-related ischemic heart disease might be most appropriately derived from the cardiac mean dose. In our present study, the average reduction in the cardiac mean dose was 444.8 cGy. The estimated 10-year risks of coronary events were 4.03 and 2.55% for our patients treated with FB and DIBH, respectively. Although the absolute risk reduction was relatively small (1.48%), our current findings may be clinically significant given the high incidence of breast cancer and the high prevalence of long-term survivors. The estimated clinical benefit of DIBH was also studied previously by Eldredge-Hindy et al. [10]. The risk of ischemic heart disease was reduced with DIBH in that study, regardless of the baseline cardiac risk, although the largest benefit was observed in the high-risk group. Korreman et al. [24] used the relative seriality model to calculate the expected reduction in cardiac mortality from the use of DIBH in 16 cases. They found that the cardiac mortality probability was reduced from 4.8% in FB to 0.1% for DIBH.
Another strategy to minimize radiation exposure is the treatment position. In the prone position, the breast is elongated and falls away from the trunk. Studies comparing supine and prone whole-breast irradiation have shown that the prone position can reduce lung volume exposure [25]. A major disadvantage of the prone setup is the gravity-induced anterior displacement of the heart toward the field edge. To address the problem of a higher heart dose in the prone position, prone DIBH has been attempted. In a study by Mulliez et al. [26], four treatment plans—supine shallow breathing, supine DIBH, prone shallow breathing, and prone DIBH—were compared. The authors found that DIBH was able to reduce the heart dose in both positions, with the results of
prone DIBH at least as favorable as those of supine DIBH. While preserving the lung-sparing ability of prone positioning, prone DIBH was able to reduce the heart dose compared with prone shallow breathing. To maximize normal tissue sparing, DIBH in the prone position could be considered, especially for young small-breasted patients who are able to perform prone DIBH.
There were some limitations to our present study. First, our analysis was limited to 32 nonrandom cases. However, it is likely that larger numbers of patients would show similar results. The strength of our current study was that exactly the same patient cohort was included in the FB and DIBH plans. Using the deformable image registration technique, the equality of treated mammary tissue was maintained. Also, both breast-conserving surgery and mastectomies were included in the analysis.
Conclusions
DIBH allows tangential treatment of left-sided breast cancer patients and considerably reduced radiation doses to the heart, lung, and LAD artery without compromising target coverage. For our study patients, the probability of a major coronary event within 10 years was reduced from 4.03–2.55%.
Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
Study concepts: JHJ, SSK, SDA. Study design: JHJ, SSK, JK. Data analysis and interpretation: JHJ, CI, S-HA, B-HS, JWL. Statistical analysis and manuscript preparation: JHJ. All authors read and approved the final manuscript.
Acknowledgements
This study was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2015M2A2A6A02045253).
Author details
1Department of Radiation Oncology, Asan Medical Center, University of Ulsan College of Medicine, 88 Olympic-ro 43-gil, Songpa-gu, Seoul 138-736, Republic of Korea. 2Department of Surgery, Asan Medical Center, University of Ulsan College of Medicine, Seoul, Korea.
Received: 4 August 2015 Accepted: 14 December 2015
Published online: 30 December 2015
References
1. Clarke M, Collins R, Darby S, Davies C, Elphinstone P, Evans E, et al. Effects of radiotherapy and of differences in the extent of surgery for early breast cancer on local recurrence and 15-year survival: an overview of the randomised trials. Lancet. 2005;366:2087–106.
2. Overgaard M, Jensen MB, Overgaard J, Hansen PS, Rose C, Andersen M, et al. Postoperative radiotherapy in high-risk postmenopausal breast-cancer patients given adjuvant tamoxifen: Danish Breast Cancer Cooperative Group DBCG 82c randomised trial. Lancet. 1999;353:1641–8.
3. Darby SC, Evertz M, McGale P, Bennet AM, Brornum LS, et al. Risk of ischemic heart disease in women after radiotherapy for breast cancer. N Engl J Med. 2013;368:897–98.
4. Nissen HJ, Appelt AL. Improved heart, lung and target dose with deep inspiration breath hold in a large clinical series of breast cancer patients. Radiother Oncol. 2013;106:28–32.
5. Vikstrom J, Hjelstuen MH, Mjøland I, Dybvik KI. Cardiac and pulmonary dose reduction for tangentially irradiated breast cancer, utilizing deep inspiration breath-hold with audio-visual guidance, without compromising target coverage. Acta Oncol. 2011;50:42–50.
6. Nielsen MH, Berg M, Pedersen AN, Andersen K, Glavivc V, Jakobsen EH, et al. Delineation of target volumes and organs at risk in adjuvant radiotherapy of early breast cancer: National guidelines and contouring atlas by the Danish Breast Cancer Cooperative Group. Acta Oncol. 2013;52:703–10.
7. Radiation therapy oncology group. Breast cancer atlas for radiation therapy planning: consensus definitions. http://www.rtog.org/CoreLab/ContouringAtlases/BreastCancerAtlas.aspx. Accessed 27 Jul 2015.
8. Radiation therapy oncology group. Atlases for organs at risk (OARs) in thoracic radiation therapy. 2011. https://www.rtog.org/CoreLab/ ContouringAtlases/LungAtlas.aspx. Accessed 27 Dec 2015.
9. Wilson PW, D’Agostino RB, Levy D, Belanger AM, Silberschatz H, Kannel WB. Prediction of coronary heart disease using risk factor categories. Circulation. 1998;98:1837–47.
10. Eldredge-Hindly HB, Duffy D, Yamaoh K, Simonne NL, Skowronski J, Dicker AP, et al. Modeled risk of ischemic heart disease following left breast irradiation with deep inspiration breath hold. Pract Radiat Oncol. 2015;5:162–8.
11. Mosca L, Benjamin EJ, Berra K, Beazons JL, Dolor RJ, Lloyd-Jones DM, et al. Effectiveness-based guidelines for the prevention of cardiovascular disease in women—2011 update: a guideline from the American Heart Association. J Am Coll Cardiol. 2011;57:1404–23.
12. Swanson T, Grills IS, Ye H, Entwistle A, Teahan M, Letts N, et al. Six-year experience routinely using moderate deep inspiration breath hold for the reduction of cardiac dose in left-sided breast irradiation for patients with early-stage or locally advanced breast cancer. Am J Clin Oncol. 2013;36:24–30.
13. Stranlz H, Zurl B. Postoperative irradiation of left-sided breast cancer patients and cardiac toxicity. Does deep inspiration breath-hold (DIBH) technique protect the heart? Strahlenther Onkol. 2008;184:354–8.
14. Hayden AJ, Rains M, Tiver K. Deep inspiration breath hold technique reduces heart dose from radiotherapy for left-sided breast cancer. J Med Imaging Radiat Oncol. 2012;56:464–72.
15. da Costa J. Pulmonary function studies in healthy Chinese adults in Singapore. Am Rev Respir Dis. 1971;104:128–31.
16. Yang TS, Peat J, Keena V, Donnelly P, Unger W, Woolcock A. A review of the racial differences in the lung function of normal Caucasian, Chinese and Indian subjects. Eur Respir J. 1991;4:872–80.
17. Gagliardi G, Costine LS, Moiseenko V, Correa C, Pierce LJ, Allen AM, et al. Radiation dose-volume effects in the heart. Int J Radiat Oncol Biol Phys. 2000;47:225–32.
18. Borger JH, Hooning MJ, Boersma LA, Snijders-Reehorst A, Aleman BM, Lintzen E, et al. Cardiotoxic effects of tangential breast irradiation in early breast cancer patients: the role of irradiated heart volume. Int J Radiat Oncol Biol Phys. 2007;69:1131–8.
19. Correa CR, Litt H, Hwang WT, Ferrari VA, Solin LJ, Harris EE. Coronary artery findings after left-sided compared with right-sided radiation treatment for early-stage breast cancer. J Clin Oncol. 2007;25:3031–7.
20. Marks LB, Yu XL, Prosnitz RG, Zhou SM, Hardenbergh PH, Blazing M, et al. The incidence and functional consequences of RT-associated cardiac perfusion defects. J Int Radiat Oncol Biol Phys. 2005;63:214–23.
21. Nilsson G, Holmberg L, Garmo H, Duvevnoy D, Sjogren I, Lagerqvist B, et al. Delineation of target volumes and organs at risk consensus definitions. http://www.rtog.org/CoreLab/ContouringAtlases/LungAtlas.aspx. Accessed 27 Jul 2015.
22. Lind PA, Pagnanelli R, Marks LB, Borges-Neto S, Hu C, Zhou S-M, et al. Myocardial perfusion changes in patients irradiated for left-sided breast cancer and correlation with coronary artery distribution. Int J Radiat Oncol Biol Phys. 2003;55:914–20.
23. Evans SB, Panigrahi B, Northrup V, Patterson J, Baldwin DE, Higgins SA, et al. Analysis of coronary artery dosimetry in the 3-dimensional era: implications for organ-at-risk segmentation and dose tolerances in left-sided tangential breast radiation. Pract Radiat Oncol. 2013;3:55–60.
24. Korreman SS, Pedersen AN, Arup LR, Nottrup TJ, Specht L, Nystrom H. Reduction of cardiac and pulmonary complication probabilities after breathing adapted radiotherapy for breast cancer. Int J Radiat Oncol Biol Phys. 2006;65:1375–80.
25. Lymberis SC, de Wyngaert JK, Parhar P, Chhabra AM, Fenton-Kerimian M, Chang J, et al. Prospective assessment of optimal individual position (prone versus supine) for breast radiotherapy: volumetric and dosimetric correlations in 100 patients. Int J Radiat Oncol Biol Phys. 2012;84:902–9.
26. Mulliez T, Veldeman L, Speleers B, Mahjoubi K, Remouchamps V, Van Geveling A, et al. Heart dose reduction by prone deep inspiration breath hold in left-sided breast irradiation. Radiother Oncol. 2015;114:79–84. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2354,
1
],
[
2354,
7859,
2
],
[
7859,
14083,
3
],
[
14083,
19450,
4
],
[
19450,
20435,
5
],
[
20435,
23238,
6
],
[
23238,
26808,
7
],
[
26808,
34300,
8
],
[
34300,
34807,
9
]
]
} |
7540e998533e6248e73804d0f27d6231f1cfc1a9 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 5,
"total-fallback-pages": 0,
"total-input-tokens": 12757,
"total-output-tokens": 3236,
"fieldofstudy": [
"Medicine"
]
} | Addressing drug safety of maternal therapy during breastfeeding using physiologically-based pharmacokinetic modeling
INTRODUCTION
Breastfeeding can have positive health consequences for both the breastfed infant and the nursing mother. However, when taking medication, there are concerns about protecting the infant from adverse events while allowing necessary maternal therapy. An adverse effect on a breastfeeding infant due to maternal medication may be caused by an interplay of factors between the mother and the nursing infant, a complex scenario that can be readily investigated using physiologically-based pharmacokinetic (PBPK) modeling.
Multiple factors, including genetic and environmental, contribute to the variability associated with an individual’s response. Exposure of mothers, particularly those with certain genotypes, to multiple medications during pregnancy and breastfeeding may place their infants at increased risk of adverse drug reactions. Consideration should also be given to the infant’s smaller mass and immature gastrointestinal, hepatic, and renal function. Indeed, at this age, neonatal drug-excretory mechanisms, both hepatic and renal, are incompletely developed. Drugs chronically administered at that time through breastfeeding may accumulate and reach toxic concentrations.
PBPK models which account for the complex interplay between physiological parameters and drug-related characteristics, represent a mechanistic approach to predict the pharmacokinetics (PKs) of drugs in different populations, including nursing mothers and infants. Pediatric PBPK models account for the development of organs, including the ontogeny of specific enzymes and transporters involved in the disposition of a specific drug. Although knowledge gaps remain, ongoing research relating to these processes in children, has allowed refinement of relevant physiological parameters and integration of more complex models. Thus, PBPK models which are increasingly used in pediatric clinical pharmacology, including drug development, are reaching maturation for applications with high regulatory impact. In this paper, we discuss how “off the shelf” PBPK models for commonly used drugs, already robustly verified in terms of their disposition, can be used to assess safety concerns in breastfeeding infants as a consequence of the nursing mothers taking medication(s). Complex case studies will be used to demonstrate the validity of the approach.
CLINICAL LACTATION STUDIES IN DRUG DEVELOPMENT
In 2019, the US Food and Drug Administration (FDA) released a guidance document for pharmaceutical companies providing recommendations on how to address the potential impact of maternal drug exposure, including assessment of levels of the drug (and metabolite) appearing in breast milk, the potential effects on breastfeeding infants, and effects of the drug on milk production. The FDA indicate that data from clinical lactation studies, supported by other relevant data, including drug physicochemical properties, mechanism of drug entry into breast milk, data from nonclinical studies, and infant factors, can be used to evaluate the safety of a drug when used by breastfeeding mothers and to develop recommendations to minimize infant exposure.
Key factors affecting the excretion of drugs into milk and methods of measuring the passage of drugs into breast milk have been described previously. The standard method of quantifying drug passage into breast milk is the administration of a drug to a nursing mother, either for the purpose of the study or because she is taking the drug therapeutically. Ideally, sufficient drug concentrations are measured to allow calculation of an area under the milk concentration–time curve (AUC) and an average milk concentration (AUC/milk sampling duration).
Once an estimate of drug concentration in milk is available, an infant daily dose assuming a daily milk intake of 150 ml/kg and a milk/plasma ratio can be calculated. Thereafter, the relative infant daily dose (RIDD; the percent of the weight-adjusted maternal dosage consumed in breast milk over 24 h) is determined. The World Health Organization (WHO) Working Group proposed that drugs with an RIDD >10% may not be safe in infants, and that those with an RIDD greater than 25% should be avoided in nursing mothers.
**PREDICTING DRUG CONCENTRATIONS IN MILK**
The amount of drug excreted into breast milk depends upon the composition of the milk, the physicochemical properties of the drug, and the mechanism of transport. The higher the lipid solubility, the greater the concentration in human milk. The majority of drugs appear to be transported into mammary blood capillaries via passive diffusion. In the absence of clinical lactation data, it may be possible to predict the passage of drugs into breast milk (M/P ratio) using only the physicochemical properties of the drug and milk characteristics. Indeed, a number of such predictive algorithms have been developed and evaluated.4,5
Integration of these M/P ratio prediction algorithms within a PBPK model can facilitate simulation of drug levels in breast milk following administration of the drug in mothers.1 Thereafter, the infant daily dose and RIDD of a drug based on ingestion via breast milk can be predicted from the simulated milk concentration profiles and used to guide neonatal/infant risk assessment where clinical lactation data are lacking. In the context of regulatory application, “well-qualified models” are required to provide assurances that the model predictions are robust and this approach can be used to inform with confidence, high-impact decisions as part of regulatory submissions.6 Although it is accepted that this is an emerging and significant area of interest, evaluation of such approaches is already ongoing and results are promising.4,4
**PREDICTING DRUG CONCENTRATIONS IN INFANTS DURING BREASTFEEDING**
When clinical lactation data are available, some of the uncertainty associated with extrapolation of the infant daily dose is removed. Here, we present two case studies where observed milk concentrations were available and the extrapolated infant daily dose was used to simulate plasma concentration time profiles in infants using a pediatric PBPK model (Johnson et al.7); one involves a drug–drug interaction for a combination therapy, and the other, the complex interplay between mother/infant and the impact of their respective CYP2B6 genotypes.
**Case study 1: Lumacaftor/ivacaftor**
Cystic fibrosis (CF) is a life-shortening genetic disorder caused by mutations in the cystic fibrosis transmembrane conductance regulator (CFTR) gene. These mutations lead to abnormal ion transport in mucous membranes throughout the body, including the respiratory tract. As a consequence of CFTR modulator therapy, there has been a significant increase in the quality of life for those with CF. Pregnancy was once discouraged for women with CF but now, even with moderately severe lung disease, women can successfully navigate pregnancy. However, with the increasing use of this medication, there is a growing need to understand the effects of these agents during pregnancy. The uncomplicated and successful pregnancy of a woman treated with lumacaftor/ivacaftor, as well as the clinical course of the infant during the first 9 months of life, was reported recently.7 Concentrations of lumacaftor and ivacaftor in maternal plasma, cord blood, breast milk, and infant plasma over time were recorded throughout. A PBPK model describing the ivacaftor/lumacaftor combination that was able to capture the induction of CYP3A4-mediated metabolism of ivacaftor by lumacaftor for a number of different dosage regimens, was reported previously.8 In the case study presented here, the published PBPK models were used to predict the exposure of both drugs in breastfeeding infants during their first 9 months of life, thus replicating the clinical scenario.7 Virtual neonates with time-varying physiology, including a CYP3A4 ontogeny, were generated and given an infant daily dose of each drug (extrapolated from the observed milk data). As milk intake via breast-feeding was not constant, various scenarios were assessed (25% of dietary intake from breast milk up to 100%; Figure 1). Although data from only a single infant were available for comparison, the results are promising especially when considering the complexity of the situation.
**Case study 2: efavirenz**
Current WHO guidelines recommend efavirenz as the preferred non-nucleoside reverse transcriptase inhibitor component of first-line antiretroviral therapy for adults across different patient populations, including nursing mothers. However, efavirenz is not licensed for use in
children <3 months old or weight \( \leq 3.5 \) kg because optimal dosing and safety have not been evaluated. Despite this, the drug is widely used by nursing mothers. An observational study was conducted to investigate maternal plasma and breast milk PKs of efavirenz and breastfed infants’ exposure in genetically defined subgroups of HIV positive nursing mothers.\(^9\) Potential variability due to genetic polymorphisms in CYP2B6, NR1I3, CYP2A6, ABCB1, ABCB5, and ABCG2 was evaluated. CYP2B6 516G>T was independently associated with efavirenz concentrations in maternal plasma, breast milk and infant plasma (\( n = 134 \)). When stratified according to CYP2B6 516G>T genotypes (\( n = 29; 11 \) GG, 10 GT, and 8 TT), efavirenz PK parameters in plasma and breast milk differed significantly between patient groups. No efavirenz-related toxicity was reported and the RIDD was reported to be <10% in most breastfed infants.
A robust PBPK model for efavirenz describing the CYP3A4- and CYP2B6-mediated auto-induction during multiple dosing was reported previously.\(^10\) In the case study presented here, the published PBPK model was used to predict the exposure of efavirenz in maternal and infant plasma accounting for the various CYP2B6 genotypes. Virtual infants with time-varying physiology, including a CYP2B6 ontogeny, were generated. The infant daily doses were estimated based on the clinically observed M/P ratio of 1.1 and efavirenz exposures in mothers carrying different CYP2B6 genotypes. The clinically significant trend toward higher infant efavirenz exposure from GG/GG to TT/TT composite maternal/infant CYP2B6 genotypes was captured reasonably well by the PBPK model (Figure 2).
### Concluding remarks
Most drug labels do not provide enough information to guide a woman and her physician in deciding whether a
medication is safe during breastfeeding. PBPK modeling can be used to predict drug exposures in both mothers and infants while accounting for complex factors, such as genetics, comediations, and time-varying physiology. Robust “off the shelf” PBPK models that have been extensively verified with supporting clinical data are already available for many commonly prescribed drugs. Along with other methods, this approach can be used to support benefit–risk decisions for both the nursing mother and the breastfeeding infant in early drug development and through practice.
**CONFLICT OF INTEREST**
K.R.Y. and X.P. are employees of Certara UK Limited (Simcyp Division) and may hold shares in Certara. As an Associate Editor for Clinical Pharmacology & Therapeutics: Pharmaceutics & Systems Pharmacology, K.R.Y. was not involved in the review or decision process for this paper.
**REFERENCES**
1. Abduljalil K, Pansari A, Ning J, Jamei M. Prediction of drug concentrations in milk during breastfeeding, integrating predictive
algorithms within a physiologically-based pharmacokinetic model. *CPT Pharmacometrics Syst Pharmacol.* 2021;10:878-889.
2. Johnson TN, Small BG, Rowland Yeo K. Increasing application of pediatric physiologically based pharmacokinetic models across academic and industry organizations. *CPT Pharmacometrics Syst Pharmacol.* 2022;11:373-883.
3. US Food and Drug Administration (FDA). Clinical lactation studies: considerations for study design. Guidance for industry. Draft guidance. [https://www.fda.gov/media/124749/download](https://www.fda.gov/media/124749/download) (2019).
4. Anderson PO, Momper JD. Clinical lactation studies and the role of pharmacokinetic modeling and simulation in predicting drug exposures in breastfed infants. *J Pharmacokinet Pharmacodyn.* 2020;47:295-304.
5. Fleishaker JC. Models and methods for predicting drug transfer into human milk. *Adv Drug Deliv Rev.* 2003;55:643-652.
6. Coppola P, Kerwash E, Cole S. Physiologically based pharmacokinetics model in pregnancy: a regulatory perspective on model evaluation. *Front Pediatr.* 2021;9:687978.
7. Trimble A, McKinzie C, Terrell M, Stringer E, Esther CR Jr. Measured fetal and neonatal exposure to Lumacaftor and Ivacaftor during pregnancy and while breastfeeding. *J Cyst Fibros.* 2018;17:779-782.
8. Tsai A, Wu SP, Haseltine E, et al. Physiologically based pharmacokinetic modeling of cftr modulation in people with cystic fibrosis transitioning from mono or dual regimens to triple-combination elexacaftor/tezacaftor/ivacaftor. *Pulm Ther.* 2020;6:275-286.
9. Olagunju A, Bolaji O, Amara A, et al. Breast milk pharmacokinetics of efavirenz and breastfed infants' exposure in genetically defined subgroups of mother–infant pairs: an observational study. *Clin Infect Dis.* 2015;61:453-463.
10. Ke A, Barter Z, Rowland-Yeo K, Almond L. Towards a best practice approach in PBPK modeling: case example of developing a unified efavirenz model accounting for induction of CYPs 3A4 and 2B6. *CPT Pharmacometrics Syst Pharmacol.* 2016;5:367-376. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3812,
1
],
[
3812,
8742,
2
],
[
8742,
10575,
3
],
[
10575,
11598,
4
],
[
11598,
13630,
5
]
]
} |
0218b5b59c26e8607ba84da3807e2d989cdae3d0 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 10,
"total-fallback-pages": 0,
"total-input-tokens": 31635,
"total-output-tokens": 12319,
"fieldofstudy": [
"Medicine"
]
} | Feasibility of using an LED-probe in third-space endoscopy: a clinical study
Oscar Víctor Hernández Mondragón*, Raúl Zamarripa Mottú, Omar Solórzano Pineda, Raúl Alberto Gutierrez Aguilar and Luís Fernando García Contreras
Abstract
Background: Third-space endoscopy is a novel, safe, and effective method for treating different gastrointestinal conditions. However, several failed endoscopic procedures are attributed to incomplete myotomy. Lighting devices are used to prevent organic injuries. We aimed to investigate the feasibility of using a hand-made LED-probe (LP) in third-space procedures.
Methods: This prospective study was conducted in a tertiary-care center in Mexico between December 2016 and January 2019. We included peroral endoscopic myotomy (POEM) and gastric peroral endoscopic myotomy (G-POEM) procedures. Pseudoachalasia, peptic ulcer, normal gastric emptying scintigraphy (GES) and prepyloric tumors were excluded. LP was used to guide or confirm procedures. Clinical and procedural characteristics were recorded and analyzed.
Results: Seventy third-space procedures were included (42 POEM, 28 G-POEM), with an average patient age of 46.7 ± 14.3 and 43.7 ± 10.1 years, respectively. For the POEM and G-POEM groups, respectively, 18/42 (42.9%) and 13/28 (46.7%) patients were males; median procedure times were 50 (interquartile range [IQR]: 38–71) and 60 (IQR: 48–77) min, median LP placement times were 5 (IQR: 4–6) and 6 (IQR: 5–7) min, mild adverse events occurred in 4 (9.4%) and 4 (14.2%) of cases, and clinical success at 6 months occurred in 100 and 85.7% of cases. Integrated relaxation pressure (IRP) improved from 27.3 ± 10.8 to 9.5 ± 4.1 mmHg (p < 0.001); retention percentage at 4 h also improved. LP was successfully placed and adequate myotomy confirmed including 14.2 and 17.8% of POEM and G-POEM difficult patients.
Conclusions: Using an LP is promising and allows guiding during third-space procedures either for submucosal tunnel creation or myotomy confirmation, with excellent safety and efficacy in clinical practice.
Keywords: Third-space endoscopy, LED-probe, Peroral endoscopic myotomy, Gastric peroral endoscopic myotomy
Background
Third-space endoscopy has emerged as a novel and effective method for the treatment of different gastrointestinal disorders such as achalasia and refractory gastroparesis [1–4]. However, difficult or incomplete myotomy has been identified in peroral endoscopy myotomy (POEM) and gastric-peroral endoscopy myotomy (G-POEM) as a result of different factors such as end-stage disease or previously treated cases (due to high submucosal fibrosis) [1, 5], inability to identify the esophagogastric junction (EGJ) throughout the submucosal tunnel during POEM [6–8] or the pyloric muscle ring (PMR) during G-POEM [9], lack of third-space endoscopy experience [2, 3, 6], and certain anatomical factors (megaeosophagus, sigmoid-type) [4, 9, 10]. These factors are associated with a failed procedure. Different techniques, such as fluoroscopy [9, 11] or double endoscopy [12, 13] have been proposed to overcome these problems and guide...
an appropriate tunnel creation and myotomy; however, low availability and high costs limit their use.
Lighting devices for surgical guidance have been investigated for years with good results. In laparoscopic colorectal and gynecological surgeries, the use of lighted ureteral stents has successfully prevented iatrogenic injuries [14, 15]. In ophthalmologic procedures, light-emitting diode (LED) technology is used for vitrectomy, with the advantage of no thermal or photodynamical harm; this provides better illumination than other light sources [16, 17]. In third-space endoscopy, the use of a dedicated LED-probe (LP) that could be inserted into the submucosal tunnel (cornerstone of the procedure) [1, 2, 8] could be used to guide the direction during the procedure or confirm a correct myotomy when combined with the endoscope, before closing the entry site. Use of an LP could be an excellent alternative during third-space endoscopic procedures. The aim of this study was to evaluate the feasibility of using LP in clinical practice, especially during POEM or G-POEM third-space procedures.
Methods
Study design and ethical considerations
This prospective study was conducted in a tertiary care center in Mexico City, Mexico between December, 2016 and January, 2019. We included patients between the ages of 18 and 90 years with naïve or previously-treated achalasia or severe refractory gastroparesis and who were treated with POEM or G-POEM, respectively, with 6 months of follow-up. Patients with pseudoachalasia were excluded from the POEM procedure. Active peptic ulcer disease, normal gastric emptying scintigraphy (GES) and prepyloric tumor lesions were excluded from G-POEM. Patients with severe clinical conditions that could be contraindications to any of these procedures were also excluded (severe chronic obstructive pulmonary disease, recent myocardial infarction). This protocol was approved by the Local Ethics Committee (R-2016-3601-192; registration number: 2016-CMN675). Informed consent was obtained from all patients.
Poem
Patients
The diagnosis of achalasia was based on the Chicago Classification [18], using high resolution manometry (HRM). Upper gastrointestinal (GI) endoscopy, computed tomography (CT) scanning, a timed barium esophagram (TBE) and the Chagas disease test were performed. Esophageal classification was evaluated according to Rezende’s classification [19]; the Eckardt score was used for clinical evaluation [20].
Procedure
The esophagus was cleaned 24 h before the POEM procedure and antibiotic prophylaxis with third-generation cephalosporines or quinolones was administered. All procedures were performed under general anesthesia. A 9.8-mm outer diameter with a 2.8-mm working channel endoscope was used (EG590WR; Fujinon, Tokyo, Japan), along with a transparent cap model (DH-28GR, Fujinon). An electrosurgical unit (ERBE VIO-200D, Tübingen, Germany), and an I-type hybrid knife (ERBE, Tübingen, Germany) were also used. Closure was performed using hemoclips (Boston Scientific, Natick, Massachusetts, USA).
The LP system was created using a sterile polyurethane non-weighted 127 cm × 20 Fr nasogastric feeding tube (AMA Proveduria, Mexico City, Mexico) that was cut at the middle. A thin strip of 150 cm long of an ultrabright slim LED strip light system of 1/8 in [3.5 mm] in diameter, with a capability of 112 lm/m (FlexfireLEDs, Costa Mesa, California, USA), was inserted throughout this catheter and attached to it with one 127 cm long strip of Scotch black tape (3 M, St. Paul, Minnesota, USA). This LP was coupled to a power supply system of 12 V that used conventional alkaline AA batteries (Duracell, Bethel, Connecticut, USA). After LP creation, it was cleaned with soapy water, rinsed and then dried. Finally, we used an antiseptic wipe (SoluPrep™, 3 M, St. Paul, Minnesota, USA), which has 2% w/v chlorhexidine gluconate and 70% v/v isopropyl alcohol, in order to clean the catheter before use (video 1).
The POEM technique was based on Inoue’s technique [21]. The technique was performed using the following procedure: (1), initially, the esophagus was cleaned if necessary; (2), injection and incision were performed with a mixture of saline solution and 0.5% methylene blue being injected 13-15 cm above the EGJ (20 cm for type III patients) and a 12-15 mm longitudinal incision being made for anterior (naïve patients) or posterior (previously-treated patients) approaches; (3), the submucosal tunnel was created, with the tunnel being created up to 3 cm below the EGJ; (4), a full-thickness myotomy was performed in all patients; (5), the LP was placed through the mouth; once it passed the cricopharyngeal muscle, it was grasped using biopsy forceps under endoscopic visualization and inserted up to the end of the submucosal tunnel; (6), intraluminal revision of the POEM procedure was performed and EGI was reviewed in retroflexion with the LP on, in order to confirm that submucosal tunnel reached gastric space and an adequate myotomy was performed. If LP on was not observed, submucosal tunnel and myotomy were considered as insufficient and they were corrected as necessary until LP on was observed. Submucosal tunnel was reviewed again to rule out adverse events secondary to LP or endoscope at this level; (7), closure with clips at the entry site was performed (Fig. 1).
Follow-up
Twenty-four hours after POEM, upper GI endoscopy and upper GI series were performed to rule out adverse
events. Antibiotics were continued by intravenous and then oral route for 7 days. A proton pump inhibitor (PPI) was administered for 4 weeks. Diet progressed from a liquid diet up to a normal one over the following 3 weeks. Follow-up continued for 6 months, with HRM, GI endoscopy, pHmetry, TBE, reflux questionnaires, and Eckardt scores evaluated at 3 and 6 months. Success was defined as an integrated relaxation pressure (IRP) < 15 mmHg, Eckardt score < 3, and TBE demonstrating adequate passage of contrast (≥ 80% at 5 min) 3 and 6 months postoperatively.
G-poem
Patients
Gastroparesis was diagnosed based on clinical evaluations and scintigraphy. Severe refractory gastroparesis was based on the presence of delayed gastric emptying-related symptoms, including nausea, retching, vomiting, abdominal pain, post-prandial fullness, early satiety and/or bloating. Patients who had failure or recurrence after receiving optimal pharmacological therapies and a Gastroparesis Cardinal Symptom Index (GCSI) score > 2.3 (score that has been validated as severe when greater than 2.3) [22] with a retention percentage at 4 h (RP4H) in GES > 10% and a mean half emptying time (MHET) > 150 min, were also diagnosed with severe refractory gastroparesis. Efficacy was evaluated based on a reduction in the self-reported gastroparetic symptoms of the patients; the absence of recurrent hospitalizations and the proportion of patients with a decrease in GCSI score < 2.3, RP4H < 10% and MHET< 150 min. Adverse events in POEM and G-POEM were graded according to the American Society for Gastrointestinal Endoscopy Lexicon [23].
Procedure
Procedures were performed in the endoscopic unit under general anesthesia. Forty-eight hours before the procedure, all patients were administered a liquid diet and antibiotic prophylaxis with third-generation cephalosporines or quinolones. Endoscopic instruments were the same as in POEM patients, including the LP. The G-POEM procedure was based on Khashab’s technique [24]. The technique was performed based on the following protocol: (1), revision and cleaning of the stomach were performed; (2), injection and incision were performed 5 cm before the pylorus for submucosal bleb creation using a combination of saline solution with 0.5% methylene blue. A longitudinal 1.5 cm incision was also performed; (3), a submucosal tunnel was performed in pyloric direction until PMR was identified. If submucosal tunnel orientation was lost during this step, LP was used and was inserted throughout the mouth, grasped with biopsy forceps and placed intraluminally into the duodenal bulb in order to guide submucosal tunnel creation and PMR identification; (4), myotomy of the circular and longitudinal muscular layers of the pylorus and the antrum was performed; the incision was 3-4 cm in length and deep up to the serosa. LP was used for myotomy confirmation in all cases. Before closure
was performed, submucosal tunnel was reviewed endoscopically to rule out complications at this level; (5), the incision was closed using the over the scope clips (OTSC) type A (OVESCO Endoscopy, AG, Tübingen, Germany) or hemoclips (Fig. 2).
Follow-up
Patients were admitted to the hospital after the procedure and given intravenous antibiotics, and then changed to oral route, in order to complete 7 days. An upper GI series and upper endoscopy were performed at 24 h to rule out adverse events. Diet progressed from a liquid diet to a normal diet over the next week. PPI was administered for 4 weeks. Both GCSI and GES were performed 3 and 6 months postoperatively.
Statistical analyses
Sample size was calculated based on an assumption that there would be at least 90% of efficacy in the completion of third-space procedures when LP is used, with a significance level of 0.05 (type I error of 5%) and a beta of 0.20 (type II error of 20%). Using an online statistically-validated program for sample size calculation (EpInfo, USA), we calculated a minimum of 25 patients for POEM and G-POEM procedures. Quantitative data were expressed as mean (standard deviation [SD]) or median with interquartile range (IQR); qualitative data were expressed as frequencies and percentages. Bivariate comparisons were done using the Friedman test, chi-squared test and a one-way analysis of variance, as appropriate. \( P < 0.05 \) was considered to be statistically significant. SPSS v.23.0 (IBM, Chicago, Illinois, USA) was used for all statistical analyses.
Results
There were 70 third-space procedures performed between December 2016 and January 2019 (42 POEM and 28 G-POEM).
Poem
Baseline characteristics
Forty-two patients were included with a mean age of 46.7 ± 14.3 years and 18 (42.9%) were male. Esophagus type grade II (16 [38%]) and achalasia subtype II (20 [47.6%]) were the most common. Thirty-two (76.2%) were naïve, while 10 (23.8%) had been previously treated, (60% had undergone LHM, 20% botulinum toxin injection, and 20% pneumatic dilation). No Chagas disease was found.
Procedure
The median total POEM time was 50 min (IQR 38–71). The mean tunnel and myotomy lengths were 12.9 ± 3.6 cm and 10.5 ± 3.1 cm, respectively. The most common mild adverse event was minor bleeding in 2 cases (4.7%), and the median length of stay (LOS) was 3 days (IQR 1–4).
Efficacy
Clinical response was observed in all cases at the 6-month follow-up. The Eckardt score decreased from 9 to
---
**Fig. 2** Animation and endoscopic image of G-POEM procedure guided and confirmed with LP. a LP is inserted intraluminally into the duodenal bulb. b Endoscopic view of LP throughout the submucosal space. Gastric and duodenal LED lights are observed with PMR at the bottom. c Myotomy is performed with LP guidance.
1 at the 3-month follow-up ($P < 0.001$) and did not change at the 6-month follow-up ($P < 0.001$). The IRP decreased from $27.3 \pm 10.8$ mmHg to $9.8 \pm 3.8$ mmHg at the 3-month follow-up ($P < 0.001$) and $9.5 \pm 4.1$ mmHg at the 6-month follow-up ($P < 0.001$); TBE showed emptying of < 50% in 100% of patients to emptying of > 50% in 100% ($p > 0.001$) after 6 months. Furthermore, 57% presented positive pHmetry, 15% had esophagitis and 12% had clinical symptoms of reflux disease (Table 1).
G-poem
**Baseline characteristics**
Twenty-eight patients with a mean age of $43.7 \pm 10.1$ years were included and 13 were male (46.4%). The most common etiology was diabetes in 12 (42.9%) and the mean duration of disease before G-POEM was $22.2 \pm 5.5$ months. The most predominant symptoms and previous therapy were: nausea and vomiting in 15 (53.5%), and medical therapy in 22 (78.7%), respectively. The median number of hospitalizations preoperatively was 2 (IQR 2-5).
**Procedure**
The median total G-POEM time was 60 min (IQR 48–77). The mean tunnel and myotomy lengths were $5.2 \pm 0.96$ cm and $3.2 \pm 0.82$ cm, respectively. The most common mild adverse event was capnoperitoneum in 2 patients (7.1%); it required abdominal decompression with a Veress needle and 1 mucosal tear 24 h after procedure and was solve endoscopically with clips. The median LOS was 2 days (IQR 1-6).
**Efficacy**
The GSCI score decreased from $3.5 \pm 0.64$ points to $1.8 \pm 0.61$ after 3 months ($P < 0.001$), and $1.2 \pm 0.43$ after 6 months ($P < 0.001$). GES test showed a decrease in RP4H from $35.3 \pm 11.6$ to $11.1 \pm 4.2$ after 3 months ($P < 0.001$), and $9.3 \pm 3.2$ after 6 months ($P < 0.001$). The half-emptying time improved from $260.2 \pm 66.9$ min to $165.9 \pm 31.2$ min after 3 months ($P < 0.001$), and $152.7 \pm 23.1$ min after 6 months ($P < 0.001$). Clinical response was observed in 24 patients (85.7%) at the 6-month evaluation. Resolution of the predominant symptoms were as follows: resolved in 16 (57.1%), 18 (64.3%) and 9 (32.1%); improved in 10 (35.8%), 5 (17.8%) and 11 (39.2%); not changed in 1 (3.6%), 3 (17.8%) and 7 (25%) and worsened in 1 (3.6%), 2 (7.2%) and 1 (3.6%), for nausea/vomiting, abdominal pain and gastric fullness, respectively. GES was normalized in 17 (60.7%) and partially improved in 8 (28.5%) of patients at the 6-month evaluation (Table 2).
**LED probe**
The median placement time for POEM and G-POEM were 5 (IQR 4-6) and 6 (IQR 5-7) min, respectively. All probes were successfully placed without adverse events and no adverse events or technical failures were observed after procedures secondary to their use. There was no damage to the submucosal space or at the intra-luminal mucosal level in both POEM and G-POEM cases, and we didn’t have any associated infections, neither when LP was placed in the mediastinal space at EGJ level in POEM cases. In general, LP use helped to adequately complete POEM and G-POEM in 11/70 (15.7%) of cases. After initial classic POEM procedure, LP on was placed and not observed in 6/42(14.2%) of cases. Therefore, submucosal tunnel and myotomy were extended up to an adequate LP confirmation. In POEM cases, placement of LP in posterior approach was relatively easier than anterior approach, but without significant differences in placement times (4 vs 6 min; $P = 0.2$).
In G-POEM cases, inadequate submucosal direction was found in 5/28(17.8%) of cases and LP use helped to correct it and confirm myotomy of the PMR in all cases. (video 2).
**Discussion**
In this study we evaluated the feasibility of using a new device, the LP, and confirmed its safe and effective use in clinical practice when performing third-space procedures (POEM and G-POEM).
Third-space endoscopy was first described by Sumiyama et al. [25]; it was first used in animals in 2007, and then used in humans. It is based on the creation of a submucosal tunnel to perform surgical procedures with confirmed safety and efficacy. It transforms the concept of endoluminal endoscopy to intramural, making many diseases that previously would have been treated by open or laparoscopic surgery endoscopically curable [1, 4].
The lumen is considered as the first space, while the peritoneum is considered the second space and the intentionally-created tunnel is the third space (space between the mucosa and muscularis propria) [2–4]. Different disorders have been addressed by this technique, including Zenker’s diverticulum, myotomy for achalasia, gastroparesis, Hirschsprung’s disease, removal of tumors arising from the muscularis propria and beyond, and stricture treatment [1, 2, 8]. Among them, achalasia and gastroparesis are the most prevalent diseases treated by this technique. However, “difficult”, “incomplete”, or even “not possible” tunnel creation or myotomy have been described and are associated with certain complexity factors such as end-stage disease (POEM) [5], previously-treated cases (POEM and G-POEM) [4, 8, 24], inability to identify EGJ (POEM) [6–8], PMR (G-POEM) [9], high submucosal fibrosis (POEM and G-POEM) [2–4, 6–8], lack of experience (POEM and G-POEM) [2, 3, 6], or anatomical factors (POEM) [1, 4, 9, 10]. These factors result in a failed procedure, even if the endoscopist believes that
the procedure was successful [1, 3]. If the tunnel is too short, the procedure is ineffective; if the length of the myotomy is too long, there is a higher risk of adverse events, including perforation or bleeding [3, 12]. Currently, there are several endoscopic landmarks, such as palisading vessels at the EGJ and the circular bundle of LES fibers in POEM (difficult use and inaccurate), or the continuous insertion and extraction of the endoscope from the tunnel, that are used to identify the PMR, which is technically challenging. A second endoscope (POEM and G-POEM) [12, 13] and fluoroscopy (G-POEM) [9, 11] are used in an attempt to overcome these problems;
| Table 1 Characteristics of the 42 POEM procedures performed with LED probe |
|---------------------------------------------------------------|
| Patients | Value |
| N = 42 | |
| Age, mean (SD), years | 46.7 ± 14.3 |
| Sex | male, n (%) |
| | 18 (42.9%) |
| Type of esophagus, n (%) | |
| Normal | 2 (5%) |
| Grade I | 8 (19%) |
| Grade II | 16 (38%) |
| Grade III | 8 (19%) |
| Grade IV | 8 (19%) |
| Previous treatments, n (%) | |
| Treatment naïve | 32 (76.2%) |
| Previously treated | 10 (23.8%) |
| + Post-LHM | 6 (60%) |
| + Botulinum toxin injection | 2 (20%) |
| + Pneumatic dilation | 2 (20%) |
| Achalasia subtype, n (%) | |
| Type I | 11 (26.2%) |
| Type II | 20 (47.6%) |
| Type III | 11 (26.2%) |
| Procedure | |
| Tunnel length, mean (SD), cm | 12.9 ± 3.6 |
| Myotomy length, mean (SD) cm | 10.5 ± 3.1 |
| LP placement time, median (IQR), min | 5 (4–6) |
| Patients with inadequate myotomy after initial classic POEM that benefited from LP use (difficult cases), n (%) | 6 (14.2%) |
| Total POEM time, median (IQR), min | 50 (38–71) |
| Adverse Events, n (%) | |
| Minor bleeding | 2 (4.7%) |
| Pneumoperitoneum | 2 (4.7%) |
| POEM outcomes | PRE-POEM | POST-POEM 3 m | POST-POEM 6 m | P value |
| Eckardt score, median (IQR), points | 9 (6–12) | 1 (0–3) | 1 (0–3) | < 0.0011 |
| IRP pressure, mean (SD), mmHg | 27.3 ± 10.8 | 9.8 ± 3.8 | 9.5 ± 4.1 | < 0.0012 |
| TBE | | < 0.0013 |
| • < 50% | 100% | 0% | 0% |
| • 50–80% | 0% | 14% | 9.5% |
| • > 80% | 0% | 86% | 90.5% |
SD standard deviation, IQR interquartile range, POEM peroral endoscopic myotomy, LP led-probe, LHM laparoscopic Heller myotomy
1 Friedman test
2 ANOVA test
3 X2 test
however, these methods are costly or are unavailable. Therefore, we decided to explore a new alternative to overcome these problems when performing third-space endoscopy.
The use of lighting devices has been explored in medicine for years. In colorectal and gynecological surgeries, for example, iatrogenic ureteric injury is a serious complication with a variable incidence between 0.7-10% [14]. The identification of ureters is challenging and the optional double J stent placement is invasive and associated with serious adverse events [15]; however, the use of fluorescence and lighted ureteral stents has overcome these problems. LED technology was invented in 1907 by H. J. Round but was commercially available in 1962 in electrical components. Modern LED technology with more practicality was used after 2010 [17]; uses in medicine are confirmed in ophthalmologic procedures where improved illumination for vitrectomy has been observed [16]. LED has advantages over incandescent light sources. It provides lower energy consumption, a longer lifetime, smaller size, faster switching, a better spectrum of light and intensity (emitting more lumens per watt compared
| Table 2 Characteristics of the 28 G-POEM procedures performed with LED probe |
|-------------------------|---------|
| Patients | Value |
| N = 28 |
| Age, mean (SD), years | 43.7 ± 10.1 |
| Sex, male, n (%) | 13 (46.4) |
| Etiology, n (%) | |
| • Diabetic | 12 (42.9%) |
| • Idiopathic | 11 (39.2%) |
| • Postsurgical | 5 (17.9%) |
| Duration of disease before G-POEM, mean (SD), months | 22.2 ± 5.5 |
| Predominant symptoms, n (%) | |
| • Nausea/vomiting | 15 (53.5%) |
| • Abdominal pain | 8 (28.6%) |
| • Gastric fullness | 5 (17.9%) |
| Previous therapy, n (%) | |
| • Medical treatment | 22 (78.7%) |
| • Botulinum toxin injection | 5 (17.8%) |
| • Transpyloric stenting | 1 (3.5%) |
| Procedure | |
| Tunnel length, mean (SD), cm | 5.2 ± 0.96 |
| Myotomy length, mean (SD), cm | 3.2 ± 0.82 |
| LP placement time, median (IQR), min | 6 (5-7) |
| Patients with inadequate submucosal tunnel direction after initial classic G-POEM procedure that benefited from LP use, n (%) | 5 (17.8%) |
| Total G-POEM time, median (IQR), min | 60 (48-77) |
| Adverse Events, n (%) | |
| • Capnoperitoneum | 2 (7.1%) |
| • Mucosal tear | 1 (3.5%) |
| • Prepyloric ulcer | 1 (3.5%) |
| G-POEM outcomes | |
| GSCI score, mean (SD), points | 35.3 ± 11.6 |
| RP4H, mean (SD), percentage | 35.3 ± 11.6 |
| MHET, mean (SD), minutes | 260.2 ± 66.9 |
| PRE-GPOEM | POST-GPOEM 3 m | POST-GPOEM 6 m | P value |
| 3.5 ± 0.64 | 1.8 ± 0.61 | 1.2 ± 0.43 | < 0.0011 |
| 35.3 ± 11.6 | 11.1 ± 4.2 | 9.3 ± 3.2 | < 0.0011 |
| 260.2 ± 66.9 | 165.9 ± 31.2 | 152.7 ± 23.1 | < 0.0011 |
SD standard deviation, IQR interquartile range, G-POEM gastric peroral endoscopic myotomy, LP led-probe, GSCI gastroparesis cardinal symptoms index, RP4H retention percentage 4 h, MHET mean half emptying time
1 ANOVA test
Hernández Mondragón et al. BMC Gastroenterology (2020) 20:132
with light bulbs), and cool light that radiates minimal heat. It is safe because mercury or other hazardous metals are not contained within it [16, 17].
Because of safety and efficiency, we decided to use a white LED-probe and orally insert it into a conventional 127 cm × 20 Fr nasogastric feeding tube. We spent between 10 to 15 min for LP building and disinfection process. Excellent visualization was obtained with the 112 lm/m of the probe; this was enough to be visualized under the submucosal tunnel or over the intraluminal space when inserted into the tunnel. We didn’t have technical problems during assembly or during procedures, neither when insertion into the patient was performed or after LP was used and procedures were finished. Therefore, based on these results, we confirmed the safety and efficacy of this device, that had a median insertion time of 5 min (4-6) for POEM and 6 (5-7) for G-POEM, without compromising total procedural times, and being similar to those observed in previous studies [5–7, 10, 11, 21, 24].
POEM was performed as described by other groups [5, 6, 21], with similar demographic characteristics. However, in our cohort 23.8% were previously treated and 38% grade III and IV. These are the subgroups theoretically more difficult to treat; therefore, with the greatest benefit if LP is used. Nonetheless, POEM was completed in 100% of cases and the mean myotomy length was 10.5 ± 3.1 cm, which is similar to the length of 9.4 ± 3.1 cm obtained in other studies [6]. Grimes et al. [13] compared double-scope vs conventional POEM in a clinical trial that included 50 patients per group. No differences in technical (98% vs 100%) or clinical success (93% vs 97%) was found, but with a 34% longer myotomy and 17 min increase in procedural times for double-scope group. In our study, the LP was 6 mm in diameter, which is similar to the length of the neonatal endoscope used in Grimes’ study. However, our LP system was advantageous in terms of cost (10 dls per LP), and placement time (5 min vs 17 min). We confirmed an adequate myotomy in all cases including 6 patients (14.2%) who were considered as difficult (4 grade IV, 1 grade III and 1 pneumatic dilation), in whom classic POEM didn’t complete myotomy and who benefited from the LP use, avoiding potential adverse events or risk of incomplete procedure. Additionally, no other endoscopy tower was needed (saving costs and space in the endoscopy room). In 2019, Grimes et al. published the follow-up of the cohort of double-scope vs conventional POEM, with a median of 3 years. They found no differences in clinical outcomes between groups (83% vs 80%; P = 1.0), without differences in reflux disease incidence, but more cases with grade B esophagitis were presented in treatment group (25% vs 4%; P = 0.049); they hypothesize that this is because a longer myotomy is performed in them (1.6 ± 1.2 cms) [26]. In our cases, the LP allowed performing an adequate EGJ myotomy and, at 6-month evaluation, clinical outcomes and the occurrence of reflux disease was similar to those of other studies [5–8, 12, 13, 21]. This suggests that the adequate confirmation of EGJ myotomy is the most important step in POEM procedures, regardless of whether an external device is used or not. Confirmation, which should be performed in all cases, mostly in early-experienced endoscopists in POEM procedure, represents LP as an excellent alternative for this purpose.
We performed the G-POEM and LP placement in all cases. Demographic characteristics were similar to other groups [8–11, 24]. The pylorus was previously manipulated in 21.4% of cases (botulinum toxin injection and transpyloric stent), potentially difficult cases. However, median G-POEM time (60 min) was similar to other groups [1, 9–12, 24]. Xue H et al. [9] compared the use of fluoroscopy-guided G-POEM vs conventional G-POEM procedure in 14 patients; all procedures achieved technical success, the PMR was identified in all 7 patients of the fluoroscopy-guided group, and only in 4(57.1%) from the control (P < 0.03). However, this was not clinically expressed, with a non-statistically significant difference between GCSI and GES. In our group, LP provided a better orientation towards PMR identification and myotomy confirmation in all cases, including 5/28 patients where the endoscopist was “lost”, during tunnel creation and PMR was not identified, where the LP allowed the completion of G-POEM procedures, representing a 17.8% benefit in them. However, besides the fact that the G-POEM outcomes were slightly better in our study, when compared with other centers, with a general clinical success (85.7% vs 69–81%) in GCSI and GES (89.2% vs 69–84.2%) at 6-month evaluations, we can’t assume that this could be explained because of the 100% PMR identification (similar to the fluoroscopy-guided group from Xue’s study). However, as stated by other authors, different gastroparesis subtypes with their corresponding physiopathology could explain the real heterogeneous mid-term results more than the simple direct effect of the PMR cutting, inclusive with LP guidance, as in our patients [1–4, 9–11, 24].
The strengths of our study include the use of LP in the two most common and important third-space procedures, the sample size that was reached in both and calculated for statistical significance, adequate and strict procedural and follow-up protocols, technical confirmation of all steps in all cases, and excellent safety without adverse events associated with LP use. Our study also has limitations that should be addressed. First, LP is not yet commercially available. Second, LP has to be made before each procedure by the medical doctor, which, in
spite of the fact that it takes only between 10 and 15 min, could be time-consuming. Third, different LED and nasogastric feeding tube brands exist around the world, which limits the availability of the system we used. Fourth, only POEM and G-POEM cases were included; pediatric and other third-space procedures were not included, and fifth, LP was used in 76.2% of naive POEM cases, which represent a subgroup of non-difficult cases in which LP could have been useless, especially when performed by highly-experienced endoscopists in third-space procedures; therefore, we think that the best advantage of LP use could be found in early-experience endoscopists in third-space procedures. However, we think that LP is a useful device for POEM and G-POEM procedures because of its simplicity, innovation, low costs, safety and the ability to make difficult procedures potentially easier.
**Conclusion**
In conclusion, we have confirmed the feasibility of using LP in third-space endoscopy as a new alternative to performing POEM or G-POEM cases, being specifically useful when classic anatomical landmarks are not completely reliable, in difficult cases, low-volume POEM and G-POEM centers, limited third-space procedures experience and when no other confirming methods are available. However, the real clinical relevance of LP use must be confirmed with longer evaluations and comparative studies. Commercialization and evaluation in other third-space procedures are necessary to elucidate potential advantages of the LP system.
**Supplementary information**
Supplementary information accompanies this paper at https://doi.org/10.1186/s12876-020-01260-9.
**Additional files**
Additional file 1: Video 1. Led Probe Construction. This is a video that we named led probe construction. In this video we show how to perform a LP before using in POEM or G-POEM cases.
Additional file 2: Video 2. LP clinical cases. In this video we show the use of LP in clinical POEM and G-POEM cases.
Additional file 3. POEM files. This is the POEM files from our cohort of patients with POEM that underwent to LP procedure.
Additional file 4. G-POEM files. This is the G-POEM files from our cohort of patients with G-POEM that underwent to LP procedure.
**Abbreviations**
LP: LED-probe; POEM: Peroral endoscopic myotomy; G-POEM: Gastric peroral endoscopic myotomy; GERD: Gastric emptying scintigraphy; IQR: interquartile range; IRP: Integrated relaxation pressure; EGI: Esophageagogastroduodenoscopy; PMR: pyloric muscle ring; LED: Light-emitting diode; HRM: High resolution manometry; Upper GI: Upper gastrointestinal; CT: Computed tomography; TBE: Timed barium esophagram; PPI: Proton pump inhibitor; GCSI: Gastroparesis Cardinal Symptom Index; RPMH: Retention Percentage 4 h; OTSC: Over the scope clip; SD: Standard deviation
**Acknowledgements**
Not applicable
**Authors’ contributions**
1.-OVHM: conception of LP protocol and idea, creation of manuscript, POEM and G-POEM cases, revision of final manuscript. 2.-RAZM: analysis and interpretation of the data, figures and tables creation. 3.-OMSP: acquisition of data and design, statistical analyses, POEM and G-POEM cases. 4.-RAGA: cases management and follow-up, analysis and interpretation of data. 5.-LFGC: POEM and G-POEM cases management and follow-up. All authors have read and approved the present manuscript
**Funding**
The authors declare not having any funding source for the development of the present study.
**Availability of data and materials**
All data generated or analyzed during this study are included in this published article [we added spv files as supplementary files].
**Ethics approval and consent to participate**
This protocol was approved by the Local Ethics Committee named: “Comité Local de Investigación y Ética en Investigación en Salud 3601 with registration number 13 CI 09 015 184 before COFEPRIS” which belongs to “Hospital de especialidades Dr. Bernardo Sepúlveda Gutiérrez, Centro Médico Nacional Siglo XXI del Instituto Mexicano del Seguro Social”. They approved our protocol with the number: R-2016-3601-192; and registration number: 2016-CMN675). Written informed consent was obtained from all patients.
**Consent for publication**
Not applicable.
**Competing interests**
OVHM, RAZM, OMSP, RAGA and LFGC, declare they do not have any competing interests.
**References**
1. Manolakis AC, Inoue H, Ueno A, Shimamura Y. 2007-2019: a “third”-space endoscopy in the endoscopic Management of Gastrointestinal Tract Diseases. Curr Treat Options Gastroenterol. 2019;17:202–20.
2. Nabi Z, Nageshwar R, Ramchandani M. Recent advances in third-space endoscopy. Gastroenterol Hepatol. 2018;14:224–32.
3. Elefteriadis N, Inoue H, Ikeda H, Onimaru M, Maselli R, Santi G. Submucosal tunnel endoscopy: Peroral endoscopic myotomy and peroral endoscopic tumor resection. World J Gastrointest Endosc. 2016;886–103.
4. Kobara H, Mori H, Ralfk K, Masaki T. Submucosal tunneling techniques: current perspectives. Clin Exp Gastroenterol. 2014;6:67–74.
5. Li QL, Wu QN, Zhang XC, Xu MD, Zhang W, Chen SY, Zhong YS, Zhang YQ, Chen WF, Qin WZ, Hu JW, Cai MY, Yao LQ, Zhou PH. Outcomes of peroral endoscopic myotomy for treatment of esophageal achalasia with a median follow-up of 49 months. Gastrointest Endosc. 2018;87:1405–12.
6. Akiyoye E, Kumar N, Obatian I, Alayo QA, Thompson CC. Peroral endoscopic myotomy: a meta-analysis. Endoscopy. 2016;48:599–608.
7. Werner YB, Rösch T. POEM and submucosal tunneling. Curr Treat Options Gastroenterol. 2016;14:163–7.
8. Parikh MP, Gupta NM, Sanaka MR. Esophageal third space endoscopy: recent advances. Curr Treat Options Gastroenterol. 2019;17:63–75.
9. Xue HB, Fan HZ, Meng XM, Cristofaro S, Mekaroonkamol P, Dacha S, Li LY, Fu XL, Zhan SH, Cai Q. Fluoroscopy-guided gastric peroral endoscopic pyloromyotomy (G-POEM): a more reliable and efficient method for treatment of refractory gastroparesis. Surg Endosc. 2017;31:4617–24.
10. Shlomovitz E, Pescarus R, Casseia MA, Shaitara AM, Reavis KM, Dunst CM, Swanström LL. Early human experience with per-oral endoscopic pyloromyotomy (POP). Surg Endosc. 2015;29:543–51.
11. Koul A, Dacha S, Mekaroonkamol P, Li X, Li L, Shahnazav N, Kellin S, Willsomming FF, Christie J, Cai Q. Fluoroscopic gastric peroral endoscopic myotomy (G-POEM) in patients with failed gastric electrical stimulator. Gastroenterol Rep. 2018;6:122–6.
12. Hong HJ, Song QW, Ko WJ, Jim NH, Hahn KB, Hong SP, Cho JY. Double-scope Peroral endoscopic Myotomy (POEM) for esophageal achalasia: the first trial of a new double-scope POEM. Clin Endosc. 2016;49:383–6.
13. Grimes KL, Inoue H, Onimaru M, Ikeda H, Tansawet A, Bechara R, Tanaka S. Double-scope per oral endoscopic myotomy (POEM): a prospective randomized trial. Surg Endosc. 2016;30:1344–51.
14. Boyan WP Jr, Lavy D, Dinallo A, Otero J, Roding A, Hanos D, Dressner R, Avranitis M. Lighted ureteral stents in laparoscopic colorectal surgery: a five-year experience. Ann Transl Med. 2017;5:44–8.
15. Hamilton AER, Westwood DA, Cuda T, Stevenson ARL. Identification of the ureter during robotic colorectal surgery using lighted stents – a video vignette. Color Dis. 2018;20:163–4.
16. Koellbl PS, Lingenfelder C, Krauhl CW, Kampmeier J, Koch FH, Kim YK, Hessling M. An intracutural micro light-emitting diode device for endo-illumination during pans plane vitrectomy. Eur J Ophthalmol. 2019;29:75–81.
17. Pan JW, Su YC, Chen YS. Secondary optical element design for intracoreoreal LED illumination system. Opt Lett. 2014;39:224–7.
18. Kahrilas PJ, Bredenoord AJ, Fox M, Gyawali CP, Roman S, Smout AJ, Pandolfino JE. The Chicago classification of esophageal motility disorders, v3.0. Neurogastroenterol Motil. 2015;27:160–74.
19. Rezende JM. Classificação radiológica do megaesôfago. Rev Goiana Med. 1982;28:187–91.
20. Eckardt VM, Aignherr C, Bernhard G. Predictors of outcome in patients with achalasia treated by pneumatic dilation. Gastroenterology. 1992;103:1732–8.
21. Inoue H, Minami H, Kobayashi Y, Sato Y, Kaga M, Suzuki M, Satodate H, Oda N, Itoh H, Kudo S. Peroral endoscopic myotomy (POEM) for esophageal achalasia. Endoscopy. 2010;42:265–71.
22. Khashab MA, Steint E, Clarke JO, Saxena P, Kumbhari V, Chander Roland B, Kallol AN, Stavropoulos S, Pasricha P, Inoue H. Gastric peroral endoscopic myotomy for refractory gastroparesis first human endoscopic pyloromyotomy (with video). Gastrointest Endosc. 2013;78:764–8.
23. Cotton PB, Eiseon GM, Ababken L, Baron TH, Hutter MM, Jacobson BC, Megnere K, Nemcek A Jr, Petersen BT, Petrini JL, Pike IM, Rabeneck L, Romagnuolo J, Vargo JJ. A lexicon for endoscopic adverse events: report of an ASGE workshop. Gastrointest Endosc. 2010;71:446–54.
24. Sumiyama K, Gostout CJ, Rajan E, Bakken TA, Knipschield MA, Marler RJ. Submucosal endoscopy with mucosal flap safety valve. Gastrointest Endosc. 2007;65:688–94.
25. Grimes KL, Bechara R, Shimamura Y, Ikeda H, Inoue H. Gastric myotomy length affects severity but not rate of post-procedure reflux: 3-year follow-up of a prospective randomized controlled trial of double-scope per oral endoscopic myotomy (POEM) for esophageal achalasia. Surg Endosc Aug. 2019;28. https://doi.org/10.1007/s00464-019-07079-0.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Ready to submit your research? Choose BMC and benefit from:
• fast, convenient online submission
• thorough peer review by experienced researchers in your field
• rapid publication on acceptance
• support for research data, including large and complex data types
• gold Open Access which fosters wider collaboration and increased citations
• maximum visibility for your research: over 100M website views per year
At BMC, research is always in progress.
Learn more biomedcentral.com/submissions | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3118,
1
],
[
3118,
8592,
2
],
[
8592,
11507,
3
],
[
11507,
14308,
4
],
[
14308,
19602,
5
],
[
19602,
21924,
6
],
[
21924,
25206,
7
],
[
25206,
30919,
8
],
[
30919,
37519,
9
],
[
37519,
40767,
10
]
]
} |
2637a5d4e068060a6507c01b5e471981eb037682 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 8,
"total-fallback-pages": 0,
"total-input-tokens": 27983,
"total-output-tokens": 10841,
"fieldofstudy": [
"Medicine",
"Biology"
]
} | Apolipoprotein-A-I for severe COVID-19-induced hyperinflammatory states: A prospective case study
Stanislas Faguer1,2,3*, Arnaud Del Bello1, Chloé Danet4, Yves Renaudineau2,5,6, Jacques Izopet2,5,7 and Nassim Kamar1,2,5
1Referral Center for Rare Kidney Diseases, Department of Nephrology and Organ Transplantation, University Hospital of Toulouse, Toulouse, France, 2Faculty of Medicine, University Paul Sabatier—Toulouse 3, Toulouse, France, 3French National Institute of Health and Medical Research, U1297 (Institute of Metabolic and Cardiovascular Diseases), Toulouse, France, 4Department of Clinical Pharmacy, University Hospital of Toulouse, Toulouse, France, 5French National Institute of Health and Medical Research, U1291 (INFINITY), Toulouse, France, 6Laboratory of Immunology, University Hospital of Toulouse, Toulouse, France, 7Laboratory of Virology, University Hospital of Toulouse, Toulouse, France
Viral infections can promote cytokine storm and multiorgan failure in individuals with an underlying immunosuppression or specific genetic background. Hyperinflammatory states, including critical forms of COVID-19, are characterized by a remodeling of the lipid profile including a dramatic decrease of the serum levels of apolipoprotein-A-I (ApoA-I), a protein known for its capacity to reduce systemic and lung inflammation, modulate innate and adaptive immunity, and prevent endothelial dysfunction and blood coagulation. In this study, four immunocompromised patients with severe COVID-19 cytokine storm that progressed despite standard-of-care therapy [Omicron (n = 3) and Delta (n = 1) variants] received 2–4 infusions (10 mg/kg) of CER-001, an ApoA-I-containing HDL mimetic. Injections were well-tolerated with no serious adverse events. Three patients treated while not on mechanical ventilation had early clinical and biological improvement (oxygen withdrawal and correction of hematological and inflammatory parameters, including serum levels of interleukin-8) and were discharged from the hospital 3–4 days after CER-001 infusions. In the fourth patient who received CER-001 after orotracheal intubation for acute respiratory distress syndrome, infusions were followed by transient respiratory improvement before secondary worsening related to ventilation-associated pneumonia. This pilot uncontrolled exploratory compassionate study provides initial safety and proof-of-concept data from patients with a COVID-19 cytokine storm receiving ApoA-I. Further randomized controlled trial evaluation is now required to ascertain whether ApoA-I has any beneficial effects on patients with a COVID-19 cytokine storm.
Abbreviations: ApoA-I, apolipoprotein-A-I; ARDS, acute respiratory distress syndrome; HDL, high-density lipoprotein; VOC, variant of concern.
Introduction
Severe SARS-CoV-2-associated diseases (COVID-19) are characterized by acute respiratory distress syndrome (ARDS) with local and systemic inflammation; complement activation; infiltrating neutrophils, monocytes, and macrophages; and pulmonary microangiopathy with fibrin thrombi and activated platelets (Kessel et al., 2021). In fatal cases, autopsies demonstrated the development of significant vasculopathy and increased vascular congestion in the lungs (Villalba et al., 2022). In addition, extensive analyses of COVID-19 ARDS identified phenotypes and molecular changes that distinguish it from other causes of ARDS (Empson et al., 2022). In rare cases, a COVID-19-associated cytokine storm may culminate in a hyperinflammatory state similar to, but still distinct from, autoinflammatory macrophage activation syndrome (Kessel et al., 2021).
COVID-19 evolved as a biphasic disorder including first underlying inborn or acquired immunodeficiency (type I/III-interferon response deficiency) leading to viral escape to immune defenses, and then a hyperinflammatory response promoting lung injury, endotheliopathy, and coagulopathy (Asano et al., 2021; Carapito et al., 2021; Paludan and Mogensen, 2022). Among other features, critical COVID-19 is characterized by high circulating levels of interleukin (IL)-1Ra, IL-6, IL-8, TNF-α, and ICAM-1 and low levels of FasL (Kessel et al., 2021; del Valle et al., 2020). This finding prompted the use of immunomodulatory approaches (e.g., corticosteroids or IL-1, IL-6, or JAK inhibitors) to prevent or treat COVID-19 ARDS and secondary lung fibrosis and ultimately to prevent refractory respiratory failure (van de Veerdonk et al., 2022). These treatments, used alone or in combination, are associated with some degree of improvements but have unpredictable effects. In addition, they may be associated with an increased risk of secondary infection, including life-threatening opportunistic infections mitigating their positive effects (Gangneux et al., 2022). This is particularly true in individuals with underlying immunosuppression, like those who received solid organ transplantation.
Targeted and unbiased metabolomic approaches have identified low serum levels of high-density lipoprotein (HDL) cholesterol and apolipoprotein-A-I (ApoA-I) as strong predictive factors of severe forms of COVID-19 (Sun et al., 2020; Begue et al., 2021; Hilser et al., 2021). Alterations of the lipoprotein plasma composition were demonstrated (for instance, downregulation of apolipoproteins, clusterin, and paraoxonase) (Begue et al., 2021). In addition, SARS-CoV-2 infection also triggers a humoral response against ApoA-I that may modulate the outcome of COVID-19 (Pagano et al., 2021). Interestingly, several lines of evidence point to the role of ApoA-I in modulating inflammation and innate and adaptive immunity in various settings, suggesting a potential therapeutic use in COVID-19 (Sorokin et al., 2020). Therefore, ApoA-I can inhibit the activity of monocytes (Hyka et al., 2001; Smythies et al., 2010), inhibit the cross talk between dendritic cells and natural killer cells in terms of IL-12 and IFN-γ (Kim et al., 2005), decrease T-lymphocyte activation by activated macrophages (Hyka et al., 2001), and reduce the inflammatory response of type II pneumocytes to a viral challenge (van Lenten et al., 2004). In mice, an ApoA-I mimetic reduced the severity of influenza-related pneumonia (van Lenten et al., 2002). Very recently, Kelesidis et al. (2021) reported that the ApoA-I mimetic peptide 4F attenuates in vitro the replication of SARS-CoV-2 and associated apoptosis, oxidative stress, and inflammation (IL-6 production) in epithelial cells.
CER-001 is an engineered, pre-β HDL particle that contains human recombinant ApoA-I together with natural phospholipids, combined into a single small discoidal particle (Keyserling et al., 2017). CER-001 was formerly developed for secondary prevention of cardiovascular diseases, but we recently reported that it can be proposed in patients with inherited lecithin-cholesterol-acyl-transferase deficiency to prevent kidney disease progression (Faguer et al., 2021). A preliminary study by Tanaka et al. (2022) reported a good tolerance of CER-001 in a critically ill patient with severe COVID-19 and secondary infection and a reduction in inflammatory markers. In addition, native HDL may exert a potent antiviral effect against SARS-Cov-2 (Cho et al., 2021). Altogether, these findings put forward the hypothesis that ApoA-I supplementation may prevent the progression of COVID-19 toward critical forms and/or reverse the cytokine storm induced by the SARS-CoV-2 infection.
In this study, we aimed to assess the tolerance of ApoA-I supplementation in four critically ill individuals who developed a COVID-19-associated hyperinflammatory state and were included in an ApoA-I compassionate-access program. As a secondary objective, their outcomes were reported.
Patients and methods
Approval and patients’ inclusion
The four patients included in this study were treated at the University Hospital of Toulouse (France) under a compassionate use program that was approved by the French Agency for the Safety of Drugs and Health Products (Agence Française de Sécurité du Médicament et des Produits de Santé [ANSM]);
authorization #2021-104249; #2022-107250; #2022-108293; #2022-108518). All patients provided informed consent to receive CER-001 and to be included in the Nephrogene Biobank which was approved by the French National Ethical Review Board (DC-2011-1388). The study was conducted from 15 December 2021 to 31 January 2022. Patients had documented COVID-19 (nasopharyngeal PCR) and hyperinflammatory state characterized by a serum level of ferritin higher than 1000 μg/L and inflammation-related organ injury (respiratory failure, coma, cytopenia, and hepatitis). They were also characterized by an ApoA-I serum level below 0.9 g/L (normal value > 1.1 g/L).
Drugs delivery
CER-001 was generously offered by Abionyx Pharma. Abionyx Pharma had no access to the data during the treatment period and did not participate in the article writing. Standard-of-care treatment was pursued, as appropriate.
Clinical follow-up
Patients were followed up throughout their hospitalization stay and underwent physical examinations and routine blood sampling (complete blood count, arterial blood gases, inflammatory markers, kidney and liver functions, and lipid tests). Cytokine measurements (IL-1β, IL-6, IL-8, and TNF-α) were performed immediately before and at several time points after the first administration of CER-001, using the ELLA nanofluidic system (Bio-Techne, France). Clinical and biological characteristics prior to and following CER-001 administration were compared descriptively.
The major endpoints were survival and adverse events (safety part of the study). The secondary endpoints were the length of hospitalization, the evolution of inflammatory parameters (ferritin and cytokines), and the oxygen supports in patients with ARDS.
Results
Cases histories
Patient 1 was a 52-year-old male patient with a history of IgA vasculitis, diabetes mellitus, and ischemic heart disease and had received a kidney transplant in 2018. He had been given three doses of mRNA vaccine but developed only weak anti-SARS-CoV-2 immunity (anti-spike antibodies 15.5 BAU/mL). He developed symptoms of COVID-19 on 17 December 2021 (fever, diarrhea, and dyspnea) and was admitted to the hospital on December 25. Oxygen saturation was 92% in room air, and oxygen supplementation was started (1 L/min).
The chest CT scan showed a bilateral interstitial lung disease compatible with COVID-19 (parenchyma extension 25%). Nasopharyngeal PCR identified SARS-CoV-2 (variant-of-concern (VOC) Delta). Blood tests showed a hyperinflammatory state (ferritin 5,037 μg/L and C-reactive protein 34 mg/L), liver test abnormalities (AST and ALT 2.5 and 3.5 times the upper limit normal (ULN) values, respectively), and thrombocytopenia. Tacrolimus was pursued, mycophenolate mofetil was withdrawn, and dexamethasone was introduced (6 mg/day) with antibiotics. On day 2, the blood tests showed pancytopenia and progression of the hyperinflammatory state (ferritin 6,870 μg/L and C-reactive protein 55 mg/L). He received one infusion of the monoclonal anti-IL-6R antibody tocilizumab (8 mg/kg i.v.) and one infusion of neutralizing monoclonal anti-SARS-CoV-2 antibodies (casirivimab/imdevimab). On day 4, ferritin increased to 19,219 μg/L, AST and ALT increased to 17 and 14 times the ULN values, respectively, and arterial lactates were at 2.7 mmol/L. Bone marrow aspirate showed features of hemophagocytosis. Blood PCR of SARS-CoV-2 was weakly positive. Worsening hypoxia required increased oxygenation (4 L/min; PaO2 62 mmHg), and the CT scan showed progressive lung lesions typical of COVID-19 (50% of the parenchyma). Despite increasing dexamethasone to 10 mg/day, serum triglycerides and ferritin increased to 3.2 mmol/L and 27,394 μg/L, respectively, on day 6.
Patient 2 was a 38-year-old female patient with a history of systemic lupus erythematosus and being overweight and had received a kidney transplant in 2011. She had been given three doses of mRNA vaccine but developed no anti-SARS-CoV-2 immunity. She developed symptoms of COVID-19 on 4 January 2022 (cough, chills, diarrhea, and fever) and was admitted to the transplantation ward on January 14. Nasopharyngeal PCR identified SARS-CoV-2 (VOC Omicron). Upon admission, SaO2 was 94% while receiving 9 L/min of oxygen with a facial mask. The chest CT scan showed typical lesions of COVID-19 (extension 50%). Blood tests showed hepatitis with cytolysis and cholestasis (7–10 times the ULN values, respectively), acute kidney injury (KDIGO stage 1), and hyperinflammation (ferritin 2,000 μg/L and C-reactive protein 107 mg/L). High-flow oxygen supplementation, awake prone position, dexamethasone (10 mg/day), tocilizumab (8 mg/kg once), and antibiotics were started. Everolimus was withdrawn, and tacrolimus was pursued. On day 4, despite full-code therapy, high-flow oxygen supplementation was still required, and the hyperinflammatory state worsened (ferritin 2,800 μg/L).
Patient 3 was a 47-year-old female patient with a history of diabetes mellitus, adrenal Cushing’s syndrome, hypertension, and end-stage kidney disease requiring chronic kidney replacement therapy since 2020. She did not receive anti-SARS-CoV-2 vaccination and had no anti-SARS-CoV-2 immunity at the time of admission to the hospital. She developed symptoms of COVID-19 on 15 January 2022.
(cough, dyspnea, abdominal pain, and fever) and was admitted to the hospital on January 19. Nasopharyngeal PCR identified SARS-CoV-2 (VOC Omicron). The chest CT scan showed mild to moderate lung lesions typical of COVID-19 (10%–25%). She did not require oxygen supplementation. Blood tests showed hyperinflammatory syndrome (ferritin 4,350 μg/L and C-reactive protein 55 mg/L) with a moderate increase in AST and ALT (2 and 1.5 times the ULN values, respectively) and mild thrombocytopenia and anemia. Dexamethasone (6 mg/day) was introduced. On day 3, hyperferritinemia (4,142 μg/L) and liver test abnormalities persisted, and she developed encephalopathy leading to admission to the intensive care unit.
**Patient 4** was a 59-year-old male patient with a history of hepatitis B, liver transplantation in 2006, HHV8-negative Kaposis’s sarcoma (complete remission), and end-stage kidney disease requiring chronic kidney replacement therapy since 2020. He had received three doses of mRNA vaccines but developed no anti-SARS-CoV-2 antibodies. Owing to familial exposure to SARS-CoV-2, nasopharyngeal PCR was performed on 6 January 2022, identifying the VOC Omicron variant. He had no respiratory symptoms. The chest CT scan showed mild to moderate lung lesions typical of COVID-19 (10%–25%). On January 17, dyspnea, cough, and fever developed. Upon admission, PaO₂ was 54 mmHg in room air, his respiratory rate was 30 cycles/min, and body temperature was 38.5°C. Blood tests showed hyperferritinemia (1,223 μg/L) and leukopenia (1,080 cells/mm³). A CT scan showed progression of lung lesions (25%–50%). Oxygen supplementation, dexamethasone (10 mg/day), tocilizumab (8 mg/kg, once), antibiotics, and fresh frozen plasma from convalescent patients were given. Mycophenolate mofetil was withdrawn, and tacrolimus was pursued. On day 5, acute respiratory failure developed requiring orotracheal intubation and mechanical ventilation with neuromuscular blocking. Blood tests showed a hyperinflammatory state (ferritin 4,535 μg/L) with increased AST and ALT (three times the ULN values). At that time, the bronchoalveolar fluid culture was negative, suggestive of critical COVID-19 only. The PaO₂ to FiO₂ ratio was in the range of 150–180. Antibiotics were pursued.
### General safety
Patients 1, 2, and 3 did not develop any serious adverse events. Patient 4 developed two episodes of ventilation-associated pneumonia (VAP; *Klebsiella pneumoniae* and *Aspergillus fumigatus* plus mucormycosis) and one bacteremia (*Staphylococcus haemolyticus*).
### Bioefficacy: lipid profiles
As shown in Figure 1, all four patients had very low serum levels of ApoA-I (range 0.74–0.79 mg/L, normal value > 1.1 g/L) and HDL (range 0.26–0.35, normal value > 0.45 g/L) and high serum levels of triglycerides (range 2.16–3.4 g/L, normal value < 1.5 g/L) when CER-001 was started. Lipid tests were not available at the time of admission to the hospital. Following infusion of CER-001, ApoA-I and HDL levels normalized in all patients at day 2 but remained in the lower range of the normal values in most inflammatory patients. In patient 4, who developed ventilator-associated pneumonia 3 days after the start of CER-001, ApoA-I subsequently decreased below the normal values.
### Inflammation kinetic
At baseline, IL-1β was normal in all individuals, IL-6 was increased in the three patients who previously received tocilizumab and was normal in the latter (3.3–1.295 pg/ml), and TNF-α was moderately increased (9.7–42.1 pg/ml). IL-8 was the only inflammatory cytokine universally increased (>10 pg/ml; 14.8–64.5 pg/ml) (Figure 1). Following CER-001, IL-8 normalized in patients 1, 2, and 3. In patient 4, IL-8 decreased immediately after the injections and re-increased at the time of a ventilator-associated pneumonia. Serum levels of ferritin decreased from 6,616 ± 8,696 to 1,712 ± 815 μg/L, 6 days after the start of CER-001. The administration of anti-IL6R antibodies before CER-001 in 3 out of 4 patients precluded the analysis of C-reactive protein. Body temperature remained below 37.5°C in all patients.
### Clinical outcomes
CER-001 administration was followed by a rapid improvement of the clinical condition of patients 1, 2, and 3, allowing them to be discharged from the hospital 3–4 days after the CER-001 infusions (Figure 1). In patients 1 and 2, oxygen
---
**Dosing**
According to the available information regarding its safety and pharmacokinetic/pharmacodynamic (Keyserling et al., 2017), CER-001 was given intravenously over 0.5–1 h at a dose of 10 mg/kg at hours 0 and 12 (patient 1) and hours 0, 12, 24, and 48 (patients 2, 3, and 4). In order to address the safety of the procedure, patient 1 received only two infusions of CER-001, whereas patients 2–4 received four infusions. Administration was preceded by anti-histaminic prophylaxis with hydroxyzine (50 mg i.v.). In all patients, dexamethasone was pursued.
supplementation was withdrawn 2 and 3 days after the administration, respectively. In patient 3, confusion resolved within 2 days. In these three patients, inflammatory parameters, liver tests, and blood cell count improved until discharge. Patient 4 received mechanical ventilation for 3 days when CER-001 was introduced. After a first phase of improvement (neuromuscular blocker withdrawal and sedation lightening) for 3 days, he secondarily developed several ventilator-associated pneumonia infections and ultimately died 1 month later. These infections were considered unrelated to the CER-001 treatment.
Discussion
In this study, we reported the outcomes of four individuals with COVID-19-induced cytokine storm who received ApoA-1 supplementation as salvage therapy. In addition to a very good
acute tolerance of CER-001, as already observed in other settings outside critical care units (Nicholls et al., 2018; Faguer et al., 2021), we observed a rapid improvement in respiratory status, a decrease in inflammatory parameters, and the normalization of blood cell counts, paralleling the normalization of ApoA-I levels after CER-001 in 3 out of 4 patients. On the contrary, they developed critical COVID-19-related cytokine storm, and they could be discharged home, without oxygen support, as soon as 3–4 days after CER-001 infusions. After the completion of this compassionate-use access, Tanaka et al. (2022) also reported a case of severe COVID-19 in which CER-001 administration was followed by a dramatic decrease of inflammatory parameters during infusion. These preliminary clinical results and data obtained in vitro (Kelesidis et al., 2021) strongly support the development of a randomized double-blind clinical trial testing CER-001 in patients with hyperinflammatory COVID-19, especially in those at risk of developing a critical disease.
Several studies have reported that ApoA-I and HDL-C are less abundant in COVID-19 patients (Poynard et al., 2020; Sun et al., 2020; Begue et al., 2021; Hilser et al., 2021), especially in the most severe forms, and that HDL-C from COVID-19 patients is less protective in endothelial cells submitted to inflammatory triggers and does not protect them from apoptosis (Begue et al., 2021). Low serum levels of ApoA-I may increase both triggers and does not protect them from apoptosis (Begue et al., 2021). Such a decrease in ApoA-I or HDL-C is a common finding in cytokine storms and was observed in virus-induced and familial hemophagocytic lymphohistiocytosis (HLH) (Henter et al., 1991; Kraskovsky et al., 2021) and in dengue shock syndrome (Marin-Palma et al., 2019). Thus, the results derived from this study may potentially be valid in other settings of hyperinflammatory states. Beyond its potential ability to prevent severe forms of COVID-19, ApoA-I also modulates virologic control by hosts and their immune responses against various viruses (e.g., herpes simplex virus and dengue virus) (Srinivas et al., 1990; Coelho et al., 2021). Our data thus support future trials in other forms of virus-induced hyperinflammatory states, like viral HLHs or dengue hemorrhagic fever/shock syndrome.
Among the various inflammatory cytokines, IL-8 was the only cytokine that was universally increased (>10 pg/ml), confirming its ability to identify patients developing critical COVID-19 (Kessel et al., 2021). IL-6 was also increased though the previous use of tocilizumab which precluded firm conclusions (Nishimoto et al., 2008). Our proof-of-concept study was not designed to distinguish whether hyperinflammation and COVID-19 were indeed reversed by the ApoA-I supplementation itself or whether it was only a fortuitous association, but, following CER-001, we observed a rapid decrease in IL-8 in the three patients with a favorable outcome, paralleling the clinical and biological improvement. In patient 4, after a first phase of clinical improvement accompanied by ApoA-I normalization and IL-8 decrease, ventilation-associated pneumonia and clinical deterioration were accompanied by C-reactive protein and IL-8 increase and ApoA-I decrease.
In this study, patients received four infusions of CER-001 (10 mg/kg), but the use of a higher dose for the first injection (e.g., 15 mg/kg) may help reach the optimal concentrations of ApoA-I and non-oxidized HDL more rapidly to achieve maximal therapeutic effects. Also, the pharmacokinetic of CER-001 has only been described in healthy individuals (Keyserling et al., 2017). In a phase 1 clinical study, a 10 mg/kg dose led to an increase of ApoA-I in the range of 0.1–0.2 g/L in the first 12 h followed by rapid normalization (Keyserling et al., 2017) that prompted us to inject CER-001 at hours 0, 12, 24, and 48 to reach optimal values of blood ApoA-I in a setting of low baseline values. Whether its half-life is extended in critically ill patients with liver failure is currently unknown.
This study has several limitations including its uncontrolled design and the small size of the cohort which could be included in the compassionate access program. This did not allow us to identify COVID-19 patients with the highest probability to benefit from CER-001 and whether specific sub-phenotypes (according to the degree of inflammation, vasculopathy, or other parameters to be determined) may better respond to ApoA-I supplementation. This will require additional analyses on larger cohorts. Second, one patient had a COVID-19 hyperinflammatory state but not respiratory failure. Our purpose was first to confirm the feasibility and tolerance of ApoA-I supplementation in the setting of critically ill COVID-19 patients. Here, we report the rapid improvement of some patients with COVID-19 ARDS or a hyperinflammatory state.
Conclusion
In summary, this pilot uncontrolled exploratory compassionate study provides initial safety and proof-of-concept data from patients with a COVID-19 cytokine storm receiving ApoA-I. Further randomized controlled trial evaluation is now required to ascertain whether ApoA-I has any beneficial effects on patients with COVID-19 cytokine storm.
Data availability statement
The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author.
Ethics statement
The studies involving human participants were reviewed and approved by the four patients included in this study who were treated at the University Hospital of Toulouse (France) under a compassionate use program that was approved by the French Agency for the Safety of Drugs and Health Products (Agence Française de Sécurité du Médicament et des Produits de Santé [ANSM]); authorization #2021-104249; #2022-107250; #2022-108293; #2022-108518). All patients provided informed consent to receive CER-001 and to be included in the Nephrogene Biobank, which was approved by the French National Ethical Review Board (DC-2011-1388). The patients/participants provided their written informed consent to participate in this study.
Author contributions
SF designed the study, followed up on the patients, acquired and analyzed the data, and wrote the manuscript; AD followed up on the patients and reviewed the manuscript; CD prepared the medications and managed the compassionate access forms; YR performed immunological analyses; JK followed patients, analyzed the data, and reviewed the manuscript. All the co-authors approved the last version of the manuscript.
Funding
SF received personal consulting fees from Abionyx Pharma, speaker fees from Asahi and Vifor Pharma, and travel funds from Sanofi-Genzyme. NK has received speaker fees and participated in the advisory board for Astellas, AstraZeneca, Biotest, CSL Behring, Chiesi, ExVIR, Hansa, Merck Sharp and Dohme, Glasgow Smith Kline, Novartis Pharma, Sanofi-Genzyme, Sandoz, and Takeda.
Acknowledgments
The authors greatly acknowledge the Agence Française de Sécurité du Médicament et des Produits de Santé (ANSM) for their helpful comments and support in obtaining the supply of CER-001.
Conflict of interest
SF has received personal consulting fees from Abionyx Pharma for the development of CER-001 in LCAT deficiency related-glomerulopathy.
The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
References
Asano, T., Bosson, B., Onodi, F., Mattuzzo, D., Moncada-Velez, M., Maglouris Renkilaraj, M. R. L., et al. (2021). X-linked recessive TLR7 deficiency in ~1% of men under 60 years old with life-threatening COVID-19. *Sci. Immunol.* 6, eabl4348. doi:10.1126/sciimmunol.abl4348
Begue, F., Tanaka, S., Mouktadi, Z., Rondoue, P., Veeren, B., Dietel, N., et al. (2021). Altered high-density lipoprotein composition and functions during severe COVID-19. *Sci. Rep.* 11, 2291. doi:10.1038/s41598-021-81638-1
Carapito, R., Li, R., Helms, J., Carapito, C., Guja, S., Rolli, V., et al. (2021). Identification of driver genes for critical forms of COVID-19 in a deeply phenotyped young patient cohort. *Sci. Transl. Med.* 14, eabf521. doi:10.1126/scitranslmed.abj7521
Cho, K. H., Kim, J. R., Lee, I. C., and Kwon, H. J. (2021). Native high-density lipoproteins (HDL) with higher paraoxonase exerts a potent antiviral effect against SARS-CoV-2 (COVID-19), while glycerated HDL lost the antiviral activity. *Antioxidants (Basel)* 10, 209–211. doi:10.3390/antiox10020209
Codho, D. R., Carneiro, P. H., Mendes-Moniziero, J., Conde, J. N., Andrade, I. Cao, T., et al. (2021). ApoA1 neutralizes proinflammatory effects of dengue virus NS1 protein and modulates viral immune evasion. *J. Virol.* 95, e0197420. doi:10.1128/JVI.01974-20
del Valle, D. M., Kim-Schulze, S., Huang, H. H., Beckmann, N. D., Niremberg, S., Wang, B., et al. (2020). An inflammatory cytokine signature predicts COVID-19 severity and survival. *Nat. Med.* 26, 1636–1643. doi:10.1038/s41591-020-1051-9
Empson, S., Rogers, A. J., and Wilson, J. G. (2022). COVID-19 acute respiratory distress syndrome: One pathogen, multiple phenotypes. *Crit. Care Clin.* 38, 505–519. doi:10.1016/j.ccc.2022.02.001
Faguer, S., Colombat, M., Chauveau, D., Bernadet-Montrozier, P., Beq, A., Delas, A., et al. (2021). Administration of the high-density lipoprotein mimetic CER-001 for inherited lecithin-cholesterol acyltransferase deficiency. *Annu. Intern. Med.* 174, 1022–1025. doi:10.7326/M21-1300
Gangneux, J.-P., Dannaoui, E., Fekkar, A., Luyt, C. E., Botterel, F., De Frost, N., et al. (2022). Fungal infections in mechanically ventilated patients with COVID-19 during the first wave: the French multicentre MYCOVID study. *Lancet. Respir. Med.* 10, 180–190. doi:10.1016/S2213-2600(21)00442-2
Henter, J. I., Carlsson, L. A., Soder, O., Nilsson-Ehle, P., and Elinder, G. (1991). Lipoprotein alterations and plasma lipoprotein lipid reduction in familial hemophagocytic lymphohistiocytosis. *Acta Paediatr.* 80, 675–681. doi:10.1111/j.1651-2227.1991.tb11928.x
Hilser, J. R., Han, Y., Buwas, S., Gukasyan, J., Cai, Z., Zhu, R., et al. (2021). Association of serum HDL-cholesterol and apolipoprotein A1 levels with risk of severe SARS-CoV-2 infection. *J. Lipid Res.* 62, 100061. doi:10.1194/jlr.R00061
Hyka, N., Dayer, J. M., Modoux, C., Kohno, T., Edwards, C. K., Roux-Lombard, P., et al. (2001). Apolipoprotein A-I inhibits the production of interleukin-1beta and tumor necrosis factor-alpha by blocking contact-mediated activation of monocytes by T lymphocytes. Blood 97, 2381–2389. doi:10.1182/blood.v97.8.2381
Kelesidis, T., Madhav, S., Petcherski, A., Cristelle, H., O’Connor, E., Hultgren, N. W., et al. (2021). The ApoA-I mimetic peptide 4F attenuates in vitro replication of SARS-CoV-2, associated apoptosis, oxidative stress and inflammation in epithelial cells. Virulence 12, 2214–2227. doi:10.1080/21505594.2021.1964329
Kessel, C., Vollenberg, R., Majoosthumann, K., Hinze, C., Wittkowski, H., Debaughnes, F., et al. (2021). Discrimination of COVID-19 from inflammation-induced cytokine storm syndromes using disease-related blood biomarkers. Arthritis Rheumatol. 73, 1791–1799. doi:10.1002/art.41763
Keyserling, C. H., Barbaras, R., and Benghozi, R. (2017). Development of CER-001: Preclinical dose selection through to phase I clinical findings. Clin. Drug Investig. 37, 483–491. doi:10.1007/s40261-017-0506-3
Kim, K. D., Lim, H. Y., Lee, H. G., Yoon, D. Y., Choe, Y. K., Choi, I., et al. (2005). Apolipoprotein A-I inhibits IL-10 and PGE2 production in human monocytes and inhibits dendritic cell differentiation and maturation. Biochem. Biophys. Res. Commun. 338, 1126–1136. doi:10.1016/j.bbrc.2005.10.065
Kraskovsky, V., Harhay, J., and Mador, M. J. (2021). Case of haemophagocytic lymphohistiocytosis following Epstein-Barr virus infection. BMJ Case Rep. 202109-2150OC
Marin-Palma, D., Stroop, C. M., Urquidi-Inchima, S., and Hernandez, J. C. (2019). Inflammatory status and severity of disease in dengue patients are associated with lipoprotein alterations. PLoS ONE 14, e0214245. doi:10.1371/journal.pone.0214245
Nicholls, S. J., Andrews, J., Kastelein, J. J. P., Merkely, B., Nissen, S. E., Ray, K. K., et al. (2018). Clinical implications of CER-001, a pre-beta high-density lipoprotein amphipathic peptide analogs. JAMA Cardiol. 3, 815–822. doi:10.1001/jamacardio.2018.2121
Nishimoto, N., Terao, K., Mima, T., Nakahara, H., Takagi, N., and Kakehi, T. (2008). Mechanisms and pathologic significances in increase in serum interleukin-6 (IL-6) and soluble IL-6 receptor after administration of an anti-IL-6 receptor antibody, tocilizumab, in patients with rheumatoid arthritis and Castleman disease. Blood 112, 3959–3964. doi:10.1182/blood-2008-05-155846
Pagano, S., Yerly, S., Meyer, B., Julliard, C., Suh, N., Le Terrier, C., et al. (2021). SARS-CoV-2 infection as a trigger of humoral response against apolipoprotein A-1. Eur. J. Clin. Invest. 51, e13661. doi:10.1111/eci.13661
Paludan, S. R., and Mogensen, T. H. (2022). Innate immunological pathways in COVID-19 pathogenesis. Sci. Immunol. 7, eabm5505. doi:10.1126/sciimmunol.abm5505
Poynard, T., Deckmyn, O., Rudler, M., Peta, V., Ngo, Y., Vautier, M., et al. (2020). Performance of serum apolipoprotein-A1 as a sentinel of Covid-19. PLoS One 15, e0242306. doi:10.1371/journal.pone.0242306
Smythies, L. E., White, C. R., Maheshwari, A., Palgunachari, M. N., Ananthathamaiah, G. M., Chaddha, M., et al. (2010). Apolipoprotein A-I mimetic 4F alters the function of human monocyte-derived macrophages. Am. J. Physiol. Cell Physiol. 298, 1538–1548. doi:10.1152/ajpcell.00467.2009
Sorokin, A. v., Karathanasis, S. K., Yang, Z. H., Freeman, D., Kotani, K., and Remaley, A. T. (2020). COVID-19-Associated dyslipidemia: Implications for mechanism of impaired resolution and novel therapeutic approaches. FASEB J. 34, 9843–9855. doi:10.1096/fj.201901451
Srinivas, R. V., Birkedal, B., Owens, R. J., Ananthathamaiah, G. M., Segrest, J. P., and Comans, R. W. (1990). Antiviral effects of apolipoprotein A-I and its synthetic amphipathic peptide analogs. Virology 176, 48–57. doi:10.1016/0042-6822(90)90229-k
Sun, J. T., Chen, Z., Nie, P., Ge, H., Shen, L., Yang, F., et al. (2020). Lipid profile features and their associations with disease severity and mortality in patients with COVID-19. Front. Cardiovasc. Med. 7, 584987. doi:10.3389/fcvm.2020.584987
Tanaka, S., Buge, F., Veenen, B., Robert, T., Faille, D., Tashk, P., et al. (2022). First recombinant high-density lipoprotein particles administration in a severe ICU COVID-19 patient, a multi-omics exploratory investigation. Biomolecules 10, 754. doi:10.3390/biomolecules10040754
van de Veerdonk, F. L., Giarellas-Bourboulis, E., Pickkers, P., Derde, L., Leavis, H., van Crevel, R., et al. (2022). A guide to immunotherapy for COVID-19. Nat. Med. 28, 39–50. doi:10.1038/s41591-021-01643-9
van Lenten, B. J., Wagner, A. C., Ananthathamaiah, G. M., Garber, D. W., Fuhhein, M. C., Adhikary, L., et al. (2002). Influenza infection promotes macrophage traffic into arteries of mice that is prevented by D-4F, an apolipoprotein A-I mimetic peptide. Circulation 106, 1127–1132. doi:10.1161/01.CIR.0000030182.35880.3e
van Lenten, B. J., Wagner, A. C., Navah, M., Ananthathamaiah, G. M., Hui, E. W. K., Nayak, D. P., et al. (2004). D-4F, an apolipoprotein A-I mimetic peptide, inhibits the inflammatory response induced by influenza A infection of human type II pneumocytes. Circulation 110, 3252–3258. doi:10.1161/01.CIR.0000147322.75456.B3
Villalba, J. A., Hildbrun, C. F., Garlin, M. A., Elliott, G. A., Li, Y., Kunotko, K., et al. (2022). Vasculopathy and increased vascular congestion in fatal COVID-19 and ARDS. Am. J. Respir. Crit. Care Med. Online ahead of Print. doi:10.1164/RCCM.202109-2150OC | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2779,
1
],
[
2779,
8105,
2
],
[
8105,
13403,
3
],
[
13403,
18332,
4
],
[
18332,
19134,
5
],
[
19134,
24619,
6
],
[
24619,
29950,
7
],
[
29950,
35483,
8
]
]
} |
528169533521c713602b9a4db138cde96b2ecd49 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 10,
"total-fallback-pages": 0,
"total-input-tokens": 26856,
"total-output-tokens": 5705,
"fieldofstudy": [
"Computer Science",
"Engineering"
]
} | Automatic Detection of Motorcycle on the Road using Digital Image Processing
Sutikno¹, Helmie Arif Wibawa², Ragil Saputra³
¹,²,³ Department of Computer Science / Informatics, Faculty of Science and Mathematics, Diponegoro University, Indonesia
Email: ¹[email protected], ²[email protected], ³[email protected]
Abstract
Traffic accident is one of the causes of death in the world. One of them is traffic accidents on motorcyclist not wearing helmet. To overcome this problem, several researchers have developed detection system of motorcyclist not wear helmet. This system consists of motorcycle detection and motorcyclist head detection. On motorcycle detection, accuracy still needs to be improved. For this reason, this paper proposed motorcycle detection by adding image improvement processes that are enhancing contrast and adding object positioning features. The proposed technique is divided into three stages: image enhancement, feature extraction, and classification. The image enhancement stage consists of enhance contrast, convert RGB image to gray scale, background subtraction, convert gray scale image to binary, closing operation, and small object removal. The features used in this paper are the object area, the circumference of the object, and the location of the object, while the method for classification process using back-propagation neural network and SVM. The proposed method resulted in an accuracy of 96.97%.
Keywords: Detection, Image Processing, Motorcycle, On-road
1. INTRODUCTION
Traffic accident is one of many death causes in the world. A data produced by World Health Organization (WHO) states that the number of people died because of traffic accident is 1.25 million every year and 20 up to 50 million experienced minor injuries and disability [1]. Data published by Statistics Indonesia that the number of accidents from 1992 to 2015 in general continues to increase [2].
One of many causes which especially leads to dead victim in riding a motorcycle is the rider does not use helmet [1]. To reduce the death risk and any kind of injury, the government had released regulation number 22 of 2009 on traffic and road transportation [3]. Meanwhile, the surveillance towards the motorcycle riders on the road has been done manually although there have been CCTV (Closed-Circuit Television). This matter might allow some riders to be undetected. The existed CCTV system on the road needs an automatic surveillance feature.
Commonly, there are two steps in the system of motorcyclist do not wear helmet namely motorcycle detection and head detection. In the research [4], there are four steps to detect the motorcycle: background detection using Adaptive Mixture of Gaussians (AMG), moving object segmentation, feature extraction using Local
Binary Pattern (LBP) descriptor and clarification process by SVM (Support Vector Machine). While in [5], there are five steps in motorcycle detection process: RGB conversion to grayscale, background subtraction, enhancement by threshold and mathematical morphology method, feature extraction with area, and clarification with Neural Network. These methods can be improved by enhancing image quality and adding influential features. Therefore, this paper added the process of enhancement contrast and it added feature of the location of the object.
In general, there are three main steps of the proposed method namely image enhancement, feature extraction, and classification. The image enhancement stage is divided into 6 processes: enhance contrast, convert RGB image to grayscale, background subtraction, convert grayscale image to binary, closing operation, and small object removal. The features used the area of the object, the circumference of the object, and the location of the object, while the classification process used back-propagation neural network and SVM.
Back-propagation neural network and SVM algorithms have been widely used for classification, identification, prediction, and detection that produce a fairly good degree of accuracy. The applications of back-propagation neural network and SVM for classification are the fruit classification, ship classification, natural gas pipeline classification, automatic text classification, cancer classification, audio sounds classification, handling binary classification, enzyme classification and object classification [6-15]. The applications of the two classifiers for identification are defect identification for simple fleshy fruits, hand writer character recognition, transcription factor binding sites identification on human genome, diagnosis of renal calculus disease, and automated speech signal analysis [16-20]. Back-propagation neural networks and SVM are also widely used for prediction and detection including breast cancer risk prediction, weld quality prediction, permeability prediction, prediction of osteosarcoma metastasis, prediction of flow rate of karstic springs, detection of tobacco disease, detection of epileptic seizure, and detection of glioblastoma brain tumor [21-28].
2. METHODS
In general, the proposed techniques are divided into 3 stages namely image enhancement, feature extraction, and classification. Image enhancement step is classified into six processes namely contrast enhancement, RGB image to grayscale conversion, background subtraction, grayscale image to binary conversion, closing operation, and small object removal. The order of the process can be seen in Figure 1.
2.1. Image Enhancement
This step is divided into 6 processes: enhancing contrast, converting RGB image to gray scale, background subtraction, convert gray scale image to binary, closing operation, and small object removal. Changes in each process are shown in Figure 2. The input data applied in this research includes the frames from the video extraction. This video file is obtained from one of the CCTV recordings with
duration of 19 minutes and 12 seconds that are installed on the roads in Ciamis Regency, West Java.
**Figure 1. The proposed method for detecting motorcycles on the highway**
2.2. **Enhancing Contrast**
The first step in image enhancement is enhancing the contrast so the image will be clearer. This process is exercised on to background and object image. Background images are the images in video frames that have no moving objects.
2.3. **Converting RGB image to grayscale:**
The next step is converting RGB image to grayscale in background and moving objects image. This process is run by collecting three basic colors (red, blue, and green) which later are summed up. This sum will be divided by three to get an average. This average is the grayscale colors.
2.4. Background subtraction:
The background subtraction is subtracts between object frame and background frame. In this study, background image used closest background frame with object frame for order minimize lighting variation.
2.5. Converting grayscale image to binary:
The next process is converting grayscale to binary image. The results of this image are the pixels in images with only two possibilities; black and white (1 and 0). The threshold value is 50, which means if the value of gray is greater than 50 then the color pixel is black and the other is white.
2.6. Closing operation:
The next step is closing operation process. This process is a dilation process which is followed by the erosion. The result of this process is combining some close objects. This operation is useful if the result of grayscale image to binary conversion process is not fragmented into some pieces. To combine some objects, some element shapes can be used such as rectangle, square, disk, etc. This research used disk with radius of 8 pixels.
2.7. Small object removal:
The last process in the image enhancement is small object removal. The aim is to remove unwanted object. The object removal is based on the object’s size in the digital image. In this research, the object will be removed if the area is less or equal to 60 pixels. Meanwhile, the object with area more than 60 pixels will not be removed.
2.8. Feature extraction
The next step is feature extraction. The used features are area, circumference and object position. The object position is taken from center point of object at horizontal and vertical axis. The object area calculated from number of white pixel at the object. Meanwhile the circumference calculated from number of outline pixel on the object. The center point of object determinates as seen at the Figure 3. The formula for this point of the X axis and the Y axis is as equation (1) and (2).
\[
\text{CenterX} = X_1 + 0.5 \times W \\
\text{CenterY} = Y_1 + 0.5 \times H
\]
(1)
(2)
Where \(X_1\) is the object’s minimum point on X axis and \(Y_1\) is the object’s minimum point on Y axis. While \(W\) is the object’s width and \(H\) is the object’s height.
2.9. Classification
The classification stage is used to distinguish between an object of motorcycle and an object not motorcycle. The input data used the object area, the area circumference, the object’s center point on X axis and the object’s center point on Y axis. These features normalized in the range 0.1 to 0.9. The used classification methods are back-propagation neural network and SVM.
The architecture of the back-propagation neural network is as seen in Figure 4. This architecture consists of four inputs namely feature of area (X1), circumference (X2), object’s center point on X axis (X3), and object’s center point on Y axis (X4). The number of hidden layer is one hidden layer, meanwhile the numbers of neuron in the hidden layer are four neurons.
The second classification method is using SVM. The kernel in the SVM is used linier. Both classifiers were used to distinguish two classes namely an object of motorcycle and an object not motorcycle. If the object is a motorcycle, there will be a square shape surrounding the object as a mark. While if the object is not a motorcycle, the object will be ignored.
3. RESULT AND DISCUSSION
In this research, there are two types of testing: testing of performance on image enhancement and testing of classifier performance.
3.1. The Testing of Performance on Image Enhancement
Purpose of this testing is to find out the performance on image enhancement technique. The image data used in this testing was taken from result of a video extraction. The used data is frames image from video. The video was obtained from recording of CCTV on a highway in Ciamis Regency, West Java. The data testing number of frames image are 176 images with the measurement of 200 x 200 pixels (102 objects of motorcycle and 74 objects of not motorcycle). Data example used in this research is as seen in Figure 5.
The result of the testing is accuracy as 93.75%, while eleven images are not detected. The enhancement technique cannot detect object that the test image have similar color with background color. Another caused is the object is too small so the object accidentally removed on the process of small object removal.
3.2. The Testing of Performance Classifier
The purpose in this test is to test performance of classifier. The used classifiers in the research are back-propagation neural network and SVM. The used data are 165 images: 91 images of motorcycle and 74 images of other object. The size image is 200 x 200 pixels as shown in Figure 5. The used validation method is K-Fold cross validation with K=5. The total data for training are 132 images and for testing are 33 images.
The parameters of back-propagation neural network used epoch limit=10.000, error limit=0.001 and learning rate=0.3. The result of the test can be seen in Table 1. This table, it can be seen that every fold can reach epoch first before it reach error limit. The smallest error is reached on fold 3, as big as 0.0116.
The network weights be saved and it used to testing, after back-propagation neural network is doing training. The SVM classifier also needs training process before it does testing. The result of classification (testing) from both the classifiers can be seen on the Table 2. From this table, it can be seen that back-propagation and SVM produced the same accuracy on each K-fold and the average result. The average accuracy produced in both classifiers is 96.97%. The error is caused too difference small color between object and background image. This problem can be reduced by increasing the contrast between the object and background color. The proposed technique can improve accuracy when it compared to previous studies using HOG and SVM [29], HAAR and SVM [30], HAAR and RBFN [30], HOG and RBFN [30], LBP and RBFN [30], and SURF and RBFN [30] methods. Comparison of proposed techniques with other techniques is shown in Table 3.
| K-fold | Epoch | Error | Time (Second) |
|--------|-------|--------|---------------|
| 1 | 10.000| 0.0173 | 37 |
| 2 | 10.000| 0.0157 | 36 |
| 3 | 10.000| 0.0116 | 36 |
| 4 | 10.000| 0.0215 | 37 |
| 5 | 10.000| 0.0208 | 39 |
| Average| 10.000| 0.1208 | 37 |
Table 2. Classification results using back-propagation neural network and SVM
| Classifier | Accuracy (%) |
|------------|--------------|
| | K-Fold |
| | 1 2 3 4 5|
| BN | 0.969 0.939 0.939 10 10 96.97 |
| N | 7 4 4 0 0 |
| SV | 0.969 0.939 0.939 10 10 96.97 |
| M | 7 4 4 0 0 |
Table 3. Comparison of the proposed method with other methods
| Methods | Accuracy (%) |
|----------------------------------|--------------|
| Proposed | 96.97 |
| HOG and SVM [29] | 96.00 |
| HAAR and SVM [30] | 92.26 |
| HAAR and RBFN [30] | 96.24 |
| HOG and RBFN [30] | 95.10 |
| LBP and RBFN [30] | 95.75 |
| SURF and RBFN [30] | 96.76 |
4. CONCLUSION
The proposed technique for motorcycle detection are divided into 3 stages namely image enhancement, feature extraction, and classification. The proposed technique resulted 96.97% of accuracy. The cause of error is too small difference color
between object and background image. This problem can be reduced by increasing contrast between object color and background color.
5. REFERENCES
[1] WHO, 2018. Road traffic injuries. Available: http://www.who.int/mediacentre/factsheets/fs358/en/
[2] Statistics Indonesia. (2018). Traffic Accident, Killed Person, Seriously Injured, Slight Injured and Expected of Material Losses Value, Indonesia 1992-2017.
[3] Yudhoyono, S.B. (2009). Undang-Undang Republik Indonesia Nomor 22 Tahun 2009 Tentang Lalu Lintas dan Angkutan Jalan.
[4] Silva, R., Aires, K., Santos, T., Abdala, K., Veras, R., and Soares, A. (2013). Automatic detection of motorcyclists without helmet: in Proc. 2013 XXXIX Laten America Computing Conference ( pp. 1–7). Naiguata: IEEE.
[5] Marayatr, T., and Kumhon, P. (2014). Motorcyclist’s helmet wearing detection using image processing. Advanced Materials Research, 932–932, 588–592.
[6] Dimililer, K., and Bush, I.J. (2017). Automated classification of fruits: Pawpaw fruit as a case study: in Proc. 5th International Conference on Man-Machine Interactions, ICMMI (pp. 365-374). Kraków: Springer.
[7] Wu, J., Zhu, Y., Wang, Z., Song, Z., Liu, X.,Wang, W., Zhang, Z., Yu, Xu, Z., Zhang, T., Zhou, J. (2017). A novel ship classification approach for high resolution SAR images based on the BDA-KELM classification model. International Journal of Remote Sensing, 38(23), 6457-6476.
[8] Sun, J., Peng, Z., and Wen, J. (2017). Leakage aperture recognition based on ensemble local mean decomposition and sparse representation for classification of natural gas pipeline. Measurement, 108, 91-100.
[9] Ranjan, N.M., and Prasad, R.S. (2017). Automatic text classification using BPLion-neural network and semantic word processin. Imaging Science Journal, 66(8), 1-15.
[10] Watsqa, D., and Marwha, M. (2017). Median filter noise reduction of image and backpropagation neural network model for cervical cancer classification. Journal of Physics, 885(1).
[11] Lu, X. and Chen, D. (2017). Cancer classification through filtering progressive transductive support vector machine based on gene expression data: in Proc. 2017 International Conference on Green Energy and Sustainable Development, GESD.
[12] Souli, S., and Lachiri, Z., (2018). Audio sounds classification using scattering features and support vectors machines for medical surveillance. Applied Acoustics, 130, 270-282.
[13] Gonzalez-Abril, L., Angulo, C., Nunez, H., and Leal, Y. (2017). Handling binary classification problems with a priority class by using Support Vector Machines. Applied Soft Computing Journal, 61, 661-669.
[14] Pradhan, D., Padhy, S., and Sahoo, B. (2017). Enzyme classification using multiclass support vector machine and feature subset selection. Computational Biology and Chemistry, 70, 211-219.
[15] Ferraz, C.T., and Gonzaga, A., Object classification using a local texture descriptor and a support vector machine. *Multimedia Tools and Applications*, 76(20), 20609-20641.
[16] Smita and Degaonkar, V. (2016). Defect identification for simple fleshy fruits by statistical image feature detection: in Proc. 4th International Conference on Advanced Computing, Networking and Informatics, ICACNI (pp. 156-172), Springer.
[17] Khalaf, M.H., Al-Khateeb, B., and Farhan, R.N. (2017). Hand written character recognition using neural network and deep belief network. *Journal of Theoretical and Applied Information Technology*, 95(19), 5070-5080.
[18] Koshki, H.B., Seyyedsalehi, S.A., and Mirakabad, F.A. (2017). Transcription factor binding sites identification on human genome using an artificial neural network: in Proc. 25th Iranian Conference on Electrical Engineering, ICEE (pp. 14-17), Tehran: IEEE.
[19] Akkasaligar, P.T. and Biradar, S. (2016). Diagnosis of renal calculus disease in medical ultrasound images: in Proc. 2016 IEEE International Conference on Computational Intelligence and Computing Research, ICCIC. Chennai: IEEE.
[20] Umapathy, S., Rachel, S., and Thulasi, R. (2017). Automated speech signal analysis based on feature extraction and classification of spasmodic dysphonia: a performance comparison of different classifiers. *International Journal of Speech Technology*, 21(1), 1-10.
[21] Singh, B.K., Verma, K., Panigrahi, L., and Thoke, A.S. (2017). Integrating radiologist feedback with computer aided diagnostic systems for breast cancer risk prediction in ultrasonic images: An experimental investigation in machine learning paradigm. *Expert Systems with Applications*, 90, 209-223.
[22] Wan, X., Wang, Y., Zhao, D. and Huang, Y. (2017). A comparison of two types of neural network for weld quality prediction in small scale resistance spot welding. *Mechanical Systems and Signal Processing*, 93, 634-644.
[23] Azizi, Y. and Manaman, N.S. (2017). Permeability prediction in one of the iranian carbonate oil reservoir using artificial neural network and support vector machine. *Journal of the Earth and Space Physics*. 43(2), 281-295.
[24] He, Y., Ma, J., and Ye, X.J. (2017). A support vector machine classifier for the prediction of osteosarcoma metastasis with high accuracy. *International Journal of Molecular Medicine*, 40(5), 1357-1364.
[25] Goyal, M.K., Sharma, A., and Katsifarakis, K.L. (2017). Prediction of flow rate of karstic springs using support vector machines. *Hydrological Sciences Journal*, 62(13), 2175-2186.
[26] Zhu, H., Chu, B., Zhang, C., Liu, F., Jiang, L., and He, Y. (2017). Hyperspectral imaging for presymptomatic detection of tobacco disease with successive projections algorithm and machine-learning classifiers. *Scientific Reports*, (7)(1).
[27] Dhif, I., Hachica, K., Pinna, A., Hochberg, S., Mhedhbi, I., and Garda, P. (2017). Epileptic seizure detection based on expected activity measurement and Neural Network classification: in Proc. 39th Annual International
Conference of the IEEE Engineering in Medicine and Biology Society, EMBC (pp. 2814-2817). Seogwipo: IEEE.
[28] Arunachalam, M., and Savarimuthu, S.R. (2017). An efficient and automatic glioblastoma brain tumor detection using shift-invariant shearlet transform and neural networks. *International Journal of Imaging Systems and Technology, 27*(3), 216-226.
[29] Mukhtar, A., and Tang, T.B., (2015). Vision based motorcycle detection using HOG feature. *Proc. 2015 IEEE International Conference on Signal and Image Processing Applications (ICSIPA)* (pp. 452-456). Kuala Lumpur: IEEE.
[30] Silva, R., Aires, K., Veras, R., Santos, T., Lima, K., and Soares, A. (2013). Automatic motorcycle detection on public roads. *CLEI Electronic Journal, 16*(3), 1-9. | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2792,
1
],
[
2792,
5901,
2
],
[
5901,
6667,
3
],
[
6667,
8857,
4
],
[
8857,
10148,
5
],
[
10148,
11964,
6
],
[
11964,
14418,
7
],
[
14418,
17206,
8
],
[
17206,
20250,
9
],
[
20250,
21005,
10
]
]
} |
e1188231004def9a44559fd986cf090117c32d6f | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 6,
"total-fallback-pages": 0,
"total-input-tokens": 16613,
"total-output-tokens": 4598,
"fieldofstudy": [
"Economics"
]
} | Factors affecting participation of women farmers in supporting family food security: case study in Pandeglang regency, Indonesia
R Megasari 1*, Y Budiawati1, A Mulyaningsih
Department of Agribisnis, Faculty of Agriculture, Universitas Sultan Ageng Tirtayasa, Jl. Raya Jakarta Km 4 Pakupatan Serang Banten Indonesia
*Corresponding author: [email protected]
Abstract. The potential of women farmers in achieving household food security must be supported by adequate female farmer capacity, optimal participation of women farmers at every stage, and eliminating and finding solutions to a number of obstacles faced by women in order to strengthen their capacity and increase their participation in achieving home food security stairs. The purpose of this study is to analyze the factors that influence the participation of female farmers in supporting family food security. The population in this study were female farmers in two sub-districts in Pandeglang District, Banten Province, namely Munjul and Cibaliung Districts. The number of samples is 125 female farmers. The research activities were carried out for three months (April to June 2019). Data analysis with the inferencing statistics used are SEM using LISREL 8.73 (Linear Structural Relationships). The results showed that the factors that influence the participation of female farmers in supporting family food security are access to resources, physical and socio-economic support and extension support. For this reason, government support is needed, by giving attention to women farmers as the main actors in achieving food security in rural households.
Keywords: participation, women farmers, family food security
1. Introduction
Socio-culturally, peasant women in Pandeglang Regency are responsible for achieving household food security. Therefore, the success of achieving household food security in Pandeglang Regency cannot neglect the role of women farmers. The potential of peasant women in achieving household food security must be supported by adequate capacity of peasant women, optimal participation of peasant women at each stage, and eliminating and finding solutions to a number of obstacles faced by women in order to strengthen their abilities and increase their participation in achieving home food security stairs.
Farmer women play an important role in household food security, both in the components of food availability, food access and food utilization. Farmer women contribute as workers in the agricultural sector. In 2010, in Latin America and the Caribbean there were approximately 20 percent of women in the agriculture sector, in Near East and North Africa and Sub-Saharan Africa nearly 50 percent, in South Asia around 35 percent, and in East and Southeast Asia nearly 50 percent. percent. Farmer women are also responsible for planning, processing, preparing, and serving food for the family [1], [9].
Farmer women are exclusively responsible for family nutrition, as producers and providers of food for families [6]. Farmer women also buy food using the income they get from working [7], [14], [4], [5], [9]. The International Center for Research on Women / ICRW states that farm women are also an integral part of efforts to reduce hunger and malnutrition because it is women who are responsible for ensuring the availability of balanced, nutritious food for their families.
Farmer women also carry out household strategies to meet food shortages (coping ability indicator) [3], [1], [7], [17], [2], [5]. The above description reinforces that the participation of women farmers in achieving household food security is not only related to increasing food production and food providers but also with increasing food and nutrition of household members. Alignment must occur between increased food production and income with improved food and nutritional status of households [2], [9]. This supports the opinion that household food security is the ability of households to meet the adequacy of food for their members to be able to live healthy lives and be able to carry out daily activities that are reflected in the consumption of nutrients (energy and protein) that meet the adequacy norms [12], [8]. According to [10] efforts to achieve household food security can be pursued through increasing food and nutrition knowledge to maintain harmony between food availability and the quality of community food consumption.
To increase one’s participation requires certain capability requirements in their implementation and analyzing social, economic and cultural factors (personal characteristics of farm women, household socioeconomic households, socio-cultural environmental support, access to resources, and support for counseling) that affect ability and participation and find a way out. Supporting the implementation of food security counseling for farm women is needed to succeed household food security, because extension workers have a very strategic role [13].
The instructor should not only understand the production aspects but also need to have adequate knowledge, attitudes and skills in terms of consumption patterns, food distribution in order to provide correct information to farmer women in relation to food consumption and distribution patterns. The achievement of household food security gives meaning to the fulfillment of the rights of all individuals in the household to quality food (quality, balanced nutrition) at all times and can live a healthy and active life, as mandated by [15] Law of the Republic of Indonesia Number 18 2012 concerning Food. Household food security will determine the achievement of national and even global food security. Food security and nutrition are the common thread connecting various elements of sustainable future development. Food insecurity can have a long-term negative impact on the growth prospects of the whole community. Therefore, the government must continue to pay attention to farm women as the main actors in achieving household food security in rural areas. The purpose of this study is to analyze the factors that influence the participation of women farmers in supporting family food security.
2. Materials and Methods
This research is quantitative research supported by qualitative data. The research design is descriptive which takes a sample in one population using a questionnaire as a primary data collection tool [16] and aims to make a description of the situation or event from sample to population so that conclusions can be drawn. The research activities will be carried out for 3 months from April to June in 2019 in two sub-districts in Pandeglang District namely Munjul District and Cibaliung District. The sample in this study was 125 peasant women from two sub-districts.
The research uses survey methods and data analysis is done by descriptive statistics and inferential statistics. Inference statistics are used to estimate or estimate the population (generalization) in order to see the extent to which independent variables influence the dependent variable and to see the compatibility of the research model designed with the actual model. Statistical inference used is SEM by using LISREL 8.73 (Linear Structural Relationships). Determination of the sample in the study was carried out through two stages, namely the first stage was to determine the number of research samples. The size of the research sample follows the rules in the analysis of Structural Equation Modeling (SEM) with a maximum likelihood estimation method requiring a minimum sample of 100-150 respondents or as much as five times the indicators in the model [11]. In this study there were 25
indicators and the number of samples taken was 5 x 25 = 125 people. The number of samples in this study met the requirements for SEM testing. The second stage is to determine respondents in each selected village. The instrument used in this study was in the form of a questionnaire containing a list of questions made on the basis of predetermined variables.
Questionnaire in the form of a list of questions and guideline questions in the form of a number of key questions to find out qualitative phenomena from respondents and informants related to the problem and research objectives. The collected data was analyzed using inferential statistics. To give an idea of the factors that influence the participation of female farmers, the variables studied are: farmer characteristics (X1), access to resources (X2), economic and physical support (X3), extension support (X4), participation rates, (Y1) and food security (Y2).
The hypothesis in this study is that the level of participation of female farmers in supporting family food security is influenced by the characteristics of farmers, access to resources, physical and socio-economic environmental support, and extension support. Structural Equation Model and measurement model with the following formula:
(1) Structural Equation Model, is:
\[ \eta = B\eta + \Gamma\xi + \zeta \]
Description :
- \( \eta \) = eta, vektor from endogenous variable (Y)
- \( B \) = beta, a coefficient matrix describing the effect of other endogenous variables
- \( \Gamma \) = gamma, a coefficient matrix describing the effect from the exogenous variable to the endogenous variable
- \( \xi \) = xi, a vector of exogenous variables (latent variables X)
- \( \zeta \) = zeta, a vector of residuals or errors in the equation
(2) Measurement Model, is:
\[ X = \Lambda x\zeta + \delta Y = \Lambda y\zeta + \epsilon \]
Description :
- \( X \) = a vector of measurement of free variables
- \( \Lambda x \) = lambda X, a matrix of loading X on the latent variable exogenous which is not observed
- \( \delta \) = delta, a vector of related measurement errors with X variables
- \( \Lambda y \) = lambda Y, a matrix of loading X on the endogenous variable not observed
- \( \epsilon \) = epsilon, a vector of related measurement errors with Y variables
3. Results and Discussion
The results of hypothesis testing indicate that the factors that influence the level of participation of women farmers in supporting family food security are access to resources (X2), physical and socio-economic environmental support (X3), and extension support (X4). However, the level of participation of female farmers was more dominantly influenced by access to resources by 0.53, when compared to the influence of physical and socio-economic environmental support, and extension support by 0.33 and 0.39, respectively. The positive influence shows that the higher access to resources, physical and socio-economic environmental support, and extension support will further increase the participation of women farmers in supporting family food security.
The estimation of structural model parameters between the tested variables, namely: \( Y1 = 0.53 \times X2 + 0.13 \times X4 \), with \( R2 = 0.57 \) meaning that the simultaneous influence of the two variables on the level of participation of women farmers in supporting family food security is 0.57. This means that the
diversity of data that can be explained by the model is 57 percent, while the rest (43%) is explained by other variables (which are not yet in the model) and errors.
Figure 1 shows the factors that influence the level of participation of women farmers in supporting family food security. Factors affecting the level of participation of female farmers were analyzed using structural equation modeling (SEM) with the help of the LISREL 8.72 program, which was initially estimated or tested on the parameters of the model (framework of thought). Testing the model using a two-step procedure (two step approach). First, testing the Goodness of fit model. Second, the results of processing for testing the goodness of fit by using alternative testing for the use of SEM indicators, namely the results of processing for testing the goodness of fit by using an alternative testing for the use of SEM indicators, namely the results of several measurement indicators test results in the conclusion that the model meets the criteria for goodness of fit.
According to the criterion size RMSEA (Root Mean Square Error of Approximation) produces a value of $0.070 \leq 0.080$ which means that the resulting model is fit. The use of other good fit criteria namely GFI (Goodness of Fit Index), AGFI (Adjusted Goodness of Fit), CFI (Comparative Fit Index), IFI (Incremental Fit Index), and NFI (Normed Fit Index) produce values $\geq 0.90$ which means the resulting model is already good fit (Table 1). The test results of several measurement indicators produce the conclusion that the model meets the criteria for goodness of fit, so that hypothesis testing can be done.
Table 1. The results of testing the goodness of fit model of factors that influence the level of participation of women farmers in supporting family food security.
| Goodness-of-Fit | Cutt-off-Value | Result | conclusion |
|-----------------|---------------|--------|------------|
| RMSEA | $\leq 0.08$ | 0.070 | Fit |
| GFI | $0.80 \geq \text{GFI} \geq 0.90$ | 0.87 | Fit |
| AGFI | $0.80 \geq \text{AGFI} \geq 0.90$ | 0.83 | Fit |
| CFI | $\geq 0.90$ | 0.97 | very Fit |
| IFI | $\geq 0.90$ | 0.97 | very Fit |
| NFI | $\geq 0.90$ | 0.94 | very Fit |
The proposed construct measurement model is fit with the data. This means that the model is able to estimate the covariance matrix of sample data. In other words, the model can be used as a basis for making generalizations about the phenomena under study. In summary based on the estimation of structural model parameters between the tested variables, it can be seen that access to resources directly influences the level of participation of women farmers in supporting family food security, this is because the input factors and farming technology support the participation of farmers in managing their farming. Physical social economic support affects the participation of women farmers, especially in terms of government policy support, support of farmer leaders, institutional support, infrastructure support, and expert support. In addition, extension support also affects the participation of farmers, especially in supporting family food security. Dal is supported by material that is suitable to the needs of farmers, high intensity of counseling and good extension agent. The participation of women farmers is reflected by the participation variable with indicators of implementation ($\lambda = 0.93$) and implementation ($\lambda = 0.80$). Farmer participation, especially in the implementation phase, is very much needed for improvement. The more farming is carried out properly and in accordance with the rules, the more weaknesses will be known and can later be corrected in the next planting season.
3.1. Level of participation
The level of participation of women farmers in supporting family food security in both districts is classified as moderate. This can be seen in Figure 1 where it can be seen that farmers from Cibaliung
and Munjul sub-districts have a moderate level of participation, however, Munjul sub-district is relatively more participatory than farmers from Cibaliung sub-district.
3.2. Farmers Women's Participation Rate
Based on Figure 1, it can be seen that the element of participation that supports family food security from the aspect of availability and distribution aspects is implementation and benefits. This shows that in general women farmers from two districts conduct farming activities to support the food security of their families so that the availability of food in their homes can be guaranteed. In addition, some of the results of his farming are distributed to be sold and bought other food needs besides rice. The participation of women farmers from the aspect of benefits is to use the results of their farming for family food sufficiency. Thus it can be concluded that the involvement of farm women in farming can support family food security, especially in the aspects of availability and distribution aspects.
4. Conclusion
Factors that influence the participation of women farmers in supporting family food security are access to resources, physical and socio-economic support and extension support. To support family food security, support from the government is needed, especially access to resources, support for physical and socio-economic facilities and extension support.
5. References
[1] Arumsari V, Rini WDE. 2008. Peran perempuan dalam mewujudkan ketahanan pangan pada tingkat rumah tangga di Kabupaten Sleman Daerah Istimewa Yogyakarta. Jurnal Ekonomi Pembangunan 13(1): 71-82.
[2] Baliwati YF, Khomsan A, Dwiriani CM. 2010. Pengantar: Pangan dan Gizi. Depok (ID): Penebar Swadaya. Berg A.1986. Peranan Gizi dalam Pembangunan. Jakarta (ID): Rajawali.
[3] Brown LR, Feldstein H, Haddad L, Pena C, Quisimbing A. 2001. Generating Food Security in the Year 2020: Women as Producers, Gatekeepers, and Sock Absorbes. Di dalam: The Unfinished Agenda: Perspective on Overcoming Hunger, Poverty, dan Environmental. Washington DC (US): International Food Policy Research Institute.
[4] [FAO] The Food and Agricultural Organization. 2011. The Role of Women in Agriculture. ESA Working Paper. No. 11-02.
[5] Hubeis AVS 2002. Tantangan dan Prospek Teknologi Informasi dan Komunikasi dalam Otonomi Daerah. Di dalam: Pambudy R, Adhi AK, editor. Pemberdayaan Sumber Daya Manusia Menuju Terwujudnya Masyarakat Madani. Bogor (ID): Pustaka Wirausaha Muda.
[6] Hubeis AVS 2010. Pemberdayaan Perempuan dari Masa ke Masa. Bogor (ID): IPB Press.
[7] Ibnoof FO. 2009. The role of women in providing and improving household food security in Sudan: Implication for reducing hunger and malnutrition. Journal of International Women’s Studies 10(4) [Internet].
[8] Jayaputra. 2001. Ketahanan Pangan Rumahtangga Petani di Daerah Kawasan Pertambangan PT Newmont Nusa Tenggara. [Tesis]. Bogor (ID): Program Pascasarjana IPB.
[9] Karl M. 2013. Inseparable: The Crucial role of women in food security revisited. ProQuest Agriculture Journals.
[10] Kusharto CM, Hardinsyah. 2012. Ketahanan dan Kemandirian Pangan. Di dalam: Merevolusi Revolusi Hijau. Pemikiran Guru Besar IPB. Bogor (ID): IPB Press.
[11] Kusnendi. 2008. "Model-model Persamaan Struktural, Satu dan Multigrup Sampel dengan LISREL". Bandung: Alfabeta.
[12] Maxwell S, TR Frankenberger. 1992. Household Food Security: Concepts, Indicators, Measurements, A Technical Review. Rome: International Fund for Agricultural Development/United Nation Children’s Fund.
[13] Ndraha T. 1990. Pembangunan Masyarakat. Jakarta (ID): Rineka Cipta.
[14] Ogunlela, Mukhtar. 2009. Gender issues in agricultural and rural development in Nigeria; The Role of Women. Humanity and Social Sciences Journal. 4 (1): 19—30. Tersedia pada: http://www.idosi.org/.
[15] [UU] Republik Indonesia Nomor 18 Tahun 2012 tentang Ketahanan Pangan.
[16] Singarimbul M, Effendi S. 2006. Metode Penelitian Survei. Jakarta: LP3ES.
[17] World Bank. 2009. Gender in Agriculture Sourcebook. The World Bank, FAO, IFAD. Washington DC (US). | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2904,
1
],
[
2904,
7663,
2
],
[
7663,
11058,
3
],
[
11058,
15134,
4
],
[
15134,
17422,
5
],
[
17422,
19263,
6
]
]
} |
9f9f97001beec48fd140630810e3a8b03b4109b5 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 16,
"total-fallback-pages": 0,
"total-input-tokens": 52601,
"total-output-tokens": 10275,
"fieldofstudy": [
"Economics",
"Mathematics"
]
} | Dynamics of Money and Income Distributions
Przemysław Repetowicz Stefan Hutzler Peter Richmond
Department of Physics, Trinity College Dublin 2, Ireland
Abstract
We study the model of interacting agents proposed by Chatterjee (2003) that allows agents to both save and exchange wealth. Closed equations for the wealth distribution are developed using a mean field approximation.
We show that when all agents have the same fixed savings propensity, subject to certain well defined approximations defined in the text, these equations yield the conjecture proposed by Chatterjee (2003) for the form of the stationary agent wealth distribution.
If the savings propensity for the equations is chosen according to some random distribution we show further that the wealth distribution for large values of wealth displays a Pareto like power law tail, i.e. \( P(w) \sim w^{1+a} \). However the value of \( a \) for the model is exactly 1. Exact numerical simulations for the model illustrate how, as the savings distribution function narrows to zero, the wealth distribution changes from a Pareto form to an exponential function. Intermediate regions of wealth may be approximately described by a power law with \( a > 1 \). However the value never reaches values of \( \sim 1.6 - 1.7 \) that characterise empirical wealth data. This conclusion is not changed if three body agent exchange processes are allowed. We conclude that other mechanisms are required if the model is to agree with empirical wealth data.
Key words: Elastic and inelastic scattering, Kinetic theory, Classical statistical mechanics, Probability theory, stochastic processes, and statistics, Dynamics of social systems, Environmental studies
PACS: 13.85.Dz, 13.85.Fb, 13.85.Hd, 25.45.De, 05.20.Dd, 05.20.-y, 02.50.-r, 87.23.Ge, 89.60.+x
Email addresses: [email protected] (Przemysław Repetowicz), [email protected] (Stefan Hutzler), [email protected] (Peter Richmond).
URLs: www.maths.tcd.ie/~przemek (Przemysław Repetowicz),
www.tcd.ie/Physics/People/Peter.Richmond (Peter Richmond).
1 Introduction
The distribution of wealth or income in society has been of great interest for many years. Italian economist Vilfredo Pareto (1897) was the first to suggest it followed a “natural law” where the higher end of the wealth distribution is described by power law, \( P(w) \sim w^{-1-\alpha} \). Repeated empirical studies by Levy Solomon (1997); Dragulescu (2001); Reed Hughes (2002); Aoyama Souma (2003) show that the power law tail exhibits a remarkable spatial and temporal stability and while the value of the exponent, \( \alpha \), may vary slightly, it changes little from the value \( \sim 1.5 \).
Even though the collected data stem from different sources and can be incomplete because of difficulties in accessibility (poor conclusions from income data in Sweden in Levy Solomon (1997) due to a too small number of wealth ranges in the data; total net capital of individual at death in the United States (US) reported to the Bureau of Census and the Inland Revenue for tax heritage purposes in Dragulescu (2001); distributions of sizes of incomes, cities, internet files, biological taxa, gene family and protein family frequencies in Reed Hughes (2002); and income distributions in the Japan in Aoyama Souma (2003)) the common conclusion which can be drawn is that the high end that exhibits the power law is characterised by several multiples or even tens of multiples of the average income/wealth (only 5% of population income-data in the US conforms to a power-law and the power law for the yearly income data in the United Kingdom sets in only for \( > 50k \£ \) Dragulescu (2001), income distributions in the Japan in 2000 exhibit power laws only for \( > 5 \cdot 10^4 \) thousands of Yen).
For around 100 years the tantalising Pareto law remained without explanation. The renewed interest by physicists and mathematicians in econo- and sociophysics has however led to publication of a number of new papers on the topic in recent years (see Slanina (2004) for an extensive literature review).
The fact that multiplicative power law processes can lead to power law distributions has been known for many years from studies as diverse as the frequency of words in text Yule (1997), economic growth Gibrat (1931), city populations Zipf (1949), wealth distribution Ijiri (1977) and stochastic renewal processes Kesten (1973).
In the analysis of these distributions Solomon (2002) has recently proposed the use of Generalised Lotka Volterra (GLV) equation that combines a multiplicative random process with an autocatalytic process. The latter redistributes a fraction of the total money to ensure the money possessed by an agent is never zero. This simulates in a simplistic way the effect of a tax. The model
equations lead to a wealth distribution $P(w)$ of the form:
$$P(w) \sim \frac{e^{(1-\alpha)/w}}{w^{1+\alpha}}$$
(1)
where and $\alpha - 1$ is a positive number that is a ratio of parameters of the model that are related to social security and some random investments respectively. For large values of income $w$ this indeed exhibits a Pareto behaviour.
However two issues arise. The first is that empirical studies of income distributions show that this function does not describe well the very low end of the income distribution which is essentially exponential [Dragulescu (2001)]. The second relates to use of the multiplicative stochastic term. It is certainly necessary to secure the right form for the distribution function but how does it arise in the first place?
More recently [Chatterjee (2003)] have developed a model of pairwise interacting agents $i$ and $j$ that exchange money by analogy with an ensemble of gas molecules that exchange momentum. In Chatterjee (2003)’s model, however, the agents are allowed to save a fraction $\lambda_i$ of their money prior to an interaction. The total money held between two agents is conserved during the interaction process. The governing equations for the evolution of wealth $w_i$ and $w_j$ of agents $i$ and $j$ respectively are given by:
$$
\begin{align*}
w_i(t+1) &= \lambda_i w_i + \epsilon [ (1 - \lambda_i) w_i + (1 - \lambda_j) w_j ] \\
w_j(t+1) &= \lambda_j w_j + [1 - \epsilon] [ (1 - \lambda_i) w_i + (1 - \lambda_j) w_j ]
\end{align*}
$$
(2)
Here each agent, $i$, has a savings propensity, $\lambda_i$. The remaining money is divided during the exchange process in a random manner determined by a uniformly distributed random number $\epsilon$ between zero and one. From their numerical calculations [Chatterjee (2003)] found the following results for the stationary wealth distribution $P(w)$. Here
(1) With no saving ($\lambda_i = 0$ for all $i$) agents behave randomly and the distribution follows the Gibbs rule $P(w) \sim \exp(-w/\langle w \rangle)$ where $\langle w \rangle$ is the average wealth of agent. $P(w)$ has a maximum when $w = 0$.
(2) If the saving propensity is non-zero and takes the same constant value for all agents ($\lambda_i = \lambda$ for all $i$) the resulting distribution can be fitted well by the heuristic function:
$$P(w) = \frac{n^n}{\Gamma(n)} w^{n-1} \exp(-nw)$$
(3)
where $\Gamma(n)$ is the gamma function and the parameter $n$ is related to the
saving propensity, $\lambda$ as follows:
$$n(\lambda) = 1 + \frac{3\lambda}{1 - \lambda} \quad (4)$$
The power, $w^{n-1}$, qualitatively changes the distribution so that it has a maximum for $w > 0$. The author does not give any theoretical arguments for the use of this distribution.
(3) If the saving propensity for the agents is chosen according to some random distribution, like uniform or power-law distributions with $0 \leq \lambda \leq 1$, the numerical output for large values of money gives $P(w) \sim w^{-1-\alpha}$. This is the celebrated Pareto law. Numerical calculations yield a value for $\alpha = 1.03 \pm 0.03$. The authors show empirical data for wealth distributions for both Japan and the USA. These data clearly exhibit power laws with values of $\alpha$ greater than this value. However the authors leave the reader wondering whether the model could fit this data better. A further calculation allowing only a fraction, $p$, of agents to save is made but the the value for the Pareto law remains unchanged. The authors do not investigate the possible changes in $\alpha$ as a result of using savings distributions that differ from uniform distributions.
This work is interesting in that it brings together within one framework the distributions of both Gibbs and Pareto. However it leaves open tantalizing questions.
(1) Is it possible to predict analytically the expressions 3 and 4?
(2) How does the value of $\alpha$ within the model depend on the nature of the savings distribution?
(3) Could it be that the value of $\alpha$ is actually unity?
(4) Is there a way of reconciling the approach based on the GLV equations and the exchange theory of Chakrabarti?
Note that caution has to be taken by fitting the models described above to income data obtained from Inland Revenues in different countries. As pointed out in Dragulescu (2000) the wealth has to be understood as a commodity that is subject to an incessant process of exchange rather then as valueables like precious metals, “hard currency”, bonds or works of art that have been deposited in a bank account in order to serve as a lifetime security. In this sense the distributions that come out of the models should be fitted to a momentary distribution of money in the society; a distribution they may or may not be in equilibrium. Since people rarely disclose their momentary wealth the statistical data one avails of regards more the total wealth of individuals, ie the wealth that has been accumulated throughout their whole lifetimes and is reported to the Revenue office only after death (to fulfill the heritage tax requirements). Since, however, individuals with small and medium wealths are rather unlikely to invest parts of their income in any sort of lifetime securities,
because their earnings are small and are spent in their total to cover the cost of living, the low end of the momentary money distribution in equilibrium should coincide with the low end of the wealth distribution obtained from the Revenue data. Differences will only be observed in the high end.
In the next section we develop the theory for the model by Chatterjee (2003) and show that it is indeed possible to demonstrate that the conjecture summarised above is, to within a certain well defined approximation, correct. We then study asymptotically the behaviour of the wealth distribution for the case where the savings propensity varies for the agents and demonstrate that if the wealth distribution \( P(w) \sim w^{1+\alpha} \) then \( \alpha \) is exactly unity for this model. We demonstrate in section 2.2 that this conclusion remains unchanged even when three agent exchange processes are allowed. The conclusions of the mean field analytic analysis are supported by exact numerical simulations shown in Figs. 5 and 6.
2 Theoretical analysis
Complete information about the processes at time \( t \) is given by the \( N \) agent distribution function \( f_N(v_1, \ldots, v_N) \). In what follows we shall assume the mean-field approximation. This implies that the \( N \)-agent distribution function:
\[
f_N(v_1, \ldots, v_N) = P \left( \bigcap_i v_i \leq V_i \leq v_i + dv \right) / (dv)^N = \prod_i f_1(v_i) \tag{5}\]
We can now invoke the Boltzmann equation Ernst (1981) for the one-agent wealth \( v \) distribution \( f_1(v; t) \) at time \( t \). Thus:
\[
\partial_t f_1(v; t) = \int dw dv' dw' (W(v w | v' w') f_1(v') f_1(w') - W(v' w' | v w) f_1(v) f_1(w)) \tag{6}\]
where the transition probabilities \( W() \) are given via the rules for the collision-dynamics (2):
\[
W(v' w' | v w) = \delta(v' - (\lambda v + \epsilon(1 - \lambda)(v + w))) \cdot \delta(w' - (\lambda w + (1 - \epsilon)(1 - \lambda)(v + w))) \tag{7}\]
Introducing the Laplace transform \( \tilde{f}_1(x; t) := \int_0^\infty f_1(v; t) \exp(-vx) dv \) we obtain an integro-differential equation for the temporal evolution:
\[
\partial_t \tilde{f}_1(x; t) + \tilde{f}_1(x; t) = \left\langle \tilde{f}_2 \left( \lambda x + \epsilon (1 - \lambda) x, \epsilon (1 - \lambda) x; t \right) \right\rangle \tag{8}\]
where the random spatial variability of the saving propensities $\lambda$ and exchange fractions $\epsilon$ is accounted for by the averaging process $\langle \rangle$ over their random distributions.
We note at this point that this model assumes elastic scattering, i.e. conservation of wealth during the exchange process (2) and the existence of a stationary solution. This is in contrast to many previous models formulated in different contexts where 'wealth' may be either lost Krapivsky (2002); Ben-Avraham (2003); Bobylev (2000); Baldassarri (2002) or gained Slanina (2004) in the exchange process and the distribution function has a power-law tail only in an asymptotic sense.
We now write the stationary solutions $\tilde{f}_1(x) = \lim_{t \to -\infty} \tilde{f}_1(x; t)$ both in terms of solutions of non-linear integral equations (Master Equations (MEs)) and in terms of expansions $\tilde{f}_1(x) = \sum_{n=0}^{\infty} (-1)^n m_n x^n$ over moments (Ms) $\langle v^n \rangle = m_n \cdot n!$ which satisfy recursion relations. It is convenient to distinguish two cases:
(I) Saving propensity: $\lambda \neq 0$ but equal for all agents:
\begin{align}
\text{ME: } x \tilde{f}_1(x) &= \frac{1}{1 - \lambda} \int_0^{(1-\lambda)x} \tilde{f}_1(\lambda x + \phi) \tilde{f}_1(\phi) d\phi \\
\text{Ms: } m_p &= \sum_{q=0}^{p} m_q m_{p-q} \tilde{C}_q^{(p)}(\lambda) \quad \text{with} \quad \tilde{C}_q^{(p)}(\lambda) = \frac{\tilde{f}_0^{(1-\lambda)}_q (\lambda + \eta)^{q+1} \eta^{p-q} d\eta}{1 - \lambda} \\
\text{and} \quad \tilde{C}_{q+1} = \frac{(1 - \lambda)^{p-q-1} - (q + 1) \tilde{C}_q^{(p)}}{p - q} \quad \text{with} \quad \tilde{C}_0^{(p)} = \frac{(1 - \lambda)^p}{p + 1}
\end{align}
(II) Random saving propensity: $\lambda \sim \rho_{\Lambda}(\lambda)$.
\begin{align}
\text{ME: } x \tilde{f}_1(x) &= \int_0^1 d\lambda \rho_{\Lambda}(\lambda) \frac{(1-\lambda)x}{1 - \lambda} \int_0^{(1-\lambda)x} \tilde{f}_1(\lambda x + \phi) \tilde{f}_1(\phi) d\phi
\end{align}
Here we waive the writing of equations for the moments since due to the wealth distribution having a power-law tail they may not of course exist. Now an assumption about an asymptotic expansion in the “wealth-domain”: $f_1(v) = \sum_{n=0}^{\infty} a_n / v^{n+\alpha+1}$ leads to a decomposition of the function in the Laplace domain into two parts
\begin{align}
\tilde{f}_1(x) &= \tilde{f}_1^{\text{reg}}(x) + \tilde{f}_1^{\text{sing}}(x)
\end{align}
with the first part being an analytic function \( \tilde{f}_{\text{reg}}^{\text{reg}}(x) = 1 - x + O(x^2) \) and the second part \( \tilde{f}_{\text{reg}}^{\text{sing}}(x) = \sum_{n=0}^{\infty} b_n x^{n+\alpha} \) having a leading term \( x^\alpha \) of order \( \alpha \).
### 2.1 Conjecture by Patriarca, Chakraborti and Kaski (PCK):
Solving the moments’ equations (10) with initial conditions \( m_0 = 1 \) and \( m_1 = 1 \) recursively, ie. expressing, via the \( p \)th equation, \( m_p \) as a function of \( \lambda \) and all previous values of \( m \), (ie \( m_0, m_1, \ldots, m_{p-1} \)), one obtains:
\[
\begin{align*}
m_2 &= \frac{\lambda + 2}{2(1 + 2\lambda)} \\
m_3 &= \frac{\lambda + 2}{2(1 + 2\lambda)^2} \\
m_4 &= \frac{72 + 12\lambda - 2\lambda^2 + 9\lambda^3 - \lambda^5}{24(1 + 2\lambda)^2(3 + 6\lambda - \lambda^2 + 2\lambda^3)}
\end{align*}
\]
The first three moments \( m_1, m_2 \) and \( m_3 \) coincide with the moments of PCKs function (3) if the relation between the parameters \( n \) and \( \lambda \) is given by (4). Indeed the coefficients of a series expansion of the Laplace transform
\[
\tilde{P}(x) = \int_{0}^{\infty} P(\xi) \exp(-\xi x) d\xi = \left( \frac{n}{x + n} \right)^n
\]
of the function (3) agree with moments (14) up to the third order subject to equation (4) being satisfied. This is shown in a nice way in Fig. 1. The deviation \( \Delta \tilde{f}_1(x) \) between the exact solution of the ME (9) and the ansatz (3) has a leading fourth order:
\[
\Delta \tilde{f}_1(x) = \frac{(n - 1)(n + 1)(n + 8)}{8n^3(10n^3 + 30n^2 + 45n - 4)} x^4 + O(x^5)
\]
It is hard to say if a more general class of functions than (3) would satisfy the ME to higher expansion orders.
### 2.2 The power-law tail:
Calculations by \[\text{Chatterjee (2003)}\] and ourselves suggest that the value of the exponent \( \alpha \) is equal to one. Let us look at this aspect in more detail. Inserting the expansion (12) into the ME (9) and comparing coefficients of order \( x^{\alpha+1} \) on both sides of the equation leads to a transcendental equation for the exponent,
Fig. 1. Deviations $\Delta(\lambda; n) = \sum_{\rho=0}^{10} \left| (m_{\rho}(\lambda) - m_{\rho}^{\text{conj}}(n))/p! \right|$ of the exact moments $m_{\rho}$ of the wealth distribution from the moments $m_{\rho}^{\text{conj}}$ derived from the conjecture plotted as a function of $\lambda$ for $n = 2, 3, \ldots, 9$. Solid lines (dot symbols) correspond to analytical (numerical) solutions of the moment equations (10). We see that the minima $\lambda = (n - 1)/(n + 2) = \{1/4, 2/5, 3/6, 4/7, 5/8, 6/9, 7/10, 8/11\}$ of the deviations do correspond to the PCK conjecture (4).
Clearly if we choose $\alpha = 1$, (17) we obtain an identity for any distribution of $\lambda$. This would seem to be true even for a distribution that assumes only a fraction $p$ of the agents save and the remainder do not save, i.e. $\rho^{(1)}_{\lambda}(\lambda) = p\rho_{\lambda}(\lambda) + (1 - p)\delta(\lambda)$.
However, whether other solutions for $\alpha$ exist is an open question and depends on the distribution of the saving propensity $\rho_{\lambda}(\lambda)$. We try to clarify this question below.
For uniformly distributed propensities $\rho_{\lambda}(\lambda) = 1/l_{2}$ for $0 \leq \lambda \leq l_{2} \leq 1$ the only solution is $\alpha = 1$ (see Fig. 2). Likewise if $\rho_{\lambda}(\lambda)$ is a normal distribution with a variable mean $l_{2}$ where $|l_{2}| \leq 1$ and the standard deviation is small (See Fig.3) or with a fixed mean and variable standard deviation (Fig.4) the exponent similarly turns out to be unity.
Now we make a stronger statement and say that there is no continuous and differentiable distribution of saving propensities $\lambda \in [0, 1]$ that would yield $\alpha \neq 1$. Indeed since every distribution $\rho_{\lambda}(\lambda)$ can be constructed as a weighted
Fig. 2. The left-hand-side of equation (17) plotted as a function of α for a uniformly random saving propensity λ with 0 < λ < l/2 for different values of l/2 (dashed lines) and the right-hand-side (rhs) of the equation (17) (solid line). As we can see there is no other solution of the transcendental equation (17) except α = 1 in the range α ∈ [0, 2].
(possibly continuous) linear combination of uniform distributions
\[ \rho_\Lambda(\lambda) = \int_0^1 w(\nu)U(0, \nu) d\nu \]
(18)
and since for a uniform distribution U(0, ν) the left-hand side of the transcendental equation (17) intersects the right-hand side only for α = 1 in the range α ∈ [0, 2] then the last statement holds also for a generic distribution ρ_Λ(λ).
Here we used conditional averaging. This means that the average in equation (17) is carried out as an average over U(0, ν) conditioned on ν first and then over the distribution w(ν) of random values of ν.
2.3 Beyond the mean-field approximation:
Many-agent distribution functions \( f_N(x_1, \ldots, x_N) \) may not be produced correctly within the mean-field approach. Furthermore the wealth-exchange model by Chatterjee (2003) may be extended to N-point interactions:
\[ w_i(t+1) = \lambda_i w_i + \epsilon_i \left[ \sum_{j=1}^{N} (1 - \lambda_j)w_j \right] \quad \sum_i c_i = 1 \]
(19)
Fig. 3. The same as in Fig. 2 but for the propensity $\lambda$ conforming to a truncated $|\lambda| \leq 1$ normal distribution with variable mean $l_2$ and standard deviation 0.01. As before dashed lines denote the left-hand side and the solid line denotes the right-hand side of equation (17). Again the only solution of the transcendental equation is $\alpha = 1$ in the range $\alpha \in [0, 2]$.
Fig. 4. The same as in Figs. 2 and 3 except that now the mean of the normal distribution of propensities $\lambda$ is fixed and equal to 0.5 and the standard deviation varies. Here again no new solutions except $\alpha = 1$ are obtained.
Here we mean that at every time step exchange processes involving any number of agents can happen – each with a certain likelihood. We perform the analysis for $N = 3$ in order to find out what kind of mathematical difficulties we will come across. Now the master equation for the 2-agent distribution function in the Laplace domain (compare with (8)) reads:
\[ \partial_t \tilde{f}_2(x, y; t) + \tilde{f}_2(x, y; t) = (1 - \sigma) \left( \tilde{f}_2(\lambda x + \lambda_1 (\epsilon x + (1 - \epsilon) y), \lambda y + \lambda_1 (\epsilon x + (1 - \epsilon) y); t) \right) + \]
\[ \frac{\sigma}{2} \left( \tilde{f}_3(\lambda x + \lambda_1 (\epsilon_1 x + \epsilon_2 y), \lambda y + \lambda_1 (\epsilon_1 x + \epsilon_2 y); t) \right) + \]
\[ \frac{\sigma}{2} \left( \tilde{f}_3(\lambda_1 (\epsilon_2 x + \epsilon_3 y), \lambda x + \lambda_1 (\epsilon_2 x + \epsilon_3 y), \lambda y + \lambda_1 (\epsilon_2 x + \epsilon_3 y); t) \right) \] (20)
where \( \lambda + \lambda_1 = 1, \epsilon + \epsilon_1 \leq 1 \) and \( \sigma \) and \( (1 - \sigma) \) denote likelihoods of three-agent and two-agent exchange processes respectively. The first (second and third) term(s) on the right-hand side in (20) account(s) for two-(three-)agent exchange processes respectively. Setting \( y = 0 \) we obtain equation (8) except for three-agent exchange terms that were neglected in the first place and now have been added appropriately. Setting \( x = y = 0 \) we obtain an identity from the normalisation condition \( f_2(0, 0) = f_3(0, 0, 0) = 1 \).
### 2.4 The power-law tail with three-agent exchange processes:
Now the transcendental equation, derived from the master equation (20), has the following form:
\[ (1 - \sigma) \left[ \langle (1 - \lambda)^\alpha \rangle + \langle \frac{1 - \lambda^{\alpha+1}}{1 - \lambda} \rangle \right] + \]
\[ \frac{\sigma}{\alpha + 2} \left[ 2 \langle (1 - \lambda)^\alpha \rangle + \langle \frac{1 - (\alpha + 2)\lambda^{\alpha+1} + (\alpha + 1)\lambda^{\alpha+2}}{(1 - \lambda)^2} \rangle \right] = \alpha + 1 \] (21)
and a \( \alpha = 1 \) is again the only solution (compare Fig.5) of this equation for arbitrary saving propensity distributions \( p_\Lambda(\lambda) \) and for any likelihood \( \sigma \in [0, 1] \) of three-agent exchange processes. This is in conformance with our numerical simulations that also show that an introduction of three-agent exchange processes do not alter the exponent.
### 2.5 Moment equations in the case of two- and three-agent exchange processes:
The expansion of the steady-state solution in terms of two-agent correlations \( \langle v^p w^q \rangle = m_{p,q} \cdot (p!q!) \) now reads \( f_2(x, y) = \sum_{p,q=0}^{\infty} (-1)^{p+q} m_{p,q} x^p y^q \) and the two-agent correlations satisfy following equations:
\[ 11 \]
Fig. 5. The second term (corresponding to three agent exchange processes) on the left-hand-side of equation (21) plotted as a function of $\alpha$ for a uniformly random saving propensity $\lambda$ with $0 < \lambda < l_2$ for different values of $l_2$ (dashed lines) and the right-hand-side (rhs) of the equation (17) (solid line). We see that three-agent exchange processes do not lead to a change of the exponent $\alpha$ from unity to a different value.
$$m_{p,q} = (1 - \sigma) \sum_{\substack{p_1 + q_1 = p \cr p_2 + q_2 = q}} \left( \begin{array}{c} p_1 + p_2 \\ p_1 \end{array} \right) \left( \begin{array}{c} q_1 + q_2 \\ q_1 \end{array} \right) m_{p_1+p_2,q_1+q_2} \tilde{C}_{p_1,q_2}^{(p,q)}(\lambda) + \sigma \sum_{\substack{p_1 + q_1 + r_1 = p \cr p_2 + q_2 + r_2 = q}} \left( \begin{array}{c} p_1 + p_2 \\ p_1 \end{array} \right) \left( \begin{array}{c} q_1 + q_2 \\ q_1 \end{array} \right) \left( \begin{array}{c} r_1 + r_2 \\ r_1 \end{array} \right) m_{p_1+p_2,q_1+q_2,r_1+r_2} \tilde{D}_{p_1,q_2}^{(p,q)}(\lambda)$$
where
$$\tilde{C}_{p_1,q_2}^{(p,q)}(\lambda) = \frac{1}{\lambda} \int_0^{\lambda_1} d\xi (\lambda + \xi)^{p_1} \xi^{q-p_1} (1 - \xi)^{q_1} (\lambda_1 - \xi)^{q-q_1}$$
$$\tilde{D}_{p_1,q_2}^{(p,q)}(\lambda) = \frac{2}{\lambda^2} \int_0^{\lambda_1} d\xi \int_0^{\lambda_1-\xi} d\eta (\lambda + \xi)^{p_1} \xi^{q-p_1} (\lambda + \eta)^{q_1} \eta^{q-q_1}$$
(23)
If we neglect ternary exchange processes ($\sigma = 0$) we end up with following equations for the moments of the 1-agent distribution function:
$$m_2 = m_{1,1} \frac{\lambda + 2}{2(1 + 2\lambda)} \quad m_3 = \frac{m_{1,2}}{1 + 2\lambda}$$
\[
m_4 = m_{1,3} \frac{(4 - 2\lambda + 2\lambda^2 + \lambda^3)}{2(3 + 6\lambda - \lambda^2 + 2\lambda^3)} - m_{2,2} \frac{-6 + 3\lambda + 2\lambda^2 + \lambda^3}{6(3 + 6\lambda - \lambda^2 + 2\lambda^3)} - m_2 - m_3
\]
\[
m_5 = \frac{((2 - 2\lambda + 3\lambda^2)m_{1,4} - 2(-1 + \lambda)m_{2,3})}{(4 + 8\lambda - 3\lambda^2 + 6\lambda^3)}
\] (24)
These equations reduce to equations (14) under the mean-field approximation \( m_{p,q} = m_p m_q \).
3 Exact computer simulations of the model
Intuitively, it is clear that the distribution function depends critically on the relative values of the mean value of the savings propensity and the spread or mean square deviation of the saving distribution function. As the spread of saving propensities tends to zero, the distribution function must change from one having a power law tail to one with an exponential tail. How does this change take place? Could it be that the effective power law region shifts to take on values of \( \alpha > 1 \)? Might this explain the empirically observed facts?
We have made computer simulations of the model for different values of these parameters. The results are described below.
A uniform distribution of the savings parameter \( \lambda \) in the model of Chatterjee (2003) results in a power law distribution of the cumulative distribution shown in the Fig. 6.
The situation is different in the case of \( \lambda \) being Gaussian distributed. Here the cumulative wealth distribution may still be approximately described by a power law for widths between 1 and 0.45 (see Fig. 7).
One thing seems clear. The region where power law behaviour is observed is fairly well marked even when the spread is small. And moreover the slope is consistent with higher values of \( \alpha \). However it does not seem that \( \alpha \) can take on values greater than around 1.2. As it stands then we conclude that this model does not offer a complete picture of the empirically observed wealth dynamics.
4 Conclusions
We have studied the model of interacting agents proposed by Chatterjee (2003) that allows agents to both save and exchange wealth. Closed equations for the wealth distribution are developed using a mean field approximation.
We have shown that when all agents have the same fixed savings propensity, subject to certain well defined approximations defined in the text, these equations yield the conjecture proposed by Chatterjee (2003) for the form of the stationary agent wealth distribution.
If the savings propensity for the equations is chosen according to some random distribution we have further shown that the wealth distribution for large values of wealth displays a Pareto like power law tail, i.e. \( P(w) \sim w^{1+a} \). However the value of \( a \) for the model is exactly 1. Exact numerical simulations for the model illustrate how, as the savings distribution function narrows to zero, the wealth distribution changes from a Pareto form to an exponential function. Intermediate regions of wealth may be approximately described by a power law with \( a > 1 \). However the value never reaches values of \( \sim 1.6 - 1.7 \) that characterise empirical wealth data. This conclusion is not changed if three body agent exchange processes are allowed. We conclude that other mechanisms are
Fig. 7. The same as in Fig. 6 but for the saving propensity being Gaussian distributed. Here the power law exponent decreases with decreasing width, but only over a small range from -1 to -1.13. Narrower Gaussian distributions do not result in wealth distributions that can be described by power law. (Note that in the limit of small widths both Gaussian and uniform distribution give the same wealth distribution.)
required if the model is to agree with empirical wealth data.
References
Pareto V, *Cours d’Economique Politique* Lausanne F Rouge 1897
Slanina F, Inelastically scattering particles and wealth distribution in an open economy, Phys. Rev. E 69, n 4, 46102-1-7 (2004)
June-Yule Lee, Signal processing of chaotic impacting series, *IEE Colloquium on Signals Systems and Chaos*, p 7/1-6 (1997)
Gibrat R, *Les Inegalites economiques*, Paris, 1931;
Zipf G K, *Human Behavior and the Principle of Least Effort*, Addison-Wesley 1949
Ijiri Y and Simon H, *Skew Distributions and the Sizes of Business Firms*, North-Holland: New York 1977
Kesten H, *Random Difference Equations and Renewal Theory for Products of Random Matrices*, Acta Mathematica, CXXXI:207-248, 1973
Solomon S et al, Theoretical analysis and simulations of the generalized Lotka-Volterra model, Phys. Rev. E **66**, n 3 1, 031102/1-031102/4, (2002); Solomon S, Richmond P, Stable power laws in variable economies; Lotka-Volterra implies Pareto-Zipf, Eur. Phys. J. B **27**, n 2, p 257-261, (2002); Richmond P, Solomon S, Power laws are disguised Boltzmann laws Int. J. Mod. Phys. C **12**, n 3, p 333-43, (2001)
Levy M, Solomon S, New evidence for the power-law distribution of wealth, Physica A **242**, 90, (1997)
Reed W J, Hughes B D, From gene families and genera to incomes and internet file sizes: Why power laws are so common in nature, Phys. Rev. E **66**, 067103, (2002)
Aoyama H, Souma W and Fujiwara Y, Growth and fluctuations of personal and company’s income, Physica A **324**, 352, (2003)
Dragulescu A and Yakovenko V M, Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States, Physica A **299**, n 1-2, p 213-221, (2001); Dragulescu A, Yakovenko V M, Evidence for the exponential distribution of income in the USA Eur. Phys. J. B **20**, n 4, p 585-589 (2001)
Dragulescu A and Yakovenko V M, Statistical mechanics of money, Eur. Phys. J. B **17**, 723–729 (2000)
Chatterjee A and Chakrabarti B K, Money in gas-like markets: Gibbs and Pareto laws, Physica Scripta T **106**, p 36-38 (2003) and [cond-mat/0311227]
Chatterjee A, Chakrabarti B K and Manna S S, Physica A **335** 155–163 (2004)
Ernst M H, Nonlinear model-Boltzmann equations and exact solutions, Phys. Rep. (Review Section of Physics Letters) **78**, No. 1, p 1-171 (1981)
Krapivsky P L and Ben-Naim E, Nontrivial velocity distributions in inelastic gases, J. Phys. A: Math. Gen. **35** L147–L152 (2002)
Ben-Avraham D, Ben-Naim E, Lindenberg K and Rosas A, Self-similarity in random collision processes Phys. Rev. E, **68**, n 5 1, p 50103/1-50103/4 (2003)
Bobylev A V, Carrillo J A and Gamba I M, On some properties of kinetic and hydrodynamic equations for inelastic interactions J. of Stat. Phys. **98**, n 3-4, p 743-73 (2000)
Baldassarri A, Puglisi A, Marini U, Marconi B, Kinetics models of inelastic gases, Mathematical Models & Methods in Applied Sciences, **12**, n 7, p 965-83 (2002) | 2025-03-06T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2052,
1
],
[
2052,
4789,
2
],
[
4789,
7259,
3
],
[
7259,
10034,
4
],
[
10034,
12337,
5
],
[
12337,
14770,
6
],
[
14770,
16873,
7
],
[
16873,
18673,
8
],
[
18673,
20000,
9
],
[
20000,
21000,
10
],
[
21000,
23440,
11
],
[
23440,
25078,
12
],
[
25078,
27304,
13
],
[
27304,
28380,
14
],
[
28380,
29427,
15
],
[
29427,
31801,
16
]
]
} |
2e18090452f495bdedfeacfbfd8715837752d1fa | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 15,
"total-fallback-pages": 0,
"total-input-tokens": 47370,
"total-output-tokens": 12140,
"fieldofstudy": [
"Medicine"
]
} | # PEER REVIEW HISTORY
BMJ Open publishes all reviews undertaken for accepted manuscripts. Reviewers are asked to complete a checklist review form ([http://bmjopen.bmj.com/site/about/resources/checklist.pdf](http://bmjopen.bmj.com/site/about/resources/checklist.pdf)) and are provided with free text boxes to elaborate on their assessment. These free text comments are reproduced below.
## ARTICLE DETAILS
| TITLE (PROVISIONAL) | Socioeconomic inequalities in health status and survival: a cohort study in Rome |
|---------------------|--------------------------------------------------------------------------------|
| AUTHORS | Dei Bardi, Luca; Calandrini, Enrico; Bargagli, Anna Maria; Egidi, Viviana; Davoli, Marina; Agabiti, Nera; Cesaroni, Giulia |
## VERSION 1 – REVIEW
| REVIEWER | Daoud, Nihaya |
|----------|---------------|
| | Ben-Gurion University of the Negev, Department of Public Health, Faculty of Health Sciences |
| REVIEW RETURNED | 26-Sep-2021 |
**GENERAL COMMENTS**
Abstract: Can be more clear to international readers. Please add a definition for the variable ‘Disease-Related Co-payment Exemption (DRCE).
Introduction: please specify what do you mean by heterogeneity. There are all kinds of heterogeneity. This is a very universal term to use in a study about inequalities. Just use direct term. What do you mean by differences? do you mean inequalities? Age class means age group?
Methods:
Please add the definition of the variable disease related co-payment exemption.
What was the % of the missing cases for different variables in the study? How was the missing treated?
Data analysis:
Some of the variables might have strong correlations? Was this examined before the multivariable analysis?
There might be interactions or confounding effect for different independent variable? Please clarify how this was examined and what decisions were made following this analysis.
How the neighborhood SES homogeneity was considered in the multivariable analysis? Would GEE be considered?
Survival analysis: please explain how the repeated measure was considered in the analysis. How lost for follow up was considered?
Table should be independent and include all the information needed to understand the content.
Table 1: include N for the P-value for significance level.
Table 2: add the total N for each of the models.
Table 3: Add foot not for the Table to define TR
| REVIEWER | Yu, Xue Qin |
|----------|-------------|
| | Cancer Council New South Wales, Cancer Research Division |
| REVIEW RETURNED | 12-Oct-2021 |
This study examines the association between socioeconomic position (SEP) and health status for a large cohort of residents in Rome and to investigate the role of SEPs on their survival. The authors found that there is a significant association between SEP and a proxy of comorbidity (DRCE) and people's survival are associated with both individual SEP and contextual SEP measures, with those having high education level or living in wealthy areas having higher survival.
I have some suggestions for the approach of statistical modelling and think that modelling SEPs (individual and contextual) separately first and then combined together may provide more insights about the impact of these SEP measures on survival.
I also think it is better to use the term survival (as in the title) consistently throughout the paper, rather than the mixed use of 'mortality' and 'survival'. For example, in the conclusion of "The association between SEP and mortality was independent of baseline health status" would be more accurate "The association between SEP and overall survival was independent of baseline health status".
Reviewer: 1
Dr. Nihaya Daoud, Ben-Gurion University of the Negev
**********
Comments to the Author:
C1: Abstract: Can be more clear to international readers. Please add a definition for the variable ‘Disease-Related Co-payment Exemption (DRCE).
A: To facilitate international readers, we rephrased the abstract and the manuscript using “chronic or rare conditions” / “chronicity” instead of “Disease-Related Co-Payment Exemption” or “DRCE”. We think it is now clearer.
C2: Introduction: please specify what do you mean by heterogeneity. There are all kinds of heterogeneity. This is a very universal term to use in a study about inequalities. Just use direct term.
A: Thank you. We changed the beginning of the introduction, deleting the sentence “Heterogeneity in the population is often reflected in heterogeneity in health”. We also rephrased the sentence “Among all the factors of heterogeneity, socioeconomic position (SEP) is often used to tackle avoidable disparities in health.” in “Among the characteristics of a population, socioeconomic position (SEP) is often used to tackle avoidable disparities in health.”.
C3: What do you mean by differences? do you mean inequalities?
A: We consider “inequality” as a dimensional concept that expresses differences, variation, or disparity in health without any political comment or moral commitment for which we would have used the word “inequity”. In this sense, “difference” or “inequality” can be considered synonyms.
C4: Age class means age group?
A: Yes, it does. To avoid misunderstandings, we agreed to substitute all the “age class” with “age group”, modifying the text, the graphs, and Table 1.
C5: Please add the definition of the variable disease related co-payment exemption.
A: We agree that the term “DRCE” does not help the readers and can be unclear, so we choose to use the term “chronic or rare conditions” / “chronicity” throughout the manuscript. We defined the variable in the section “Variables of interest” (page 4) in the following way: “The number of chronic or rare conditions was derived from the Disease-Related Co-payment Exemptions Registry from 01 Jan 2008 to 09 Oct 2011. To characterize the baseline health status of the population, a binary variable indicating the presence of chronic or rare conditions was used.”
C6: What was the % of the missing cases for different variables in the study? How was the missing treated?
A: We used the 2011 Census population, which was complete of educational attainment, age, sex, and census block of residence. We selected only those with an identifier in the Regional Health Information System. Moreover, selecting those living in residential areas, for each subject an average neighborhood real estate price was available. For these reasons, we have a dataset without missing information on any of the variables.
Data analysis:
C7: Some of the variables might have strong correlations? Was this examined before the multivariable analysis?
A: Associations between variables were not analyzed before multivariable analyses but they were during the modeling through the estimation of Variance Inflation Factors (VIF) not reported in the draft. The complete models had low VIF (lower than 2.5), but we are not reporting those results since we ran new models (please, refer to point C8). We ran VIFs for the new models and they were always lower than commonly used thresholds of 10, 5, and 2.5, hence, multicollinearity is not likely to affect estimates or confidence intervals. We described these measures either in the method section and in the results section.
C8: There might be interactions or confounding effect for different independent variable? Please clarify how this was examined and what decisions were made following this analysis.
A: In the first analysis we considered all covariates as confounders, using them to adjust the estimations of SEP. After your insightful consideration, we ran backward elimination stepwise models starting from a model with all considered variables and all possible first-level interactions. The logistic model with the highest AIC conserved all variables and all interactions. The best AIC-wise AFT model removed, in order:
- the interaction between individual and contextual SEP,
- gender and contextual SEP,
- citizenship and contextual SEP,
- citizenship and contextual SEP,
- citizenship and gender.
Looking at these results, we choose to:
- stratify all models and analyses by sex,
- remove foreign citizens from the analyses,
- analyze the interactions further.
Therefore, to analyze the interactions further, we ran explorative analyses stratifying for education first and price quintiles then, we found that all relationships in all strata have the same directions although slightly different strengths. As the main interest of this study was to find the presence (or absence) of inequalities at individual and/or contextual level, but not to analyze how the different socioeconomic indicators interact with the other variables, we choose to show the overall effect only.
It is worth noting that, with a huge dataset like ours of almost two million individuals, every interaction can result as statistically significant.
The new results are now in the manuscript pages 7 and 8, Table 2 and Table 3, Supplemental Material, Table S1, and Table S2.
C9: How the neighborhood SES homogeneity was considered in the multivariable analysis? Would GEE be considered?
A: neighborhood SEP homogeneity was not considered in the multivariable analyses. Interpreting your comment as a suggestion, we chose to run a null Random Intercept Model clustering at the neighborhood level for both logistic and survival models (that is: overall intercept plus one intercept per every neighborhood).
For the logistic models, the resulting Intraclass Correlation Coefficient (ICC) was ICC = 0.017 for females and ICC = 0.014 for males, meaning that less than 2% of the whole variance was captured by clustering at the neighborhood level. Looking at these results, we chose not to go further in the multilevel analysis for the logistic models.
In the survival models, we tried to replicate the analysis made for the logistics using nested frailty models, but several runs of the models never reached convergence. This could be due to very low intraclass correlation. Moreover, considering that only a low percentage of individuals experienced death in our 5-year follow-up (6.7% females and 7.2% males), it is unlikely to find strong correlations between time at death and neighborhood. Hence, we chose not to consider further multilevel analysis for AFT models either.
C10: Survival analysis: please explain how the repeated measure was considered in the analysis. How lost for follow up was considered?
A: Data has no repeated measure: it consists of baseline observation, date of death (when/if occurred), and date of emigration outside the municipality of Rome (when/if occurred). The status “lost to follow up” hence refers to people who emigrated outside the municipality of Rome and was considered as “no event”, i.e. right-censored, as in usual survival analysis. As discussed in the main document, we also considered people reaching their 100th birthday and living people at 31/12/2006 as right censored ("no event"). We ran a logistic model to analyze baseline differences between stayers and leavers, as discussed in the “strength and weakness” section of the draft on pages 9-10. We ran these analyses again for the new models (please refer to previous answers) and the results were similar.
C11: Table should be independent and include all the information needed to understand the content.
A: Thank you. We checked all the tables and changed them accordingly.
C12: Table 1: include N for the P-value for significance level.
A: after your comment, we discussed the utility of showing unadjusted chi-squared tests at this stage of analysis. We came up to the conclusion of showing neither chi tests nor minimum N.
We don’t find useful to show minimum N that gives significance level in the table as it could be misleading and could make the table difficult to read. Moreover, we discussed the utility of the chi-tests in this table as it is meant to describe the study population. We don’t find these tests informative at this point of the analysis, as we model and test for associations later in the draft. In addition, they could be misleading as it is not straightforward if they refer to Females-Males differences or inter-category differences.
C13: Table 2: add the total N for each of the models.
A: Although the total N is the same for every gender-strata model we ran, we agreed to show the Ns in both Table 2 and Table 3.
C1: I have some suggestions for the approach of statistical modelling and think that modelling SEPs (individual and contextual) separately first and then combined together may provide more insights about the impact of these SEP measures on survival.
A: We show the complete models as part of the supplemental material, with each indicator adjusted for every other variable in the analysis. Following your suggestion, we summarized the two measures of SEP into one, defining as “High” overall SEP all individuals with the highest individual or contextual SEP and the highest or second-highest other measure. Similarly, we defined as “Low” overall SEP all people with the lowest individual or contextual SEP and the lowest or second-lowest other measure. All those outside these definitions were categorized as “Medium” overall SEP. In Table C1 is represented the categorization, the outcome numerosity, and the resulting percentages.
Table C1: Categorization of Overall SEP variable, numerosity, and percentages by sex.
| | real estates price quintiles | overall SEP | N | % |
|----------|-----------------------------|-------------|-----|----|
| **Males** | | | | |
| | education | 1 (high) | 2 | 3 | 4 | 5 (low) | | | |
| High | | 71,461 | 48,623 | 35,421 | 26,373 | 20,553 | High | 182,728 | 22.4 |
| Medium | | 62,644 | 81,148 | 84,215 | 81,687 | 81,215 | Medium | 424,821 | 52.1 |
| Low | | 19,294 | 30,218 | 45,912 | 54,413 | 72,782 | Low | 208,410 | 25.5 |
| **Females** | | | | | | | | | |
| | education | 1 (high) | 2 | 3 | 4 | 5 (low) | | | |
| High | | 75,550 | 53,129 | 39,188 | 30,034 | 24,663 | High | 216,197 | 22.4 |
| Medium | | 87,518 | 96,323 | 93,430 | 84,750 | 79,883 | Medium | 511,237 | 53.0 |
| Low | | 31,425 | 45,936 | 65,488 | 73,981 | 82,986 | Low | 236,850 | 24.6 |
With this new variable, we ran new logistic and survival models. Results are reported respectively in Table C2 and C3 where a comparison between the three types of SEP measure can be made.
Table C2: Association between indicators of socioeconomic position and having 1+ Chronic or Rare Disease
| | **FEMALES** (N=964,284) | **MALES** (N=815,959) |
|----------|-------------------------|-----------------------|
| | OR 95%CI | OR 95%CI |
**********
Reviewer: 2
Dr. Xue Qin Yu, Cancer Council New South Wales, The University of Sydney
**********
Comments to the Author:
This study examines the association between socioeconomic position (SEP) and health status for a large cohort of residents in Rome and to investigate the role of SEPs on their survival. The authors found that there is a significant association between SEP and a proxy of comorbidity (DRCE) and people’s survival are associated with both individual SEP and contextual SEP measures, with those having high education level or living in wealthy areas having higher survival.
C14: Table 3: Add foot not for the Table to define TR.
A: We welcomed the suggestion and added a definition of TR in Table 3.
Table C3. Association between indicators of socioeconomic position and survival
| | FEMALES (N=964,284) | MALES (N=815,959) |
|-------------------------------|----------------------|-------------------|
| | TR | 95%CI | TR | 95%CI |
| age | 0.90 | 0.90 | 0.91 | 0.91 |
| education | | | | |
| High | 1 | | 1 | |
| Medium | 0.90 | 0.87 | 0.82 | 0.80 |
| Low | 0.82 | 0.80 | 0.70 | 0.68 |
| real estate | 1 (higher)| 1 | 1 | 1 |
| price quintiles | | | | |
| 2 | 0.95 | 0.93 | 0.94 | 0.92 |
| 3 | 0.92 | 0.90 | 0.88 | 0.86 |
| 4 | 0.91 | 0.89 | 0.86 | 0.84 |
| 5 (lower) | 0.86 | 0.85 | 0.82 | 0.80 |
| chronicity | none | 1 | 1 | 1 |
| one or more | 0.73 | 0.72 | 0.74 | 0.69 |
| Overall SEP | High | 1 | 1 | 1 |
| Medium | 0.89 | 0.88 | 0.85 | 0.83 |
| Low | 0.84 | 0.82 | 0.76 | 0.74 |
Times Ratios (TR) Adjusted for age.
As the estimates of Overall SEP reflect the estimates obtained with the single SEP indicators, we decided not to show these results in the paper.
C2: I also think it is better to use the term survival (as in the title) consistently throughout the paper, rather than the mixed use of ‘mortality’ and ‘survival’. For example, in the conclusion of "The
association between SEP and mortality was independent of baseline health status” would be more accurate “The association between SEP and overall survival was independent of baseline health status”.
R: We welcomed this suggestion and changed the text accordingly when possible.
**VERSION 2 – REVIEW**
| REVIEWER | Cursio, John |
|--------------|--------------|
| The University of Chicago, Public Health Sciences |
| REVIEW RETURNED | 10-May-2022 |
**GENERAL COMMENTS**
Thank you for this well-written and informative manuscript. I have a few comments regarding the research presented here:
1) The authors’ Table 1 shows age categories such as 25-34, 35-44, 45-54, and so on. However, the information in Table 2 and Table 3 treats age as a continuous variable. Did the authors consider using the age categories in the logistic and accelerated failure time models? That would make the tables and models more descriptive, and reveal if age groups adjusted for education and real estate (SEPs) show different effects on comorbid conditions and survival.
2) The authors might consider an ordinal model for the presence of chronic or rare diseases, instead of a logistic model. The categories could be 0, 1, 2, 3 or more chronic conditions based on the distribution found in the data set. In addition, a non-proportional odds model may reveal interesting patterns and effects of SEP across different levels of the ordinal outcome.
3) Table 3 shows chronicity of none versus one or more. Breaking out one or more with multiple categories 1, 2, 3 or more may reveal interesting patterns and could be useful in the accelerated failure time model. The main idea in 2 and 3 is that someone with only one comorbid condition can be very different than someone with 2, 3 or more comorbid conditions. Here the effect is treated equally for everyone with one or more comorbid condition.
**VERSION 2 – AUTHOR RESPONSE**
Reviewer: 3 Dr. John Cursio, The University of Chicago.
Comments to the Author:
Comment 0 (C0): Thank you for this well-written and informative manuscript. I have a few comments regarding the research presented here:
Reply 0 (R0): We kindly thank Reviewer 3, Dr. John Cursio, for his work and comments. We proceed to reply with a point-by-point response.
C1: The authors’ Table 1 shows age categories such as 25-34, 35-44, 45-54, and so on. However, the information in Table 2 and Table 3 treats age as a continuous variable. Did the authors’ consider using the age categories in the logistic and accelerated failure time
models? That would make the tables and models more descriptive, and reveal if age groups adjusted for education and real estate (SEPs) show different effects on comorbid conditions and survival.
R1: We agree with the Reviewer’s suggestion, and we ran new models using the 10-years age groups in all analyses. Following this choice, we modified tables 2, 3, S1, and S2, all the figures and text in the manuscript, referencing all of them accordingly.
C2: The authors might consider an ordinal model for the presence of chronic or rare diseases, instead of a logistic model. The categories could be 0,1,2,3 or more chronic conditions based on the distribution found in the data set. In addition, a non-proportional odds model may reveal interesting patterns and effects of SEP across different levels of the ordinal outcome.
R2: Unfortunately, because of the nature of the data, we do not think analyses with more than two categories (0, 1+) would be appropriate due to the definition of the measure and the low numerosity in specific categories of the variables (age group, SEP, sex).
Regarding the first aspect, we used an administrative database aimed at helping people with chronic or rare diseases to receive appropriate and free-of-charge assistance. The database was not intended for medical or statistical purposes. Hence, our definition of chronicity is quite rough, and we possibly observe only the more severe cases of illnesses. This can be noticed in Table 1, where approximately only one-third of the population of 65-74 years have one (or more) certified chronicity. Moreover, people with multiple chronic conditions may not be interested to have multiple certificates as the expenses for specialist visits or diagnostic tests could be already covered, totally or partially, by the first. Hence, there could be a big difference between who owns a chronicity certificate and who does not, and less marked differences between who has one certification and who owns more.
Then, there is an issue of numerosity because the number of people steeply decreases when considering more than one certificate by sex, age group, or other variables. As an example, looking at Table 1 in the manuscript, we notice that only 4.1% of males (N=4,500) in the 25-34 age category have at least one certified chronic condition, and only ≈500 individuals (0.5% of the 25-34 male population) have two or more certificates. In the whole study population, females owning at least one certificate are ≈23% while the percentage drops to ≈8% for females with two or more. In males, the percentages are respectively ≈21% and ≈8%. We addressed the above issues in the Discussion section (strength and weakness, page 10-11).
However, we found the Reviewer’s suggestion very interesting, and we decided to implement it, defining a three-category variable indicating the number of conditions (0, 1, 2+). We limited the variable to three categories because of numerosity and ran both ordinal and non-proportional odds models.
The results from ordinal models stratified by sex and adjusted by age are shown in Table A, while ordinal models stratified by sex and adjusted for every other variable in the table are reported in Table B.
Results from these models, those reported in Table 2, and supplementary material Table S1 appear to be almost identical. For this and the previously stated reasons, we chose to not show the results from ordinal models in the manuscript.
Table A: Association between indicators of socioeconomic position and number of Chronic or Rare Diseases. Residents aged 25-99 years. Rome, 09 Oct 2011.
| age group | FEMALES (N=964,284) | MALES (N=815,959) |
|-----------|---------------------|-------------------|
| | OR 95%CI | OR 95%CI |
| 25-34 | 1 - - | 1 - - |
| 35-44 | 1.62 1.58 1.67 | 1.69 1.63 1.75 |
| 45-54 | 2.77 2.70 2.84 | 3.63 3.51 3.75 |
| 55-64 | 5.32 5.19 5.45 | 8.72 8.44 9.00 |
| 65-74 | 7.22 7.04 7.40 | 15.34 14.86 15.83 |
| 75-84 | 7.13 6.95 7.32 | 18.76 18.15 19.38 |
| 85-99 | 4.77 4.63 4.92 | 13.47 12.93 14.02 |
| education | FEMALES | MALES |
|-----------|---------|-------|
| | OR 95%CI| OR 95%CI|
| High | 1 - - | 1 - - |
| Medium | 1.36 1.34 1.38 | 1.55 1.53 1.58 |
| Low | 1.64 1.62 1.67 | 1.68 1.65 1.71 |
| real estate | FEMALES | MALES |
|-------------|---------|-------|
| | OR 95%CI| OR 95%CI|
| 1 (higher) | 1 - - | 1 - - |
| price quintiles | FEMALES | MALES |
|-----------------|---------|-------|
| | OR 95%CI| OR 95%CI|
| 2 | 1.23 1.21 1.25 | 1.25 1.23 1.27 |
| 3 | 1.51 1.49 1.54 | 1.52 1.50 1.55 |
| 4 | 1.60 1.58 1.63 | 1.58 1.55 1.61 |
| 5 (lower) | 1.90 1.87 1.93 | 1.84 1.81 1.88 |
Odds Ratios (OR) from ordinal models Adjusted for age with 95% Confidence Intervals (95%CI).
Table B: Association between indicators of socioeconomic position and number of Chronic or Rare Diseases. Residents aged 25-99 years. Rome, 09 Oct 2011.
| | FEMALES (N=964,284) | MALES (N=815,959) |
|-------|---------------------|-------------------|
| age | OR | 95%CI | OR | 95%CI |
| 25-34 | 1 | - | 1 | - |
| 35-44 | 1.60 | 1.56 | 1.68 | 1.62 | 1.74 |
| 45-54 | 2.68 | 2.61 | 3.61 | 3.50 | 3.73 |
| 55-64 | 5.19 | 5.06 | 8.81 | 8.53 | 9.10 |
| 65-74 | 6.95 | 6.77 | 15.48 | 14.99 | 15.98 |
| 75-84 | 6.76 | 6.59 | 18.82 | 18.21 | 19.46 |
| 85-99 | 4.65 | 4.51 | 14.05 | 13.48 | 14.63 |
| age | | | | |
| education | | | | |
| High | 1 | - | 1 | - |
| Medium | 1.24 | 1.22 | 1.41 | 1.38 | 1.43 |
| Low | 1.37 | 1.35 | 1.43 | 1.40 | 1.45 |
| real estate | | | | |
| 1 (higher) | 1 | - | 1 | - |
| price quintiles | | | | |
| 2 | 1.19 | 1.17 | 1.18 | 1.15 | 1.20 |
| 3 | 1.42 | 1.40 | 1.39 | 1.37 | 1.42 |
| 4 | 1.49 | 1.46 | 1.42 | 1.39 | 1.44 |
| 5 (lower) | 1.73 | 1.70 | 1.63 | 1.60 | 1.66 |
Odds Ratios (OR) from ordinal models Adjusted for every variable in the table
The results from non-proportional odds models, stratified by sex and adjusted for every other variable in the analysis, are reported in Table C. Results do not differ in meaning, trend, and statistical significance from those of logistic models: lower educated people and people living in less expensive neighborhood are more likely to have 1 and/or 2+ certified chronicity than people highly educated or living in more expensive neighborhoods. Due to the same reasons already mentioned before, we chose to show these results to the Reviewer only.
Table C: Association between indicators of socioeconomic position and number of Chronic or Rare Diseases. Residents aged 25-99 years. Rome, 09 Oct 2011.
| 1 vs 0 | FEMALES (N=964,284) | MALES (N=815,959) |
|--------|---------------------|--------------------|
| | OR | 95%CI | OR | 95%CI |
| **age** | | | | |
| 25-34 | 1 | - | 1 | - |
| 35-44 | 1.54 | 1.50 | 1.59 | 1.53 | 1.65 |
| 45-54 | 2.41 | 2.34 | 2.97 | 2.87 | 3.08 |
| 55-64 | 3.82 | 3.71 | 5.85 | 5.65 | 6.06 |
| 65-74 | 4.46 | 4.33 | 8.77 | 8.46 | 9.08 |
| 75-84 | 4.13 | 4.01 | 9.85 | 9.49 | 10.21|
| 85-99 | 2.86 | 2.76 | 7.41 | 7.06 | 7.78 |
| **education** | | | | |
| High | 1 | - | 1 | - |
| Medium | 1.18 | 1.16 | 1.32 | 1.29 | 1.34 |
| Low | 1.26 | 1.23 | 1.37 | 1.34 | 1.40 |
| **real estate** | | | | |
| 1 (higher) | 1 | - | 1 | - |
| **price quintiles** | | | | |
| 2 | 1.15 | 1.13 | 1.19 | 1.16 | 1.22 |
| 3 | 1.30 | 1.28 | 1.32 | 1.29 | 1.35 |
| 4 | 1.34 | 1.31 | 1.32 | 1.29 | 1.35 |
| 5 (lower) | 1.52 | 1.49 | 1.51 | 1.47 | 1.54 |
| 2+ vs 0 | FEMALES (N=964,284) | MALES (N=815,959) |
|---------|---------------------|--------------------|
| | OR | 95%CI | OR | 95%CI |
| **age** | | | | |
| 25-34 | 1 | - | 1 | - |
| 35-44 | 2.10 | 1.95 | 2.41 | 2.19 | 2.65 |
| 45-54 | 4.89 | 4.57 | 8.50 | 7.78 | 9.30 |
| 55-64 | 14.42 | 13.51 | 30.07 | 27.55 | 32.82 |
| 65-74 | 22.42 | 21.00 | 23.92 | 61.58 | 56.45 | 67.19 |
|-------|-------|-------|-------|-------|-------|-------|
| 75-84 | 22.61 | 21.17 | 24.15 | 79.09 | 72.44 | 86.35 |
| 85-99 | 15.59 | 14.54 | 16.73 | 58.49 | 53.28 | 64.21 |
| education | High | | | | | |
|-----------|------|-----|-----|-----|-----|-----|
| | 1 | - | - | 1 | - | - |
| Medium | 1.44 | 1.40| 1.48| 1.56| 1.52| 1.60|
| Low | 1.65 | 1.61| 1.70| 1.55| 1.50| 1.59|
| real estate | 1 (higher) | | | | | |
|-------------|------------|-----|-----|-----|-----|-----|
| | 1 | - | - | 1 | - | - |
| price quintiles | 2 | | | | | |
|-----------------|---|-----|-----|-----|-----|-----|
| | 1.25 | 1.22 | 1.28 | 1.16 | 1.13 | 1.19 |
| | 1.63 | 1.59 | 1.67 | 1.48 | 1.43 | 1.52 |
| | 1.74 | 1.69 | 1.78 | 1.54 | 1.49 | 1.58 |
| 5 (lower) | 2.12 | 2.06 | 2.18 | 1.81 | 1.76 | 1.86 |
Odds Ratios (OR) from non-proportional odds models Adjusted for every variable in the table
C3: Table 3 shows chronicity of none versus one or more. Breaking out one or more with multiple categories 1, 2, 3 or more may reveal interesting patterns and could be useful in the accelerated failure time model.
R3: As previously stated in Reply 2, the number of individuals in the category 2+ can be small, and we are afraid of the low numerosity when adjusting for other variables, resulting in estimates based on few individuals. We previously ran accelerated failure time models with more than two categories of chronicity, and we know there is a strong negative association between survival and the number of chronic conditions.
Those analyses are presented in Table D and E. **Table D** shows the estimates stratified by sex and adjusted by age group while **Table E** shows the estimates stratified by sex and adjusted for every other variable in the table. As said, an increasingly negative effect on survival with an increasing number of chronicity is visible, although the biggest difference in effect is between the category “0” and “1” and smaller differences are visible between the category “1” and “2+”. It can also be seen that Odds Ratios of the other variables are stable and totally alike to Table 3 and Table S2. For the reasons previously stated and considering that the biggest difference in survival is between “not having” and “having” chronicity, we chose to not show the tables in the manuscript.
### Table D. Association between indicators of socioeconomic position and survival. Italian residents aged 25-99 years. Rome, 2011-2016.
| | FEMALES (N=964,284) | MALES (N=815,959) |
|----------------------|---------------------|-------------------|
| | TR | 95%CI | TR | 95%CI |
| **age group** | | | | |
| 25-34 | 1 | - - | 1 | - - |
| 35-44 | 0.43| 0.37 0.51 | 0.51| 0.46 0.58 |
| 45-54 | 0.18| 0.16 0.21 | 0.22| 0.20 0.25 |
| 55-64 | 0.08| 0.07 0.09 | 0.10| 0.09 0.11 |
| 65-74 | 0.04| 0.03 0.04 | 0.04| 0.04 0.05 |
| 75-84 | 0.01| 0.01 0.01 | 0.02| 0.01 0.02 |
| 85-99 | 0.00| 0.00 0.01 | 0.01| 0.01 0.01 |
| **education** | | | | |
| High | 1 | - - | 1 | - - |
| Medium | 0.87| 0.85 0.89 | 0.84| 0.82 0.86 |
| Low | 0.79| 0.77 0.81 | 0.71| 0.70 0.73 |
| **real estate** | | | | |
| 1 (higher) | 1 | - - | 1 | - - |
| **price quintiles** | | | | |
| 2 | 0.96| 0.94 0.98 | 0.96| 0.93 0.98 |
| 3 | 0.96| 0.94 0.98 | 0.91| 0.89 0.94 |
| 4 | 0.95| 0.93 0.97 | 0.90| 0.88 0.92 |
| 5 (lower) | 0.94| 0.91 0.96 | 0.88| 0.86 0.91 |
| **chronicity** | | | | |
| none | 1 | - - | 1 | - - |
| one | 0.79| 0.77 0.80 | 0.75| 0.74 0.77 |
| two or more | 0.66| 0.65 0.67 | 0.62| 0.61 0.64 |
Time Ratios (TR) Adjusted for age and number of chronicity with 95% Confidence Interval (95%CI)
| Table E. Association between indicators of socioeconomic position and survival. Italian residents aged 25-99 years. Rome, 2011-2016. |
|---------------------------------------------------------------|
| Females (N=964,284) |
| **age group** | **TR** | **95% CI** | **MALES (N=815,959)** | **TR** | **95% CI** |
| 25-34 | 1 | - | 1 | - | - |
| 35-44 | 0.44 | 0.38 - 0.52| 0.52 | 0.47 | 0.59 |
| 45-54 | 0.19 | 0.16 - 0.22| 0.23 | 0.21 | 0.26 |
| 55-64 | 0.08 | 0.07 - 0.10| 0.10 | 0.09 | 0.11 |
| 65-74 | 0.04 | 0.03 - 0.05| 0.04 | 0.04 | 0.05 |
| 75-84 | 0.01 | 0.01 - 0.02| 0.02 | 0.02 | 0.02 |
| 85-99 | 0.00 | 0.00 - 0.01| 0.01 | 0.01 | 0.01 |
| **education** | | | | | |
| High | 1 | - | 1 | - | - |
| Medium | 0.87 | 0.85 - 0.89| 0.84 | 0.83 | 0.86 |
| Low | 0.79 | 0.77 - 0.81| 0.71 | 0.70 | 0.73 |
| **real estate** | | | | | |
| 1 (higher) | 1 | - | 1 | - | - |
| **price quintiles** | | | | | |
| 2 | 0.99 | 0.97 - 1.01| 1.00 | 0.98 | 1.02 |
| 3 | 1.00 | 0.98 - 1.02| 0.99 | 0.96 | 1.01 |
| 4 | 1.01 | 0.98 - 1.03| 0.99 | 0.97 | 1.02 |
| 5 (lower) | 1.00 | 0.97 - 1.02| 1.00 | 0.98 | 1.03 |
| **chronicity** | | | | | |
| none | 1 | - | 1 | - | - |
| one | 0.79 | 0.78 - 0.81| 0.76 | 0.75 | 0.78 |
| two or more | 0.67 | 0.66 - 0.68| 0.63 | 0.62 | 0.64 |
Time Ratios (TR) Adjusted for every variable in the table
C4: The main idea in 2 and 3 is that someone with only one comorbid condition can be very different than someone with 2, 3 or more comorbid conditions. Here the effect is treated equally for everyone with one or more comorbid condition.
R4: We thank the Reviewer for his insightful comments, with which we agree. However, the main focus of our study was not to analyze comorbid conditions, but the effect of different measures of socioeconomic levels on health and survival.
To summarize Reply 2 and 3, we are aware of the limit in treating people with one certified morbidity and people with more than one condition equally. Unfortunately, the need to treat this variable as dichotomic (0/1+) comes from the intrinsic nature of the data we used to measure morbidity. It should not be intended as a real or substitutive measure, but only as a proxy for chronicity: due to its bureaucratical nature we are likely to underestimate mild forms of chronicity and to not observe multi-chronicity in people who have specialist visits’ or diagnostic tests’ expenses already covered by previous certificates. This, the low number of individuals with 2+ certified chronicity, and the fact that models’ results are totally alike when treating the variable as dichotomic or with multiple categories, lead us to keep the variable as presence/absence of chronicity. In future studies, if better-quality morbidity data would be available, we would not hesitate to use more categories. To better explain our reasons for the dichotomization of the variable to the readers, we chose to report part of the responses to the Reviewer in the discussion section.
VERSION 3 – REVIEW
| REVIEWER | Cursio, John |
|---------------|--------------|
| | The University of Chicago, Public Health Sciences |
| REVIEW RETURNED | 06-Jun-2022 |
| GENERAL COMMENTS | Thank you for responding to my comment accordingly and thoroughly. The authors may want to describe in the methods section that they performed ordinal models as a sensitivity analysis, and the same conclusions were found as from the logistic models due to the nature of their data. This is optional, but important for the reader to see. | | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2586,
1
],
[
2586,
5363,
2
],
[
5363,
8904,
3
],
[
8904,
12407,
4
],
[
12407,
15890,
5
],
[
15890,
17772,
6
],
[
17772,
20311,
7
],
[
20311,
23767,
8
],
[
23767,
25281,
9
],
[
25281,
27260,
10
],
[
27260,
29044,
11
],
[
29044,
31588,
12
],
[
31588,
33707,
13
],
[
33707,
36512,
14
],
[
36512,
38228,
15
]
]
} |
e61fdf6ce227065a97d2e6d4bcc3cd3788c90c0a | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 14,
"total-fallback-pages": 0,
"total-input-tokens": 50854,
"total-output-tokens": 10686,
"fieldofstudy": [
"Engineering",
"Physics",
"Environmental Science"
]
} | Exergy and Energy Analysis of Wind-Thermal System
Nima Norouzi*
Department of Energy Engineering and Physics, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, PO Box 15875-4413, Tehran, Iran
Received August 3, 2021; Accepted August 25, 2021; Published August 30, 2021
Current wind systems are intermittent and cannot be used as the baseload energy source. The research on the concept of wind power using direct thermal energy conversion and thermal energy storage, called wind powered Thermal Energy System (WTES), opened the door to a new energy system called Wind-thermal, which is a strategy for developing baseload wind power systems. The thermal energy is generated from the rotating energy directly at the top of the tower by the heat generator, which is a simple and light electric brake. The rest of the system is the same as the tower type concentrated solar power (CSP). This paper’s results suggest that the energy and exergy performance of the WTES (62.5% and 29.8%) is comparable to that of conventional wind power, which must be supported by the backup thermal plants and grid enhancement. This cogeneration nature of the WTES system makes this system suitable for using wind power as a direct heat source in several heat-demanding processes such as chemical production. Also, the light heat generator reduces some issues of wind power, such as noise and vibration, which are two main bottlenecks of the wind power technology.
Keywords: ORC cycle; Wind turbine; Energy analysis; Wind Thermal; Exergy analysis
Introduction
Due to the industrialization of most cities, energy demand grew significantly. The continuous increase in energy demand has led to the widespread use of carbon-containing fossil fuels, which has caused significant damage to the environment and human health. In recent years, many efforts and programs have been made to reduce the use of fossil fuels. Renewable energy sources such as solar and wind energy have been introduced as reliable sources for clean energy production for use. Solar power plant technology using parabolic-linear concentrators is the most significant method among thermal-electric methods for renewable energy production.
Recently, Gupta et al. [1] proposed a system consisting of an organic Rankin cycle with a triple pressure level absorption system and a parabolic-linear solar collector system in 2020. This system generates electricity and refrigeration simultaneously at two different temperatures. In this study, the effect of different inlet parameters such as solar radiation, turbine inlet pressure, turbine outlet pressure, and evaporator temperature on the designed schematic subsystems was investigated. Kerme et al. [2] thermodynamically analyzed a multiple power generation system using the thermal energy from a solar system with a parabolic-linear solar collector. The results showed that increasing the turbine inlet temperature increased the efficiency and decreased overall energy losses.
*Corresponding author: [email protected]
The results also showed that the two main sources of exergy losses are the solar system and the desalination unit.
Alirahmi *et al.* [3] proposed a multiple generation system based on the geothermal energy and a parabolic-linear solar collector system for simultaneous electricity generation, cooling load, freshwater, hydrogen, and heat. To optimize the objectives of their research, EES (engineering equation solver) and MATLAB software were interconnected using the Dynamic Exchange Data method. Finally, the system exergy efficiency and total unit cost were 29.95% and 129.7 $/GJ, respectively. Alotaibi *et al.* [4] investigated the performance of a conventional steam power plant with a regenerative system equipped with a parabolic-linear solar collector system. The system analysis results showed that the removal of the low-pressure (LP) turbine increases the performance of the steam power plant up to 9.8 MW/h. The optimal area for the solar system in these conditions was estimated at 25,850 square meters. Ehyaei *et al.* [5] conducted thermodynamic analysis, energy and exergy, and economic analysis on a linear parabolic solar collector. The optimization results showed that the exergy efficiency, energy efficiency, and costs were 29.29%, 35.55%, and $0.0142/kWh, respectively. Toghyani *et al.* [6] used a nanofluid as a cooling fluid in a parabolic-linear solar collector to cool the solar system and produce hydrogen. The results showed that hydrogen production increases under higher solar intensities because the Rankin cycle transfers more energy to the PEM.
AlZahrani and Dincer [7], in 2018, studied the energy and exergy of parabolic-linear solar collectors as part of a solar power plant under different design and performance conditions. Finally, the energy and exergy efficiency rates of 35.66% and 38.55% were reported, respectively. In 2019, Yilmaz [8] reviewed the comprehensive thermodynamic performance and economic evaluation of a combined ocean thermal energy system and a wind farm. The results showed that the hybrid system’s overall energy and exergy efficiencies are 12.27% and 34.34%, respectively. The cost of the proposed system was reported to be $3.03 per hour. Ishaq and Dincer [9] proposed a new idea for hydrogen production from methanol using the wind energy. The proposed system used industrial carbon emissions to produce methanol. EES and Aspen Plus software was used to model the system and comprehensively analyze it. Bamisile *et al.* [10] modeled a power generation system using wind, solar and biogas energy, and analyzed the energy and exergy of the system. The results showed that the system’s overall energy efficiency varies from 64.91% to 71.06%, while the exergoeconomic efficiency increases from 31.80% to 53.81%. In 2018, Kianfard *et al.* [11] investigated a renewable system based on thermal energy to produce fresh water and hydrogen. The economic analysis results showed that the investment costs per unit of reverse osmosis desalination plant were 56%. The cost of producing freshwater was estimated at 32.73 cents per cubic meter.
Alirahmi and Assareh [12] analyzed the energy, exergy, and economy and multi-objective optimization of multiple energy systems, including hydrogen production, freshwater, cooling, heating, hot water, and electricity generation of Dezful city. The two objective functions of this study were exergy and total cost, which were optimized by a genetic algorithm. Finally, the best value for the exergy efficiency was 31.66%, and the total unit rate was 21.9 $/GJ. In 2020, Mohammadi *et al.* [13] designed a combined cycle gas turbine to generate electricity, freshwater, and cooling. The results showed that the use of reverse osmosis is more economical than a combined multi effect distillation and reverse osmosis (MED-RO) system. System costs for electricity, water, and cooling were
also reported at $0.0648 per kilowatt-hour, $0.7219 per cubic meter, and $0.0402 per hour, respectively.
In the aforementioned studies, there is no numerical modeling for wind turbines. It is often assumed that the wind turbine is working under a steady operation condition, and the effect of the changing parameters of the wind turbine on the system was not studied.
In this study, a numerical modeling method is used to model a horizontal axis wind turbine coupled with a direct heat generator and a phase change material (PCM) storage to enhance baseload reliability of the wind system, including an organic Rankine cycle (ORC), a wind turbine, and a PCM storage. The model studied the effects of the different wind turbine’s operation conditions on the performance of the described system based on the energy and exergy efficiencies (2E analysis), and finally evaluated the operating conditions for the best overall technical performance of the system.
**Materials and Methods**
*Case Study*
The installation of renewable energy sources in the electricity grid creates many problems, because most renewables are intermittent [14]. This article describes a new idea called Wind Thermal Power (WTES), which was first proposed to solve network problems.
Concentrated Solar Power (CSP) is attracting attention due to its susceptibility to scattering. Some plants can operate with continuous power generation 24 hours a day. Thermal energy storage has already become the second-largest energy storage system in the United States after hydrogen. Solana, which has been online since 2013, has a massive 1,680 megawatt-hour power reserve. Total thermal energy storage will almost double in 2015 [3]. Proposals using this practical thermal energy storage are gradually increasing [4-6]. The use of energy storage is also studied from various aspects [7, 8].
---
**Fig. 1. Schematic of the system**
The use of this thermal energy storage and a low-cost and lightweight heat generator are key points of WTES. A typical shape of a “specialized thermal type” WTES is shown in Fig. 1. The rotational energy is converted into thermal energy just above the tower. The rest of the system is of the same type as the CSP turret [9]. The thermal energy generated is transferred to the base facilities by means of a heat transfer fluid (HTF) and produces steam to power the turbine generator when required.
This system is sub-divided into three subsystems and studied in the term of exergy and energy. The mentioned subsystems are wind turbine, storage system, and wind turbine system.
**Wind Turbine Energy Analysis**
If we consider a wind turbine consisting of three general parts of blades, mechanical equipment, and generator (as shown in Fig. 2), then to analyze the power in each part, energy analysis must be used. The result of using energy analysis is the following Eqs 1 to 4 for turbine power [13].
\[
\begin{align*}
p_w &= \frac{1}{2} \rho A v^3 \\
p_m &= p_w \eta_b \\
p_G &= p_m \eta_m \\
Q_G &= p_G \eta_g = \frac{1}{2} \rho A v^3 \eta_m \eta_g \eta_b
\end{align*}
\]
In the above equations, \( \eta_b \) stands for blade efficiency, \( \eta_m \) is mechanical efficiency of turbine, \( \eta_g \) is generator’s efficiency, \( V \) is wind speed, \( A \) is effective area of wind turbine, \( \rho \) is air density, \( Q_G \) is turbine output heat, \( p_G \) is power received by the generator, \( p_m \) is power received by mechanical parts, and \( p_w \) is maximum power of the wind [14].
**Wind Turbine Exergy Analysis**
The exhaust air outlet of the turbine is shown in Eq. (5):
\[
EX_{\text{air}} = EX_{\text{kinetic}} + EX_{\text{potential}} + EX_{\text{physical}} + EX_{\text{chemical}}
\]
where EX symbolizes the exergy in the above relation, and the substrates of each symbol represent the relevant part (kinetic, potential, physical, and chemical). If we consider the environment as 298 K and air at 1 atm pressure, the chemical and physical exergy of the air will be zero. Because the height of the air does not change, the potential exergy will be zero. So, the air exergy is calculated from \( EX_{\text{air}} = EX_{\text{kinetic}} \), and mass flow and airflow exergy are obtained from the following Eqs 6 and 7 [15]:
\[
\begin{align*}
m &= \rho AV_r = \rho \pi R^2 V_r \\
EX_{\text{kinetic}} &= \frac{V_r^2}{2}
\end{align*}
\]
where \( M \), \( R \), and \( V_r \) are equal to mass flow, rotor radius, and wind speed at high relationships, respectively. If we consider the turbine in the simplified form of Fig. 3, in this figure, the wind turbine consists of blades (which are assumed to be without friction), mechanical equipment (including shaft, bearing, and gearbox with \( \eta_m \) efficiency) and
heat generator with $\eta_G$ efficiency is considered. As can be seen from the figure, the energies in the flow are in the form of kinetic, work-oriented, and electrical forms that can be fully converted to work, i.e., the current exergy is equal to the content of the flow energy. If for analysis, we consider the system only as a turbine set, then the feed exergy of the system is equal to the state 1 exergy flow and the product exergy flow is equal to the exergy flow of the state 2. The flows are marked with a number on the figure. The exergy of the flows will be in the form of the following Eqs 7 to 12 [16]:
\[
EX_1 = m\left(\frac{v_{in}^2}{2}\right)
\]
(7)
\[
EX_2 = m\left(\frac{v_{out}^2}{2}\right)
\]
(8)
\[
EX_3 = EX_1 - EX_2
\]
(9)
\[
EX_4 = \eta_m EX_3
\]
(10)
\[
EX_5 = \text{constant in let water} \sim 0
\]
(11)
\[
EX_6 = \eta_G EX_5\left(1 - \frac{T_5}{T_6}\right)
\]
(12)
In the above equations, $EX$ represents the flow of exergy (multiplied by mass flow), and $V_{in}$ and $V_{out}$ are equal to the velocity of the inlet and outlet winds, respectively.
In a wind turbine, the part of the input wind power that is out of the turbine’s reach is called the exergy loss and will be equal to the flow exergy of state 1. Also, the part of the exergy, which is lost in the equipment and different parts of the conversion turbine due to friction and inefficiencies of that component and turns into other forms of energy (such as heat), is called exergy destruction which is equal to the difference in exergy level between inlet and output flow (as defined by Eq. (13) [17]):
\[
EX_D = EX_{in} - EX_{out}
\]
(13)
In the above relation, $EX_{in}, EX_{out},$ and $EX_D$ are equal to the output current exergy, the input current exergy, and the exergy degradation, respectively. Therefore, the
degradation of the exergies of different parts in a turbine can be calculated from Eqs 14 to 16:
\[
EX_D = EX_3 - EX_4 = EX_3 - \eta_m EX_3 = EX_3(1 - \eta_m)
\]
\[
EX_{DG} = EX_4 - EX_6 = \eta_m EX_3 - \eta_G EX_4 = \eta_m EX_3 - \eta_G \eta_m \left(1 - \frac{T_5}{T_6}\right) EX_3
\]
\[
EX_{DG} = EX_3 \eta_m \left(1 - \eta_G \left(1 - \frac{T_5}{T_6}\right)\right)
\]
where \(EX_D\), \(EX_{DG}\) and \(EX_D\) are the total exergy damage, the generator exergy degradation, and the exergy degradation of the mechanical part, respectively. For each part, a quantity called the degradation ratio is defined, which is equal to the degradation ratio of that part to the system feed exergy. It is defined in Eqs 17 to 20 [18]:
\[
y_{D,t} = \frac{E_{D,t}}{E_f}
\]
\[
y_{D,G} = \frac{E_{D,G}}{E_f}
\]
\[
y_{D,m} = \frac{E_{D,m}}{E_f}
\]
\[
y_{D,tot} = \frac{E_{D,tot}}{E_f}
\]
where \(y_{D,t}\) is equal to the degradation ratio in the \(t\) part and \(t\) can be equal to \(G\), \(m\) and \(tot\), which represent the generator, the mechanical part and the whole system, respectively. Also, the exergy efficiency of the whole turbine system is defined as the ratio between the output current exergy to the feed flow exergy as calculated in Eq. (21):
\[
extergy\ efficiency_{sys} = \frac{e_p}{e_f} = \frac{EX_6}{EX_1} = \frac{\eta_G \eta_m \left(1 - \frac{T_5}{T_6}\right) EX_3}{EX_1}
\]
Replacing the new system requires an analysis of many different aspects. Therefore, in the first step of designing the power generation system, the desired system should be adapted to thermodynamics’ rules and principles. Due to the CHP system’s combination with two different types of generators as the prime movers, energy analysis must be performed. The purpose of these calculations is to determine the best type of combination with the highest output power, recycled heat, overall efficiency, and the lowest fuel consumption of the system.
Storage Exergy Analysis
Having some practical considerations, a commercial PCM melting point of which is 250 °C (PlusICE H250) is used as a case study. The supplied exergy by HTF during the charging period, the output exergy at discharging cycle, and the exergetic efficiency of PCM storage can be expressed by the following equations, where \(T_0\), \(T_6\), \(T_7\), and \(T_m\) refer to temperatures of ambient, HTF inlet, HTF outlet, and PCM melting point, respectively. Storage heat-loss is considered to be negligible [19]:
Charging is calculated in Eq. (22):
\[
EX_{pcm,i} = \dot{m}_{HTF} C_{HTF} \left[\left(T_6 - T_7\right) - T_0 \ln\left(T_6/T_7\right)\right]
\]
Discharging is calculated in Eq. (23):
\[ EX_{pcm,o} = \dot{m}_{HTF} C_{HTF} [(T_7 - T_6) - T_0 \ln(T_7/T_6)] \]
Charge and Discharge are calculated in Eq. (24):
\[ T_7 = T_m + (T_7 - T_m)e^{-\frac{h_{pcm} A_{pcm}}{m_{pcm} c_{pcm}}} \]
Exergetic PCM storage efficiency is calculated in Eq. (25):
\[ \eta_{pcm} = \frac{EX_{pcm,o}}{EX_{pcm,i}} \]
where \( m_{HTF} = 6.2 \text{ (kg/s)} \). Also, it is assumed that the isothermal PCM melts, and the sensible heat of the PCM is negligible. Moreover, to minimize any unsatisfactory conditions, it is considered that the controlling system would block the storage tank’s path as soon as the difference between \( T_7 \) and \( T_m \) falls below 30°C. The total exergetic outcome of the system with PCM storage is determined as shown in Eq. (26):
Total output exergy = \( EX_u + EX_{pcm,o} \)
Finally, the overall exergetic efficiency of the whole system is measured by dividing the sum of all output exergy by the amount of input exergy of the solar system.
Results showed that using “PlusICE H250” as the latent heat storage (LHS) for the Shiraz power plant is suitable due to both PCM physical properties and power plant working conditions, such as HTF temperature (see Table 1)[20].
| Table 1. Selected LHS with PlusICE H250 exergetic analysis results |
|---------------------|----------|---------|
| Parameter | unit | value |
| Exergetic efficiency| (%) | 85.54 |
| Exergy Loss | (W) | 30200 |
| \( EX_{pcm,o} \) | (W) | 103448 |
| \( EX_{pcm,i} \) | (W) | 133567 |
| Density | (kg/m³) | 2380 |
| Latent heat | (kJ/kg) | 280 |
| Specific heat | (kJ/kg K)| 1.525 |
| Max working temperature| (°C) | 600 |
| Melting point | (°C) | 250 |
| Material | | PlusICE H250 |
**Rankin cycle**
The heat given to the ORC heat exchanger can be calculated by balancing the energy between the operating fluid and the wind tower fluid at the heat exchanger inlet and outlet obtained from Eq. (27) (see Fig. 4).
\[ \dot{Q}_6 = \dot{m}_{turbine}(h_7 - h_5) = \dot{m}_{ORC}(h_8 - h_{11}) \]
where \( \dot{m}_{turbine} \) is the mass flow rate of geothermal water, and \( \dot{m}_{ORC} \) is the mass flow rate of the ORC cycle. By applying the energy balance, the production capacity of the turbine is obtained from Eq. (28).
\[ \dot{W}_t = \dot{W}_{t,isen} \eta_t = \eta_t \dot{m}_{ORC} ((h_8 - h_9)) \]
The heat given to the cooling water in the condenser is calculated from Eq. (29).
$$\dot{Q}_C = \dot{m}_{ORC} (h_{10} - h_9)$$
(29)
The consumption of pumps in the cycle is calculated from Eq. (30).
$$\dot{W}_P = \dot{W}_{P_1} = \frac{m_{ORC}}{\eta_P} (h_{11} - h_{10})$$
(30)
The net generated power of the ORC cycle is obtained from the algebraic sum of the turbine-generated power and the pump consumption, which is injected into the grid directly as $E_{product}$ calculated in Eq. (31).
$$\dot{W}_{net} = \dot{W}_t - \dot{W}_P = \dot{E}_{Product}$$
(31)
The energy efficiency of the Rankin cycle is calculated from Eq. (32)[21].
$$\eta_{ORC} = \frac{\dot{W}_{net}}{\dot{Q}_{HX}}$$
(32)
**Results and Discussion**
**Validation**
In this section, before presenting the results, the values and results obtained are first validated. The purpose of accreditation is to ensure the simulation and its results.
Implementing the 2E method can allow us to make satisfactory predictions about the energy produced under different conditions and calculate the wind speed behind the wind turbines to measure the energy and energy efficiency.
Figure 5 shows the comparison between the real-state power measurement and the power calculated by the 2E code. As shown in Figure 5, the 2E code has a good ability to predict the power output. Increasing the wind speed from 4 m/s to 15 m/s results in a
higher power output at all three tilt angles, whereas after reaching a peak at wind speeds of 11.5 m/s, it has an opposite effect on the power output. On the other hand, increasing the bank angle decreases the power output at all wind speeds. This reduction makes more sense at higher wind speeds. Wind turbines are expected to have the highest performance at a wind speed of 12 m/s and a tilt angle of 5 degrees, producing a power of 140 kW.
**Fig. 5.** Comparison of output power between BEM model and experimental data
**Wind Turbine’s Energy and Exergy Analyses**
As seen in Table 2, the wind speed significantly affects the wind turbine’s performance based on energy and exergy efficiencies. It causes a steady rise in exergy flow and destruction. The maximum exergy and energy efficiencies are 44.9 % and 46.7 % at wind speed 11.5 m/s, respectively.
| Wind speed (m/s) | Energy efficiency (%) | Exergy efficiency (%) | Exergy flow (W) | Exergy destruction (W) |
|------------------|------------------------|-----------------------|-----------------|------------------------|
| 6 | 15.1 | 13.8 | 55833.8 | 12037.2 |
| 7 | 34.7 | 31.5 | 86571.5 | 18203.9 |
| 8 | 43.8 | 41.6 | 127209.6 | 24587.9 |
| 9 | 44.8 | 43.1 | 179150 | 33692.4 |
| 10 | 46.8 | 45.2 | 243812.1 | 44596.7 |
| 11 | 45.7 | 44.4 | 322612.5 | 56701.1 |
| 12 | 46.7 | 44.9 | 416960.3 | 71283.5 |
| 13 | 32.8 | 32.1 | 528321.2 | 74462.9 |
| 14 | 25 | 24.6 | 658063.4 | 75354.3 |
| 15 | 18.3 | 18 | 807607.5 | 71847.3 |
Table 3 shows that increasing the pressure change can decrease the wind turbine exergy efficiency while increasing the temperature can increase the exergy efficiency from 42.1% at 5°C to 43% at 35°C. However, these changes are not noticeable from the velocity’s affect on the wind turbine’s exergy efficiency.
Table 3. The effect of pressure changes and temperature on the exergy efficiency of wind turbine
| Variables | Exergy efficiency (%) |
|-----------|-----------------------|
| P= 100 Kpa | 44.9 |
| P= 150 Kpa | 44.7 |
| P= 200 Kpa | 44.6 |
| P= 250 Kpa | 44.2 |
| T= 5°C | 44.5 |
| T= 20°C | 44.7 |
| T= 25°C | 44.9 |
| T=35°C | 45.2 |
Results of the System
By comparing the references and the present work presented in Table 4, it can be seen that there is a good accuracy for the results of the calculated parameters in the present work.
Table 4. Performance parameters of organic Rankine cycle with feed fluid recovery and heating
| Parameter | Value |
|--------------------------------|-----------|
| Fluid agent | R236fa |
| Heat Exchanger load (kW) | 112 |
| Condenser load (kW) | 34.9 |
| Turbine output power (kW) | 77.0 |
| Pump power consumption (kW) | 2.9 |
| Net power output (kW) | 69.9 |
| Energy efficiency (%) | 62.4 |
| Mass flow rate of operating fluid (kg/s) | 1.1 |
Table 5 shows the performance characteristics of the system. All these values are calculated for four different operating fluids. It is observed that the operating fluid R245fa has the highest energy and exergy efficiency with 49.8% and 27.8%, respectively. Operating fluids R114, R600 and R236fa are also in the next categories in terms of performance characteristics. Table 5 shows the lost exergy rate of system components for all operating fluids. Examining the system’s exergy based on the above tables shows that the exchanger and the inductive generator have the highest exergy destruction (heat degradation), because both fuels’ exergy flow rate and temperature differences are very high. It is also observed that with the change of operating fluid, the exergy loss in the exchanger decreases. This trend is to increase the power by reducing the loss of exergy in the exchanger. Comparing the operating fluids exegetically, it is observed that the operating fluid R245fa has the lowest exergy loss and the operating fluid R236fa has the highest exergy loss in the exchanger. Therefore, it can be concluded that the operating fluid that has less exergy loss in the exchanger produces more power and produces higher exergy loss in the wind turbine (see Table 6).
Table 5. System performance characteristics
| Performance characteristic | R236fa | R600 | R114 | R245fa |
|-----------------------------------|--------|-------|-------|--------|
| Direct power to grid (kW) | 69.9 | 69.9 | 69.9 | 69.9 |
| Exchanger heat (kW) | 112 | 112 | 112 | 112 |
| Condensing heat (kW) | 36.99 | 36.52 | 34.93 | 35.56 |
| Turbine power (kW) | 75.01 | 75.48 | 77.07 | 76.44 |
| Pump power (kW) | 5.11 | 5.58 | 7.17 | 6.54 |
| Total thermal efficiency (%) | 67.0 | 67.4 | 68.8 | 68.3 |
| Rankine cycle exergy efficiency (%)| 63.7 | 64 | 65.4 | 64.9 |
| Exergy efficiency with wind system (%)| 28.7 | 28.8 | 29.4 | 29.2 |
Table 6. Loss of exergy rate of different system components
| System components | R236fa | R600 | R114 | R245fa |
|-------------------|--------|-------|-------|--------|
| Pump | 5.21 | 5.66 | 7.33 | 6.54 |
| Storage | 12.76 | 13.21 | 13.44 | 13.51 |
| Turbine | 5.24 | 6.64 | 5.97 | 6.71 |
| Condenser | 116.2 | 114.1 | 109.6 | 109.2 |
| Generator | 45.3 | 46.1 | 46.4 | 47.1 |
CONCLUSIONS
Thermal backup systems and plants or some energy storage systems are essential when a considerable amount of wind power is injected into the grid. The findings of other studies showed energy costs of the wind with backup thermal, the wind with battery energy storage, and Wind Powered Thermal Energy System (WTES), which employs inductive heat generators and thermal energy storage systems, are comparable. Also, the results of this study show that the energy and exergy performance of the WTES system is also comparable with conventional wind and other energy storage systems. The results of the 2E analysis show that the exergy efficiency of the system is 28.9%, which is more than solar thermal system exergy efficiency. WTES becomes much more attractive when constructed besides CSP and/or bio-mass plants since many elements can be shared. The configuration of WTES has many variations. Employment of the electric and heat generator enables flexible operation. It can even absorb surplus energy from the grid. Employment of the superconducting heat generator realizes high working temperature, i.e., high thermal to electric conversion efficiency. Those variations, including simple thermal specialized types, have lots of room to be investigated.
Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
REFERENCES
[1] Gupta, D. K., Kumar, R., and Kumar, N. (2020). Performance analysis of PTC field based ejector organic Rankine cycle integrated with a triple pressure level vapor absorption system (EORTPAS). *Engineering Science and Technology, an International Journal*, 23(1), 82-91. DOI: https://doi.org/10.1016/j.jestch.2019.04.008
[2] Kerme, E. D., Orfi, J., Fung, A. S., Salilih, E. M., Khan, S. U.-D., Alshehri, H., Ali, E., and Alrasheed, M. (2020). Energetic and exergetic performance analysis of a solar driven power, desalination and cooling poly-generation system. *Energy*, 196, 117150. DOI: https://doi.org/10.1016/j.energy.2020.117150
[3] Alirahmi, S. M., Rahmani Dabbagh, S., Ahmadi, P., and Wongwises, S. (2020). Multi-objective design optimization of a multi-generation energy system based on geothermal and solar energy. *Energy Conversion and Management*, 205, 112426. DOI: https://doi.org/10.1016/j.enconman.2019.112426
[4] Alotaibi, S., Alotaibi, F., and Ibrahim, O. M. (2020). Solar-assisted steam power plant retrofitted with regenerative system using Parabolic Trough Solar Collectors. *Energy Reports*, 6, 124-133. DOI: https://doi.org/10.1016/j.egyr.2019.12.019
[5] Ehyaeei, M. A., Ahmadi, A., El Haj Assad, M., and Salameh, T. (2019). Optimization of parabolic through collector (PTC) with multi objective swarm optimization (MOPSO) and energy, exergy and economic analyses. *Journal of Cleaner Production*, 234, 285-296. DOI: https://doi.org/10.1016/j.jclepro.2019.06.210.
[6] Toghyani, S., Afshari, E., Baniasadi, E., and Shadloo, M. S. (2019). Energy and exergy analyses of a nanofluid based solar cooling and hydrogen production combined system. *Renewable Energy*, 141, 1013-1025. DOI: https://doi.org/10.1016/j.renene.2019.04.073
[7] AlZahrani, A. A., and Dincer, I. (2018). Energy and exergy analyses of a parabolic trough solar power plant using carbon dioxide power cycle. *Energy Conversion and Management*, 158, 476-488. DOI: https://doi.org/10.1016/j.enconman.2017.12.071
[8] Yilmaz, F. (2019). Energy, exergy and economic analyses of a novel hybrid ocean thermal energy conversion system for clean power production. *Energy Conversion and Management*, 196, 557-566. DOI: https://doi.org/10.1016/j.enconman.2019.06.028
[9] Ishaq, H., and Dincer, I. (2020). Evaluation of a wind energy based system for cogeneration of hydrogen and methanol production. *International Journal of Hydrogen Energy*, 45(32), 15869-15877. DOI: https://doi.org/10.1016/j.ijhydene.2020.01.037
[10] Bamisile, O., Huang, Q., Li, J., Dagbasi, M., Desire Kemena, A., Abid, M., and Hu, W. (2020). Modelling and performance analysis of an innovative CPVT, wind and biogas integrated energy system: An energy and exergy approach. *Energy Conversion and Management*, 209, 112611. DOI: https://doi.org/10.1016/j.enconman.2020.112611
[11] Kianfard, H., Khalilarya, S., and Jafarmadar, S. (2018). Exergy and exergoeconomic evaluation of hydrogen and distilled water production via combination of PEM electrolyzer, RO desalination unit and geothermal driven dual fluid ORC. *Energy Conversion and Management*, 177, 339-349. DOI: https://doi.org/10.1016/j.enconman.2018.09.057
[12] Alirahmi, S. M., and Assareh, E. (2020). Energy, exergy, and exergoeconomics (3E) analysis and multi-objective optimization of a multi-generation energy system for day and night time power generation - Case study: Dezful city. *International Journal of Hydrogen Energy*, 45(56), 31555-31573. DOI: https://doi.org/10.1016/j.ijhydene.2020.08.160
[13] Mohammadi, K., Khaledi, M. S. E., Saghaififar, M., and Powell, K. (2020). Hybrid systems based on gas turbine combined cycle for trigeneration of power, cooling, and freshwater: A comparative techno-economic assessment. *Sustainable Energy Technologies and Assessments*, 37, 100632. DOI: https://doi.org/10.1016/j.seta.2020.100632
[14] Okazaki, T., Shirai, Y., and Nakamura, T. (2015). Concept study of wind power utilizing direct thermal energy conversion and thermal energy storage. *Renewable Energy*, 83, 332-338. DOI: https://doi.org/10.1016/j.renene.2015.04.027
[15] Razmi, A. R., and Janbaz, M. (2020). Exergoeconomic assessment with reliability consideration of a green cogeneration system based on compressed air energy storage (CAES). *Energy Conversion and Management*, 204, 112320. DOI: https://doi.org/10.1016/j.enconman.2019.112320
[16] Rashidi, H., and Khorshtidi, J. (2018). Exergoeconomic analysis and optimization of a solar based multigeneration system using multiobjective differential evolution algorithm. *Journal of Cleaner Production*, 170, 978-990. DOI: https://doi.org/10.1016/j.jclepro.2017.09.201
[17] Nemati, A., Sadeghi, M., and Yari, M. (2017). Exergoeconomic analysis and multi-objective optimization of a marine engine waste heat driven RO desalination system integrated with an organic Rankine cycle using zeotropic working fluid. *Desalination*, 422, 113-123. DOI: https://doi.org/10.1016/j.desal.2017.08.012
[18] Naseri, A., Bidi, M., Ahmadi, M. H., and Saidur, R. (2017). Exergy analysis of a hydrogen and water production process by a solar-driven transcritical CO2 power cycle with Stirling engine. *Journal of Cleaner Production*, 158, 165-181. DOI: https://doi.org/10.1016/j.jclepro.2017.05.005
[19] Norouzi, N. (2021). The Pahlev Reliability Index: A measurement for the resilience of power generation technologies versus climate change. *Nuclear Engineering and Technology*, 53(5), 1658-1663. DOI: https://doi.org/10.1016/j.net.2020.10.013
[20] Khajehpour, H., Norouzi, N., Bashash Jafarabadi, Z., Valizadeh, G., & Hemmati, M. H. (2021). Energy, exergy, and exergoeconomic (3E) analysis of gas liquefaction and gas associated liquids recovery co-process based on the mixed fluid cascade refrigeration systems. *Iranian Journal of Chemistry and Chemical Engineering (IJCCE)*. ‘Article in Press’ DOI: 10.30492/ijccee.2021.141462.4442
[21] Habibollahzade, A., Gholamian, E., Ahmadi, P., and Behzadi, A. (2018). Multi-criteria optimization of an integrated energy system with thermoelectric generator, parabolic trough solar collector and electrolysis for hydrogen production. *International Journal of Hydrogen Energy*, 43(31), 14140-14157. DOI: https://doi.org/10.1016/j.ijhydene.2018.05.143
**Article copyright:** © 2021 Nima Norouzi. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use and distribution provided the original author and source are credited. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3047,
1
],
[
3047,
6934,
2
],
[
6934,
8835,
3
],
[
8835,
11744,
4
],
[
11744,
13673,
5
],
[
13673,
16328,
6
],
[
16328,
18789,
7
],
[
18789,
20192,
8
],
[
20192,
22770,
9
],
[
22770,
25302,
10
],
[
25302,
27942,
11
],
[
27942,
29711,
12
],
[
29711,
32935,
13
],
[
32935,
34495,
14
]
]
} |
98ec1a748c896d4c02f147a85b7bee06bf7d608c | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 7,
"total-fallback-pages": 0,
"total-input-tokens": 21696,
"total-output-tokens": 4665,
"fieldofstudy": []
} | Adsorption Effectivity Test of Andisols Clay-Zeolite (ACZ) Composite as Chromium Hexavalent (Cr(VI)) Ion Adsorbent
Pranoto¹, A Masykur, Y A Nugroho
Research Group of Analytical and Environmental Chemistry, Faculty of Mathematics and Natural Sciences
Universitas Sebelas Maret, Ir. Sutami street No. 36 A, Surakarta, Central Java, 57126, Indonesia.
E-mail: [email protected]
Abstract. Adsorption of chromium hexavalent (Cr(VI)) ion in aqueous solution was investigated. This research was purposed to study the influence of the composition of ACZ, temperature activation, and contact time against adsorption capacity of Cr(VI) ion in aqueous solution. Determination of adsorption effectivity using several parameter such as composition variation of ACZ, contact time, pH, activation temperature, and concentration. In this research, andisol clay and zeolite has been activated with NaOH 3 M and 1 M, respectively. Temperature variation used 100, 200, and 400 °C. While composition variation ACZ used 0:100, 25:75, 50:50, 75:25, 100:0. The pH variation was used 2 – 6 and concentration variation using 2, 4, 6, 8, 10, and 12 ppm. Characterization in this research used such as UV-Vis, Surface Area Analyzer (SAA) and Acidity Analysis. Result of this research is known that optimum composition of ACZ was 50:50 with calcination temperature 100 °C. Optimum adsorption of Cr(VI) at pH 4 with removal percentage 76.10 % with initial concentration 2 ppm and adsorption capacity is 0.16 mg/g. Adsorption isotherm following freundlich isotherm with value $K_f = 0.17$ mg/g and value $n$ is 0.963. Based on results, ACZ composite can be used as Cr(VI) ion adsorbents in aqueous solutions.
1. Introduction
Chromium hexavalent (Cr(VI)), is toxic and suspected to carcinogenic for all life form [1,2], Cr(VI) usually found in electroplating, leather tanning, paint, steel fabrication, and textile dyeing [3]. Cr(III) and Cr(VI) state usually exist on environment. Cr(VI) have more high mobility then Cr(III) and is known to capable of permeating cell membrane and is a powerful mutagen for human and animal [4]. According to the Regulation of the Minister of Environment of Indonesia on the Standard of Wastewater Quality that the maximum limit of Cr(VI) ions in waste is 0.1 mg/L.
Conventional methods for the removal of Cr(VI) ion from wastewater include adsorption [5], coagulation-flocculation [6], ion exchange [7], filtration [8], and reverse osmosis [9]. The adsorption process is well known to be one of the most effective techniques and low cost for the removal of Cr(VI) ion in wastewater. The adsorption capacity of the sorbent is related to the radius, the specific surface area and the number of pores [4]. A few materials that can be used as adsorbent for Cr(VI) removal and easy to be found such as zeolite and andisol clay [10,11]. According to Sugiyarto (2013), andisol clay could be good adsorbent for heavy metals removal including Cr(VI) ion and could be
¹ [email protected]
found in few mountain in java island such as Mt Papandayan, Mt Wilis, and Mt Arjuna. In andisol clay usually found allophane minerals that have high specific surface area, porosity and ion exchange capacity and could be apply to wastewater treatment [10]. Zeolite are the crystalline microporous aluminosilicates that have molecular sieve and adsorbing ability for small molecules such as water. Zeolite are good adsorbent for removal heavy metals ion and contamination/pollution control [12]. Zeolite have SiO$_4$ and AlO$_4$ tetrahedral framework that forming stable arrangement through oxygen atom [13].
Andisol clay is still considered to have a lower adsorption capacity against Cr(VI) ions than zeolites. So, the modification of andisol clay by forming andisol-clay-zeolite composite is used to improve andisol clay adsorption capacity [14]. This is due to the excess of zeolites that have better adsorption capability than soil andisol may help to increase the adsorption capacity of the andisol soil [15].
In this research, zeolite will be added to the andisol clay to form the ACZ composite as Cr(VI) ion adsorbent and to study the effect of composition, activation, and contact time on Cr(VI) ion adsorption process in aqueous solution. ACZ composite are expected to have a better adsorption capacity that could be applied in industrial wastewater treatment.
2. Experimental
2.1. Adsorbent Preparation
Natural andisol clay from Mt. Lawu and zeolite from Wonosari are dried in the free air. After drying the soil andisol and zeolite mashed and sifted with 150 mesh then washed with aquades then dried with temperature 105 °C for 4 hours. Dry andisol clay was activated by soaked in 3 M NaOH solution and stirred with heating 70 °C for 5 hours then washed with aquades until the pH of andisol clay was neutral then dried at 105 °C. The dried natural zeolite was activated by soaking in 1 M NaOH solution and stirred with 90 °C for 1 hour then washed with aquades until the pH of the zeolite was neutral then dried at 105 °C.
2.2. ACZ Composite Preparation
Activated andisol soils and zeolite were mixed into 100 ml aquadest with weight variation (g/g) 0:100 (ZAA), 25:75 (ZAB), 50:50 (ZAC), 75:25 (ZAD), 100: 0 (ZAE). The mixture is then stirred for 1 hour. Each mixture was activated with temperature variations of 100, 200, and 400 °C for 3 hours. The composite is used as the Cr(VI) ion adsorbent in the aqueous solution.
2.3. Testing Adsorption effectivity of ACZ to Cr(VI) ion
0.1 g of ACZ composite was introduced into 10 ml Cr(VI) solution 2 mg/L with pH 2, 3, 4, 5 and 6 variations. The best pH variations were tested using variation of contact time 20, 40, 60, 80, 100, and 120 minutes. The obtained mixture was filtered and the filtrate was added 1.5-Diphenylcarbazide and was performed by determining Cr(VI) values using UV-VIS Spectroscopy following SNI 6989.71: 2009.
2.4. Isotherm Adsorption analysis of ACZ composite
0.1 g of ACZ composite was introduced into 10 ml Cr(VI) solution with variation of concentration 2, 4, 6, 8, 10, 12 mg/L. The obtained mixture was filtered and the filtrate was added with 1.5-Diphenylcarbazide and determination of Cr(VI) values using UV-VIS spectroscopy.
3. Result and Discussion
3.1. Characterization of ACZ
3.1.1. Surface area, Acidity and Pore Size Characterization. Surface area, acidity and pore size characterization is used to determine effectivity of andisol-clay composite adsorption against Cr(VI) ion. Acidity of Adsorbent is used to determine active site of adsorbent that used to adsorb Cr(VI) ion. Surface area, acidity, pore size characterization of Andisol clay and zeolite will be showed in table 1.
Table 1. Surface area, acidity and pore size characterization of Andisol Clay and Zeolite
| Adsorbent | Surface Area (m²/g) | Acidity (mmol/g) | Pore Size (Å) |
|-------------------|---------------------|------------------|---------------|
| Natural Andisol | 91.30 | 0.47 | 25.06 |
| Clay | | | |
| Activated Andisol | 54.36 | 1.24 | 51.94 |
| Clay | | | |
| Natural Zeolite | 45.95 | 3.88 | 76.56 |
| Activated Zeolite | 55.68 | 4.82 | 86.91 |
| ACZ Composite | 48.61 | 4.94 | 95.90 |
Table 1 showed that andisol clay and zeolite activated with NaOH could increase surface area and acidity of andisol clay and zeolite. Increasing surface area and pore size of andisol clay and zeolite showed that impurities on andisol clay and zeolite dissolved during the activation process. Increasing of acidity showed that active site from andisol clay and zeolite increase during activated process and could increase adsorption capacity.
3.2. Adsorption Effectivity of ACZ Composite on Cr(VI). The adsorbent effectivity test on Cr(VI) ion was performed to determine the optimum capability of the ACZ composite adsorbent. This adsorption effectivity test includes several tests such as the effect of contact time, pH, and the activation temperature of the ACZ composite. Adsorption effectivity of ACZ against Cr(VI) ion with variation composition and variation temperature will showed in figure 1 and 2.
Figure 2. Adsorption effectivity of ACZ Composite against Cr(VI) ion with variation temperature
In figure 1 show that ZAC is optimum composition of ACZ composite with the optimum contact time of adsorption is 60 munites. At this composition, Cr(VI) ion removal is 76.10 % with initial concentration is 2 mg/L. ZAC that activated with different temperature showed in figure 2 that optimum temperature is 100 °C. It is caused by more higher temperature could broke the structure of ACZ composite. Rouzière et al. (2016) state the andisol clay would be broken in temperature above 500 °C caused –OH group release during calcination process [16,17]. Therefore, the adsorption capacity of ACZ composite would be decrease when temperature increase. The adsorption capacity of ZAC with temperature variation and pH variation will showed in figure 3 and 4.
Figure 3. Adsorption capacity of ZAC with temperature variation
In figure 3 show that adsorption capacity of ZAC at 100 °C is 0.16 mg/g. Decrease of adsorption capacity caused by increasing activated temperature of ZAC that could breake the composite structure. In figure 4 show that the optimum condition of Cr(VI) ion adsorption at pH 4. In aqueous solution, Cr(VI) occur in few ion such as \( \text{Cr}_2\text{O}_7^{2-} \), \( \text{HCrO}_4^- \) and \( \text{CrO}_4^{2-} \) [18]. In pH 4, the dominant species of Cr(VI) is \( \text{HCrO}_4^- \) that will interact with active site on ZAC. Reaction mechanism between ZAC with Cr(VI) ion will showed in scheme 1.
\[
\begin{align*}
\text{Al-OH} & \xrightarrow{\text{H}^+} \text{Al-OH}_2^+ + \text{HCrO}_4^- \\
\text{Al-OH}_2^+ + \text{HCrO}_4^- & \rightarrow \text{Al-OH} + \text{HCrO}_4
\end{align*}
\]
Scheme 1. Reaction mechanism between ZAC surface with Cr(VI) ion
In scheme 1 showed that interaction between ZAC surface with Cr(VI) ion that aluminol group will protonized and form \( \text{–OH}_2^+ \) which facilitate to form metal binding with \( \text{HCrO}_4^- \). In ZAC surface, aluminol group will have different characteristic in different pH. Aluminol group could protonized at pH below 5, while at pH above 5 could relase \( \text{H}^+ \) ion and make aluminol group have negative charge [19].
3.3. Isotherm Adsorption Analysis of ACZ Composite. Isotherm adsorption analysis is used to determine adsorption perform on ZAC. Type of isotherm adsorption of ZAC against Cr(VI) ion will showed in figure 5 and figure 6.
In figure 5 showed that freundlich isotherm adsorption of ZAC against Cr(VI) ion. Freundlich isotherm analysis based on physically adsorption which assumed formed multilayer of adsorbed molecules on adsorbent surface. Freundlich isotherm of ZAC showed that r value is 0.994 with $K_f$ value is 0.17 mg/g and n values is 0.963 which mean the adsorption process is favorable [1].
In figure 6 showed that Langmuir isotherm adsorption of ZAC against Cr(VI) ion. Langmuir isotherm analysis based on chemically adsorption which assumed formed monolayer of adsorbed molecules on adsorbent surface. Langmuir isotherm of ZAC showed that r value is 0.327 with $Q_{\text{max}}$ 1.25 mg/g and b value is 0.169 L/g. The isotherm adsorption for ZAC will showed in table 2.
| Isotherm | $Q_{\text{max}}$ (mg/g) | $K_f$ (mg/g) | $n$ | $r$ |
|----------|------------------------|--------------|-----|-----|
| Langmuir | 1.25 | 0.17 | 0.963 | 0.327 |
| Freundlich | | | | 0.994 |
In table 2 show that adsorption of ZAC against Cr(VI) ion following freundlich isotherm which means the adsorption process occurs in physically adsorption where the interaction between ZAC surface with Cr(VI) ion is van der waals bonding [20].
4. Conclusion
Result of this research is optimum composition of ACZ composite is 50:50 (ZAC) with activation temperature 100 °C and optimum contact time is 60 minute. Adsorption capacity of ZAC is 0.16 mg/g with removal of Cr(VI) ion is 76.10 %. Isotherm adsorption result is showed that adsorption process of Cr(VI) ion followed freundlich isotherm or adsorption on physically with freundlich coefficient \( (K_f) \) is 0.17 mg/g and \( r \) value of freundlich isotherm is 0.994. Physically adsorption based on weak van der waals interaction between ZAC adsorbent with Cr(VI) ion in aqueous solution. From this result we known that ZAC can be used as water treatment in wastewater.
Reference
[1] Bhattacharyya K G and Gupta S Sen 2006 Ind. Eng. Chem. Res. 45 7232–40
[2] Wu X-W, Ma H-W and Zhang Y-R 2010 Appl. Clay Sci. 48 538–41
[3] Ren Z, Xu X, Wang X, Gao B, Yue Q, Song W, Zhang L and Wang H 2016 J. Colloid Interface Sci. 468 313–23
[4] Song W, Shi T, Yang D, Ye J, Zhou Y and Feng Y 2015 J. Environ. Manage. 162 96–101
[5] Mthombeni N H, Onyango M S and Aoyi O 2015 J. Taiwan Inst. Chem. Eng. 0 1–10
[6] Haydar S and Aziz J A 2009 J. Hazard. Mater. 168 1035–40
[7] Sardohan T, Kir E, Gulec A and Cengeloglu Y 2010 Sep. Purif. Technol. 74 14–20
[8] Zhao Y, Kunieda M, Obi N and Watanabe S 2017 Precis. Eng. 49 211–9
[9] George J S, Ramos A and Shipley H J 2015 J. Environ. Chem. Eng. 3 969–76
[10] Sugiyarto K 2013 J. Environ. Earth Sci. 3 48–56
[11] Nguyen T C, Loganathan P, Nguyen T V, Vigneswaran S, Kandasamy J and Naidu R 2015 Chem. Eng. J. 270 393–404
[12] Ates A and Akgül G 2016 Powder Technol. 287 285–91
[13] Erdem E, Karapınar N and Donat R 2004 J. Colloid Interface Sci. 280 309–14
[14] Shukla A and Kumar A 2007 Sep. Purif. Technol. 52 423–9
[15] Churchman G J, Gates W P, Theng B K G and Yuan G 2006 Developments in Clay Science vol 1pp 625–75
[16] Rouzière S, Amara M S, Painneau E and Launois P 2016 Nat. Commun. 7 254–78
[17] Wada K 1978 Developments in Sedimentology vol 26, ed C Oliver and M C Janur (Totowa, NJ: Humana Press) pp. 147–87
[18] Tandon R K, Crisp P T, Ellis J and Baker R S 1984 Talanta 31 227–8
[19] Wang G, Hua Y, Su X, Komarneni S, Ma S and Wang Y 2016 Appl. Clay Sci. 124–125 111–8
[20] Atkins P W 1990 Physical chemistry (Oxford: Oxford Univ. Press) | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2992,
1
],
[
2992,
6680,
2
],
[
6680,
8502,
3
],
[
8502,
9417,
4
],
[
9417,
10937,
5
],
[
10937,
11971,
6
],
[
11971,
14513,
7
]
]
} |
67f60073af207eaa05705a41d6352f4d5caab026 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 12,
"total-fallback-pages": 0,
"total-input-tokens": 37826,
"total-output-tokens": 11326,
"fieldofstudy": [
"Medicine",
"Biology"
]
} | Determination of CSF GFAP, CCN5, and vWF Levels Enhances the Diagnostic Accuracy of Clinically Defined MS From Non-MS Patients With CSF Oligoclonal Bands
Fay Probert†, Tianrong Yeo*, Yifan Zhou†, Megan Sealey†, Siddharth Arora†, Jacqueline Palace†, Timothy D. W. Claridge†, Rainer Hillenbrand†, Johanna Oechtering†, Jens Kuhle†, David Leppert† and Daniel C. Anthony
1 Department of Chemistry, University of Oxford, Oxford, United Kingdom, 2 Department of Pharmacology, University of Oxford, Oxford, United Kingdom, 3 Department of Neurology, National Neuroscience Institute, Singapore, Singapore, 4 Duke-National University of Singapore (NUS) Medical School, Singapore, Singapore, 5 Translational Stem Cell Biology Branch, National Institutes of Health, Bethesda, MD, United States, 6 Wellcome Medical Research Council (MRC) Trust Stem Cell Institute, University of Cambridge, Cambridge, United Kingdom, 7 Department of Mathematics, University of Oxford, Oxford, United Kingdom, 8 Nuffield Department of Clinical Neurosciences, John Radcliffe Hospital, University of Oxford, Oxford, United Kingdom, 9 Biomarker Development, Novartis Pharma AG, Basel, Switzerland, 10 Neurologic Clinic and Policlinic, Multiple Sclerosis (MS) Center and Research Center for Clinical Neuroimmunology and Neuroscience Basel (RC2NB), Departments of Clinical Research and Biomedicine, University Hospital Basel, University of Basel, Basel, Switzerland
Background: Inclusion of cerebrospinal fluid (CSF) oligoclonal IgG bands (OCGB) in the revised McDonald criteria increases the sensitivity of diagnosis when dissemination in time (DIT) cannot be proven. While OCGB negative patients are unlikely to develop clinically definite (CD) MS, OCGB positivity may lead to an erroneous diagnosis in conditions that present similarly, such as neuromyelitis optica spectrum disorders (NMOSD) or neurosarcoïdosis.
Objective: To identify specific, OCGB-complementary, biomarkers to improve diagnostic accuracy in OCGB positive patients.
Methods: We analysed the CSF metabolome and proteome of CDMS (n=41) and confirmed non-MS patients (n=64) comprising a range of CNS conditions routinely encountered in neurology clinics.
Results: OCGB discriminated between CDMS and non-MS with high sensitivity (85%), but low specificity (67%), as previously described. Machine learning methods revealed CCN5 levels provide greater accuracy, sensitivity, and specificity than OCGB (79%, +5%; 90%, +5%; and 72%, +5% respectively) while glial fibrillary acidic protein (GFAP) identified CDMS with 100% specificity (+33%). A multiomics approach improved accuracy further to 90% (+16%).
Conclusion: The measurement of a few additional CSF biomarkers could be used to complement OCGB and improve the specificity of MS diagnosis when clinical and radiological evidence of DIT is absent.
Keywords: diagnosis, metabolomics (OMICS), multiple sclerosis (MS), proteomics, oligoclonal band
INTRODUCTION
There remains no single pathognomonic clinical feature or diagnostic test for MS. Diagnosis relies on the integration of clinical, imaging, and laboratory findings within the framework of the McDonald criteria. The present criteria recognize the need to demonstrate clinical and/or radiological dissemination in space (DIS) and time (DIT) and to exclude alternative diagnoses. In 2017, revisions to the McDonald criteria introduced the presence of cerebrospinal fluid (CSF)-specific oligoclonal IgG bands (OCGB) as a proxy of DIT to establish MS diagnosis in patients with a typical clinically isolated syndrome (CIS) and with only evidence of DIS. The OCGB appear to arise from CSF-persistent, clonally related B cell populations, which appears, at least partially, independent of B cell targeted therapy (1). While these revisions have increased the sensitivity of the McDonald criteria, to facilitate earlier treatment, they have reduced the specificity for clinically definite MS (CDMS) (2).
While CSF OCGB are present in a high proportion of individuals with CDMS (3), they are also detectable in the CSF of individuals with other autoimmune and infectious diseases of the CNS including syndromes with clinical and radiographic overlap with MS (4, 5), and in other non-inflammatory neurological diseases such as migraine (6). Indeed, migraine, fibromyalgia, psychogenic disorders, and neuromyelitis optica spectrum disorders, have all been highlighted as the true cause of illness in patients misdiagnosed with MS (7–9). A recent meta-analysis gave a sensitivity of 84% and a specificity of 54% when using OCGB to predict conversion to CDMS, with a corresponding positive predictive value of 0.64 and a NPV of 0.77 (10). Therefore, when DIT cannot be proven clinically or radiologically, other biomarkers would be useful to improve the specificity of MS diagnosis.
We have previously shown that we can distinguish between individuals with MS and healthy controls with very high accuracy (100%) using NMR-based metabolomics on blood samples (11). However, except for radiologically isolated syndrome (RIS), it is rare that the subject of an investigation for suspected demyelinating disease is healthy on presentation. Thus, the need to distinguish between individuals with MS and the heterogeneous cross-section of non-MS patients encountered in neurology clinics is the normal challenge. A multi-omics approach on samples CSF combined with cross platform multivariate pattern recognition methods affords an opportunity to identify new biomarkers for MS diagnosis.
Here we sought to discover if a CSF-based multivariate diagnostic test combining proteomics, metabolomics, and OCGB could improve the diagnostic accuracy of MS from the heterogeneous mix of neurological diseases encountered in a clinical setting. Using an integrative approach, we looked for diagnostic biomarkers that are independent of OCGB and highly specific for CDMS. Such biomarkers could be added to the 2017 McDonald criteria, alongside highly sensitive OCGB, to improve diagnostic specificity and the positive predictive value in patients where DIT cannot be proven clinically or radiologically. We report a multivariate model which out-performs, not only OCGB status, but all identified metabolite and protein biomarkers when measured in isolation. All models were validated on independent test data using 10-fold cross validation and permutation testing to ensure significance was not a result of the model overfitting the data.
MATERIALS AND METHODS
Study Participants
CSF samples from 41 patients with CDMS (Poser criteria (12)) and 64 patients with non-MS diagnoses (with spinal taps performed as part of their diagnostic investigations) were collected at the Department of Neurology, University Hospital Basel to identify biomarkers specific for CDMS that are independent of OCGB status. Those with a non-MS diagnosis were chosen to represent the heterogenous range of neurological conditions observed in a typical generalist neurology clinic including epilepsy, functional neurological disorders, primary headache syndromes, inflammatory neurological conditions, and infections amongst others (Table 1). In summary, the confirmed diagnoses of the non-MS cohort were: primary headache disorder [n=13], functional neurological disorder [n=12], sensory disturbance [n=8], epilepsy [n=5], polynuropathy [n=5], motor paresis [n=3], neuroinfection [n=3], meningitis [n=2], movement disorder [n=2], myasthenia gravis [n=2], polyradiculitis [n=2], white matter lesions/leukoencephalopathy [n=2], gait disorder [n=1], neuralgic amyotrophy [n=1], OCGB+ve normal pressure hydrocephalus [n=1], systemic lupus erythematosus [n=1], visual disturbance [n=1].
Standard Protocol Approvals, Registrations, and Patient Consents
Written informed consent was obtained from all patients according to the Declaration of Helsinki. Ethical approval was obtained by the local ethics committee (University Hospital Basel ethics # 332/06).
CSF Sample Collection
CSF samples were centrifuged at 400 × g for 10 minutes at room temperature, and the cell-free supernatant stored at -80°C within 2 hours of collection according to a consensus protocol (13). Standard laboratory procedures measured leukocytes [cells/mm3] and total protein concentration [mg/dL]. CSF/serum albumin was calculated using concurrent serum samples. Detection of OCGB was by isoelectric focusing on agarose gel and subsequent immunoblotting using IgG-specific antibody staining (14). Patterns two or three were considered OCGB positive (15).
NMR Spectroscopy and Data Processing for Metabolomics Analysis
100 μL of CSF was diluted with 450 μL of 75 mM sodium phosphate buffer D2O (pH 7.4) containing 1 mM maleic acid as an internal reference standard. Samples were centrifuged at 3,000 x g for 5 minutes before transferring to a 5-mm NMR tube. NMR spectra were acquired at 310 K using a 700-MHz Bruker AVIII spectrometer operating at 16.4 T equipped with a 1H [13C/15N] TCI cryoprobe (Department of Chemistry, University of Oxford) and processed as previously described (16).
NMR metabolite measures were converted to absolute concentrations using the internal reference standard (1 mM maleic acid) as previously described (16). To validate the quantification of the metabolites by NMR, the glucose and lactate levels in all CSF samples were measured using a Cobas® 8000 modular analyser (Roche Diagnostics, Switzerland) coupled with the Gluc3 and LAC2 assays, respectively.
Protein Profiling by SomaScan™
Protein biomarker profiling was performed using SomaScan® (SomaLogic, USA), a multiplexed proteomic tool that measures more than 5000 protein analytes that recognise 4,137 distinct human gene targets (17, 18).
Statistical Analysis
Multivariate orthogonal partial least squares discriminant analysis (OPLS-DA) was performed in R software (R foundation for statistical computing, Vienna, Austria) (R Development Core Team, 2019) using in-house R scripts and the ropls package (19). All models were validated on independent data using an external 10-fold cross-validation strategy with repetition coupled with permutation testing as previously described (20). Thus, it should be noted that all models are tested on data that was excluded from model building and that the training and test cohorts never overlap. An in-depth description of this analysis approach can be found in our previous publication (21). Variables responsible for the observed class separation are extracted by inspection of the average variable importance (VIP) scores.
Two-sample t-tests or two-way ANOVA were used for continuous variables and Chi-square tests for categorical variables. A multiple comparisons correction (Bonferroni) was applied throughout. Receiver operator curves (ROC), area under the curve (AUC), 95% confidence intervals, optimal thresholds for diagnosis, and p values (relative to a null distribution ROC curve with AUC = 0.5) were calculated for each discriminatory variable using the pROC package (22). Hierarchical clustering was performed on the discriminatory proteins to identify clusters similarly expressed and correlated proteins using the ‘pheatmap’ and ‘corrplot’ packages. Joint-pathway hypergeometric enrichment analysis was performed on the discriminatory proteins and metabolites identified by the multivariate analysis (described above) using MetaboAnalyst 5.0 [http://metaboanalyst.ca, last accessed 05/05/21]. Degree centrality was used as the topology measure along with the combined queries integration method.
RESULTS
High Sensitivity and Low Specificity of CSF OCGB When Discriminating Between Clinically Definite MS and Other Non-MS Neurological Diseases
CSF samples from 105 patients seen in the neurology clinic were investigated: 41 with a diagnosis of CDMS and 64 with a confirmed non-MS diagnosis. Demographic and clinical chemistry data can be found in Table 1.
Thirty-five of 41 (85%) CDMS patients were positive for OCGB, in the non-MS set this was the case for 21 of 64 patients (32%) (Figure 1A). Thus, while the sensitivity of OCGB status alone is high (85%) the specificity in this cohort is only 67% resulting in an overall accuracy and AUC of 74% and 0.74, respectively.
The CSF Metabolite Profile of CDMS Is Distinct From That of Non-MS Neurological Diseases and Independent of OCGB Positivity
OPLS-DA identified patterns of NMR-detectable metabolites which differ significantly between the CDMS and non-MS cohorts.
**FIGURE 1** (A) Confusion matrix illustrating low specificity of OCGB status for CDMS. (B) Representative OPLS-DA scores plot illustrating discrimination between CDMS (blue square, n=41) and non-MS (white circle, n=64) CSF metabolite profiles. Box plots illustrating CSF concentrations of the discriminatory metabolites identified by the OPLS-DA model for OCGB positive (striped) and OCGB negative (solid color) CDMS (blue) and non-MS (white). The optimal cut-off for each metabolite identified by ROC analysis is represented by a dashed line for (C) myo-inositol, (D) isoleucine, (E) leucine, (F) glutamine, (G) creatine, (H) creatinine, (I) citrate, and (J) glucose. Bonferroni corrected 2-way ANOVA p-values for disease (MS v. non-MS) effect less than 0.05, and 0.001 are represented by *, and *** respectively. +ve; oligoclonal band positive, -ve; oligoclonal band negative.
independently of OCGB status, age, and non-MS diagnosis (Figure S1) Models identified CDMS and non-MS patients in the test data with accuracy, sensitivity, and specificity of 70 ± 4%, 73 ± 6%, and 70 ± 4% respectively (Figure 1B) and permutation testing confirmed that these values are significantly higher than expected from random chance alone (Figure S2).
Inspection of the VIP scores illustrated that leucine, isoleucine, glutamine, citrate, creatine, creatinine, glucose, and myo-inositol are significantly decreased in CDMS (Table 2). Interestingly, all the metabolites identified discriminate between CDMS and the other neurological conditions independently of OCGB status as confirmed by two-way ANOVA in which no significant interaction between diagnosis (CDMS/non-MS) and OCGB status was observed for any of the biomarkers. Furthermore, no metabolite reached significance when comparing the levels in OCGB+ve samples to OCGB-ve and the OPLS-DA was able to separate MS from non-MS irrespective of OCGB status (Figure S1B).
The CSF Proteomics Profile of CDMS Is Distinct From That of Non-MS Neurological Conditions and Independent of OCGB Positivity
Next, we investigated the CSF proteomics profiles of the CDMS and non-MS patients. OPLS-DA was able to discriminate between CDMS and other neurological conditions with accuracy, sensitivity, and specificity of 75 ± 4%, 75 ± 4%, and 77 ± 5% respectively independently of OCGB status, age, and non-MS diagnosis (Figure S3). This is an improvement on the specificity of OCGB alone which is 67%. Once again, the permutation test confirmed these values are significantly higher than expected from random chance alone (Figure S4).
Table 2 | List of significant CSF metabolites identified by OPLS-DA which drive the discrimination between CDMS and Controls ranked from highest to lowest specificity.
| Metabolite | CDMS v non-MS (fold change) | OCGB+ve v. OCGB-ve [p-value] | Interaction [p-value] | AUC | Acc (%) | Sens (%) | Spec (%) | PPV | NPV | TP | FN | TN | FP |
|------------|-----------------------------|-----------------------------|-----------------------|-----|---------|---------|---------|-----|-----|----|----|----|----|
| Myo-inositol | **1*** (0.87) | ns [0.67] | ns [0.41] | 0.74 | 73 | 49 | 89 | 0.74 | 0.73 | 20 | 21 | 57 | 7 |
| Isoleucine | **1*** (0.83) | ns [0.65] | ns [0.08] | 0.71 | 72 | 49 | 88 | 0.71 | 0.73 | 20 | 21 | 56 | 8 |
| Leucine | **1*** (0.81) | ns [0.74] | ns [0.18] | 0.74 | 73 | 61 | 81 | 0.68 | 0.76 | 25 | 16 | 52 | 12 |
| Glutamine | **1*** (0.89) | ns [0.28] | ns [0.75] | 0.76 | 74 | 73 | 75 | 0.65 | 0.61 | 30 | 11 | 48 | 16 |
| OCBG | NA | NA | NA | 0.74 | 74 | 85 | 67 | 0.63 | 0.88 | 35 | 6 | 43 | 21 |
| Creatine | **1*** (0.83) | ns [0.76] | ns [0.96] | 0.75 | 71 | 78 | 67 | 0.6 | 0.83 | 32 | 9 | 43 | 21 |
| Creatinine | **1*** (0.83) | ns [0.25] | ns [0.39] | 0.76 | 71 | 80 | 66 | 0.6 | 0.84 | 33 | 8 | 42 | 22 |
| Citrate | **1*** (0.90) | ns [0.25] | ns [0.55] | 0.61 | 62 | 63 | 61 | 0.51 | 0.72 | 26 | 15 | 39 | 25 |
| Glucose | **1*** (0.95) | ns [0.05] | ns [0.5] | 0.66 | 62 | 71 | 56 | 0.51 | 0.75 | 29 | 12 | 36 | 28 |
2-way ANOVA p-values less than 0.001, and 0.05 following Bonferroni correction for multiple comparisons are represented by ***, and * respectively. ns, not significant; ↓, decrease in CDMS relative to non-MS Control. Diagnostic accuracy of OCGB status is included for comparison. AUC, receiver operator curve area under the curve; PPV, positive predictive value; NPV, negative predictive value; OCGB, CSF oligoclonal bands; PPV, positive predictive value; NPV, negative predictive value; TP, true positive; FN, false negative; FP, false positive; TN, true negative.
NA, not applicable.
Measurement of the CCN5 concentration resulted in a greater AUC (0.85, + 0.11), accuracy (79%, +5%), sensitivity (90%, +5%), and specificity (72%, +5%) than OCGB status alone (Table 3). Glial fibrillary acidic protein (GFAP) (increased in CDMS) results in 100% specificity (+33% relative to OCGB) (Table S2). Following threshold optimisation, the top protein VIPs together clearly separate the non-MS OCGB+ve and the CDMS OCGB+ve groups (Figures 2B–D).
JAK-STAT Pathways Are Upregulated in CDMS Patients While BCAA Degradation and Tyrosine Metabolism Are Down Regulated
Hierarchical clustering reveals four highly correlated groups of proteins within the 40 biomarkers identified which separate the CDMS patients from non-MS independently of OCGB status (Figure 3A). In contrast, fewer significant correlations were observed between the metabolite and protein hits (Figure 3B).
No correlations were observed between any of the metabolite hits and IgG associated proteins, consistent with our earlier observation that the identified discriminatory metabolites are independent of OCGB status.
Integrative metabolomics and proteomics enrichment analysis revealed several potentially perturbed pathways in the CDMS group (Figure 4A). Of note, upregulation of the JAK-STAT and glycolysis pathways is consistent with an increased inflammatory response and perturbed energy metabolism in the CDMS cohort.
A Combination of CCN5, vWF, and GFAP CSF Levels Discriminates Between OCGB+ve MS and OCGB+ve Non-MS With 91% Accuracy
Finally, we investigated if a multivariate diagnostic test combining proteomics, metabolomics, and OCGB measures could improve the diagnosis of MS. A combination of CCN5, vWF, GFAP, and
TABLE 3 | List of the top 14 protein biomarkers identified by OPLS-DA which outperform OCGB for discriminating between CDMS and Controls ranked from highest to lowest AUC.
| Uniprot # | Gene | Protein | CDMS v Non-MS (fold change) | OCGB-ve v OCGB-ve [p-value] |
|----------|---------------|---------------------------------------------------|-----------------------------|-----------------------------|
| | | | Interaction [p-value] | AUC (%) | Sens (%) | Spec (%) | PPV (%) | NPV (%) | TP (%) | FN (%) | FP (%) | TN (%) |
| O76076 | CCN5 | CCN family member 5 (WISP-2) | ↓*** (0.61) | ns [3.18] | ns [4.72] | 0.85 | 79 | 90 | 72 | 67 | 92 | 37 | 4 | 18 | 46 |
| O76996 | CDDC80 | Cleaved-coil domain-containing protein 80 | ↓*** (0.79) | ns [30.58] | ns [3.21] | 0.83 | 76 | 71 | 80 | 69 | 81 | 29 | 12 | 13 | 51 |
| Q6B821 | IGFL4 | Insulin growth factor-like family member 4 | ns (1.57) | ns [0.1] | ns [27.79] | 0.81 | 80 | 73 | 84 | 75 | 83 | 30 | 11 | 10 | 54 |
| O96531 | NTN1 | Nectin-1 | ↓*** (0.86) | ns [32.8] | ns [23.25] | 0.81 | 73 | 85 | 66 | 61 | 88 | 35 | 6 | 22 | 42 |
| P01602 | IKGV1-5 | Immunoglobulin kappa variable 1-5 | ns (1.24) | ns [0.91] | ns [39.39] | 0.8 | 81 | 68 | 89 | 80 | 81 | 28 | 13 | 7 | 57 |
| P01857 | IGHG1 | Immunoglobulin heavy constant gamma 1 | ↑*** (1.79) | *** [-0.001] | ns [14.77] | 0.77 | 77 | 76 | 78 | 69 | 83 | 31 | 10 | 14 | 50 |
| Q9NPF7 | IL23A | Interleukin-23 subunit alpha | ns (1.51) | ** [0.006] | ns [14.39] | 0.77 | 78 | 80 | 77 | 69 | 86 | 33 | 8 | 15 | 49 |
| Q6UX9 | NPNT | Nephrin | ↓*** (0.82) | ns [30.61] | ns [34.37] | 0.77 | 73 | 76 | 72 | 63 | 82 | 31 | 10 | 18 | 46 |
| P04275 | VWF | von Willebrand factor (VWF) | ↓*** (0.63) | ns [0.45] | ns [6.22] | 0.77 | 70 | 88 | 59 | 58 | 88 | 36 | 5 | 26 | 38 |
| Q9UBT3 | DKK4 | Dickkopf-related protein 4 | ↑*** (0.59) | ns [37.37] | ns [13.99] | 0.76 | 70 | 90 | 56 | 57 | 90 | 37 | 4 | 28 | 36 |
| Q9BS26 | ERP44 | Endoplasmic reticulum resident protein 44 | ↓** (0.83) | ns [1.01] | ns [0.17] | 0.75 | 73 | 83 | 67 | 62 | 86 | 34 | 7 | 21 | 43 |
| P21860 | ERBB3 | Receptor tyrosine-protein kinase erbB-3 | ↓** (0.81) | ns [11.22] | ns [22.35] | 0.75 | 71 | 78 | 67 | 60 | 83 | 32 | 9 | 21 | 43 |
| Q9BQ41 | SCST | Sclerostin | ↓ (0.78) | ns [15.21] | ns [14.8] | 0.75 | 68 | 80 | 59 | 56 | 83 | 33 | 8 | 26 | 38 |
| O75828 | CBR3 | NADPH-dependent carbonyl reductase 3 | ↑ (0.71) | ns [3.75] | ns [2.89] | 0.74 | 72 | 66 | 77 | 64 | 78 | 27 | 14 | 15 | 49 |
| NA | NA | OCGB | NA | NA | NA | NA | 0.74 | 74 | 85 | 67 | 63 | 88 | 35 | 6 | 43 | 21 |
2-way ANOVA p-values less than 0.001, 0.01, and 0.05 following Bonferroni correction for multiple comparisons are represented by ***, **, and * respectively. ns, not significant: ↓ decrease in CDMS CSF relative to Control, ↑, increase in CDMS CSF relative to non-MS control. AUC, receiver operator curve area under the curve; PPV, positive predictive value; NPV, negative predictive value; TP, true positive; FN, false negative; FP, false positive; TN, true negative.
OGB status provided the greatest overall accuracy when discriminating between CDMS and non-MS CSF samples (Figures S5A–D). Indeed, OPLS-DA analysis using only these 4 variables resulted in an accuracy, sensitivity, and specificity or 91%, 89%, and 92% respectively on independent data which is significantly higher than the accuracy, sensitivity, and specificity of OCGB alone (+16%, +4%, and +25% respectively). The multivariate model out-performed, not only OCGB status, but all identified metabolite and protein biomarkers when measured in isolation (Figure 4B). For the OCGB-ve patients, the multivariate model correctly identified one (15%) of OCGB-ve CDMS patients as MS while all 43 (100%) OCGB-ve non-MS patients remained correctly identified as non-MS. However, the greatest clinical utility of this approach is in the identification of non-MS patients who test positive for OCGB (improved PPV). Indeed, the model correctly identified 16 (76%) OCGB+ve non-MS patients (Figure 4C) and 35 (100%) of OCGB+ve CDMS patients. This illustrates that the addition of the identified proteins to complement the use of OCGB status, within the context of the McDonald criteria, could greatly improve specificity and PPV without sacrificing sensitivity or NPV in the instance when DIT cannot be demonstrated radiologically or clinically, although this remains to be confirmed in a cohort of early MS patients. Interestingly, vWF may be substituted for either myo-inositol or TMEM40 in the multi-omics model with no significant drop in accuracy (Table S3).
DISCUSSION
Here, we have identified a small number of independent biomarkers, using feature selection coupled with a pattern recognition multivariate analysis framework and multimomics data, that may be used to support a diagnosis of MS with an accuracy of 90% (91% in the OCGB+ve patients and 90% in the OCGB-ve patients). The combination of CCN5, VWF, GFAP, and OCGB provides a significant increase in PPV; the model is able to accurately discriminate between OCGB+ve CDMS and OCGB+ve non-MS neurological conditions. While this combination yielded the highest accuracy, it is of note that other combinations could produce similar accuracies – for example, the substitution of myo-inositol for vWF. In each case, the levels of the newly identified biomarkers – CCN5, GFAP, and vWF – were independent of OCGB levels and outperformed OCGB alone.
CCN5 (previously known as WISP-2), which was decreased in the CSF of CDMS patients, is a member of the connective tissue growth factor/cysteine-rich 61/nephroblastoma overexpressed (CCN) family which play important roles in cell growth, adhesion, and migration. However, the function of CCN5 is not well understood. In an EAE model of MS, CCN5 mRNA was found to be significantly upregulated in spinal cord tissue, but as the tissue was collected in end-stage disease, its relevance to early-stage disease in MS is questionable (23).
Interestingly, a significant positive correlation has been reported between levels of the related protein CCN3 in matched plasma and CSF of MS patients, which was absent in a comparator group of idiopathic intracranial hypertension patients (24). CCN3 plays various roles in the immune system and CCN5 and CCN3 have been reported to have antagonistic effects (25). CCN3 is a regulator of cytokine expression in both the periphery and CNS (26), where it can promote astrocyte activation (27), but it is not clear what effect CCN5 has on these processes.
The connection between the biology of multiple sclerosis and vWF, which was decreased in the CSF of CDMS patients compared to non-MS, is less opaque; vWF and/or Weibel-Palade bodies negatively regulate BBB permeability changes in MS-like lesions (28). It is not clear why the levels should be reduced in the CSF of MS patients, but one might speculate that increased release from endothelial cells into the blood might lead to a reduction in the CSF.
For GFAP, which was increased in the CDMS group, the connection with MS pathogenesis is now well established. Here, GFAP provided 100% specificity (+33% relative to OCBG), which suggests that measurement of this protein biomarker could be particularly useful in diagnosing MS in OCBG positive patients. GFAP is highly specific for astrocytic damage, and, as astrogliosis is a central component in MS pathogenesis, it is perhaps unsurprising that this protein should be highlighted in this analysis. However, it is important to note that other conditions have also been shown to be associated increase GFAP levels in the CSF. During acute NMO exacerbations, for example, CSF GFAP levels are significantly elevated (29) and after trauma (30). GFAP levels also increase with age, but, following an adjustment for age, MS patients have been shown to have higher GFAP levels compared with controls, and the adjusted levels correlate with neurological disability and disease progression (31). In studies on early MS, it has been reported that there are no significant differences in CSF GFAP levels between CIS and RRMS, but that GFAP does seem to be a good biomarker for highly active CNS inflammation in patients with CIS and RRMS (32). This would appear to highlight the need for a small panel of biomarkers rather than relying on one or another to aid in a diagnosis.
 | Correlation plots. (A) Protein-protein correlations and (B) metabolite-protein correlations. Correlations with self (diagonal) represented in grey. Significant Pearson’s R correlations prior to multiple comparison correction are displayed below the diagonal while those which remain significant following correction for multiple comparisons are above the diagonal.
Myo-inositol is a component of all cell membranes and oligodendrocyte myelin and is involved in intracellular signalling in many CNS cell populations. It has been found to be increased in CSF in RRMS/CIS patients compared to healthy controls (33, 34), and in the brain of animals with EAE (35). The reduction in the CSF observed here could, therefore, reflect the sum difference between the anabolic and catabolic processes in MS versus other neurological disease where a relative loss in MS is present. Interestingly, myo-inositol levels can be used to accurately discriminate between RRMS and antibody mediated-NMOSD (36), where the further reduction in myo-inositol in antibody-mediated NMOSD may reflect demyelination and increased loss of astrocyte membrane. Hierarchical clustering revealed four highly correlated groups of proteins, but these did not fit with any known disease associated clusters. Pathway analysis revealed increased JAK-STAT signalling and glycolysis pathways in the MS cohort. The JAK-STAT pathway is activated by many cytokines, and its activation is key in almost all immune responses. The increase in glycolysis would be consistent with increased energy metabolism associated with inflammation.
For patients who are incorrectly diagnosed with MS, 50% have been found to carry the misdiagnosis for at least 3 years, and more than 5% were found to be misdiagnosed for over 20 years (37). This can lead to the administration of inappropriate and potentially harmful disease modifying therapies. Our results have shown how the inclusion of a small number of additional laboratory tests complement the high sensitivity of OCGB by increasing specificity and PPV and, thus, could significantly improve confidence in an MS diagnosis when DIT cannot be confirmed either radiologically or clinically. NMR metabolomics is a cheap and rapid analysis method, requiring minimal sample preparation and with the advantage that a host of additional small molecules can be quantified in the same analysis. Indeed, we have shown that NMR metabolomics is able to identify relapse (38), predict conversion (16), and diagnose progression (39) in MS and so, in future, it may be possible to apply multiple tests to a single sample. Future work...
will develop a chip-based assay to measure only the top biomarkers identified here in the hopes of improving translatability of this method. However, as CSF is routinely collected as part of the 2017 McDonald criteria, the addition of a small number of biomarker measurements to complement and improve the specificity of the already measured OCGB would be of benefit in a clinical setting. One limitation of this study might be considered to be that we used a cohort from one site which was limited in size (n=105). It is clear that a further prospective study in a larger independent cohort, collected across multiple centres, of early MS/clinically isolated syndrome patients, focused on the principal metabolite and protein biomarkers identified here, is now warranted. Should the results be conserved in a larger and broad population, the use of these markers in addition to OCGB could provide a valuable new diagnostic test for the presence of MS.
DATA AVAILABILITY STATEMENT
The datasets presented in this article are not readily available because they contain identifiable information from human subjects that cannot be shared in open access repositories for legal reasons. Anonymized data will be shared upon request from any qualified investigator. Requests should be directed to the corresponding authors.
ETHICS STATEMENT
The studies involving human participants were reviewed and approved by University Hospital Basel local ethics committee. The patients/participants provided their written informed consent to participate in this study.
AUTHOR CONTRIBUTIONS
FP was involved in the design/conception of the study, performed the NMR data acquisition, developed in house R scripts, performed and interpreted the analysis of the results, and drafted the manuscript. TY was involved in the design/conception of the study, preparation of samples for NMR data acquisition, interpretation of results, and manuscript preparation. JK was involved in the design/conception of the study, was involved in clinical data acquisition, interpretation of results, and manuscript preparation. DL was involved in the design/conception of the study, was involved in clinical data acquisition, interpretation of results, and manuscript preparation. DA was involved in the design/conception of the study, was involved in clinical data acquisition, interpretation of results, and was a major contributor to writing the manuscript. All authors contributed to the article and approved the submitted version.
REFERENCES
1. Greenfield AL, Danekar R, Ramesh A, Wu H, Laurent S, Harkin M, et al. Longitudinally Persistent Cerebrospinal Fluid B Cells can Resist Treatment in Multiple Sclerosis. *JCI Insight* (2019) 4:e126599. doi: 10.1172/jci.insight.126599
2. van der Vaart de Vries RM, Mescheriakova JY, Wong YYM, Runia TF, Jafari N, Samijn JP, et al. Application of the 2017 Revised McDonald Criteria for Multiple Sclerosis to Patients With A Typical Clinically Isolated Syndrome. *JAMA Neurol* (2018) 75:1392–8. doi: 10.1001/jamaneurol.2018.2160
3. Schwenkenbecher P, Sarkidi A, Wurster U, Bronzilik P, Suhs KW, Raab P, et al. McDonald Criteria 2010 and 2005 Compared: Persistence of High Oligoclonal Band Prevalence Despite Almost Doubled Diagnostic Sensitivity. *Int J Mol Sci* (2016) 17:1592–602. doi: 10.3390/ijms17091592
4. Chu AB, Sever JL, Madden DL, Iivanainen M, Leon M, Wallen W, et al. Oligoclonal IgG Bands in Cerebrospinal Fluid in Various Neurological Diseases. *Ann Neurol* (1983) 13:434–9. doi: 10.1002/ana.410130410
5. Hegen H, Zinganell A, Auer M, Deisenhammer F. The Clinical Significance of Single or Double Bands in Cerebrospinal Fluid Isoelectric Focusing. A Retrospective Study and Systematic Review. *PlOS One* (2019) 14:e0215410. doi: 10.1371/journal.pone.0215410
6. Pannewitz-Makaj K, Wurster U, Jendretzky KF, Gingele S, Suhs KW, Stangel M, et al. Evidence of Oligoclonal Bands Does Not Exclude Non-Inflammatory Neurological Diseases. *Diagnostics (Basel)* (2020) 11:1–13. doi: 10.3390/diagnostics11010037
7. Solomon AJ, Bourdette DN, Cross AH, Applebee A, Skild PM, Howard DB, et al. The Contemporary Spectrum of Multiple Sclerosis Misdiagnosis: A Multicenter Study. *Neurology* (2016) 87:1393–9. doi: 10.1212/WNL.0000000000003152
8. Solomon AJ, Naismith RT and Cross AH. Misdiagnosis of Multiple Sclerosis: Impact of the 2017 McDonald Criteria on Clinical Practice. *Neurology* (2019) 92:26–33. doi: 10.1212/WNL.0000000000006383
9. Carmosino MJ, Brousseau KM, Arciniegas DB, Corboy JR. Initial Evaluations for Multiple Sclerosis in a University Multiple Sclerosis Center: Outcomes and
Role of Magnetic Resonance Imaging in Referral. Arch Neurol (2005) 62:585–90. doi: 10.1001/archneur.62.5.485
10. Robson R, Ramagopalan S, Davis A, Giovannoni G. Cerebrospinal Fluid Oligoclonal Bands in Multiple Sclerosis and Clinically Isolated Syndromes: A Meta-Analysis of Prevalence, Prognosis and Effect of Latent. J Neuro Neuropsychiatry (2013) 84:999–14. doi: 10.1136/jnnp-2012-304695
11. Dickens AM, Larkin JR, Griffin JL, Cavey A, Matthews L, Turner MR, et al. A Type 2 Biomarker Separates Relapsing-Remitting From Secondary Progressive Multiple Sclerosis. Neurology (2014) 83:4192–9. doi: 10.1212/2.41369.0000000000000090
12. Poser CM, Paty DW, Scheinberg I, McDonald WI, Davis FA, Ebers GC, et al. New Diagnostic Criteria for Multiple Sclerosis: Guidelines for Research Protocols. Ann Neurol (1983) 13:227–31. doi: 10.1002/ana.41013020
13. Teunissen CE, Petzold A, Bennett JL, Berven FS, Brundin L, Comabella M, et al. A Consensus Protocol for the Standardization of Cerebrospinal Fluid Collection and Biobanking. Neurology (2009) 73:1914–19. doi: 10.1212/2.01360.1318147c2
14. Keir G, Luxton RW and Thompson EL. Isoelectric Focusing of Cerebrospinal Fluid Immunoglobulin G: An Annotated Update. Ann Clin Biochem (1990) 27 (Pt 5):346–43. doi: 10.1097/0000000000000325
15. Andersson M, Alvarez-Cermeño J, Bernardi G, Cogato I, Fredman P, Frederikson J, et al. Cerebrospinal Fluid in the Diagnosis of Multiple Sclerosis: A Consensus Report. J Neurol Neuropsychiatry (1994) 57:889–902. doi: 10.1136/jnnp.57.8.889
16. Probert F, Yeo T, Zhou Y, Sealey M, Arora S, Palace J, et al. Integrative Biochemical, Proteomics and Metabolomics Cerebrospinal Fluid Biomarkers Predict Clinical Conversion to Multiple Sclerosis. Brain Commun (2021) 3: fca084. doi: 10.1093/braincomms/fca084
17. Gold I, Ayers D, Bertino J, Bock C, Bock A, Brody EN, et al. APTamer-Based Multiplexed Proteomics Technology for Biomarker Discovery. PLoS One (2010) 5:e15004. doi: 10.1371/journal.pone.0015004
18. Emnilson V, Ikkov M, Lamb JR, Finkel N, Gudmundsson EF, Pitts R, et al. Co-Regulatory Networks of Human Serum Proteins Link Genetics to Disease. Science (2018) 361:769–73. doi: 10.1126/science.aad3127
19. Thevenot EA, Roux A, Xu Y, Ezan E, Junot C. Analysis of the Human Adult Biochemical, Proteomics and Metabolomics Cerebrospinal Fluid Biomarkers. Frontiers in Immunology | www.frontiersin.org February 2022 | Volume 12 | Article 811351
this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
Copyright © 2022 Probert, Yeo, Zhou, Sealey, Arora, Palace, Claridge, Hillenbrand, Oechtering, Kahle, Leppert and Anthony. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2938,
1
],
[
2938,
9470,
2
],
[
9470,
11893,
3
],
[
11893,
13339,
4
],
[
13339,
17070,
5
],
[
17070,
18776,
6
],
[
18776,
26379,
7
],
[
26379,
29142,
8
],
[
29142,
31397,
9
],
[
31397,
36006,
10
],
[
36006,
38440,
11
],
[
38440,
39121,
12
]
]
} |
0a2ef4a9dda7a1bba89e817aaed282c6ee3e7de4 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 13,
"total-fallback-pages": 0,
"total-input-tokens": 39188,
"total-output-tokens": 13297,
"fieldofstudy": [
"Economics"
]
} | Declining Large-Cardamom Production Systems in the Sikkim Himalayas
Climate Change Impacts, Agroeconomic Potential, and Revival Strategies
Ghanashyam Sharma1*, Uma Partap2, D. R. Dahal1, Durga P. Sharma1, and Eklabya Sharma2
*Corresponding author: [email protected]
1 The Mountain Institute–India, Abhilasha, Development Area, Gangtok, Sikkim 737101, India
2 International Centre for Integrated Mountain Development (ICIMOD), Khumaltar, Lalitpur, GPO Box 3226, Kathmandu, Nepal
(C) 2016 Sharma et al. This open access article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). Please credit the authors and the full source.
Large cardamom (Amomum subulatum) is an economically valuable, ecologically adaptive, and agro-climatically suitable perennial cash crop grown under tree shade in the eastern Himalayas. In Sikkim, India, the focus of this study, large-cardamom production peaked early in the 21st century, making India the largest producer in the world, but dropped sharply after 2004; Nepal is now the largest producer. This crop is an important part of the local economy, contributing on average 29.2% of the income of households participating in this study. Farmers and extension agencies have worked to reverse its decline since 2007, and thus, there is a steady increase in production and production area. After reviewing the literature, we carried out extensive field research in 6 locations in Sikkim in 2011–2013 to investigate the causes of this decline and measures being undertaken to reverse it, using a combination of rapid rural appraisal, participatory rural appraisal, structured questionnaire, and field sampling techniques. Study participants attributed the decline in large-cardamom farming to 4 broad types of drivers: biological, socioeconomic, institutional/governance-related, and environmental/climate-change-related. Altered seasons, erratic or scanty rainfall, prolonged dry spells, temperature increase, soil moisture loss, and increasing instances of diseases and pests were prominent factors of climate change in the study region. Multistakeholder analysis revealed that development and implementation of people-centered policy that duly recognizes local knowledge, development of disease-free planting materials, training, subsidies, and improved irrigation facilities are central to improving cardamom farming and building socioeconomic and ecological resilience.
Keywords: Large cardamom; climate change impacts; household economy; revival strategy; Sikkim Himalayas.
Introduction
Large cardamom (Amomum subulatum) is the most important perennial cash crop in the eastern Himalayan region (Sharma et al 2000). It is used as a spice or condiment, flavoring agent, and preventive and curative agent for sore throats, lung congestion, digestive disorders, and pulmonary tuberculosis in Unani and Ayurvedic medicine (Sharma et al 2009). This crop is believed to have been first domesticated by the indigenous Lepcha tribe and then by other communities such as the Bhutias and Nepalis of Sikkim, and was later passed on to the neighboring district of Darjeeling in India and to southern Bhutan and eastern Nepal (Sharma et al 2000; Sharma et al 2007). The agroclimatic range of large cardamom farming is similar to the altitudinal range of Himalayan alder (Alnus nepalensis) and mixed agroforestry species, which are widely used as a shade trees (Sharma et al 1994). India is now the second largest producer and the largest exporter of large cardamom, contributing about 37% of the world’s production, while Nepal is the world’s largest producer with a share of more than 53% (Sharma et al 2009; Singh and Pothula 2013; Subedi et al 2014). Sikkim contributes up to 88% of India’s production of large cardamom. The cash income earned from this crop in Sikkim increased from US$ 1.9 million in 1975 to US$ 13.8 million in 2005 and as high as US$ 50 million in 2010 (Sharma et al 2009; Sharma and Acharya 2013; Partap et al 2014). Sikkim is also fast becoming known in India for its organic farming, and organic large cardamom has a potentially strong international market (FSADD and HCDD 2012). For more than a decade now (2004 onwards), however, more than 60% of the cardamom plantations in Sikkim have become barely productive, resulting in a tremendous decline in cultivated area as well as total production in the state (DESME 2002, 2005, 2006, 2010; HCCDD 2010). The income of marginal and cardamom-dependent farmers in the eastern Himalayan
region has dramatically declined, jeopardizing their livelihoods (Srinivasa 2006; Sharma et al 2009; Singh and Pothula 2013). This decline is an example of the long-term environmental and ecological implications of farming that relies on a single cash crop, the impact on farmers’ livelihoods, and the unprecedented challenges for sustaining and improving production capacity.
This study had 4 goals: (1) investigate the current status of large-cardamom farming and its contribution to the livelihoods of marginal farmers, (2) assess local actors’ perceptions of the decline in large-cardamom production area and productivity, (3) analyze crop cycle, adaptive management, and revival strategy for cardamom-based farming systems, and (4) analyze the challenges and opportunities emerging from different drivers of change.
**Materials and methods**
**Study sites**
The households that participated in the study belong to 6 study sites based on their dependence on large cardamom-based traditional farming systems (Figure 1; Table 1). Of the 88 households participating in the study, 22 were at Sumik-Khamdong, 14 at Sang-Martam, and 14 at Dhanbari-Tumin, in the East District of Sikkim; 14 at Lingee-Sokpay in the South District; and 12 each at Hee-Pechreak and Hee-Martam in the West District. These sites are situated between 1000–2200 masl and have large cardamom as their principal cash crop. They are located within larger cardamom-growing areas (also shown in Figure 1) that range in elevation from 500 to 2300 m; agroclimatic conditions vary with elevation.
Farmers have, in addition to large-cardamom farming, adopted innovative intercropping of farm trees (fodder, fuelwood, timber, or fruit trees), other fodder crops, and beans, and in some areas grow a wider range of crops (pulses, oilseeds, soybeans, yams, and vegetables), multipurpose agroforestry species, and medicinal plants (Sharma et al 2016). Annual rainfall averages 3500 mm across the study sites, 2000–4000 mm in the higher elevations, and 1000–2000 mm in the lower elevations (Rahman et al 2012; Seetharaman 2012; També et al 2012). The study sites are mostly southwest facing; slopes range from 10 to 30°. The upper reaches of Dhanbari-Tumin, Sumik-Khamdong, and Lingee-Sokpay experience occasional snowfall, hailstorms, and frost during winter.
**Methods**
We carried out an extensive secondary literature survey, and data on the 6 study sites were pooled to estimate the large-cardamom plantation area, production, and productivity (DESME 2002, 2005, 2006, 2010; HCCDD 2010).
A multistage, stratified sampling technique was followed to select the sample households in the 6 study sites. A total of 88 households were selected for detailed study during 2011–2013, representing different ethnic communities, landholding sizes (1.5 to 3 ha), social and economic relationships, and farming practices. The primary livelihood source for all households was traditional large-cardamom-based agriculture. The households were surveyed using structured questionnaires to investigate the range of livelihood options associated with large-cardamom-based farming systems and the contribution of each option to household income, using rapid rural appraisal to obtain scientific evidence through quicker and more cost-effective qualitative techniques that could not be gathered by quantitative research, and participatory rural appraisal for data-gathering by way of participatory mapping, visual sharing techniques, and other self-determined community-based methods (Chambers and Blackburn 1996). Focus group discussions were used together with extensive field sampling and observation to document climate change impacts, traditional management practices, and adaptation strategies for the revival of the system.
Furthermore, 20 key informants—progressive cardamom farmers and panchayat (elected representatives of the village, self-government) members from other cardamom-growing areas in Sikkim, academics, large-cardamom scientists, extension and development workers, researchers, and professionals at the policy and planning level—were interviewed regarding their perceptions of the changes in large-cardamom plantation area, total production, and yield per hectare and climate change impacts, as well as existing extension services and the challenges and opportunities associated with cardamom farming.
During participatory rural appraisal/rapid rural appraisal and focus group discussions, respondents were also asked about the incidence of viral diseases (including chirkey, furkey, pahenley, and rhizome rot) and dry spells. Plants infected by furkey (bushy dwarf) disease have shorter stems and the spikes become stunted, crop production declines rapidly, and the whole cardamom bush dies within 2 to 3 years. A plant infected by chirkey (mosaic streak) produces brownish spots all over the leaves, and in time the entire leaves become brown and eventually dry out. Pahenley is a Phoma leaf spot disease that rapidly spreads during continuous rain, resulting in severe damage of cardamom bushes. Long dry spells were defined as periods without rainfall lasting from November through April.
Qualitative information collected in the surveys was complemented with information collected during the literature review. Information on competitive marketing and auctions was obtained from the North Eastern Regional Agricultural Marketing Cooperation in Sikkim. Data were collected on the various household income options and the amount of income they provided, demographic features, literacy, ethnic community composition, education level, occupational structure,
landholdings, cropping patterns, and crop yield. The total yield was converted into monetary value based on current market rates. Each household’s total annual cash income from other sources—such as the Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA), a 100-day employment scheme of the Government of India (MGNREGA 2005), and other off-farm employment—was also recorded.
Data analysis
We analyzed the household livelihood options based on empirical socioeconomic, biophysical, and institutional data. The average landholding of the cardamom growers was calculated by adding the total landholdings of the respondents and dividing the sum by the number of households. We used Microsoft Excel for data computation and SPSS version 10 to conduct analysis of variance and regression analysis. The study sites did not vary much with regard to management practices, climate change indicators, diseases, and pest infestations, and thus data were pooled, extrapolated, and interpreted for these factors.
Results
Large-cardamom area and yields
According to the Spices Board of India and the Horticulture and Cash Crops Development Department Government of Sikkim, the total area under large cardamom in Sikkim in 1997 was 26,734 ha. The plantation area is the total plantation area under large cardamom, not all of which gives yield. Production area is the actual area that provides an agronomic yield on a yearly basis. The actual cardamom production area in 1999 was only 19,912 ha, but increased to 20,023, 21,797, and 22,714 ha in 2001, 2002, and 2003, respectively. As a consequence of long dry spells and disease infestations during 2004–2007, the production area and yield decreased each year, with an especially sharp drop (37%) to 12,500 ha from 2006 to 2007 (Figure 2). Revival strategies were then initiated by improving the management of the farms: application of manures before flowering and after harvesting, irrigation during dry winter months, uprooting infected plants, and manual management of pests and diseases followed by application of biopesticides. Farmers planted cardamom in new fields, leaving the old plantations fallow, while the Sikkim Government Horticulture and Cash Crops Development Department and Spices Board provided them with incentives for reviving large cardamom. This led to a gradual increase in production area and yield in the next 6 years (Figure 2).
Total production of cardamom in Sikkim has fluctuated (Figure 2). In 2002, Sikkim produced a record large-cardamom yield (almost 5227 metric tonnes [t], up from 3710 t in 1999), and thus India became the largest producer worldwide, accounting for about half of the world’s production (SDR 2008). However, with the consistent decline in plantation area after 2004, production declined to 2745 t in 2008, and India dropped to second place, after Nepal. Production gained momentum from 2008 to 2013, owing to increased awareness, farmers’ innovations and motivation, and the government’s provision of extension services. Accordingly, the total large-cardamom production area in 2013 was about 14% greater than in 2007, with an average production of 3312 t per year. The average cardamom production area increased from 12,500 ha in 2007 to 16,010 ha in 2013. Large-cardamom yield was very low (average 148 kg ha$^{-1}$) during the early 1990s, increased a bit later in that decade (average 228 kg ha$^{-1}$), decreased again during 2006–2007 (average 220–225 kg ha$^{-1}$), and showed good improvement during 2012–2013 (with 238 kg ha$^{-1}$) (Figure 2). Linear regression modeling showed a positive correlation between cardamom-yielding area and year for 2007–2013 ($y = 661.64x - 1E+06, R^2 = 0.95, P < 0.001$).
Data sources for rainfall and humidity calculated from Tambe et al 2012, Rahman et al 2012, Seetharam 2012, and field recordings.
| Study area | Altitude (m) | Aspect | Slope (°) | Rainfall (mm) | Humidity (%) | Climate events | Ambient air temperature (°C) |
|------------------|--------------|----------------------|-----------|---------------|--------------|----------------|------------------------------|
| East district | | | | | | | |
| Sumik-Khamdong | 1500–1900 | West, southwest | 15–30 | 1000–2100 | 70–98 | Hailstorms and frost | 10–23 |
| Sang-Martam | 1000–1700 | West, southwest | 10–20 | 1000–1800 | 60–90 | Hailstorms | 13–25 |
| Dhanbali-Tumin | 1700–2200 | Southwest | 10–20 | 2000–4000 | 70–99 | Frost, snowfall, and erratic rainfall | 6–20 |
| South district | | | | | | | |
| Lingee-Sokpay | 1000–2300 | East, southwest | 15–30 | 1000–4000 | 60–99 | Snowfall, hailstorms, and erratic rainfall | 6–23 |
| West district | | | | | | | |
| Hee-Pechreak | 1400–2000 | West, southwest | 15–30 | 1000–2000 | 70–98 | Hailstorms | 10–24 |
| Hee-Martam | 1200–1800 | West, southwest | 15–30 | 1000–2000 | 70–95 | Frost in upper reaches | 14–27 |
TABLE 1 Characteristics of the 6 study sites.
*Data sources for rainfall and humidity calculated from Tambe et al 2012, Rahman et al 2012, Seetharam 2012, and field recordings.
Total production also showed a positive correlation ($P < 0.001$) for data computed from 2007–2013 ($y = 0.287x - 831.49$, $R^2 = 0.94$, $P < 0.001$). This was attributed to the revival strategies that were initiated after 2007 by cardamom farmers and extension agencies. By 2013 the production area had increased to 16,010 ha, with a total production of 3842 t and yield per ha of 240 kg (SOM 2014).
Economic sustainability of household incomes
Of the 6 major household livelihood sources identified, services and remittances contributed the most to household income (Table 2). Services refer to employment in the government sector, nongovernmental organizations, or in pharmaceutical and hydropower companies. Large cardamom was the second largest contributor (generating on average US$ 911 per year per household), followed by livestock. The remaining sources of income were crops, other cash crops, beekeeping, and employment under the Mahatma Gandhi National Rural Employment Guarantee Act, which together contributed only 4% of household income.
Annual household income among large-cardamom farmers participating in the study was highest at Hee-Martam, followed by the adjacent village Hee-Pechreak (Table 2), which is credited to the cultivation of the new disease-tolerant and high-yielding local cultivar *Seremna*, supported by income from services and remittances. The farmers raise nurseries of *Seremna* cultivars and supply good quality planting materials to progressive farmers and to the Horticulture and Cash Crops Development Department and Spices Board at Gangtok, Sikkim, to generate cash income. Another effective cultivar is *Dzongu-golsai*, used in Lingee-Sokpay. The contribution of large cardamom to household income was only 7, 9, and 21% in Dhanbari-Tumin, Sang-Martam, and Sumik-
### Table 2: Average annual household income (in US$) and contribution of different income sources.
| Income source | Study site | % of total |
|------------------------|---------------------|------------|
| | Sumik-Khamd | Sang-Martam | Dhanbari-Tumin | Lingee-Sokpay | Hee-Pechreak | Hee-Martam | |
| Cropsa) | 3.04 | 56.75 | 138.23 | 12.17 | 24.07 | 24.69 | 1.38 |
| Large cardamom | 508.33 | 223.61 | 168.78 | 1318.19 | 1035.49 | 2206.79 | 29.20 |
| Other cash cropsb) | 7.15 | 205.03 | 4.64 | 27.51 | 22.38 | 14.81 | 1.51 |
| Beekeeping | 10.52 | 0.00 | 0.00 | 12.57 | 3.09 | 0.00 | 0.14 |
| Livestock | 298.28 | 301.59 | 461.59 | 203.76 | 193.67 | 854.78 | 12.37 |
| Servicesc) and remittances | 1482.32 | 1583.99 | 1616.93 | 952.38 | 1496.91 | 2793.21 | 53.07 |
| Labor under the MGNREGAd) | 104.38 | 10.32 | 107.94 | 39.68 | 101.85 | 70.68 | 2.33 |
| Total | 2414.02 | 2381.29 | 2498.11 | 2566.26 | 2877.46 | 5964.96 | 100.00 |
a) Rice, maize, wheat, millets, and pulses.
b) Orange, ginger, inflorescence of broom grass, and small cash crops such as fruit and vegetables sold on the market.
c) Services refer to employment in the government sector, nongovernmental organizations, or in pharmaceutical and hydropower companies.
d) MGNREGA = Mahatma Gandhi National Rural Employment Guarantee Act. Income source calculated in Indian rupees and converted into US$, 1 US$ = INR 60.
### Figure 3: Contribution of large cardamom to total income in the study sites.
90%). As many as 85–100% key informants stated that the number of farm laborers) than other farming options (85–90%) were labor intensive (using only 10–15% of the total material and poor management practices. The contribution of services and remittances was high in Hee-Martam (28.1%), remained within the range of 14–16% in Dhanbari-Tumin, Sang-Martam, and Sumik-Khamdong, while it was low in Lingee-Sokpay, with 9.6%.
Based on yield per hectare and 2014 market prices (US$ 24 kg⁻¹), the income from large cardamom can be estimated at US$ 3246–5610 per household. One-way analysis of variance showed significant variation among the range of livelihood options across the 6 study sites ($F_{6,35} = 15.54, P < 0.001$). Large-cardamom farming was less labor intensive (using only 10–15% of the total number of farm laborers) than other farming options (85–90%).
**Local and improved cultivars**
The local farmers in Sikkim grow more than 8 different local cultivars of cardamom developed, tested and practiced in different agroclimatic situations and under different farm management conditions. Of them, 6 varieties are widely grown between 600 and 2300 m throughout Sikkim and some parts of the Darjeeling hills. *Seremna*, a variety developed by the Limboo tribes of Hee-Bermiok, West Sikkim, is a location-specific cultivar that is tolerant to diseases and pests and gives a high yield (300–450 kg ha⁻¹). Another disease-tolerant cultivar that is cultivated widely is *Dzongu-golsai*, developed by the Lepchas of Dzongu, North Sikkim. The local cultivar *Bhurlangey* is best suited to the middle and higher altitudes (1500–2000 m) and has a high market value due to its high productivity, large capsule size, good aroma, and characteristic and marketable maroon color. The Indian Cardamom Research Institute of the Spices Board in Gangtok identified the potentially disease-tolerant varieties *Sikkim I* and *Sikkim II* in 2000 on farmers’ cardamom farms, but they have not yet scientifically confirmed that these varieties are disease and pest resistant as well as high yielding, and farmers have not yet tested them.
**Perceived drivers of cardamom crop decline**
Factors that study participants perceived as driving the decline of large-cardamom farming could be grouped into 4 main categories: environmental or climate-related, biological, socioeconomic, and institutional or governance-related (Table 3). The study looked at views expressed by both key informants and cardamom growers. As many as 85–100% key informants stated that extreme heat or cold, erratic/un timely rainfall, reduction in temporal spread of rainfall, shift in seasons, long dry spells lasting until flowering, drying springs, and temperature rise were the factors responsible for decline of cardamom. Interestingly, almost 100% cardamom growers consider drying springs or streams in and around plantations as the main factor for decline while 53% further said that it is due to erratic/un timely rainfall, and 63% argued that it was due to long dry spells (Table 3).
Similarly mixed observations were recorded for biological drivers of change. The cardamom growers were very specific regarding factors based on their farm experiences: 77–94% observed emergence of diseases, pests, and insects, decreased number of pollinators, and inadequate pollination due to climatic variations (erratic rainfall) as the major reasons for decline, while 85–100% of key informants consider all of these as the cause of decline. Around 80–100% of key informants perceived weak shade management, absence of good planting material, old and exhausted farms, low soil fertility, and loose soils as contributing to crop decline. In contrast, the majority of cardamom growers (60–89%) did not consider these as major reasons for the decline. Both key informants (100%) and cardamom growers (77–94%) considered diseases and pests and decrease in pollinators as the main reasons for plantation decline. As many as 55–95% key informants said that low soil fertility, loose soil, old farms, weak shade management, and lack of disease-free planting material contributed to the decline, while 95–98% of growers did not consider these reasons for plantation decline. Sixty to 85% of key informants considered socioeconomic factors important in the decline of cardamom farms. In contrast, 84–96% of cardamom growers did not consider socioeconomic factors—family fragmentation, low productivity on farms, and weak farm management—the drivers of decline.
Sixty-five percent of growers considered lack of irrigation facilities a major cause of decline. Fifty-two percent of growers commented on the lack of appropriate policy support, 69% pointed to lack of extension services, and 89% to the lack of training, disease management, and irrigation facilities. Around 65–75% of key informants said that there were issues related to governance that needed to be taken into consideration. Of the 30 key indicators of climate change identified, the key informants and cardamom growers had contradictory responses for 21 factors and provided similar responses on 9 factors.
**Diseases and pests**
Crop development, plantation management, pest or disease outbreaks, and climate-change–related challenges for cardamom farming are presented in Table 4. Farmers have innovated several climate-smart adaptive measures that increase yield and improve performance of cardamom growth. Six prominent diseases were found to be prevalent in cardamom bushes: leaf streak (*Pestalotiopsis* sp.), fungal disease (*Colletotrichum gloeoporioides*), leaf spot...
TABLE 3 Respondents’ perceptions of the principal drivers of the decline in large-cardamom farming.
| Type of driver | Specific driver | Mentioned by study participants |
|---------------------------------|--------------------------------------------------------------------------------|---------------------------------|
| | | Key informants \((n = 20)\) | Cardamom growers \((n = 88)\) |
| Environmental or climate-related| Regional Erratic/untimely rainfall | 19 (95%) | 47 (53%) |
| | Reduction in even temporal distribution of rainfall | 19 (95%) | 11 (13%) |
| | Long dry spells during winter, lasting until flowering | 20 (100%) | 56 (64%) |
| | Temperature rise | 20 (100%) | 30 (34%) |
| | Air pollution | 13 (65%) | 6 (7%) |
| | Frost or hail | 12 (60%) | 17 (19%) |
| | Snowfall | 11 (55%) | 10 (11%) |
| | Shift in seasons | 19 (95%) | 11 (13%) |
| | Extreme heat or cold | 17 (85%) | 6 (7%) |
| | Drying springs or streams in and around plantations | 19 (95%) | 88 (100%) |
| Biological | *Chirkey, furkey, fungal blight, and pahenley* | 20 (100%) | 83 (94%) |
| | Insect pests | 20 (100%) | 72 (82%) |
| | Mammalian pests | 16 (80%) | 2 (2%) |
| | Low soil nutrient content or fertility | 19 (95%) | 4 (5%) |
| | Loose soil due to alder tree roots | 11 (55%) | 2 (2%) |
| | Decreased number of pollinators (due to climate change impacts) | 19 (95%) | 68 (77%) |
| | Old and nutrient-exhausted farms | 17 (85%) | 7 (8%) |
| | Inadequate pollination | 17 (85%) | 56 (64%) |
| | Lack of appropriate shade management | 18 (90%) | 4 (5%) |
| | Lack of disease-free planting materials | 16 (80%) | 17 (19%) |
| Socioeconomic | Weak farm management | 17 (85%) | 14 (16%) |
| | Fragmentation of land ownership | 12 (60%) | 5 (6%) |
| | Low crop productivity | 17 (85%) | 2 (2%) |
| | Lack of irrigation facilities | 14 (70%) | 57 (65%) |
| Institutional or governance-related| Lack of policy support for cardamom farming | 14 (70%) | 46 (52%) |
| | Lack of extension services (financial/material support) | 12 (60%) | 61 (69%) |
| | Low level of research on mitigating disease problems | 15 (75%) | 9 (10%) |
| | Lack of local institutions for growers (cooperatives and farmers’ clubs) | 15 (75%) | 3 (3%) |
| | Lack of forward and backward linkages | 13 (65%) | 12 (14%) |
| | Lack of training in selection of disease-free planting material, growth management of cardamom for increased productivity, technical knowhow for disease management, and irrigation facilities | 13 (65%) | 78 (90%) |
disease (*Phoma hedericola*), *furkey* (bushy dwarf), *pahenley* (*Fusarium oxysporum, F. solani*), and *chirkey* (mosaic streak) (Table S1). Around 70% of the farmers said that *chirkey* and *furkey* were the only diseases they were somehow able to manage for some years and produce some yield. Soon after, rhizome decay emerged, both *chirkey* and *furkey* also became unmanageable, and entire plantations were damaged. Four insect pests (leaf caterpillar, shoot fly, stem borer, and white grub) and 6 mammalian pests (Himalayan palm civet, crestless porcupine, monkey, Himalayan black bear, wild boar, and barking deer) were causing damage to cardamom bushes (Table S1, *Supplementary material*, http://dx.doi.org/10.1659/MRD-JOURNAL-D-14-00122.S1).
The average crop loss from diseases and pests ranged from US$ 200 to 800 across the study sites, with especially heavy losses at Lingee-Sokpay. Although in Hee-Pechreak, Hee-Martam, and Lingee-Sokpay, the contribution of cardamom was high, crop losses by diseases and pests were also comparatively higher in these sites. The per capita
### TABLE 4
Annual calendar of large cardamom’s growth cycle, management regime, and major farming challenges.
| Month | Crop development | Plantation management | Pest outbreaks |
|-------|------------------|-----------------------|---------------|
| Jan. | | Removing diseased plants | In some areas, monkeys destroy cardamom bushes and break new spikes |
| Feb. | | Manuring of bushes | |
| Mar. | Flowering starts, moving from lower to higher altitudes | Irrigating using sprinklers | |
| Apr. | Pollination starts | Monitoring and management of diseases | |
| May | | Replanting/gap filling with healthy suckers | |
| June | Pollination continues | Weeding, bush clearing, etc. during flowering and fruiting | Rodents and birds damage flowers |
| July | Fruiting starts, moving from lower to higher altitudes | Developing nurseries | Caterpillars attack leaves |
| Aug. | Spikes start maturing, beginning at lower altitudes | Transplanting in new locations | Porcupines destroy crops |
| Sept. | | Harvesting and curing, beginning at lower altitudes | Civet cats eat the mature capsules, causing heavy loss |
| Oct. | New spikes start to appear | Selling during festivals | |
| Nov. | | Harvesting in higher altitudes | Monkeys, bears, porcupines, and boars destroy the bushes |
| Dec. | | Monitoring diseased and healthy plants | |
### TABLE 4 Extended
| Month | Disease outbreaks | Climate-related challenges |
|-------|------------------|---------------------------|
| Jan. | Decay and drying of rhizome due to low soil moisture | Prolonged dry period |
| Feb. | | Hailstones destroy crops |
| Mar. | Onset of *chirkey*, *furkey*, and fungal disease | Loss of soil moisture |
| Apr. | | Drying of the leaves or even rhizomes due to sunburn |
| May | *Collectotrichum* blight, phoma leaf spot disease, and leaf streak disease | Strong winds sometimes destroy plants |
| June | | Hailstorms also damage crops during April and May |
| July | Incidence of stem borer, capsule borer | Erratic (heavy) rainfall causes flower fall or decay |
| Aug. | | Excessive rainfall causes loss of soil fertility; mudslides and landslides occur |
| Sept. | Wilting of leaves and spikes due to disease during dry periods; white grubs continue to infect rhizomes | Dry period starts, loss of moisture |
| Oct. | Some rhizomes infected by fungus dry during winter; leaves and pseudo-stem also dry | Sunny days burn the cardamom leaves |
| Nov. | | Frost and snowfall destroy crops |
Mountain Research and Development 294 http://dx.doi.org/10.1659/MRD-JOURNAL-D-14-00122.1
landholding under cardamom of the respondent households was highest (2.83 ha) at Lingee-Sokpay, followed by Hee-Martam (1.82 ha) and Hee-Pechreak (1.28 ha). The farmers here have established cardamom farms in new productive areas and are thus earning more than farmers on other sites.
Sustainability challenges and adaptive measures
Of the respondents surveyed, 91% (mostly from mid- and lower elevations) said that the weather at the onset of the cardamom flowering season was becoming drier. Around 95% of respondents said that during peak flowering season (May through July), erratic rainfall caused flower fall and decay, resulting in a loss of fruiting intensity from September to November. Almost all respondents observed that the climatic conditions are changing and that rising temperatures are causing the cardamom harvest to begin around 10–15 days earlier; around 80% said that flowering was occurring 5–10 days earlier.
The majority of cardamom farmers have developed adaptive measures, applying traditional knowledge to cope with the impacts of climate change to revive cardamom (Figure 4). The major adaptive measures are the development and introduction of improved or disease-tolerant cultivars; replanting on new farmland; bringing cardamom into home gardens where it replaces food crops; using manure to maintain soil fertility; irrigating during dry seasons; and managing diseases and pests by uprooting, drying, and burning infected plants.
With the consistent decline of large-cardamom production as the main source of income for households, the farmers have converted cardamom farms to production of food crops or fodder crops such as broom grass. In areas where cardamom yield has declined, the younger people have started looking for jobs in cities and progressive farmers at Hee-Pechreak and Hee-Martam have initiated development of Seremna nurseries.
Discussion
The agricultural economy in the Sikkim Himalayas is largely based on high-value cash crops, of which large cardamom is the most important. Rural farming families have, by and large, depended on the income generated from large cardamom to pay for food, housing, education, health, social activities, and farm management; the loss of cardamom production has therefore had a direct impact on local livelihoods (Sharma and Sharma 1997; Hunsdorfer 2013; Singh and Pothula 2013). Cardamom was the second largest contributor to household income after services and remittances (Table 2). Sharma and Sharma (1997) reported that the contribution of large cardamom to household income was 45% for small households and 54% for larger households. However, this contribution declined from 50% in 1997 (Sharma and Sharma 1997) to 38% in 2000 (Sharma et al 2000), while this study estimated that it had dropped to 29%. Sharma et al (2000) reported that during the 1990s the gross
income of households in large-cardamom-dominated systems was almost double that of households in traditional mixed-forestry systems. Awaseth et al (2011) also reported that household income in cardamom-dominated systems was almost double that of income from mixed-forestry-based traditional farming systems in Sikkim. Of the 111,830 households in Sikkim, 16,037 (14.34%) grow large cardamom as well as traditional crops (DESME 2010). Around 95% of the households in the study area have cardamom plantations. Around 40–70% of the farmland is under large cardamom; the remaining area is under traditional crops.
Climate change is becoming a well-known phenomenon in the Himalayas and is causing unpredictable and erratic rainfall, warmer weather, early flowering, less snow in the mountains and rapid melting of snow, early onset of summer and monsoon, and the drying up of water sources (Partap and Partap 2009; Chaudhary and Bawa 2011; Chaudhary et al 2011; Bawa and Ingy 2012; Sharma and Rai 2012), which is also impacting severely on cardamom-based farming systems. Climate change affects agriculture, biodiversity, and water availability and quality, among other things (Chaudhary et al 2011; Chettri et al 2012; Sharma and Rai 2012). In the Kanchenjunga landscape, to which the current study sites also belong, an annual increase in temperature at the rate of 0.01 to 0.015°C per year has been reported (Chettri et al 2012).
Study participants, both key informants and cardamom growers, perceived an increasing impact of climate change on agriculture in the form of erratic or untimely rainfall, reduction of the temporal distribution of rainfall, long dry spells from winter through autumn, rising temperature, frost and hailstorms, air pollution, a shift in seasons, extreme cold and heat, and drying springs and streams. The respondents felt strongly that research and development institutions such as the Sikkim Government Food Security and Agriculture Development Department/Horticulture and Cash Crops Development Department, and the Spices Board Gangtok, Sikkim, need to develop a strategic plan to address these challenges to revive cardamom farming.
This study has revealed the significance of local knowledge for management of large cardamom. Of the 30 factors that were identified and discussed, more than 55% of the key informants argued that all of them were responsible for the decline of large-cardamom plantation area and productivity. More than 60% of cardamom growers argued that rapid drying up of springs, spread of diseases, decreased number of pollinators (due to climate change impacts), long dry spells lasting until the flowering season, and lack of training in selection of disease-free planting material, lack of growth management of cardamom for increased productivity, lack of technical knowhow for disease management, and lack of irrigation facilities were reasons for crop decline.
The difference in responses revealed that recognition of local knowledge is extremely important while developing adaptation and management plans for reviving large cardamom in the region. Farmers in the study sites have introduced new cash crops such as broom grass and ginger and nitrogen-fixing Alnus nepalensis trees to help maintain soil fertility. They have also planted horticultural trees in the stands where cardamom crops have completely vanished. These interventions have helped reduce soil loss by more than 22% (Rai and Sharma 1998).
The revival strategies applied through innovative knowledge systems at Hee-Pechreak and Hee-Martam led to an increase in both yield and plantation area of large cardamom: farmers have now brought cardamom from forested farmlands where they were growing it earlier to the open cultivated farmlands where they were otherwise growing cereal crops, vegetables, and pulses. They eventually applied irrigation, timely manuring, disease control measures, and appropriate shade conditions. The sharp decline in the productivity of large cardamom in several areas of Sikkim was mainly due to weak management and a change in household livelihood options followed by migration for off-farm employment (Partap et al 2014). The innovative, adaptive climate-smart management practices can be replicated in other cardamom-growing areas. This study identified 6 diseases, 4 insect pests, and 6 mammalian pests that are damaging cardamom crops. Saju, Deka, et al (2011) and Saju, Mech, et al (2011) have also reported the incidence of diseases and some biocontrol measures to eradicate infestations. The emergence of new diseases and pests in cardamom crops has been increasing for the last 15 years. Mammalian pests including palm civets, black bears, wild boars, Assamese macaque, and deer were reported to be damaging cardamom and other crops. Thus, human–wildlife conflict has become a serious issue in the cardamom-growing areas of Sikkim. The incidence of disease was higher at lower elevations, while pest infestations were higher at higher elevations in our study sites. The management of plantations, including shade conditions, moisture (under-canopy and soil), and altered climatic patterns have significantly altered the crop cycle. Thus, the system is now demanding more labor, increased investment in irrigation, high-quality planting materials, manure, and periodic replantation in new locations. Indeed, the impact of age on a cardamom plantation is important for optimum yield: when the stands mature the yield also deteriorates (Sharma et al 2002a, 2002b). Cardamom farmers can design periodic replantation by establishing more than one plantation stand in subsequent years, so that when the first stand becomes old, they can still continue with the other stands and earn from them while they can fallow and re-develop the first stand in a rotation system.
Climate change-induced changes in local weather are reported to increase the incidence of diseases and pests in various crops in different areas. In 1998–1999, a dry spell of about 7 months had a visible adverse effect on the large cardamom, ginger, and orange crops in Sikkim (SHDR 2001). Sharma and Rai (2012) emphasized that traditional ecological knowledge, agrobiodiversity, multiple land uses, and diversification of livelihoods allow local communities to cope with changes and will each play an important role in adaptation to climate change. Innovative approaches involving traditional knowledge or in vitro approaches to developing disease-free planting material for improvement of large cardamom can enhance the livelihoods of cardamom growers in the region (Pradhan et al 2014). The low performance of large-cardamom production resulted in frustration for farmers in several areas of Sikkim, and as a result, young farmers are either migrating or shifting into alternative livelihoods. Thus, a significant amount of household income is shifting away from cardamom. Nevertheless, large-cardamom farming continues to be the second largest contributor of farm income as farmers continue to drive efforts to revive and maintain their cardamom farms.
Conclusion
Cardamom-based farming in the Sikkim Himalayas is undergoing a rapid transformation owing to environmental/climatic, biological, socioeconomic, and governance/institutional drivers of change. There is a need to reduce climate change impacts by establishing adaptation and mitigation strategies, taking into consideration local and indigenous knowledge. Some future objectives could be to develop disease-free, high-quality planting materials and establish certified nurseries, increase the spread of best management practices, improve disease and pest control, facilitate a more efficient farmer innovation process through communication, provide irrigation facilities, enhance conservation of effective pollinator species, improve product quality through improved post-harvest technology, and increase market channel efficiency, which are some of the immediate interventions that are required by the farmers.
This study has clearly established the fact that the local situations, issues, and challenges of cardamom farming are better understood by the growers than the institutions. Some contradictory responses of key informants and the cardamom growers revealed that recognition of traditional knowledge and participatory and focused approaches are critical for reviving cardamom farming in the region. The biggest threat to cardamom is the continuation of one-crop-based alder-cardamom agroforestry in India, Nepal, and Bhutan. This system now requires inclusion of mixed-species cardamom with diversification of other crops including medicinal and aromatic plants. Although cardamom farming is considered a one-crop-based but productive farming method in the region, its long-term environmental and ecological implications in the wake of climate change should be a high priority in investment for research and development.
ACKNOWLEDGMENTS
The authors thank the International Centre for Integrated Mountain Development for support and The Mountain Institute, India, for use of its facilities. The Indian Cardamom Research Institute, Gagntok, Sikkim, of the Spices Board of Government of India, and the Food Security & Agriculture Development Department, and Horticulture & Cash Crops Development Development Department, and Horticulture & Cash Crops Development of the Government of Sikkim provided secondary data and information on initiatives and extension services. We thank the local communities and institutions for information and Benjamin C. Hunsdorfer for help with the field survey.
REFERENCES
Awasthie RK, Singh KK, Tomar JHS. 2011. Large cardamom (Amomum subulatum Roxb), based agroforestry systems for production, resource conservation and livelihood security in the Sikkim Himalayas. Indian Journal of Soil Conservation 39(2):155–160.
Bawa KS, Ingty T. 2012. Climate change in Sikkim: A synthesis. In: Arrawatia ML, Tambe S, editors. Climate Change in Sikkim: Patterns, Impacts and Initiatives. Gangtok, India: Information and Public Relations Department, Government of Sikkim, pp 413–424.
Chambers R, Blackburn J. 1996. The Power of Participation: PRA and Policy. IDS Policy Briefings 7. Brighton, United Kingdom: Institute of Development Studies (IDS), University of Sussex.
Chaudhary P, Bawa KS. 2011. Local perceptions of climate change validated by scientific evidence in the Himalayas. Biology Letters 7:767–770. doi:10.1098/rsbl.2011.0269.
Chaudhary P, Rai S, Wangdi S, Mao A, Rehman N, Chettri S, Bawa KS. 2011. Consistency of local perceptions of climate change in the Kangchenjunga Himalaya landscape. Current Science 101:504–513.
Chhetri N, Shakya B, Lepcha R, Chettri R, Rai KR, Sharma E. 2012. Understanding the linkages: Climate change and biodiversity in the Kanchenjunga landscape. In: Arrawatia ML, Tambe S, editors. Climate Change in Sikkim: Patterns, Impacts, Initiatives. Gangtok, India: Government of Sikkim, pp 161–178.
DESME [Department of Economics, Statistics, Monitoring & Evaluation]. 2002. Sikkim: A Statistical Profile 2002. Gangtok, India: DESME, Government of Sikkim.
DESME [Department of Economics, Statistics, Monitoring & Evaluation]. 2005. Sikkim: A Statistical Profile 2005. Gangtok, India: DESME, Government of Sikkim.
DESME [Department of Economics, Statistics, Monitoring & Evaluation]. 2006. State Economic Census 2006. Gangtok, India: DESME, Government of Sikkim.
DESME [Department of Economics, Statistics, Monitoring & Evaluation]. 2010. Sikkim: A Statistical Profile 2009–10. Gangtok, Sikkim: DESME, Government of Sikkim.
FSADD, HCCD [Food Security and Agriculture Development Department, Horticulture and Cash Crop Development Department]. 2012. Sikkim Towards
Sharma G, Rai, LK. 2012. Climate change and sustainability of agrobiodiversity in traditional farming of the Sikkim Himalaya. In: Arawatia ML, Tambe S, editors. Climate Change in Sikkim: Patterns, Impacts, Initiatives. Gangtok, India: Information and Public Relations Department, Government of Sikkim, pp 193–218.
Sharma G, Sharma R, Sharma E. 2009. Traditional knowledge systems in large cardamom farming: Biophysical and management diversity in Indian mountainous regions. Indian Journal of Traditional Knowledge 8(1):17–22.
Sharma G, Sharma E, Sharma R, Singh KK. 2002a. Performance of an age series of Annuus-cardamom plantations in the Sikkim Himalaya. Biodiversity, productivity and energetics. Annals of Botany 89:261–272.
Sharma G, Sharma E, Sharma R, Singh KK. 2002b. Performance of an age series of Annuus-cardamom plantations in the Sikkim Himalaya: Nutrient dynamics. Annals of Botany 89:273–282.
Sharma HR, Sharma E. 1997. Mountain Agricultural Transformation Processes and Sustainability in the Sikkim Himalayas. India. Mountain Farming Systems’ Discussion Paper 97/2. Kathmandu, Nepal: International Centre for Integrated Mountain Development.
Sharma R, Sharma E, Purushott Mann. 1994. Dry matter production and nutrient cycling in agroforestry systems of cardamom grown under Anuus and natural forest. Agroforestry Systems 27:293–306.
Sharma R, Xu X, Sharma G. 2007. Traditional agroforestry in the eastern Himalayan region: Land management system supporting ecosystem services. Tropical Ecology 48(2):189–200.
SHDR [Sikkim Human Development Report]. 2001. Sikkim Human Development Report. Gangtok and Delhi, India: Social Science Press.
Singh AI, Pothula AK. 2013. Postharvest processing of large cardamom in the eastern Himalayas. Mountain Research and Development 33(4):453–462.
SDM [Sikkim Organic Mission]. 2014. Comprehensive Progress Report 2014: Sikkim Organic Mission. Tadong, India: Sikkim Organic Mission Food Security & Agriculture Department and Horticulture & Cash Crop Development Departments, Government of Sikkim.
Srivastava HS. 2006. Large Cardamom Cultivation in India. Report of the Spices Board, Regional Office, Gangtok, India. Unpublished report, available from the corresponding author of the present article.
Subedi BP, Ghimire PL, Koontz A, Khanal SC, Katwal P, Sthapit KR, Khadka SM. 2014. Private Sector Involvement and Investment in Nepal’s Forestry Sector: Status, Prospects and Ways Forward. Study Report Multistakeholder Forestry Programme (MSFP), Kathmandu, Nepal: Services Support Unit, Babarmahal. Tambe S, Kharel G, Arawatia ML, Kulkarni H, Mahmuni K, Ganeriwala AK. 2012. Reviving drying springs: Climate change adaptation experiments from the Sikkim Himalaya. In: Arawatia ML, Tambe S, editors. Climate Change in Sikkim: Patterns, Impacts and Initiatives. Gangtok, India: Information and Public Relations Department, Government of Sikkim, pp 333–350.
Supplemental material
TABLE S1 Infestations and control measures in large-cardamom plantations.
Found at DOI: 10.1659/MRD-JOURNAL-D-14-00122.S1 (22 KB PDF). | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4562,
1
],
[
4562,
10201,
2
],
[
10201,
10590,
3
],
[
10590,
15938,
4
],
[
15938,
16339,
5
],
[
16339,
19722,
6
],
[
19722,
25318,
7
],
[
25318,
30180,
8
],
[
30180,
34039,
9
],
[
34039,
36895,
10
],
[
36895,
42721,
11
],
[
42721,
48628,
12
],
[
48628,
51703,
13
]
]
} |
6dad5f8fcfe6c1d4b3e768fbcf036324947c64fb | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 44416,
"total-output-tokens": 12501,
"fieldofstudy": [
"Physics"
]
} | Autoresonant excitation of Bose-Einstein condensates
S.V. Batalov* and A.G. Shagalov†
Institute of Metal Physics, Ekaterinburg 620990, Russian Federation and
Ural Federal University, Mira 19, Ekaterinburg 620002, Russian Federation
L. Friedland‡
Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
Controlling the state of a Bose-Einstein condensate driven by a chirped frequency perturbation in a one-dimensional anharmonic trapping potential is discussed. By identifying four characteristic time scales in this chirped-driven problem, three dimensionless parameters are defined describing the driving strength, the anharmonicity of the trapping potential, and the strength of the particles interaction, respectively. As the driving frequency passes the linear resonance in the problem, and depending on the location in the parameter space, the system may exhibit two very different regimes, i.e. the quantum energy ladder climbing (LC) and the classical autoresonance (AR). These regimes are analysed both in theory and simulations with the emphasis on the effect of the interaction parameter. In particular, the transition thresholds on the driving parameter and their width in both the AR and LC regimes are discussed. Different driving protocols are also illustrated, showing efficient control of excitation and de-excitation of the condensate.
PACS numbers: 03.75.Kk, 05.45.-a, 05.45.Xt
I. INTRODUCTION
Unique properties of Bose-Einstein condensates (BEC) attracted enormous interest in the last decades as a very flexible framework for experimental and theoretical research in many-body physics and a promising basis for new technologies. Modern applications require understanding of nonlinear dynamics of the condensates. Nonlinear dynamics is especially interesting in anharmonic trapping potentials, when motion of the center of mass is coupled to internal degrees of freedom, and may even become chaotic. In this paper we take advantage of the anharmonic potential to excite a quasi-one-dimensional condensate from the ground state to a high energy level. The basic idea is to use a driving perturbation with a slowly varying frequency to transfer the population from the ground quantum state to the first excited state, then to the second, and so on. This dynamical process, when only two energy eigenstates are resonantly coupled at a time, is the ladder climbing (LC) regime.
The classical counterpart of the ladder climbing is the autoresonance (AR), the phenomenon discovered by Veksler and McMillan in 1944 [1] and referred to as the phase stability principle at the time. Nowadays, the AR has multitude of applications in such diverse areas as hydrodynamics, plasmas, magnetism, nonlinear optics, molecular physics, planetary dynamics etc. The AR in BECs was previously studied in [2] for the case of oscillating scattering length. The excitation of a BEC from the ground state to the first energy eigenstate using optimal control was investigated experimentally in Ref. [3].
In this paper we consider Gross-Pitaevskii model [4]
\[ i\hbar \frac{\partial \Psi}{\partial t} + \frac{\hbar^2}{2m} \nabla^2 \Psi - (U + g|\Psi|^2) \Psi = 0, \]
\[ U(x, t) = m\omega_0^2 \left( \frac{x^2}{2} - \beta \frac{x^4}{4} \right) + \varepsilon \cos \varphi(t), \]
which describes a BEC in a trap with the anharmonic potential \( U(x, t) \) perturbed by a small amplitude oscillating drive. Here \( \beta > 0 \) is the anharmonicity parameter assumed to be small. The frequency of the drive \( \omega(t) = \dot{\varphi}(t) = \omega_0 - \alpha t \) slowly decreases in time (\( \alpha > 0 \)) and passes through the linear resonance frequency \( \omega_0 \) in the problem at \( t = 0 \). We assume that the wave function is normalized to unity and, thus, parameter \( g \) is proportional to the total number of particles in the condensate.
Both the classical AR and the quantum LC in the linear limit \( (g = 0) \) of Eq. (1), i.e., the quantum Duffing oscillator, were studied in Refs. [4, 14–21].
In this work, we focus on the nonlinear effects due to the interaction of the particles in the condensate. As a first step, we adopt the notations used in Ref. [19] to allow comparison with the linear case. To this end, we classify different dynamical regimes of Eq. (1) in terms of parameters \( P_1, P_2 \) used in Ref. [19] and introduce a new parameter \( P_3 \), characterizing the nonlinearity in the problem. These parameters are constructed using four characteristic time scales in the problem: the inverse Rabi frequency \( T_R = \sqrt{2m\hbar\omega_0/\varepsilon} \), the frequency sweep time scale \( T_S = \alpha^{-1/2} \), the anharmonic time scale \( T_A = 3\hbar\beta/(4m\alpha) \) of the trapping potential, and the nonlinear time scale \( T_N = g/(\hbar\omega_0) \), where \( \ell = \sqrt{\hbar/m\omega_0} \) is the characteristic width of the harmonic oscillator. Time \( T_A \)
* [email protected]
† [email protected]
‡ [email protected]
anharmonic frequency shift between the first two levels of the energy ladder. Similarly, $T_N$ is the time of passage through the nonlinear frequency shift. Then, our three dimensionless parameters are defined as
$$P_1 = \frac{T_S}{T_R} = \frac{\varepsilon}{\sqrt{2m\hbar^2\omega_0}}, \quad P_2 = \frac{T_A}{T_S} = \frac{3\hbar\beta}{4m\hbar},$$
$$P_3 = \frac{T_N}{T_S} = \frac{g}{\hbar\sqrt{\alpha}}$$
and characterize the strength of the drive, the anharmonicity of the trapping potential and the nonlinearity of the condensate, respectively. We limit our discussion to the case of the positive nonlinearity (repulsion), $P_3 > 0$. The scope of the paper is as follows. In Sec. II we study the dynamics of our system in the energy basis of the quantum harmonic oscillator and find a domain in $P_1, P_2, P_3$ parameter space where the successive quantum energy ladder climbing process takes place. In Sec. III, we discuss the opposite limit of semiclassical dynamics. The details of our numerical simulations are presented in Sec. IV and the conclusions are summarized in Sec. V.
II. QUANTUM LC REGIME
Here we focus on the LC regime, where the quantum nature of the system is mostly pronounced. In this case, it is convenient to express Eq. (1) in the energy basis of the linear harmonic oscillator $\Psi(x,t) = \sum_n c_n(t)\psi_n(x)$, yielding
$$i\hbar \frac{dc_n}{dt} = E_n c_n + \frac{\varepsilon}{\sqrt{2}} \left( \sqrt{n+1} c_{n+1} + \sqrt{n} c_{n-1} \right) \cos \varphi$$
$$+ g \sum_{klm} c_k c_l c_m^* \int_{-\infty}^\infty \psi_k(x)\psi_l(x)\psi_m(x) dx,$$
where the approximate energy levels up to linear terms in $\beta$ are given by [22]
$$E_n \approx \hbar \omega_0 \left[ n + \frac{1}{2} - \frac{3\beta}{8\omega_0} \left( n^2 + n + \frac{1}{2} \right) \right].$$
Introducing new variables $B_n = c_n e^{i(\beta\xi + n\varphi)}$, we rewrite Eq. (4) in the form
$$i\hbar \frac{dB_n}{dt} = \left[ \hbar \omega_0 - \frac{3\beta}{8\omega_0} n(n+1) \right] B_n$$
$$+ \frac{\varepsilon}{2\sqrt{2}} \left( \sqrt{n+1} B_{n+1} e^{-i\varphi} + \sqrt{n} B_{n-1} e^{i\varphi} \right) \left( e^{-i\varphi} + e^{i\varphi} \right)$$
$$+ g \sum_{klm} B_k B_l B_m^* e^{i(n+m-k-l)\varphi} \int_{-\infty}^\infty \psi_k(x)\psi_l(x)\psi_m(x) dx$$
We also define the dimensionless time $\tau = \sqrt{\alpha} t$, coordinate $\xi = x/\ell$, and basis functions $\chi_n(\xi) = \sqrt{\ell} \psi_n(x)$, and use the rotating wave approximation (preserve only stationary terms in the driving and nonlinear components in Eq. (6)) to get a dimensionless system
$$i\frac{dB_n}{d\tau} = \Gamma_n B_n + \frac{P_1}{2} \left( \sqrt{n+1} B_{n+1} + \sqrt{n} B_{n-1} \right)$$
$$+ P_3 \sum_{k,l} B_k B_l B_{n+k-l}^* \int_{-\infty}^\infty \chi_n(x)\chi_k(x)\chi_l(x) e^{d\xi}$$,
where the frequencies $\Gamma_n$ are $\Gamma_n = n\tau - \frac{P_1}{2} \sqrt{n+1} (n+1)$. The resonant population transfer between levels $n-1$ and $n$ [the Landau-Zener (LZ) transition [23]] takes place when their time-dependent characteristic frequencies are matched: $\Gamma_{n-1}(\tau_n) \approx \Gamma_n(\tau_n)$, i.e. in the vicinity of $\tau_n = nP_2$. In terms of Eq. (4) this corresponds to the resonance condition $E_n - E_{n-1} \approx \hbar \omega(\tau_n)$. Note that the anharmonicity parameter determines the time interval between successive LZ transitions $\Delta \tau = \tau_n - \tau_{n-1} = P_2$. These transitions can be treated independently provided their duration is much shorter than $\Delta \tau$. As suggested in [19] for the linear case ($P_3 = 0$), the well-separated LZ transitions are expected when
$$P_2 \gg 1 + P_1,$$
where the right hand side is a typical duration of a LZ transition in both adiabatic (slow passage through resonance) and fast transition limits [24]. This inequality defines the domain of essentially quantum dynamics in the parameter space $P_1, P_2$, if $P_3 = 0$. Later in this Section, we discuss how relation (7) is modified in the case of the nonlinear LZ transitions ($P_3 \neq 0$).
Neglecting all states in (6), but those with amplitudes $u = B_{n-1}$ and $v = B_n$, we obtain the nonlinear LZ-type equations describing the isolated transition between the two states:
$$i\frac{du}{d\tau} = \Gamma_{n-1} u + P_3 \left( |u|^2 I_{n-1} + 2|v|^2 J_n \right) u + \frac{P_1}{2} \sqrt{n} v,$$
$$i\frac{dv}{d\tau} = \Gamma_n v + P_3 \left( |v|^2 I_n + 2|u|^2 J_{n-1} \right) v + \frac{P_3}{2} \sqrt{n} u,$$
where $J_n = \int |\chi_{n-1}|^2 |\chi_n|^2 d\xi$, $I_n = \int |\chi_n|^4 d\xi$. The nonlinear LZ model attracted significant attention recently [25–27], especially in the context of BECs in optical lattices. Nonlinearity may change the dynamics of the system significantly compared to the linear case. One deviation from the linear case is the breakdown of adiabaticity due to the bifurcation of nonlinear stationary states [28, 29]. In this paper we focus on another property of the nonlinear LZ model, namely, the AR.
Equations (8) can be simplified using the conservation of the total probability $K_n = |u|^2 + |v|^2$. Introducing the fractional population imbalance $S = (|v|^2 - |u|^2)/K_n$ and the phase mismatch $\delta = \arg(v/u)$, we obtain a set
of real equations
\[
\frac{dS}{d\tau} = -\mu_n \sqrt{1 - S^2} \sin \delta,
\]
\[
\frac{d\delta}{d\tau} = \frac{P_3 K_n f_n}{2} S - (\tau - \tau_s) + \frac{P_1 \sqrt{n} S}{\sqrt{1 - S^2}} \cos \delta,
\]
where \( f_n = 4 J_n - I_{n-1} - I_n \) and \( \tau_s = n P_2 - P_3 K_n (I_n - I_{n-1})/2 \). The AR in a similar system was studied in [13]. Its main characteristic is a continuing phase locking as the phase mismatch \( \delta \) remains bounded due to a persistent self-adjustment of the nonlinear frequency of the driven system to slowly varying driving frequency, i.e., \( P_3 K_n f_n S/2 \approx (\tau - \tau_s) \). However, the slow passage through resonance does not guarantee the AR. Indeed, if one assumes that only state \( u \) is populated initially, that is \( S \to -1 \), then the AR requires the driving parameter \( P_1 \) to exceed a certain threshold [13]
\[
P_1 > P_{1, cr} = \frac{0.82}{\sqrt{n} P_{3, cr} f_n K_n}.
\]
This condition (10) shows that the AR is an essentially nonlinear phenomenon and disappears when \( P_3 \to 0 \).
A typical dynamics of the nonlinear LZ model is illustrated in Fig. 1. For a given nonlinearity \( P_3 \), the threshold condition (10) separates two different types of evolution of the system. If \( P_1 < P_{1, cr} \) (see Fig. 1a), the passage through the resonance at \( \tau \approx \tau_s - P_3 K_n f_n/2 \approx 50 \) yields a small excitation and a fast growth of the phase mismatch \( \delta \) between the two states (see solid line in Fig. 1a). In contrast, we observe synchronization and nearly complete transition between the states when the coupling parameter exceeds the threshold, \( P_1 > P_{1, cr} \). Figures 1b and 1c illustrate this effect just beyond the threshold and far from the threshold, respectively. One can see that above the threshold the phase mismatch is bounded, exhibiting the phase-locking phenomenon characteristic of the AR. One can also see that the amplitudes vary significantly during the transition from \( n - 1 \) to \( n \) state. The phase-locking is destroyed only after the system almost completely transfers to the new state. As long as the phase-locking is sustained, the population imbalance increases on average as \( S(\tau) \approx 2(\tau - \tau_s)/P_3 f_n K_n \) with some superimposed modulations. In particular, \( |u|^2 \approx |v|^2 \) at time \( \tau \approx \tau_s \). Since the maximal change of the population imbalance is \( \Delta S = 2 \), the duration of the complete autoresonant transition can be estimated as
\[
\tau_{AR} = P_3 f_n K_n.
\]
The most important characteristic of the LZ model is the transition probability \( W_n = |v(\infty)|^2/K_n \) for finding the system in the upper state if it was in the lower state initially. In the linear limit, this probability is given by the famous LZ formula
\[
W_n = 1 - e^{-\tau^2/\gamma}.
\]
The numerical integration of the nonlinear LZ model (8) gives the transition probability shown in Fig. 2. The curve corresponding to \( P_3 = 0 \) coincides with the linear LZ result (11). The transition probability steepens as the nonlinearity \( P_3 \) increases and tends to a step-like function in the strongly nonlinear limit. The front of this step corresponds to the onset of the AR at \( P_1 \approx P_{1, cr} \). Once phase-locked, the system remains in this state until almost complete population inversion is achieved, as indicated by transition probability (the height of the step) close to unity in Fig. 2. This means that the threshold (10) obtained in Ref. [13] in a small-amplitude limit, i.e., assuming \( S \approx -1 + \delta S, \delta S \ll 1 \), is applicable to the fully nonlinear equations (9) as well.
For interpreting numerical simulations covering both the linear and nonlinear LZ transitions we redefine the threshold \( P_{1, cr} \) as the \( P_1 \) value corresponding to 50% transition probability, i.e., \( W_n(P_{1, cr}) = 1/2 \). Using this definition we numerically solve Eq.(8) to find the threshold values \( P_{1, cr} \) and compare these results with the theoretical prediction (10) in Fig. 3. One can see that in the strongly nonlinear limit \( P_{3, cr} f_n \gg 1 \) the numerical
The equation \( W(P_1, P_3) = 1/2 \) defines the threshold \( P_{1,LC}(P_3) \) for this LC process. As it was found numerically [19] in the linear \( P_3 = 0 \) case, the product (12) quickly converges for \( N \geq 5 \) and one finds \( P_{1,LC} \approx 0.79 \).
On the other hand, in the strongly nonlinear limit one can approximate the transition probability by the Heaviside step function \( W_n(P_1, P_3) \approx H(P_1 - P_{1,cr}(P_3, n)) \), where \( P_{1,cr} \) is given by Eq. (10). Since \( P_{1,cr} \) decreases with the transition number \( n \) and every transition leads to nearly complete population inversion, the product (12) can be replaced by the single \( n = 1 \) term \( W \approx W_1 \) and the capture into the LC regime occurs after the first transition.
In this approximation the threshold is simplified
\[
P_{1,LC} \approx P_{1,cr}(P_3, n = 1) = \frac{0.82}{\sqrt{P_3 f_1 K_1}}.
\]
Note that the threshold width, defined as the inverse slope of the transition probability at \( W = 1/2 \), equals \( \Delta P_{1,LC} = 0.66 \) in the linear case [19] and tends to zero in the strongly nonlinear regime.
Similarly to the linear case, we can assume that the successive transitions in the nonlinear regime will well-separated, provided the time between two successive transitions satisfies \( \Delta \tau \gg \tau_{AR} \), i.e., \( P_2 \gg f_1 K_1 P_3 \). This estimate can be simplified because \( f_1 = \sqrt{2/\pi}/8 \approx 0.1 \) and we can set \( K_1 = 1 \). Combining the above inequality with the linear result (7) we find the condition for essentially quantum dynamics in the \( P_{1,2,3} \) parameter space:
\[
P_2 \gg 1 + P_1 + 0.1 P_3.
\]
This inequality together with the condition \( P_1 > P_{1,LC} \) defines the region of the parameter space, where efficient excitation of quantum states in the model (1) via the autoresonant LC is achieved.
III. SEMICLASSICAL REGIME
If the anharmonicity parameter \( P_2 \) of the trap decreases, the two-level approximation employed in the previous section breaks down as several levels can resonate with the drive simultaneously. In the limit \( P_2 \ll 1 \), the number of coupled levels is so large that the dynamics becomes semiclassical. The linear \( P_3 = 0 \) case in this problem was already studied in Ref. [19]. It was shown that the autoresonant excitation of BEC oscillations is possible provided the drive strength \( P_1 \) exceeds the classical autoresonance threshold for the Duffing oscillator [30]
\[
P_{1,AR} = \frac{0.82}{\sqrt{P_2}}.
\]
In this regime, the center of mass of the condensate oscillates in the trap with an increasing amplitude. The frequency of these oscillations remains close to the driving frequency during the whole excitation process, despite the variation of the driving frequency. In this section we discuss the threshold value \( P_{1,AR} \) in the nonlinear case \( P_3 > 0 \).
Consider the Wigner representation of our problem [31]:
\[
\frac{\partial f(x, p, t)}{\partial t} = \{H, f\}_{MB},
\]
where \( f(x, p, t) \) is the Wigner function, \( H \) is the Hamiltonian
\[
H = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} + U(x, t) + g|\Psi(x, t)|^2
\]
and \( \{H, f\}_{MB} \) denotes the Moyal bracket. Since the Moyal bracket reduces to the Poisson bracket in the semi-classical limit \( h \to 0 \): \( \{H, f\}_{MB} \approx \{H, f\} + O(h^2) \), equation (15) reduces to the Liouville equation
\[
\frac{\partial f}{\partial t} + \frac{p}{m} \frac{\partial f}{\partial x} - \frac{\partial}{\partial x} \left( U + g|\Psi|^2 \right) \frac{\partial f}{\partial p} \approx 0, \tag{16}
\]
where in addition to the external potential \( U(x, t) \), we have the self-potential \( V = g|\Psi|^2 \). This equation is reminiscent of the Vlasov equation for an ensemble of particles in the combined external and self-potentials. Note that the self-potential can be expressed via the Wigner function
\[
|\Psi(x, t)|^2 = \int_{-\infty}^{\infty} f(x, p, t) dp,
\]
transforming (16) into a closed integro-differential form.
The characteristics (classical trajectories) for Eq. (16) are given by
\[
\frac{d^2x}{dt^2} + \frac{1}{m} \frac{\partial U}{\partial x} + \frac{g}{m} \frac{\partial |\Psi|^2}{\partial x} = 0. \tag{17}
\]
Suppose one starts in a localized state, so that the Wigner function has a local maximum at the phase-space point \([x_0, p_0]\). In the semiclassical limit, the Wigner function is expected to continue having a local maximum near the phase-space point \([x(t), p(t)]\) moving along the classical trajectory starting at \([x_0, p_0]\). Near this point,
\[
|\Psi(x + s, t)|^2 \approx const - \kappa s^2 / 2
\]
and, thus, the term \((g/m)\partial |\Psi|^2/\partial x\) in Eq. (17) vanishes along the trajectory of the maximum of \( f \). Consequently, the nonlinearity (characterized by parameter \( P_3 \)) in the semiclassical regime does not affect the evolution of the maximum. Then it also does not change the threshold of the AR (14) and should not shift the transition probability versus \( P_1 \) in contrast to the quantum regime (see Fig. 2). We confirm these conclusions in numerical simulations in the following section.
**IV. NUMERICAL SIMULATIONS**
In this section we present numerical simulations of the original Gross-Pitaevskii equation (1) in our driven problem. We rewrite this equation in a dimensionless form using the same \( \xi = x / \ell \), but a different dimensionless time \( T = \omega_0 t \):
\[
i\Phi_T + \frac{1}{2} \Phi_{\xi \xi} - \left( \hat{U} + Q_3|\Phi|^2 \right) \Phi = 0, \tag{18}
\]
\[
\hat{U}(\xi, T) = \frac{\xi^2}{2} - Q_2 \frac{\xi^4}{4} + Q_1 \xi \cos \varphi(T),
\]
where \( \Phi = \sqrt{\xi} \Psi, \quad \hat{\alpha} = \alpha / \omega_0^2, \quad Q_1 = \sqrt{2\hat{\alpha}} P_1, \quad Q_2 = \frac{4}{3} \sqrt{\hat{\alpha}} P_2, \quad Q_3 = \sqrt{\hat{\alpha}} P_3 \) and \( \varphi(T) = T - \hat{\alpha} T^2 / 2 \). The simulations are based on the standard pseudo-spectral method [32] with explicit 4-th order Runge-Kutta algorithm and adaptive step size control. The ground state of the harmonic oscillator was used as the initial condition:
\[
\Phi(\xi, 0) = \pi^{-1/4} e^{-\xi^2 / 2}. \tag{19}
\]
The state of the condensate was analyzed by calculating the amplitudes \( c_n(t) \) in the basis of Hermite functions, and the Wigner distribution.
In order to study various regimes of excitation of a condensate, we performed a series of numerical simulations by varying parameters \( P_1 \) and \( P_2 \) in the linear \( (P_3 = 0) \) and nonlinear cases. The results of the simulations are presented in Fig. 4. The circles in the figure correspond to parameters yielding 50% probability of capture into either the classical AR or the quantum LC regime. The classical autoresonance threshold (14) is shown by the black long-dashed line. The two roughly horizontal lines \( P_2 = 1 + P_1 + 0.1 P_3 \) separate the regions of the quantum and semiclassical dynamics in the linear \( (P_3 = 0, \) red line) and nonlinear \( (P_3 = 100, \) blue line) regimes. The vertical lines show the theoretical LC transition thresholds \( P_{1,LC} \) for the linear and nonlinear regimes.
One can see that the classical AR threshold (14) yields a good approximation for the transition boundary for \( P_2 \) versus \( P_1 \) in both the linear and the nonlinear cases. In the case \( P_3 = 100 \), the nonlinear ladder climbing transitions emerge at significantly smaller values of the driving parameter \( P_1 \) and larger anharmonicity \( P_2 \), compared to the linear case. This is in agreement with the shift of the threshold in the nonlinear model of the autoresonant LZ transitions discussed above (see Fig. 2).
The important change due to the nonlinearity in the problem is the decrease of the width of the transition region. This effect is illustrated in Fig. 5 for the case of the semiclassical autoresonant transition. The width of the transition for the nonlinear case decreases rapidly with the increase of the nonlinearity parameter $P_3$ and the transition probability assumes a nearly step-like shape for $P_3 > 15$. One also observes that the threshold location, where the probability crosses 50%, only slightly changes with the variation of $P_3$ as discussed at the end of Sec. II.
The effect of the narrowing of the transition width in the semiclassical regime with the increase of the nonlinearity parameter can be associated with the improved stability of the autoresonant classical trajectories described by Eq. (17). Indeed, in dimensionless variables, Eq. (17) for the characteristics of Eq. (16) becomes
$$\xi_{TT} + \xi - Q_2 \xi^3 + Q_3 \frac{\partial |\Phi(\xi,T)|^2}{\partial \xi} + Q_1 \cos \varphi(T) = 0.$$ (20)
Let the trajectory of the autoresonant maximum of the Wigner function be $\xi_0(T)$. The dynamics of this trajectory is described by
$$\eta_{TT} + \xi_0 - Q_2 \xi_0^3 + Q_1 \cos \varphi(T) = 0$$ (21)
subject to $\xi_0 = \xi_{OT} = 0$ at large negative $T$ and is not affected by the nonlinearity, as described above. For studying the the evolution of a deviation $\eta = \xi - \xi_0(T)$ from $\xi_0(T)$, we linearize Eq. (20) around $\xi_0$ and assume $|\Phi(\xi,T)|^2 \approx \text{const} - \kappa \eta^2/2$ near the maximum, to get
$$\eta_{TT} + [1 - 3Q_2 \xi_0^2 - \kappa Q_3] \eta = 0.$$ (22)
We analyze the solutions of system (21), (22) in the Appendix. Numerically, in the vicinity of the threshold for $P_3 = 0$, we observe the development of instability of $\eta$. By writing $\xi_0 = a \cos \theta$, Eq. (22) assumes the form of the Mathieu-type equation with slowly varying parameters
$$\eta_{TT} + \left\{1 - \frac{3Q_2 a^2}{2} - \kappa Q_3 - \frac{3}{2} Q_2 a^2 \cos[2\theta(T)]\right\} \eta = 0.$$ (23)
We show in the Appendix that this equation predicts parametric-type instability for $P_3 = 0$ and we attribute the existence of the width in the transition to autoresonance as seen in Fig. 5 to this effect. Note that the addition of the nonlinearity (the term $-\kappa Q_3$ in the last equation) shifts the eigenfrequency so that the parametric resonance can be avoided and characteristic trajectories with nearby initial conditions remain close to the classical autoresonant trajectory, narrowing the transition width as seen in Fig. 5. For the parameters in this figure, the system stabilizes at $P_3 > 0.3$ (see the Appendix). Nonetheless, the deviation from the autoresonant state is still large until $P_3 > 10$, when the autoresonant transition width practically disappears.
Our next numerical simulation shows that the system can be fully controlled by the AR in both the quantum and semiclassical regimes. Two protocols of such a control of the LC dynamics are shown in Fig. 6. Parameters $P_i$ are chosen so that both condition (13) and $P_i > P_{i,LC}$ are satisfied. Due to a relatively strong anharmonicity, the nonlinear LZ transitions are well separated in time. One can see that the energy in the system grows step-by-step from one energy level to another. In the first protocol, the linear frequency variation with a constant chirp rate $\alpha$ [red dashed line in Fig. 6(a)] results in the excitation of the condensate to the sixth energy level. In the second protocol (solid line) we first excite the system to the fourth energy state by decreasing driving frequency until $T = 1.8 \times 10^5$, then keep the driving frequency constant for the time span of $\Delta T = 4 \times 10^4$, and finally return the system to the ground state by increasing the driving frequency back to its original value. One can see that the quantum state of (1) can be efficiently controlled as long as the LC autoresonant conditions are met and the frequency and phase of the driving are continuous. The quantum state in the first protocol at $T = 2 \times 10^5$ is further illustrated in Figs. 6 (b) and (c) showing the distribution of populations of different levels and the Wigner function. Small deviations of the solution from the fourth eigenfunction $\chi_4(\xi)$ of the linear harmonic oscillator are due to the anharmonicity and the nonlinearity in the problem.
A similar control protocols for the semiclassical case are illustrated in Fig. 7. One can see that resulting wave function has a Gaussian (Poissonian in the early stages of dynamics) population distribution, characteristic of coherent states. The Wigner function is positive everywhere (on the computational grid) and close to the $n$-squeezed coherent state. The second protocol (solid line in Fig. 7) demonstrates that a more complex control scenarios are possible in the semiclassical case, as long as the driving parameter is within the region of autoreso-
V. CONCLUSIONS
In conclusion, we have studied the effect of the particles interaction on the excitation of Bose-Einstein condensate in an anharmonic trap under chirped-frequency perturbation. We have identified three dimensionless parameters $P_{1,2,3}$ [see Eqs. (3)] characterizing the driving strength, the anharmonicity and the strength of the interaction to show that there exist two very different regimes of excitation in this parameters space, i.e., the quantum-mechanical ladder climbing (LC) and the semiclassical autoresonance (AR). The transition boundary to the semiclassical AR in the $P_{1,2}$ parameter space is independent of the nonlinearity parameter $P_3$. In contrast, the LC transition boundary is significantly affected by the strength of the interaction of the particles, because the underlying nonlinear Landau-Zener (LZ) transitions behave differently than their linear counterpart. In the limit of strong interaction, the nonlinear LZ transition probability as a function of the driving strength parameter $P_1$ approaches the Heaviside step function due to the nonlinear phase-locking. We have also found that in both the quantum and the semiclassical regimes the width $\Delta P_1$ of the transition decreases as the strength of the interaction increases. In the quantum limit this effect is related to the autoresonance of the nonlinear LZ transitions, while in the semiclassical limit, the effect is due to the wave packet stability enhancement by avoiding parametric resonance between the center-of-mass motion and the internal dynamics of the condensate.
Possible applications of the results of this paper may include a control of the quantum state of BECs and the implementation of precision detectors based on either the LC or the AR. Unlike the noninteracting case [33], the resolution of such a detector is not limited by quantum fluctuations if the particles interaction is strong enough.
ACKNOWLEDGEMENTS
This work was supported by the Russian state assignment of FASO No.01201463332 and by the Israel Science Foundation Grant No. 30/14.
APPENDIX: STABILITY OF AUTORESONANT TRAJECTORIES.
FIG. 8. The energy $E = \frac{1}{2} (\eta^2 + \eta)$ averaged over the integration time versus $P_3$ from the numerical solution of Eqs. (20),(23) near the threshold of the autoresonance. The lines with squares and circles correspond to $\alpha = 10^{-4}$ and $\alpha = 10^{-6}$, respectively.
Here we discuss the Mathieu-type Eq. (23)
$$\eta_{TT} + [B - C \cos(2\theta)]\eta = 0,$$ \hspace{1cm} (24)$$
where $B = 1 - \frac{3Q_2a^2}{2} - \kappa Q_3$, $C = \frac{3}{2}Q_2a^2$, describing the deviation $\eta$ of the trajectory from the autoresonant solution $\xi_0 = a \cos \theta$ given by Eq. (21).
For sufficiently small amplitudes $a$ this solution is described by [34]
$$\frac{da}{dT} = (Q_1/2) \sin \Phi, \hspace{1cm} (25)$$
$$\frac{d\Phi}{dT} = \alpha T - (3Q_2/8)a^2 + (Q_1/2a) \cos \Phi, \hspace{1cm} (26)$$
where $\Phi = \theta - \bar{\varphi} + \pi$ is the phase mismatch, which starts at zero initially (at large negative $t$, where $a$ is also zero). We are interested in passage through resonance when parameter $Q_1$ is close to the autoresonance threshold $Q_{1th}$ (from either above or below). In both of these cases, $\Phi$ slowly increases initially and then passes $\pi/2$. Then when slightly above the threshold, $\Phi$ starts oscillating, but remains bounded ($|\Phi| < \pi$), while below the threshold $\Phi$ continues to increase reaching $\pi$ and the oscillator fully dephases from the drive.
At this point we observe that there are three parameters ($\alpha, Q_1, Q_2$) in system (25), (26). However, by introducing the slow time $\tau = \alpha^{1/2}T$ and rescaled amplitude $A = \sqrt[4]{3/8} \alpha^{-1/4} Q_2^{1/2}$ we obtain a single parameter system
$$\frac{dA}{d\tau} = \mu \sin \Phi, \hspace{1cm} (27)$$
$$\frac{d\Phi}{d\tau} = \tau - A^2 + (\mu/A) \cos \Phi, \hspace{1cm} (28)$$
where
$$\mu = \sqrt{\frac{3}{32}} Q_1 Q_2^{1/2} \alpha^{-3/4}. \hspace{1cm} (29)$$
The autoresonant threshold in this system is $\mu_{th} = 0.41$ [34], which upon the return to the original parameters $P_{1,2}$ yields (14). Note that at the threshold ($\mu = \mu_{th}$) the rescaled problem has no free parameters.
Next we discuss Eq. (24). Here, using (26), we have
$$\frac{d\theta}{dT} = \frac{d\bar{\varphi}}{dT} + \frac{d\Phi}{dT} = 1 - \alpha T + \frac{d\Phi}{dT} = 1 - \frac{3}{8}Q_2a^2 + \frac{Q_1}{2a} \cos \Phi \hspace{1cm} (30)$$
and assume that $S = -\frac{3}{8}Q_2a^2 + \frac{Q_1}{2a} \cos \Phi$ is small compared to unity in the region of dephasing. This suggests to transform from $T$ to $\theta$ in (24) and approximate the problem by the Mathieu equation with slow coefficients
$$\frac{d^2 \eta}{d\theta^2} + [B' - C' \cos(2\theta)]\eta \approx 0 \hspace{1cm} (31)$$
where to lowest order in small parameters
$$B' = \frac{B}{(1 + S)^2} \approx 1 - \frac{3}{4}Q_2a^2 - \frac{Q_1}{a} \cos \Phi - \kappa Q_3 \hspace{1cm} (32)$$
$$C' = \frac{C}{(1 + S)^2} \approx C = \frac{3}{2}Q_2a^2 \hspace{1cm} (33)$$
From the theory of the Mathieu equation (with fixed parameters, which we assume locally in our case), the stability condition of the solution of (31) is [35]
$$B' < 1 - C'/2 \hspace{1cm} (34)$$
or
$$\kappa Q_3 > \max\left(-\frac{Q_1}{a} \cos \Phi\right) \hspace{1cm} (35)$$
Finally, in the last equation we use the rescaled amplitude $A$ instead of $a$ to get the dimensionless condition
$$\kappa P_3 > P_1 P_2^{1/2} \max\left(-\frac{\cos \Phi}{A}\right)_{\mu = \mu_{th}} \hspace{1cm} (36)$$
where the rescaled parameters are $P_1 = Q_1/(2a)^{1/2}$, $P_2 = (3/4)Q_2/\alpha^{1/2}$, $P_3 = Q_3/\alpha^{1/2}$ and the value of
\[ \max \left( \frac{\cos \Phi}{\mu} \right)_{\mu=\mu_0} = 0.37 \] is found numerically by solving (27), (28). Thus, for \( \kappa = 0 \), the solution remains stable only if \( \Phi < \pi/2 \) and, since we approach this value in the vicinity of the threshold as mentioned above, one encounters instability near the threshold, explaining the appearance of the width of the autoresonance transition as some initial conditions dephase. On the other hand, a sufficiently large \( \kappa P_3 \) stabilizes the solution and the width of the autoresonance threshold disappears. For the parameters of Fig. 5 one finds that the solution is stable for \( P_3 > 0.27 \). Finally we check these conclusions by solving the set (21) and (22) numerically. The results of these simulations are presented in Fig. 8, showing the energy \( E = \frac{1}{2} (\eta^2 + \eta) \) averaged over the integration time versus \( P_3 \) for the parameters of Fig. 5 and initial conditions \( \eta = 1, \eta_T = 0 \) and integrating between \( T = -2 \times 10^4 \) and \( 4 \times 10^4 \) for \( \alpha = 10^{-4} \) and \( T = -2 \times 10^5 \) and \( 4 \times 10^5 \) for \( \alpha = 10^{-6} \). One can see the transition to instability at \( P_3 < 0.3 \).
[1] J. F. Dobson, Phys. Rev. Lett., 73, 2244 (1994).
[2] H. Ott, J. Fortagh, S. Kraft, A. Günther, D. Komma, and C. Zimmermann, Phys. Rev. Lett., 91, 040402 (2003).
[3] V. I. Veksler, Doklady Akad. Nauk SSSR, 43, 346 (1944); E. M. McMillan, Phys. Rev., 68, 144 (1945).
[4] L. Friedland, Physical Review E, 59, 4106 (1999).
[5] L. Friedland and A. G. Shagalov, Physics of Fluids, 14, 3074 (2002).
[6] M. Assaf and B. Meerson, Phys. Rev. E, 72, 016310 (2005).
[7] J. Fajans, E. Gilson, and L. Friedland, Phys. Rev. Lett., 82, 4444 (1999).
[8] R. R. Lindberg, A. E. Charman, J. S. Wurtele, L. Friedland, and B. A. Shadwick, Physics of Plasmas, 13, 123103 (2006).
[9] O. Yaakobi, L. Friedland, R. R. Lindberg, A. E. Charman, G. Penn, and J. S. Wurtele, Physics of Plasmas, 15, 032105 (2008).
[10] L. A. Kalyakin, M. A. Shamsutdinov, R. N. Garifullin, and R. K. Salimov, The Physics of Metals and Metallography, 104, 107 (2007).
[11] S. V. Batalov and A. G. Shagalov, The Physics of Metals and Metallography, 114, 103 (2013).
[12] G. Klughertz, L. Friedland, P.-A. Hervieux, and G. Manfredi, Phys. Rev. B, 91, 104433 (2015).
[13] A. Barak, Y. Lambot, L. Friedland, and M. Segev, Phys. Rev. Lett., 103, 123901 (2009).
[14] G. Marcus, L. Friedland, and A. Zigler, Phys. Rev. A, 69, 013407 (2004).
[15] L. Friedland, The Astrophysical Journal, 547, L75 (2001).
[16] A. I. Nicolin, M. H. Jensen, and R. Carretero-Gonzalez, Physical Review E, 75, 036208 (2007).
[17] R. Bücker, T. Berrada, S. van Frank, J.-F. Schaff, T. Schumun, J. Schmiedmayer, G. Jäger, J. Grond, and U. Hohenester, J. Phys. B: At. Mol. Opt. Phys., 46, 104012 (2013).
[18] F. Dalfovo, S. Giorgini, L.P. Pitaevskii, and S. Stringari Rev. Mod. Phys., 71, 463 (1999).
[19] I. Barth, L. Friedland, O. G. Ghalog, and A. G. Shagalov, Phys. Rev. A, 84, 013837 (2011).
[20] G. B. Andrews, M. D. Ashkezari, M. Baquero-Ruiz et al, Phys. Rev. Lett., 106 025002 (2011).
[21] Y. Shalibo, Y. Rofe, I. Barth, L. Friedland, R. Bialczak, J. M. Martinis, and N. Katz, Phys. Rev. Lett., 108, 037701 (2012).
[22] L. Landau and E. Lifshitz, Quantum Mechanics: Non-relativistic Theory (Butterworth-Heinemann, 1977).
[23] L. Landau, Phys. Z. Sowietunion, 2, 46 (1932); C. Zener, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 137, 696 (1932).
[24] N. V. Vitanov and B. M. Garraway, Phys. Rev. A, 53, 4288 (1996).
[25] J. Liu, L. Fu, B.-Y. Ou, S.-G. Chen, D.-I. Choi, B. Wu, and Q. Niu, Phys. Rev. A, 66, 023404 (2002).
[26] Q. Zhang, P. Hänggi, and J. Gong, New Journal of Physics, 10, 073008 (2008).
[27] F. Trimborn, D. Witthaut, V. Kelg, and H. J. Korsch, New Journal of Physics, 12, 053010 (2010).
[28] B. Wu and Q. Niu, Phys. Rev. A, 61, 023402 (2000).
[29] O. Zobay and B. M. Garraway, Phys. Rev. A, 61, 033603 (2000).
[30] J. Fajans and L. Friedland, Am. J. Phys., 69, 1096 (2001).
[31] B. Hiley, in Proc. Int. Conf. Quantum Theory: Reconsideration of Foundations, Vol. 2 (2004) pp. 267.
[32] C. Canuto, M. Y. Hussaini, A. M. Quarteroni, and T. A. Zang, Spectral methods (Springer-Verlag, Berlin, 2006).
[33] K. W. Murch, R. Vijay, I. A. G. Shagalov, and A. M. Quanta, L. Friedland, and I. Siddiqi, Nat. Phys, 7, 105 (2010).
[34] L. Friedland, Scholarpedia 4, 5473 (2009).
[35] C. Hayashi, Nonlinear Oscillations in Physical Systems (Princeton University Press, Princeton, 1985). | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
5017,
1
],
[
5017,
10209,
2
],
[
10209,
14401,
3
],
[
14401,
17596,
4
],
[
17596,
22127,
5
],
[
22127,
27278,
6
],
[
27278,
29207,
7
],
[
29207,
32994,
8
],
[
32994,
37588,
9
]
]
} |
1d9644f64fd8f67b53a4af28f75299ab283dec8f | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 27691,
"total-output-tokens": 11026,
"fieldofstudy": [
"Medicine"
]
} | SPINK1 Mutation in Idiopathic Chronic Pancreatitis: How Pertinent Is It in Coastal Eastern India?
Subhra S. Jena 1, Girish K. Pati 2, Kanishka Uthansingh 1, G Vyhab Venkatesh 3, Pradeep Mallick 3, Manas Behera 3, Himmy Narayan 3, Debakanta Mishra 3, Shobhit Agarwal 3, Manoj K. Sahu 1
1. Molecular Diagnostic and Research Center, Institute of Medical Sciences and SUM Hospital, Siksha ‘O’ Anusandhan Deemed to be University, Bhubaneswar, IND 2. Department of Gastroenterology, Institute of Medical Sciences and SUM Hospital, Siksha ‘O’ Anusandhan Deemed to be University, Cuttack, IND 3. Department of Gastroenterology, Institute of Medical Sciences and SUM Hospital, Siksha ‘O’ Anusandhan Deemed to be University, Bhubaneswar, IND
Corresponding author: Manoj K. Sahu, [email protected]
Abstract
Background and aim
Idiopathic chronic pancreatitis (ICP) is said to be present when no identifiable etiology can be identified. Robust evidence suggested that the serine protease inhibitor nucleus Kazol type 1 (SPINK1) N34S mutation was frequently associated with ICP. As there is a paucity of data on genetic studies in ICP cases from the coastal eastern region of India, we performed this study with an aim to evaluate the SPINK1 genetic mutations and other associated clinical correlates in ICP cases.
Material and methods
Consecutive ICP cases attending the department of gastroenterology, Institute of Medical Sciences (IMS) and SUM Hospital, were enrolled and evaluated for the pertinent clinical history and undergone detailed biochemical and radiological evaluations. Two ml of venous blood in ethylenediaminetetraacetic acid (EDTA) vials were collected from each case and subjected to a polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) test for genetic analysis.
Result
In this study, the mean age of the cases at the first consultation with us and the age of the first clinical presentation were 34.52±6.44 and 28.73±5.52 years, respectively. Males outnumbered females (Male:Female = 2.12:1). Out of the total of 200 cases, 50% had no SPINK1 mutation, whereas 40% and 10% cases had SPINK1 N34S heterozygous and homozygous mutations, respectively. The mean age of clinical presentation, severe abdominal pain, exocrine and endocrine insufficiency, and parenchymal atrophy were significantly more common in mutants as compared to non-mutants (p-value <0.05).
Conclusion
In our region, 50% of ICP cases had the SPINK1 N34S mutation. The SPINK1 mutants had a relatively more severe variety of pancreatitis as compared to non-mutants.
Introduction
Chronic pancreatitis (CP) is described as a chronic inflammatory complex disorder of the pancreas, resulting in irreversible morphological changes and manifests usually with recurrent or chronic abdominal pain initially and with exocrine and/or, endocrine insufficiencies in the long run [1-2]. Most patients with CP usually suffer from a relapsing and remitting type of abdominal pain initially and may suffer from maldigestion, diabetes mellitus, and pancreatic cancer later on if they were improperly managed [3].
Although a lot of putative factors for the development of CP were described in the literature, in nearly 10%-30% of the cases, no identifiable cause could be identified, and these cases were labeled as idiopathic chronic pancreatitis (ICP) [4]. A lot of research has been carried out on acute and CP as a whole, but very few studies have characteristic disposition on ICP, a distinct form of CP, which remains a mystery to date. A previous report suggested that ICP was prevalent only in certain geographic regions of India [4]. In the preceding few years, many cases of ICP have been reported not only from different regions of the western world but also from most states of India too [5]. It was hypothesized that ICP is a complex disorder, which may occur due to varied interaction of genetic mutations and the environment [6-7]. Various genetic mutations in different putative genes such as the cationic trypsinogen (PRSS1) gene, serine protease inhibitor nucleus Kazol type 1 (SPINK1) gene, cystic fibrosis transmembrane conductance regular (CFTR) gene, and cathepsin B gene have
How to cite this article
Jena S S, Pati G K, Uthansingh K, et al. (April 12, 2021) SPINK1 Mutation in Idiopathic Chronic Pancreatitis: How Pertinent Is It in Coastal Eastern India?. Cureus 13(4): e14427. DOI 10.7759/cureus.14427
been well-described in acute, recurrent, and chronic pancreatitis [8]. ICP is usually associated with a mutation in the SPINK1 gene, but its true prevalence in the community over different geographic regions was not well-studied to date due to the non-availability of molecular and genetic laboratories in the concerned regions. The SPINK1 gene is usually located on chromosome 5 and acts as the first line of defense against the development of pancreatitis, as it limits the premature activation of trypsinogen inside the zymogen granules of the pancreas by competitively blocking the active site of trypsin, by which the autodigestion of pancreatic parenchyma could be prevented [8-9]. In case of a SPINK1 mutation or alteration, pancreatitis may set in due to the unabated activity of trypsin [10]. Previous studies by Gomez-Lira M et al. and Shetty S et al. revealed that genetic mutation may be the most important causative factor of ICP [7,11]. Usually, the most common mutation in the SPINK1 gene occurs in exon 3 at codon 34, which results in a change of amino acid from asparagine to serine (N34S), by which trypsin inhibitory capacity gets compromised. Previous studies suggested that the SPINK1 N34S mutation was fairly common in ICP cases [6,12-13]. To date, as there is a paucity of genetic studies in ICP cases from this part of the coastal eastern region, we carried out this targeted genetic study with an aim to evaluate the prevalence of the SPINK1 N34S mutation in cases with ICP and to correlate it with different clinical and morphological presentations.
**Materials And Methods**
This study was a facility-based, cross-sectional, open-labeled, non-interventional cohort study that was carried out for a duration of 11 months in 2020.
In this study, consecutive ICP cases attending the department of gastroenterology, Institute of Medical Sciences (IMS) and SUM Hospital, Bhubaneswar, Odisha, were enrolled and evaluated in detail about pertinent clinical presentations and family history; and their genetic studies were carried out in the Molecular Diagnostic and Research Center, IMS and SUM Hospital. Written informed consent was obtained from all the cases, and the study protocol was approved by the institutional ethical committee. All the cases were subjected to pertinent biochemical tests and radiological evaluation by abdominal ultrasonography and contrast-enhanced computed tomography (CECT) study. Complications of CP such as diabetes mellitus (DM), steatorrhea, distal biliary stricture, and pseudocyst were diagnosed on the basis of standard clinical, biochemical, and radiological criteria. Chronic pancreatitis was said to be present when at least two separate episodes of pancreatic type of abdominal pain and typical radiological findings such as pancreatic parenchymal calcifications, parenchymal atrophy, intraductal stones, and ductal dilations were noted [5]. All these structural abnormalities may be variably present in ICP cases. Pertinent clinical history included etiology, type, and severity of pain, age of first clinical presentation, total disease duration, presence or absence of fatty diarrhea (steatorrhea) and diabetes mellitus, etc. CP cases with underlying etiological factors, such as a history of significant alcohol drinking (daily intake ≥ of 80 gram of ethanol for at least two years), cholelithiasis, infection, trauma, medications, surgery, metabolic disorders, such as hypercalcemia (serum calcium > 12 mg/dl) and hypertriglyceridemia (serum triglyceride > 1000 mg/dl), and a family history of pancreatitis (presence of at least two affected first-degree relatives or three or more second-degree relatives in two or more generations) [5,14-15] were excluded from the study. Steatorrhea was diagnosed subjectively, whenever patients passed oily and/or sticky stool. Diabetes mellitus (DM) was diagnosed if fasting blood glucose (FBS) value was ≥126 mg/dl and/or two-hour plasma glucose (two-hour post-glucose blood sugar (PGBS)), or random blood glucose (RBS) value ≥200 mg/dl [16].
**Procedures for mutational analysis**
The genotyping procedure starts from the collection of the patient’s peripheral blood sample in EDTA-containing tubes, extraction of deoxyribonucleic acid (DNA), carrying out polymerase chain reaction (PCR) by using the targeted primer for SPINK1 and restriction fragment length polymorphism (RFLP) by using the BsrDI and PstI restriction enzymes. The mutational changes were assayed by analyzing the developed digested and undigested products in form of bands through the Biorad gel doc imaging system.
1. **Sample collection**: Approximately 2 ml of venous blood was collected from each of the participants for genetic analysis. The peripheral blood samples were collected in EDTA-containing tubes followed by storage in a refrigerator for further processing.
2. **DNA extraction**: Genomic DNA was extracted and purified from whole blood by using the salting-out method, which was further utilized for polymerase chain reaction (PCR) to study genetic polymorphism. The isolated DNA was converted to a concentration of 80-100 ng for further PCR analysis.
3. **Polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP)**: The N34S mutation was assayed by the PCR-RFLP technique. Designed primers were used to amplify exon 3 on the basis of specific nucleotide sequences (GenBank, NM-003122). Proofreading activity may be carried out from the 3’ to 5’ location during the PCR test for the elimination of any PCR-related error if required. PCR was performed by using a genomic DNA template. The forward and reverse primer sequences were 5’-TTC TGT TTA ATT CCA TTT TTA GGC CAA ATG CTG CA-3’ and 5’-GGC TTA CAT ACA AGT GAC TTC T-3’, respectively. The primers were designed to introduce a PstI endonuclease restriction site in sequences having N34S mutation and a BsrDI endonuclease restriction site at wild-type sequences. Before doing PCR, we made the aliquot; the powder form of primer by taking nuclease-free water and stock primer. The isolated DNA was converted
to a concentration of 80-100 ng for further steps. Subsequently, for further PCR procedure, we used the Dream Taq Green PCR master mix to assess the reaction. Denaturation was done by setting the heat temperature to 93°C-95°C; the reaction mixture was heated at 95°C for a brief period to denature the double-stranded target DNA into a single-stranded form, which can act as a template for DNA synthesis. The annealing temperature was set to 55°C-60°C; the same mixture subsequently quickly cooled to a defined temperature, which is used to permit the primer/s to bind target groups on both the strands of flanking targeted DNA. The extension temperature was set to 71°C-72°C; during this step, the temperature of the reaction mixture was again elevated to 72°C to allow the enzyme to synthesize the single-stranded template DNA. Finally, the extension temperature was set at 72°C. Initially, the stock primer was converted to a working primer according to the protocol sheet by Thermo Fisher Scientific Company (Waltham, Massachusetts) by adding 90 µl nucleus-free water with 10 µl stock primer (forward and reverse). After preparation of the master mix, it was mixed properly by the use of a vortex, and out of it, 9.5 µl and 12.5 µl were transferred to PCR tubes sequentially to assess the reaction. Then the PCR tubes were made bubble-free by tapping and rotated for proper mixing. Following completion of all the PCR steps, we assayed the amplified bands in 2% gel by running gel electrophoresis. The image developed in the gel was visualized under gel doc. All the PCR byproducts were subjected to digestion procedures by the use of restriction endonucleases PstI and BsrDI as per the protocol. Subsequently, it was thawed vigorously and incubated at 55°C for 1 hour. Then, the products were analyzed by agarose gel electrophoresis by the use of 3% (w/v) Nusieve 3:1 agarose. The genotypes were determined on the basis of the expected product size {A/A Genotype (Asn 34 Asn) - 320bp, G/G Genotype (Ser 34 Ser) - 286bp, A/G Genotype (Asn 34 Ser) - 320,286 and 34}.
4. Statistical analysis: All the results were expressed as mean ± standard deviation (SD) or frequency (in percent). The quantitative and categorical variables were compared by using the student’s t-test and chi-square test, respectively. All the analyses were performed by using the Statistical Package for the Social Sciences (SPSS) 22 software (IBM Corp., Armonk, NY). A p-value of <0.05 was considered statistically significant.
Results
In this study, 200 consecutive ICP cases were included. Males outnumbered females (Males:Females - 2.12:1). The mean age of presentation at baseline and first clinical presentation were 34.52±6.44 and 28.73±5.52 years, respectively. The mean disease duration was 5.94±3.36 years. The different characteristics of ICP cases and their comparative analysis are described in Tables 1-2, respectively. Most (95.5%) of the cases presented with the pancreatic type of abdominal pain. Exocrine insufficiency in the form of steatorrhea was complained of by 20.5% cases, whereas 19% of cases suffered from endocrine insufficiency in the form of type 2 DM. The clinical presentations of ICP cases and their comparative analyses are presented in Tables 3-4, respectively. The presence of a distal biliary stricture and pancreatic pseudocyst was noticed in 11.5% and 14% cases, respectively. Most (70.5%) cases had a pancreatic structural abnormality in form of parenchymal calcifications; whereas 34.5% cases had parenchymal atrophy. Sixty-five point five percent (65.5%) and 60.5% cases had a dilated pancreatic duct and intraductal calculi, respectively. The structural changes of ICP cases and their comparative analyses were illustrated in Tables 5-6 respectively. In our study subjects, 50% of cases had no mutational changes or wild-type sequences of the SPINK1 gene, whereas 40% and 10% cases had SPINK1 heterozygous and homozygous mutations, respectively. A comparative analysis of all the characteristics in between SPINK1 mutated and un-mutated cases is described in Table 7.
| Characteristics | Total cases (n – 200) | Cases with homozygous mutation (n – 20) | Cases with heterozygous mutation (n – 80) | Un-mutated cases (n – 100) |
|----------------------------------------|-----------------------|----------------------------------------|------------------------------------------|---------------------------|
| Male:Female ratio | 2.12:1 | 4:1 | 1.85:1 | 2.12:1 |
| Mean age of presentation at baseline in years | 34.52±6.44 | 26.7±5.32 | 32.49±5.82 | 37.71±5 |
| Mean age of first clinical presentation in years | 28.73±5.52 | 21.75±2.24 | 25.94±3.51 | 32.36±4.59 |
| Mean disease duration in years | 5.94±3.36 | 4.95±3.35 | 6.54±3.19 | 5.65±3.45 |
**TABLE 1: Different characteristics of ICP cases**
ICP: idiopathic chronic pancreatitis
| Characteristics | p-value in between homozygote and heterozygote | p-value in between homozygote and un-mutated cases | p-value in between heterozygote and un-mutated cases |
|---------------------------------------------|------------------------------------------------|---------------------------------------------------|-----------------------------------------------------|
| Male:female ratio | 0.19 | 0.25 | 0.67 |
| Mean age of presentation at baseline in years | 0.0001 | 0.0001 | 0.0001 |
| Mean age of first clinical presentation in years | 0.0001 | 0.0001 | 0.0001 |
| Mean disease duration in years | 0.051 | 0.4 | 0.07 |
**TABLE 2: Comparative analysis of different characteristics of ICP cases**
ICP: idiopathic chronic pancreatitis
| Clinical presentations | Total cases (%) (n – 200) | Cases with homozygous mutation (%) (n – 20) | Cases with heterozygous mutation (%) (n – 80) | Un-mutated cases (%) (n – 100) |
|------------------------|---------------------------|---------------------------------------------|-----------------------------------------------|--------------------------------|
| Abdominal Pain | 95 | 100 | 100 | 94 |
| Non-Severe Abdominal Pain | 64 | 25 | 52.55 | 84 |
| Severe Abdominal Pain | 31 | 75 | 47.5 | 10 |
| Passage of Fatty Stool | 20.5 | 45 | 25 | 12 |
| Presence of Diabetes Mellitus | 19 | 35 | 25 | 11 |
**TABLE 3: Clinical presentations of ICP cases**
n - Number
ICP: idiopathic chronic pancreatitis
| Clinical presentations | p-value in between homozygote and heterozygote | p-value in between homozygote and un-mutated cases | p-value in between heterozygote and un-mutated cases |
|------------------------|------------------------------------------------|---------------------------------------------------|-----------------------------------------------------|
| Non Severe Abdominal Pain | 0.03 | <0.0001 | <0.0001 |
| Severe Abdominal Pain | 0.02 | <0.0001 | <0.0001 |
| Passage of Fatty Stool | 0.07 | 0.0004 | 0.02 |
| Presence of Diabetes Mellitus | 0.36 | 0.0006 | 0.01 |
**TABLE 4: Comparative analysis of clinical presentations of ICP cases**
ICP: idiopathic chronic pancreatitis
| Structural changes | Total cases (%) (n – 200) | Cases with homozygous mutation (%) (n – 20) | Cases with heterozygous mutation (%) (n – 80) | Un-mutated cases (%) (n – 100) |
|-------------------------|---------------------------|---------------------------------------------|----------------------------------------------|-------------------------------|
| Parenchymal Calcification| 70.5 | 100 | 53.75 | 78 |
| Parenchymal Atrophy | 34.5 | 25 | 50 | 24 |
| Intraductal Calculi | 60.5 | 90 | 60 | 55 |
| Dilated Pancreatic Duct | 65.5 | 90 | 63.75 | 62 |
| Distal Biliary Stricture| 11.5 | 25 | 13.75 | 7 |
| Pseudocyst | 14 | 20 | 18.75 | 9 |
**TABLE 5: Structural changes in ICP cases**
n - Number
ICP: idiopathic chronic pancreatitis
| Structural changes | p-value in between homozygote and heterozygote | p-value in between homozygote and un-mutated cases | p-value in between heterozygote and un-mutated cases |
|-------------------------|-------------------------------------------------|---------------------------------------------------|-----------------------------------------------------|
| Parenchymal Calcification| 0.0001 | 0.02 | 0.0004 |
| Parenchymal Atrophy | 0.04 | 0.92 | 0.003 |
| Intraductal Calculi | 0.01 | 0.003 | 0.5 |
| Dilated Pancreatic Duct | 0.02 | 0.01 | 0.89 |
| Distal Biliary Stricture| 0.18 | 0.01 | 0.17 |
| Pseudocyst | 0.83 | 0.14 | 0.07 |
**TABLE 6: Comparative analysis of structural changes of ICP cases**
ICP: idiopathic chronic pancreatitis
| Characteristics | SPINK1 mutated cases | SPINK1 un-mutated cases | p-value |
|-----------------------------------------|----------------------|-------------------------|---------|
| Male:Female Ratio | 2:1 | 2.12:1 | 0.88 |
| Mean Age of Presentation at Baseline in Years | 31.33±6.16 | 37.71±5 | 0.0001 |
| Mean Age of First Clinical Presentation in Years | 25.1±3.69 | 32.36±4.59 | 0.0001 |
| Mean Disease Duration in years | 6.22±3.27 | 5.65±3.45 | 0.23 |
| Abdominal Pain (%) | 100 | 90 | 0.012 |
| Severe Abdominal Pain (%) | 52 | 10 | <0.0001 |
| Passage of Fatty Stool (%) | 29 | 12 | 0.0029 |
| Presence of Diabetes Mellitus (%) | 27 | 11 | 0.0039 |
| Parenchymal Calcification (%) | 64 | 78 | 0.02 |
| Parenchymal Atrophy (%) | 49 | 24 | 0.0002 |
| Intraductual Calculi (%) | 66 | 55 | 0.11 |
| Dilated Pancreatic Duct (%) | 69 | 62 | 0.29 |
| Distal Biliary Stricture (%) | 16 | 07 | 0.04 |
| Pseudocyst (%) | 19 | 09 | 0.04 |
**TABLE 7: Comparative analysis between SPINK1 mutated and un-mutated cases**
**SPINK1: serine protease inhibitor nucleus Kazol type 1**
**Discussion**
Males outnumbered females in our study, as similarly reported by other Indian studies by Shetty S et al. [11] and Balakrishnan V et al. [17]. The mean age of presentation at baseline was 34.52±6.44 years, which was consistent with study findings by Shetty S et al. [11], Balakrishnan V et al. [18], and Garg PK et al. [19]. The mean duration of the disease in our cases was 5.94±3.36 years, whereas it was 51 months, 48 months, and 27 months as reported by Shetty S et al. [11], Garg PK et al. [20], and Midha S et al. [21]. Abdominal pain was the most common clinical presentation in our study, which was in agreement with the findings by Balakrishnan V et al. [18], Midha S et al. [21], and Layer et al. [22]. History suggestive of steatorrhoea was present in 20.5% of our study population, whereas its prevalence was 5%, 15%, and 5% in studies by Midha et al. [21], Shetty S et al. [11], and Garg PK et al. [20], respectively, which indicated that steatorrhoea was relatively more common in ICP cases from our region as compared to other regions. We noticed that 19% of our study population had type 2 DM, whereas its prevalence was 35%, 26%, and 27% as observed by Shetty S et al. [11], Garg PK et al. [20], and Midha S et al. [21], respectively, which suggested that ICP cases from our region had a lower prevalence of DM in comparison to cases from other geographic regions. We observed that 70.5%, 65.5%, and 60.5% of cases from our region had pancreatic parenchymal calcification, dilated pancreatic duct (PD), and intraductal calculi respectively; on the contrary, Shetty S et al. noticed that 87.87%, 75%, and 21% of cases had these type of structural abnormalities respectively in his study group [11]. We observed that, amongst all the ICP cases from our region, 50% cases had no genetic mutation in the SPINK1 gene or had the wild variety of the SPINK1 gene, whereas the rest 50% cases had the SPINK1 N34S mutation (40% were heterozygous, and 10% were homozygous). Shetty S et al. [11], Garg PK et al. [20], Bhatia et al. [23], and Chandak GR et al. [24] showed that 36.36%, 42%, 40%, and 32.5% of their cases had the SPINK1 mutation, respectively, which supported our study findings. We noticed that out of all the 100 SPINK1 N34S mutated cases, 20% of cases were homozygote, which was consistent with the result reported by Chandak GR et al. [24], who found that 18.42% of SPINK1 N34S mutated cases were homozygotes. The prevalence of the SPINK1 mutation in ICP cases from our region was 50%, which was relatively higher compared to findings of other published reports such as 6.4% by Chen JM et al. [25], 18.0% by Threadgold J et al. [26], 21.0% by Drenth JP et al. [27], and 40.4% by Pfutzer et al. [6]. We also noticed that 64% of cases with SPINK1 mutation had parenchymal calcification, which was much less in comparison to findings by Shetty S et al. [11], who found parenchymal calcification in all the SPINK1 mutated cases in his study group. We also observed that 49% of cases with SPINK1 mutation had parenchymal atrophy, which was much less compared to the study result by Shetty S et al. [11], who reported 75% of cases with the SPINK1 mutation had parenchymal atrophy. In our study, although the mean age of the first clinical presentation and presentation at baseline in mutated cases were significantly earlier as compared to non-mutated cases, the mean disease duration was not significantly different (p>0.05) in between them. Mutated cases had a higher...
occurrence of severe abdominal pain, steatorrhea, and type 2 DM as compared to un-mutated cases. We also observed that mutated cases had a significantly higher prevalence of pancreatic parenchymal atrophy, distal biliary stricture, and pancreatic pseudocyst in comparison to their un-mutated counterparts, although the prevalence of intraductal calculi and dilated pancreatic duct were not significantly different in between them. We also observed that homozygote cases had a relatively earlier mean age of first clinical presentation and presentation at baseline when compared to heterozygote cases. Although homozygote cases had a higher occurrence of severe abdominal pain as compared to heterozygote, they had no significant difference in the prevalence of fatty diarrhea and type 2 DM in between them. We, too, found that homozygote had a significantly higher prevalence of parenchymal calcification, ductal dilatation, and intraductal calculi as compared to heterozygote, although the prevalence of pancreatic pseudocyst and distal biliary stricture was not different between them. Surprisingly we found that un-mutated cases had a significantly higher prevalence of pancreatic parenchymal calcification as compared to mutated cases and heterozygote had a higher prevalence of pancreatic parenchymal atrophy as compared to homozygote, which suggests that, possibly, SPINK1 mutation is not a predominant disease inducer as earlier presumed; rather, it may be a disease modifier too and its effect may be modified by the environment and other associated mutated genes if present. Truninger K et al. [28] suggested that a stronger genetic abnormality may be an etiologic event for early-onset ICP as compared to late-onset ICP, but the study by Chandak GR et al. [24] did not support his finding. Chandak GR et al. [24] found no significant phenotypical differences between SPINK1 mutated and un-mutated cases and between SPINK1 N34S heterozygote and homozygote, although he observed that homozygote had a higher prevalence of type 2 DM as compared to heterozygote. Threadgold J et al. [26] reported that the SPINK1 N34S mutation was neither associated with earlier disease onset nor a severe type of chronic pancreatitis. He also noted that there were no significant differences between N34S mutated and un-mutated cases in terms of age of onset of pancreatic exocrine and endocrine insufficiency, frequency and duration of attacks, number of hospitalizations, age of first surgery, and surgical repair for complicated pancreatitis [26]. In contrast to the above study findings, the study by Muller N et al. reported that SPINK1 mutated cases had a higher prevalence of acute pancreatic episodes, more abdominal pain, higher pancreatic morphological abnormalities, and were more prone to suffer from pancreatic exocrine and endocrine insufficiency as compared to un-mutated ICP cases [29]. Singh S et al. [30] reported that the N34S heterozygous mutation was relatively more prevalent as compared to the homozygous mutation, which was consistent with our study result. He also found that no significant phenotypical differences could be noticed between homozygote and heterozygote [30]. Threadgold J et al. suggested that the prevalence of the SPINK1 N34S mutation was higher in ICP cases (18%) as compared to normal individuals (2.5%), and familial ICP cases had a higher prevalence of this specific genetic mutation as compared to true or non-familial ICP patients (86% vs. 12.6%, respectively) too [26].
Limitations
We have some limitations in our study. We have neither assayed mutations in any other associated susceptible genes or ruled out any other susceptible locus mutations except targeted N34S mutation of the SPINK1 gene because of logistic issues and our study inclusion criteria. We have not stratified our cases into familial and true ICP cases, as our diagnosis of ICP was based only on the absence of known etiological factors, including heredity. We have assayed exocrine insufficiency only symptomatically and not objectively by subjecting the cases neither for fecal fat estimation or the elastase test due to the non-availability of these facilities in our region.
Conclusions
From the study findings, we conclude that the SPINK1 N34S mutation was fairly common in ICP cases and the prevalence of the heterozygous mutation was relatively more common in comparison to the homozygous mutation. Although the disease onset was earlier in mutated cases as compared to un-mutated cases, and mutants had a relatively severe type of pancreatitis, clinical severity, and structural abnormality cannot be decided solely on the basis of this targeted genetic defect of the SPINK1 gene; rather, there might be some other hidden factors, a variable role of the environment, and other associated, unknown genetic mutations, which might have a contributory role in the phenotypical and morphological presentations of the disease, which needs to be meticulously addressed in future studies. However, a larger number of ICP cases should be subjected to detailed genetic testing to validate our findings in the future, and in the current context, we cannot advocate our study findings would be applicable globally, as we too observed variable types of results in our study population, which cannot be explained on the grounds of genetic mutation only and need further, long-term prospective studies to find out a definitive, conclusive answer in the future.
Additional Information
Disclosures
Human subjects: Consent was obtained or waived by all participants in this study. Institutional Ethics Committee, IMS & SUM Hospital, S O’A Deemed to be University, Bhubaneswar issued approval NA. Animal subjects: All authors have confirmed that this study did not involve animal subjects or tissue. Conflicts of interest: In compliance with the ICMJE uniform disclosure form, all authors declare the following: Payment/services info: All authors have declared that no financial support was received from any organization for the submitted work. Financial relationships: All authors have declared that they have no
financial relationships at present or within the previous three years with any organizations that might have an interest in the submitted work. **Other relationships:** All authors have declared that there are no other relationships or activities that could appear to have influenced the submitted work.
**Acknowledgements**
We are grateful to Prof Manojranjan Nayak, Honorable President, Sikkha ‘O’ Anusandhan (SOA) Deemed to be University, for providing us wholehearted support to undertake this genetic research in the well-equipped Institutional Molecular Lab. We are also thankful to Miss S Muthamil and Dr. Santhosh Mani for their technical support during the lab work. Last, but not least, we express our heartiest gratitude to all the study subjects, who consented to this revolutionary genetic study, without whom this study won’t have become reality.
**References**
1. Steer ML, Waxman I, Freedman S: Chronic pancreatitis. N Engl J Med. 1995, 332:1482-90. 10.1056/NEJM199506013522206
2. Somogyi L, Martin SP, Venkatesan T, Ulrich CD 2nd: Recurrent acute pancreatitis: an algorithmic approach to identification and elimination of inciting factors. Gastroenterology. 2001, 120:708-17. 10.1053/gast.2001.22333
3. Emmad B, Whitcomb DC: Chronic pancreatitis: diagnosis, classification, and new genetic developments. Gastroenterology. 2001, 120:682-707. 10.1053/gast.2001.22586
4. Yadav D, Lowenfels AB: The epidemiology of pancreatitis and pancreatic cancer. Gastroenterology. 2013, 144:1252-61. 10.1053/j.gastro.2013.01.068
5. Yadav D, Timmons L, Benson JT, Dierkhising RA, Charl ST: Incidence, prevalence, and survival of chronic pancreatitis: a population-based study. Am J Gastroenterol. 2011, 106:2192-9. 10.1058/ajg.2011.328
6. Pelaye-Luna M, Robles-Diaz G, Canizales-Quinteros S, Tusú-Luna MT: PRSS1 and SPINK1 mutations in idiopathic chronic and recurrent acute pancreatitis. World J Gastroenterol. 2014, 20:11778-92. 10.3748/wjg.v20.i35.11788
7. Gómez-Lira M, Bonamini D, Castellani C, Unis L, Cavallini G, Assael BM, Pigatti PF: Mutations in the SPINK1 gene in idiopathic pancreatitis Italian patients. Eur J Hum Genet. 2003, 11:543-6. 10.1038/sj.ejhg.5200989
8. Sobczyńska-Tomaszewka A, Bak D, Oralewska B, et al.: Analysis of CFTR, SPINK1, PRSS1 and AAT mutations in children with acute or chronic pancreatitis. J Pediatr Gastroenterol Nutr. 2006, 43:299-306. 10.1097/01.mpg.0000232570.48773.df
9. Whitcomb DC: Genetic predispositions to acute and chronic pancreatitis. Med Clin North Am. 2000, 84:531-547. 10.1016/s0025-7125(00)70238-8
10. Esposito I, Friess H, Bückler MW: Molecular mechanisms in chronic pancreatitis [Article in German]. Zentralbl Chir. 2001, 126:867-72. 10.1055/s-2001-19158
11. Shetty S, Leelakrishnan V, Krishnaveni S, et al.: A study of SPINK1 mutation and other clinical correlates in idiopathic chronic pancreatitis. JOP. 2016, 17:607-611.
12. Witt H, Luck W, Hennies HC, et al.: Mutations in the gene encoding the serine protease inhibitor, Kazal type 1 are associated with chronic pancreatitis. Nat Genet. 2000, 25:213-6. 10.1038/76088
13. Audrézet MP, Chen JM, Le Maréchal C, et al.: Determination of the relative contribution of three genes-the cystic fibrosis transmembrane conductance regulator gene, the cationic trypsinogen gene, and the pancreatic secretory trypsin inhibitor gene-to the etiology of idiopathic chronic pancreatitis. Eur J Hum Genet. 2002, 10:100-6. 10.1038/sj.ejhg.5200736
14. Ammann RW: A clinically based classification system for alcoholic chronic pancreatitis. Summary of an international workshop on chronic pancreatitis. Pancreas. 1997, 14:215-21. 10.1097/00006676-199704000-00001
15. Pfützer R, Myers E, Applebaum-Shapiro S, et al.: Novel cationic trypsinogen (PRSS1) N29T and R122C mutations cause autosomal dominant hereditary pancreatitis. Gut. 2002, 50:271-2. 10.1136/gut.50.2.271
16. Mellitus D: Diagnosis and classification of diabetes mellitus. Diabetes Care. 2005, 28:5.
17. Balakrishnan V, Unnikrishnan AG, Thomas V, et al.: Chronic pancreatitis. A prospective nationwide study of 1,086 subjects from India. JOP. 2008, 9:593-600.
18. Balakrishnan V, Nair P, Radhakrishnan L, Narayanan VA: Tropical pancreatitis - a distinct entity, or merely a type of chronic pancreatitis?. Indian J Gastroenterol. 2006, 25:74.
19. Garg PK, Tandon RK: Survey on chronic pancreatitis in the Asia-Pacific region. J Gastroenterol Hepatol. 2004, 19:999-1004. 10.1111/j.1440-1746.2004.03426.x
20. Garg PK: Chronic pancreatitis: the AIMS, New Delhi experience. Chronic Pancreatitis and Pancreatic Diabetes in India. Balakrishnan V (ed): The Indian Pancreatitis Study Group, Kochi, Kerala, India; 2006. 952.
21. Midha S, Singh N, Sachedev V, Tandon RK, Joshi YK, Garg PK: Cause and effect relationship of malnutrition with idiopathic chronic pancreatitis: prospective case-control study. J Gastroenterol Hepatol. 2008, 23:1578-83. 10.1111/j.1440-1746.2008.04349.x
22. Layer P, DiMagno EP: Early and late onset in idiopathic and alcoholic chronic pancreatitis: different clinical courses. Surgical Clinics. 1999, 79:847-860. 10.1016/s0039-6109(05)77047-7
23. Choudhari G, Bhatia E, Sikora SS, Alexander G: Tropical pancreatitis in North India. Chronic Pancreatitis and Pancreatic Diabetes in India. Balakrishnan V (ed): The Indian Pancreatitis Study Group, Kochi, Kerala, India; 2006. 53-59.
24. Chandak GR, Idiris MM, Reddy DN, Mani KR, Bhaskar S, Rao GV, Singh L: Absence of PRSS1 mutations and association of SPINK1 trypsin inhibitor mutations in hereditary and non-hereditary chronic pancreatitis. Gut. 2004, 53:723-8. 10.1136/gut.2003.026536
25. Chen JM, Mercier B, Audrezet MP, Raguenes O, Quere I, Ferec C: Mutations of the pancreatic secretory
trypsin inhibitor (PSTI) gene in idiopathic chronic pancreatitis. Gastroenterology. 2001, 120:1061-4. 10.1053/gast.2001.23094
26. Threadgold J, Greenhalf W, Ellis I, et al.: The N34S mutation of SPINK1 (PSTI) is associated with a familial pattern of idiopathic chronic pancreatitis but does not cause the disease. Gut. 2002, 50:675-81. 10.1136/gut.50.5.675
27. Drenth JP, te Morsche R, Jansen JB: Mutations in serine protease inhibitor Kazal type 1 are strongly associated with chronic pancreatitis. Gut. 2002, 50:687-92. 10.1136/gut.50.5.687
28. Truninger K, Witt H, Kück J, et al.: Mutations of the serine protease inhibitor, Kazal type 1 gene, in patients with idiopathic chronic pancreatitis. Am J Gastroenterol. 2002, 97:1153-1157. 10.1016/S0002-9270(02)04029-7
29. Muller N, Sarantitis I, Rouanet M, et al.: Natural history of SPINK1 germline mutation related-pancreatitis. EBiomedicine. 2019, 48:581-9. 10.1016/j.ebiom.2019.09.032
30. Singh S, Choudhuri G, Agarwal S: Frequency of CFTR, SPINK1, and cathepsin B gene mutation in North Indian population: connections between genetics and clinical data. Sci World J. 2014, 2014:763195. 10.1155/2014/763195 | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4428,
1
],
[
4428,
10508,
2
],
[
10508,
15779,
3
],
[
15779,
19706,
4
],
[
19706,
22838,
5
],
[
22838,
28140,
6
],
[
28140,
34263,
7
],
[
34263,
39980,
8
],
[
39980,
41139,
9
]
]
} |
96048c4fdeed6fc421ace3161ddd5b709cb768f8 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 20,
"total-fallback-pages": 0,
"total-input-tokens": 36708,
"total-output-tokens": 9241,
"fieldofstudy": [
"Economics"
]
} | Hiding Behind Machines:
When Blame Is Shifted to Artificial Agents
Till Feier∗ Jan Gogoll† Matthias Uhl‡
January 28, 2021
Abstract
The transfer of tasks with sometimes far-reaching moral implications to autonomous systems raises a number of ethical questions. In addition to fundamental questions about the moral agency of these systems, behavioral issues arise. This article focuses on the responsibility of agents who decide on our behalf. We investigate the empirically accessible question of whether the production of moral outcomes by an agent is systematically judged differently when the agent is artificial and not human. The results of a laboratory experiment suggest that decision-makers can actually rid themselves of guilt more easily by delegating to machines than by delegating to other people. Our results imply that the availability of artificial agents could provide stronger incentives for decision makers to delegate morally sensitive decisions.
“Once the rockets are up, who cares where they come down? That’s not my department” says Wernher von Braun.
– Tom Lehrer
∗ TUM School of Governance, TU Munich, Richard-Wagner-Straße 1, 80333 Munich, Germany, [email protected]
† Bavarian Institute for Digital Transformation / TU Munich, Gabelsbergerstr. 4, 80333 Munich, Germany, [email protected]
‡ ZD.B Junior Research Group “Ethics of Digitization”, TUM School of Governance, TU Munich, Richard-Wagner-Straße 1, 80333 Munich, Germany, [email protected]
1 Introduction
In 2017, the airline AirBerlin, Lufthansa’s biggest competitor for German domestic flights, went bankrupt. Lufthansa passengers soon noticed a significant spike in ticket prices. The resulting backlash was enormous and subsequently led to an investigation by Germany’s Federal Cartel Office (FCO). Lufthansa was quick to blame its automated booking system, which had allegedly responded to a spike in demand. This did little to quell the public outrage and FCO president Andreas Mundt famously said that “companies can’t hide behind algorithms” (Busse, 2017). Our article tests the empirical content of this normative statement.
Algorithms have become an integral part of society and are responsible for more tasks than ever before (Manyika et al., 2017). This is not only pushing the frontiers of technology but also challenging our traditional concepts of guilt and responsibility. The diffusion of responsibility between a multitude of actors has long been a trademark of modern institutions. The challenge of locating responsibility within a complex system may even become exponentially more difficult when moral agency is distributed between human operators and autonomous agents (Nissenbaum, 1996). The fact that even the designers of algorithms cannot fully explain their decisions (e.g., black box models in machine learning) adds to this complexity (Rudin, 2019).
Normative ethics raise a fundamental question with respect to the increasing use of artificial agents in decision-making. In which sense can artificial agents also be moral agents and therefore be responsible for their actions? Philosophers and engineers started pondering this question decades ago when computers were merely functioning as calculators (Moor, 1979). There is still little consensus on the matter and the idea of “moral machines” remains under debate (Allen and Wallach, 2012). In any case, the philosophical discussion is predominantly concerned with normative aspects and the question of who ought to be held responsible or blamed if a machine brings about moral evil.
Although these normative questions are of obvious importance, the behavioral impact that the interaction with artificial agents has on the operator’s conduct is not well understood either. It seems crucial, however, for research on behavioral consequences to feed back into the ethical debate. Human operators might get
trapped between the increasing capabilities and autonomy of artificial agents on one hand and our rigid moral understanding of guilt and responsibility on the other. Operators may end up merely filling responsibility gaps in various systems instead of actually being in charge. They might also over-utilize artificial agents even when they are not the ideal choice for a given task, because they wish to use machines as scapegoats (Danaher, 2016).
This study investigates whether delegators will be able to successfully shift blame by delegating tasks to artificial agents. Our investigation focuses on whether people judge delegations to human and artificial agents differently in light of given outcomes. We find no differences between judgments toward human and artificial agents in the event of good outcomes. This means that the morally beneficial delegation to an artificial agent was considered neither better nor worse than the beneficial delegation to a human agent. However, if a bad outcome occurred, delegators fared significantly better if a machine agent caused the failure. Interestingly, participants did not seem to anticipate this pattern as we did not find significant differences regarding delegation decisions themselves. In fact, decisions involving human and artificial agents seem driven by the expected utility of the delegation for the affected party.
Our article proceeds as follows. In Section 2, we will derive our research question. In section 3, we will outline the experimental setup to test it. We will discuss our results in Section 4 and conclude in Section 5.
2 Background and Research Question
A substantial amount of literature is available on the parameters that influence automation use in teams of human supervisors and the machines at their disposal (Dzindolet et al., 2002). In recent years, a number of studies investigated how those parameters change once decisions have moral undertones, i.e., an impact on third parties. Goldbach et al. (2019) found people to be hesitant to delegate decisions to algorithms that affect both the decision-maker herself as well as third parties. Similarly, a study by Niszczota and Kaszás (2020) suggests that algorithm aversion
extends to the financial sector, and that people especially prefer human over artificial agents when it comes to making financial decisions with moral undertones. In a laboratory study, Gogoll and Uhl (2018) identified a strong aversion against delegating morally relevant tasks to algorithms. It seems that people were less willing to delegate tasks to machines if those decisions imposed monetary externalities on third parties. While their study checked for “perceived utility” of the artificial agent and the trust in that agent, they were unable to determine the exact causes of the profound algorithm aversion.
Other studies also support the idea that a lack of trust is unlikely to be the cause of aversion towards machine use. If anything, there seems to be over-reliance and over-trust in machines, even if the lives of people are at stake (Robinette et al., 2016). This suggests that there have to be other causes for machine aversion in decisions with moral implications. We hypothesize that responsibility is a key concept in understanding this phenomenon. Perceived responsibility is already an important research topic in relation to machine use, probably most prominently in the context of automated driving (Hevelke and Nida-Rümelin, 2015). However, little attention has been paid to the question of how the introduction of machine agents might affect the blame and praise that people ascribe to the delegator in light of a given outcome. Understanding how the use of artificial agents is judged would be an important first step in gaining a deeper understanding of how their availability might influence people’s motivation to delegate morally sensible tasks. This is closely linked to the idea that avoiding blame or shirking responsibility can be pivotal factors in delegation decisions.
Strategies of blame avoidance and responsibility shifting have long been discussed in the political sciences (Weaver, 1986). Instances of so-called blame games can frequently be observed in political systems with regard to policy making and implementation in the European Union (Heinkelmann-Wild and Zangl, 2020) or between officials from different levels of government in the United States (Maestas et al., 2008). Unsurprisingly, similar strategies can also be observed in the private sector, for instance, when it comes to upholding employment standards within franchise networks (Hardy, 2019). The idea that responsibility shifting can in fact be
a pivotal factor in delegation decisions plays an especially prominent role in public choice theory (Fiorina, 1986).
Experimental evidence of this phenomenon comes from Fischbacher et al. (2008), who showed that responsibility attribution can sometimes be effectively shifted and that this constitutes a powerful motive for decision-makers. Other experiments provide evidence that this is true even if the agent in question is effectively powerless (Hill, 2015), or the delegation by the principal eliminated the possibility of a fair outcome (Oexl and Grossman 2013). But does this also hold true for artificial agents?
Popular culture places a strong emphasis on human responsibility despite an empirical decline of human control in many areas (Elish and Hwang, 2015). The concept of “algorithmic outrage asymmetry” suggests that people are less morally outraged by algorithmic wrongdoing than by human wrongdoing, for instance, in cases of discrimination by age, race or gender (Bigman et al., 2020). If, however, people seek to attribute blame, some argue that it will not be placed on algorithms but that humans could emerge as “moral crumple zones.” In human-machine teams, humans would then have to take on blame even for accidents outside of their control (Elish, 2019).
While some argue that humans will bear all of the responsibility and none of the control when working with machines, others think that machines are perfectly suited to be used as scapegoats. So far very limited empirical evidence has been provided to back either position. Strobel and Kirchkamp (2017) investigated whether choices in a dictator game and perceived guilt change when players can share responsibility with machines. The authors report that perceived responsibility and guilt did not vary significantly when comparing purely human teams with human-machine teams. They write that people tend to make fewer selfish decisions when partnered with machines, though that effect was insignificant.
So while responsibility shifting has long been established as an integral part in delegation decisions, empirical evidence of whether the introduction of artificial agents is rendering this motive mute or even more important is lacking. This constitutes a serious research gap, the implications of which exceed academic relevance.
A better understanding of responsibility shifting to artificial agents could explain over and underreliance on machines and profoundly influence legal decision-making regarding automation and digitization. For instance, administrators are struggling to provide governance strategies for automated vehicles, because of the ambiguity with respect to liability (Taeihagh and Lim, 2019). A better understanding of how people actually attribute responsibility is likely to help create guidelines that are not only more effective but also more likely to gain consensus.
Deeper insights into the phenomenon might also help to shield human operators from unjust recrimination. As mentioned above, our classic understanding of human-machine teams has cemented a focus on human responsibility despite a decline of human control in various areas (Elish and Hwang, 2015). This is especially troubling since responsibility has proven to be an important factor in understanding and predicting punishment patterns. (for example (Fehr and Schmidt, 1999; Bolton and Ockenfels, 2000)). It seems that human operators are in fact in harms way and might become scapegoats in cases of technical failure.
In contrast, machine use might emerge as a strategy for self-exculpation in critical situations. This could have detrimental effects if it leads to an overuse of machines - a bleak prospect given the growing capabilities of algorithms and the potential harm this implies for workers and consumers. In sum, there are plenty of reasons to investigate attributions of blame and praise in the context of automation.
To shed light on this problem, we will test the following conjecture in a laboratory experiment.
**Conjecture:** Delegators are rewarded differently for delegating other-regarding tasks to artificial as compared to human agents.
On one hand, the delegation of a task that could carry severe consequences for a third party to an unmonitored machine might be considered careless and result in punishment or defamation. On the other hand, principals might be exculpated entirely since people deem the failure of machines to be even more outside of their control than when delegating to another human. Either way, a better understand-
ing of public reservations regarding the introduction of novel technology is likely to prove useful in future moral and legal considerations. The experiment designed to test the above conjecture will be outlined in the following chapter.
Additionally, we will explore whether the effect of perceived utility on delegation decisions varies depending on the agent’s artificial or human nature. Based on a definition by Dzindolet et al. (2002), we define the perceived utility of employing an artificial agent as the difference between the perceived reliability of an automated device and the perceived reliability of manual control. Furthermore, we will include risk attitudes into our analysis (O’Donoghue and Somerville 2018).
3 Design
The experiment consisted of (1) a logic task, (2) a delegation decision, (3) an evaluation of the delegation decision, (4) a self-assessment of one’s performance and elicitation of risk attitudes. Subjects received a 40 ECU show-up fee increased by the outcome of the delegation (successful or not), plus (minus) their reward (their punishment) for their decision to delegate or not and the bonus for the accuracy of their self-assessment and the lottery as payment for the experiment. An experimental currency unit was used (ECU) with the exchange rate of 10 ECU for 1 EUR.
Subjects received their instructions on-screen and were fully informed about the rules of the game. They were randomly matched according to perfect stranger matching, i.e., no two participants interacted more than once during the experiment. The experimental manipulation consisted of changing the nature of the agent to which a task could be delegated: it was either another human participant or an artificial agent (see 3.2). Table 1 gives an overview over the four stages of the experiment.
3.1 Logic Task
The main task of the experiment was a logic puzzle. We asked participants to complete ten puzzles within a five-minute time frame. Each puzzle consisted of a
### Table 1: Overview of experimental stages
| Stage | Human (Machine) Treatment |
|----------------------------------------|------------------------------------------------------------------------------------------|
| (1) Solve logic task | Participants solve a series of logic puzzles |
| (2) Make delegation decision | Participants decide whether to delegate to another human (a machine) or to have their own work count |
| (3) Evaluate delegation decision | Participants reward or punish decision to delegate or not |
| (4) Self-assess & choose lotteries | Participants guess how many errors they made in logic task and reveal their risk attitude by choosing between lotteries |
sequence of three patterns and a placeholder for the missing fourth pattern. The right answer had to be derived from the given sequence and selected from a set of four alternatives. To identify the right answer, participants always had to focus on the circles, while ignoring differently shaped symbols and any colors (see Figure 1). Because we assumed that delegation decisions would heavily depend on the agent’s perceived capabilities, we chose a task involving visual perception to foster participants’ intuition that the algorithm could err. Participants had to complete ten of the tasks listed above before they could continue to the second stage of the experiment.
3.2 Delegation Decision
After the logic task had been completed, participants were randomly assigned to one of two treatments: the “human” or the “machine” treatment. Only at this point did subjects learn about the nature of the agent to whom they could delegate the task.
To give participants an idea of their potential delegatee’s capability, they were shown representations of the agent’s performance. In the human treatment, the $n$ participants were shown a histogram displaying the performance of the other $(n - 1)$ participants based on the actual results of the running session. In the machine treatment, participants were shown a histogram with information about how often the algorithm failed to give correct answers in $n$ trial runs. The algorithm was programmed such that it mirrored the performance of the human participants in the room. The performance of the artificial agent was therefore as good as that of the participants in the respective session. This process ensured that the delegation decisions were based on the agent’s nature instead of any assumptions about differing capabilities.
Participants were then asked to make the delegation decision. They chose whether their own performance or that of their human or artificial agent (depending on the treatment) would determine the third party’s payoff. The delegation decision would thus not affect the payment of the delegator but that of another participant. Conditional on participants’ decisions to delegate or not, one of the ten solutions to the ten puzzles was randomly chosen from the answers of their agent or their own answers. If the selected puzzle was solved correctly, the third party received an additional payoff. If it was solved incorrectly, the third party did not receive an additional payoff.
3.3 Evaluation of the Delegation
Participants were now given the opportunity to punish or reward another participant’s decision to delegate or not. Participants did not know the actual decision
Figure 2: Delegation decision for human and machine treatment
of the participant that they evaluated, nor whether this decision had resulted in a
good or bad outcome for themselves. They were asked to alter the payment of the
participant upwards or downwards by at most 40 ECU. Reward and punishment
choices were contingent on the two possible decisions to delegate or not and the two
possible outcomes of success or failure. Thus, in any case, four choices had to be
made. Only the one that applied to the actual decision of the evaluated participant
combined with actual outcome did finally apply (Selten, 1967). Table 2 depicts the
table that subjects saw on their screen.
| Lower or increase subjects payoff given that: | Amount |
|-----------------------------------------------------------------------------------|-----------------|
| Subject used own work – outcome: success | *enter amount* |
| Subject used own work – outcome: failure | *enter amount* |
| Subject delegated (machine/human) – outcome: success | *enter amount* |
| Subject delegated (machine/human) – outcome: failure | *enter amount* |
Table 2: Decision to increase or decrease the delegator’s pay-off
3.4 Self-Assessment and Risk Attitudes
Subsequently, participants were asked to assess their own performance by estimating
how many mistakes they had made during the logic task in the experiment’s first
part. This estimate was incentivized by an additional payment of 50 ECU if they
guess correctly. This procedure allowed us to analyze the effect of self-assessments
on delegation decisions. As is standard in incentivized economic experiments, the
experiment was concluded by an elicitation of participants’ risk attitudes.¹
4 Results
The experiment took place in a major German university between February and May 2019. A total of 149 subjects participated in six sessions, 43% were female and the average age was $23.08 \text{ years (sd = 3.83)}$. Participants received a show-up fee of €4.00 and could earn additional money in the experiment. A session lasted about 45 minutes and the average payment was about €13.50 per participant. The experiment was programmed in z-Tree (Fischbacher 2007) and subjects were recruited via ORSEE (Greiner et al. 2004). Data analysis was conducted using Python’s numpy, scipy, and statsmodels.api libraries. The preprocessed data set and the code are available online².
Remember that after the delegation decision, all participants were asked to evaluate the decision of the participant who was responsible for their own pay-off. Responsibility arose from the decision to either delegate (to a human or machine) or rely on one’s own work (in both treatments). Notice again that participants were informed whether they were randomly assigned to the human or machine treatment, but not whether the other participant had actually delegated or not. They were therefore asked to judge the decision with respect to the four possible outcomes according to the so-called strategy method (see Section 3.3). This means that subjects could increase (or deduct) the payment of their responsible participant by an integer between 0 and 40 for the cases of her (1) having brought about a good outcome herself or (2) having brought about a bad outcome herself. Furthermore, they were increasing (or deducting) the payment for the case of her (3) having delegated to an agent causing a good outcome on her behalf or (4) having delegated to an agent causing a bad outcome on her behalf.
¹We used the procedure introduced by Holt and Laury (2002). The task is based on ten choices between pairs of lotteries. The potential payoffs for the safe lottery range from €2.5 to €1.6 and are therefore always less extreme than those for the risky lottery that range from €4.35 to €0.10. For the first pair of lotteries, the probability of the high payoff is equally low in both lotteries but equally increases for both lotteries with each new pair. A participant should switch to the risky lottery once the probability for the high payoff is sufficiently high according to his or her personal risk attitude. The later a participant switches to the risky lottery, the more risk averse he or she is.
²https://doi.org/10.5281/zenodo.4446581
To test our conjecture that delegators are rewarded differently for delegating other-regarding tasks to artificial as opposed to human agents, we contrast evaluations between both treatments.
Let us first consider the good-outcome case. In the human treatment, participants that did not delegate and caused the good outcome themselves were, on average, rewarded 20.28 ECU (sd = 20.85). Participants that delegated to another human who then brought about the good outcome on their behalf were rewarded 20.94 ECU (sd = 21.34). This difference is insignificant (p = 0.720, paired t-test).
In the machine treatment, participants that did not delegate and caused the good outcome themselves were on average rewarded 23.78 ECU (sd = 20.14). Participants that delegated to a machine were rewarded 27.00 ECU (sd = 16.71). This difference is again insignificant (p = 0.106, paired t-test).
Result 1: Delegators did not lose any recognition for a good outcome if it was caused by either their human or their artificial agent.
Let us now consider the bad-outcome case. In the human treatment, participants that did not delegate and caused the bad outcome themselves were on average rewarded 7.29 ECU (sd = 22.59 ECU). Participants that delegated to another human were on average rewarded with 8.26 ECU (sd = 21.56 ECU). This difference is insignificant (p = 0.559, paired t-test).
In the machine treatment, participants that did not delegate and caused the bad outcome themselves were on average rewarded 8.53 ECU (sd = 26.52). Participants that delegated to a machine were on average rewarded 12.96 ECU (sd = 24.44). This difference is significant (p = 0.041, paired t-test).
In the machine treatment, delegators earned higher rewards if a machine agent caused the failure. This confirms our conjecture stated in Section 2. Principals are rewarded differently for delegating tasks depending on the nature of the agent. More specifically, they fare better if a machine agent caused a bad outcome than if they did so themselves.
Result 2: Delegators did not successfully shift blame for a bad outcome if their human agent caused it instead of themselves. They did, however, successfully shift blame for a bad outcome if their artificial agent caused it instead of themselves.
Figure 3 illustrates this asymmetry in terms of rewards between the human and the machine treatment for the bad-outcome case.
To see whether participants exploited this incentive to delegate to machine agents that does not exist for human agents, we compare the proportions of delegators in both treatments. In the human treatment, 35 out of 76 (46.1%) delegated the task to another human participant, whereas 41 out of 73 (56.2%) delegated to the machine agent in the machine treatment. The difference in the proportions of delegators is insignificant (p = 0.28?, Chi-Square Test for Independence). The similar proportions of delegators in both treatments suggests that the decision to delegate to the agent is not primarily driven by strategic concerns of avoiding blame in the event of a bad outcome.
This is corroborated by the logistic regression reported in Table 3. The propensity to delegate (1 = yes) is positively predicted by participants’ self-assessment of
the number of errors they believe they have committed in the logic task (p < 0.001). “Machine” captures whether the agent is human (0) or artificial (1), which does not significantly influence this result. The effect to which self-assessment predicts the delegation decision is robust to controlling for risk attitude, although participants who are more risk averse are also more likely to delegate (p < 0.017).
It thus appears that the expected utility of delegating was the driving factor for participants’ decisions to do so or not regardless of the nature of their agent. Those who were less confident regarding their own performance were more likely to delegate the task. Their estimated number of errors, which they stated in an incentivized self-assessment, had a significant impact on their delegation decision.
As Table 4 shows, the self-assessment of participants is also predicted by the actual number of a subject’s errors in the logic task. Whether they have a human or an artificial agent at their avail did not influence their self-assessment. Also, subjects’ risk attitudes have no impact on their self assessment. These findings indicate that participants have a realistic impression about their own performance. Subjects who performed better in the logic task were accordingly less likely to delegate.
5 Conclusion
Our findings indicate that delegators may be judged with more leniency in the event of a bad outcome if they delegate tasks to artificial agents instead of human
agents. It does therefore stand to reason that machine agents can be successfully used to avoid ostracism. The FCO president’s statement quoted at the beginning, i.e. that companies cannot hide behind algorithms, might not hold true empirically. Companies might well capitalize the effective shift of responsibility to algorithms if they fail. This is all the more true if they do not suffer any comparable loss of prestige as a result of the delegation in the event of success, as our data also suggest. The fact that the delegator in a between-subjects design receives a discharge if the agent is artificial but not if the agent is human at least suggests that the corresponding judgment is not reflective, but that it is a subtle behavioral tendency. If this is true, the discharge is not ethically desired by the evaluator.
Our results might indicate the importance of institutional solutions that hold companies and ultimately individuals liable for the moral wrongs that their artificial agents bring about. These institutions grow even more important if they have to compensate for consumers’ behavioral reluctance to attribute blame in such cases. A deeper inquiry into the reluctance to punish that we observe seems warranted by the idea that extrinsic social motivation is an important factor in moral decision-making (Cappelen et al., 2017). The ability to use artificial agents as a smoke screen might encourage various decision makers to engage in more activities that are considered undesirable by stakeholders. The reassuring fact that delegators in this experiment did not exploit the effective release from blame does not imply that others will not—especially if they see through this behavioral tendency.
Our experiment is subject to limitations. One is its rather explorative nature,
which is owed to the lack of a well-established theoretical framework: Scientists have only recently started to address the influence of algorithms on human decision-making empirically. To the best of our knowledge, the projects by Gogoll and Uhl (2018) and Strobel and Kirchkamp (2017) cited above are the only experiments dedicated to the issue so far. Furthermore, the stylized setting used in our experiment limits the scope of the conclusion that we can draw. This concern is best explained in relation to internal and external validity. Internal validity means that the experiment is designed in such a way that it warrants conclusions about the behavior of its participants inside of the laboratory, for instance, by keeping relevant factors constant (ceteris paribus) or omitting irrelevant influences (ceteris absenteibus). Experiments are externally valid if their design produces findings that are informative about behavior outside of the laboratory (Guala, 2002). Some authors posit an inverse relationship between internal and external validity (Guala et al., 2005; Loewenstein, 1999). Our findings provide a first indication that the nature of the agent has an effect on the reward and punishment that the delegator receives. The phenomenon we observed would have to be replicated in other contexts inside and outside of the laboratory to eliminate the possibility of it being a mere artifact.
We believe that our findings represent an early step in understanding delegation decisions in a domain that is gaining relevance, i.e., the use of artificial agents in moral decision-making. More generally, our experimental results illustrate the necessity of investigating the interaction between humans and machines in behavioral settings. It is insufficient to rely on ethicists’ armchair arguments and on surveys that study laymen’s intuitions regarding the ethical implications of algorithms, because ethically relevant implications may arise as unintended results from the interactions between people and machines. The emerging phenomena might then be difficult to anticipate and sometimes even counter-intuitive. Further research is urgently needed to create a more conclusive picture of the subtle factors that drive our behavior when cooperating (and competing) with machines.
References
Allen, C. and W. Wallach (2012). Moral machines: contradiction in terms or abdication of human responsibility. *Robot Ethics: The Ethical and Social Implications of Robotics, MIT Press, Cambridge (MA)*, 55–68.
Bardsley, N., R. Cubitt, G. Loomes, P. Moffatt, C. Starmer, and R. Sugden (2020). *Experimental economics: Rethinking the rules*. Princeton University Press.
Bénabou, R. and J. Tirole (2002). Self-confidence and personal motivation. *The quarterly journal of economics* 117(3), 871–915.
Bigman, Y., K. Gray, A. Waytz, M. Arnestad, and D. Wilson (2020). Algorithmic discrimination causes less moral outrage than human discrimination.
Bolton, G. E. and A. Ockenfels (2000). ERC: A theory of equity, reciprocity, and competition. *American economic review* 90(1), 166–193.
Busse, C. (2017). Bundeskartellamt rügt lufthansa. https://www.sueddeutsche.de/wirtschaft/nach-air-berlin-pleite-bundeskartellamt-ruegt-lufthansa-1.3806188.
Cappelen, A. W., T. Halvorsen, E. Ø. Sørensen, and B. Tungodden (2017). Face-saving or fair-minded: What motivates moral behavior? *Journal of the European Economic Association* 15(3), 540–557.
Danaher, J. (2016). Robots, law and the retribution gap. *Ethics and Information Technology* 18(4), 299–309.
Dzindolet, M. T., L. G. Pierce, H. P. Beck, and L. A. Dawe (2002). The perceived utility of human and automated aids in a visual detection task. *Human Factors* 44(1), 79–94.
Elish, M. and T. Hwang (2015). Praise the machine! punish the human! the contradictory history of accountability in automated aviation. *Punish the Human*.
Elish, M. C. (2019). Moral crumple zones: Cautionary tales in human-robot interaction. *Engaging Science, Technology, and Society* 5, 40–60.
Fehr, E. and K. M. Schmidt (1999). A theory of fairness, competition, and cooperation. *The quarterly journal of economics* 114(3), 817–868.
Fiorina, M. P. (1986). Legislator uncertainty, legislative control, and the delegation of legislative power. *JL Econ. & Org.* 2, 33.
Fischbacher, U. (2007). z-tree: Zurich toolbox for ready-made economic experiments. *Experimental economics* 10(2), 171–178.
Fischbacher, U. et al. (2008). Shifting the blame: On delegation and responsibility. Technical report, Institute for Empirical Research in Economics-University of Zurich.
Gogoll, J. and M. Uhl (2018). Rage against the machine: Automation in the moral domain. *Journal of Behavioral and Experimental Economics* 74, 97–103.
Goldbach, C., D. Kayar, T. Pitz, and J. Sickmann (2019). Transferring decisions to an algorithm: A simple route choice experiment. *Transportation research part F: traffic psychology and behaviour* 65, 402–417.
Greiner, B. et al. (2004). The online recruitment system orsee 2.0-a guide for the organization of experiments in economics. *University of Cologne, Working paper series in economics* 10(23), 63–104.
Guala, F. (2002). On the scope of experiments in economics: comments on siakantaris. *Cambridge Journal of economics* 26(2), 261–267.
Guala, F. et al. (2005). *The methodology of experimental economics*. Cambridge University Press.
Hardy, T. (2019). Shifting risk and shirking responsibility? the challenge of upholding employment standards regulation within franchise networks.
Heinkelmann-Wild, T. and B. Zangl (2020). Multilevel blame games: Blame-shifting in the european union. *Governance* 33(4), 953–969.
Hevelke, A. and J. Nida-Rümelin (2015). Responsibility for crashes of autonomous vehicles: an ethical analysis. *Science and engineering ethics* 21(3), 619–630.
Hill, A. (2015). Does delegation undermine accountability? experimental evidence on the relationship between blame shifting and control. *Journal of Empirical Legal Studies* 12(2), 311–339.
Holt, C. A. and S. K. Laury (2002). Risk aversion and incentive effects. *American economic review* 92(5), 1644–1655.
Konow, J. (2000). Fair shares: Accountability and cognitive dissonance in allocation decisions. *American economic review* 90(4), 1072–1091.
Loewenstein, G. (1999). Experimental economics from the vantage-point of behavioural economics. *The Economic Journal* 109(453), F25–F34.
Maestas, C. D., L. R. Atkeson, T. Croom, and L. A. Bryant (2008). Shifting the blame: Federalism, media, and public assignment of blame following hurricane katrina. *Publius: The Journal of Federalism* 38(4), 609–632.
Manyika, J., M. Chui, M. Miremadi, J. Bughin, M. George, P. Willmott, and M. Dewhurst (2017). A future that works: Automation, employment and productivity. *McKinsey*.
Moor, J. H. (1979). Are there decisions computers should never make. *Nature and System* 1(4), 217–229.
Nissenbaum, H. (1996). Accountability in a computerized society. *Science and engineering ethics* 2(1), 25–42.
Niszczota, P. and D. Kaszás (2020). Robo-fund aversion: People prefer it when humans and not computers make investment decisions with moral undertones.
O’Donoghue, T. and J. Somerville (2018). Modeling risk aversion in economics. *Journal of Economic Perspectives* 32(2), 91–114.
Oexl, R. and Z. J. Grossman (2013). Shifting the blame to a powerless intermediary. *Experimental Economics* 16(3), 306–312.
Robinette, P., W. Li, R. Allen, A. M. Howard, and A. R. Wagner (2016). Overtrust of robots in emergency evacuation scenarios. In 2016 11th ACM/IEEE International Conference on Human-Robot Interaction (HRI), pp. 101–108. IEEE.
Rudin, C. (2019). Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. *Nature Machine Intelligence* 1(5), 206–215.
Selten, R. (1967). Die strategiemethode zur erforschung des eingeschränkt rationalen verhaltens im rahmen eines oligopolexperiments, s. 136–168. *Beiträge zur experimentellen Wirtschafts-Forschung. Tübingen: JCB Mohr.*
Strobel, C. and O. Kirchkamp (2017). Sharing responsibility with a machine.
Taeihagh, A. and H. S. M. Lim (2019). Governing autonomous vehicles: emerging responses for safety, liability, privacy, cybersecurity, and industry risks. *Transport Reviews* 39(1), 103–128.
Weaver, R. K. (1986). The politics of blame avoidance. *Journal of public policy*, 371–398. | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
1478,
1
],
[
1478,
3877,
2
],
[
3877,
6089,
3
],
[
6089,
8548,
4
],
[
8548,
10866,
5
],
[
10866,
13096,
6
],
[
13096,
15080,
7
],
[
15080,
16698,
8
],
[
16698,
18686,
9
],
[
18686,
20513,
10
],
[
20513,
23120,
11
],
[
23120,
25143,
12
],
[
25143,
26363,
13
],
[
26363,
27862,
14
],
[
27862,
29667,
15
],
[
29667,
31963,
16
],
[
31963,
33697,
17
],
[
33697,
35514,
18
],
[
35514,
37117,
19
],
[
37117,
38102,
20
]
]
} |
509f2e01ee1e8d8041b1d937eed47588a74df735 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 6,
"total-fallback-pages": 0,
"total-input-tokens": 15851,
"total-output-tokens": 4111,
"fieldofstudy": [
"Physics"
]
} | Optical properties of gallium phosphide (GaP) nanowires
Satyendra Singh · Pankaj Srivastava
Abstract The linear and non-linear optical properties of different geometrical structures of gallium phosphide (GaP) nanowires have been studied by employing ab initio method. We have calculated the optical response of four different GaP nanowires, viz., two atom linear wire, two atom zigzag wire, four atom square wire and six atom hexagonal wire. We have investigated imaginary part of the $zz$ component of the linear dielectric tensor and second order susceptibility for different structures along with bulk material. We revealed that strongest absorption occurs for four atom square nanowire configuration.
Keywords Gallium phosphide nanowires · Linear and non-linear optical properties
Introduction
Optical properties of nanowires have become a major area of research for optoelectronic devices. When an electron absorbs a photon from the incident light, it makes a transition to the next higher unoccupied state and emits a photon of frequency less than or equal to the frequency of incident light; this phenomenon is known as linear optical transitions. It is found that there is significant shift in the optical absorption spectra toward the shorter wavelengths referred to as the blue shift as the particle size is reduced.
The existence of the exciton has a strong influence on the electronic properties of the semiconductor and its optical absorption. The second-order response or non-linear property is a two photon process where the excited electron absorbs another photon of the same frequency and makes a transition to another allowed state at higher energy. When this electron is falling back to its original state, it emits a photon of frequency, which is twice the frequency of that of the incident light (Srivastava and Singh 2008). A linear phenomenon is somewhat simple but non-linear phenomenon corresponds to the appearance of a frequency component in the intense light beam that is exactly twice the input. The high aspect ratio of 1-D semiconductors gives rise to anisotropy in the electronic and optical properties; it may further enhance the long range dipolar interaction and produces significant changes in the transition states. Semiconducting nanowires have received much attention due to their potential application as building blocks of miniaturized electrical (Wang et al. 2005), nanofluidic (Karnik et al. 2005) and optical devices (Sirbuly et al. 2005). Nanowire photonic circuitry made from 1-D nanostructures offers numerous opportunities for the development of next generation optical information processors. The wave guiding property of individual nanowires depends on the wavelength of the emitted light.
Gallium phosphide (GaP) is a semiconducting compound with an indirect band gap of 2.26 eV. It is one of the most promising optical materials having refractive index of about 3.37 in the visible region and it decreases to 3.2 in the infra red region. Thus, it can be utilized for manufacturing low and standard brightness, i.e., red, orange and green light emitting diodes (LED). It is also a low cost material with excellent optical properties. Thus, it can prove to be the best material for manufacture of optoelectronic devices in economic mode. The development of
newer non-linear optical materials for their possible applications in technological areas like optoelectronics, optical signal processing, optical computing is of crucial importance. Earlier, many efforts have been made to explore the linear and non-linear optical properties of different materials in the bulk state as well as in nanostate. Experimentally, Gupta et al. (2003) have studied the surface optical phonons in GaP nanowires using Raman scattering. Synthesis of GaP nanowires by heating Ga$_2$O$_3$ and red phosphor powders has been done by Baoyu et al. (2004). A complete Raman scattering study on GaP nanowires has been done by Chapelle et al. (2005). They gave evidence that Raman spectra are affected by the one-dimensional shape of the nanowires. The morphology and microstructure of GaP nanowires by scanning electron microscopy and transmission electron microscopy have been observed by Xiong et al. (2003). Lee et al. (2003) studied the interband optical transitions in GaP nanowires encapsulated in GaN nanotubes.
Four different geometrical structures of GaP nanowires are considered and the linear and non-linear optical properties of considered structures are being presented in this paper. The linear and non-linear spectra for considered structures are investigated and finally the optical transition in different energy regions is discussed. The details about the geometrical structures have been given in our earlier published paper (Srivastava et al. 2011). The considered geometrical structures of GaP nanowires are shown in Fig. 1.
Fig. 1 Optimized structures of GaP nanowires. a Two atom linear wire, b two atom zigzag wire, c four atom square wire, d six atom hexagonal wire.
Methodology used
ABINIT code (Hohenberg and Kohn 1964; Kohn and Sham 1965) has been used for the computational work. The ab initio DFT calculations (Martin 2004; Gonze et al. 2002) are employed within the plane-wave pseudopotential method to investigate the linear and non-linear optical properties of GaP nanowires. As is evident from the above literature that the pseudopotential method has been very successful in exploring the structural, electronic and optical properties of various materials (Martin 2004); in this calculation, the generalized gradient approximation and the exchange–correlation functional of Perdew, Burke, and Ernzerhof were applied (Perdew et al. 1996). The exchange correlation potential of Troullier and Martins (1991) has been used and these pseudopotentials were taken from ABINIT web page (Gonze et al. 2002). The potentials were tested by performing calculations on bulk GaP material in which the results were found to be consistent with the experimental ones.
All the calculations were performed in a self-consistent manner. The studied structures were optimized for Hellmann–Feynman forces as small as $10^{-3}$ eV/Å on each atom and the calculations were performed with a kinetic energy cut off of 30 Hartree. The wires were positioned in a supercell of side 20 au along the $x$ and $y$ directions; the axis of the wire was taken along the $z$ direction and the periodic boundary conditions were applied. The Monkhorst–Pack method with 15 k-points sampling along the $z$ direction was used in the integration of the Brillouin zone, all atoms were allowed to relax without any imposed constraint. In order to check the self-consistent calculations, we have determined the self-consistent optimized value for the lattice parameter of bulk GaP materials, the magnitude of atomic relaxation depends on the plane cut-off energy and one has to obtain the convergence with respect to cut-off energy too.
Results and discussion
The linear and non-linear susceptibility equations have both real and imaginary parts for calculating the optical spectra of any of the nanowires; here, both real and imaginary parts can be important for the gain and loss of energy density in the electromagnetic field at some particular frequency. In the current investigation, only the imaginary part of the susceptibility equation is responsible for the exchange of energy in the electromagnetic field, therefore, the imaginary part of the results so obtained is analyzed.
The imaginary parts of the $zz$ component of the linear dielectric tensor or linear susceptibility for various GaP nanowires along with bulk are shown in Fig. 2. The linear optical response of bulk seems to be quite smooth, whereas the linear susceptibility gradually increases with energy. In the case of two atom linear wire, response reflects a strong peak around 4.6 eV, with some other small and large peaks towards the higher energy side. For two atom zigzag wire structure, a strong absorption with one high magnitude peak at 4.2 eV with several small peaks towards higher energy side is observed. It is found that the four atom square wire linear spectra have the strongest peak around 4.4 eV, and there are other weak peaks also at higher energy region. In the case of six atom hexagonal wire structure, the spectra have its highest peak at 4.2 eV but is of less magnitude as compared to that of the other structures; however, there are many other peaks seems in between 4.0 and 6.0 eV. In conclusion, the analysis of linear spectra for all considered structures reveals that strongest absorption occurs for the two atom linear wire, two atom zigzag wire and four atom square wire, respectively.
The non-linear response of bulk spectra is as shown in Fig. 3. It can be seen that the total second order susceptibility is zero towards the low energy region up to 4 eV. Whereas in the high energy region between the energy levels 4.0 and 6.0 eV, the SHG optical spectra are dominated by intra $(2\omega)$ contribution towards the positive
 Calculated imaginary part of the $zz$ component of the linear dielectric tensor for different GaP nanowires along with bulk GaP material.
The non-linear optical spectra of different structures of GaP nanowires are presented in Figs. 4, 5, 6 and 7. Various contributions to the imaginary part of $\chi^{zzz}(2\omega,\omega,\omega)$ are taken and the non-linear spectra of two atom linear wire are shown in Fig. 4. It is observed that the total SHG peaks are dominant near lower energy values having magnitude of the order of 90, which reduces almost 7 near 3.2 eV on positive side. On the positive side, major contributions come from intra ($2\omega$) transition and intra ($\omega$) transition, whereas the intra ($2\omega$) transition plus the total transition are obtained in the negative region of the graph.
The second-order susceptibility values for two atom zigzag wire are seen to be rather complicated as shown in Fig. 5. It can be observed that so many prominent peaks lying between 0.0 and 6.0 eV energy range and it is found that the total SHG susceptibility is dominant near lowest energy region having magnitude of the order of 17, which reduces almost 2 factors near 5.2 eV. Here, the major contributions come from intra ($2\omega$) transition, and inter ($\omega$) transition plus total transition are obtained towards the upper level, whereas the intra ($2\omega$) transition and the total transition are obtained towards the lower level.
The non-linear response for a four atom square wire cross section is shown in Fig. 6. The total absorption as
well as intra \((2\omega)\) transitions has greater contribution near lower energy region as compared to higher energy region and the magnitude of SHG spectra is high at around 137.5 (total SHG). The highest absorption spectra come from intra \((2\omega)\) transition and inter \((2\omega)\) transition in the lower energy region of the positive side, whereas in the negative side SHG spectra, the highest contribution comes from intra \((\omega)\) transition plus total transition.
The optical spectrum for a six atom hexagonal wire is depicted in Fig. 7. It is observed that the total SHG spectra are dominant near lower energy side having the magnitude of the order of 14, which reduces almost 2.5 near 3.7 eV in the positive side. Here, the major contributions come from intra \((\omega)\) transition and inter \((2\omega)\) transition towards positive side and intra \((2\omega)\) transition towards negative side having a magnitude of the order of 67.5 eV.
Through SHG analysis, it can be concluded that strongest absorption occurs for a four atom square wire configuration. As reported [110] for the same material, it is predicted that four atom square wire structure has the stable structure; thus it can be concluded that stable structure configuration also has the strongest SHG absorption.
### Conclusion
We have calculated and analyzed the linear and non-linear optical response of four different structures of GaP nanowires. The aim of our analysis was to explore the best possible configuration of GaP nanowire to be applied in photonic and optoelectronic devices. First, we have analyzed the linear response of considered structures. The analysis of linear spectra reveals that strongest absorption occurs for two atom linear wires, two atom zigzag wire and four atom square wires, respectively. Second, we have investigated the SHG susceptibility spectra of these structures. In SHG spectra, we observe remarkable features for all structures. We predict that strongest absorption occurs for four atom square nanowire configuration. We also revealed that the calculated peaks not only get sharper but also show pronounced energy shift. This is mainly due to interband contribution to the imaginary part of the dielectric function. All SHG spectra comprise of total, inter and intra band contributions. The SHG spectra are rather complicated due to various microscopic features observed. We have not come across any of the experimental or theoretical results to compare such type of linear and SHG optical spectra for various structures of GaP nanowires. The present investigation is important, because size, shape and structure are the important criteria in nano regime, and one must not ignore so far as nanowires are concerned.
### Acknowledgments
The authors are thankful to Computational Nanoscience and Technology Laboratory (CNTL) of ABV-Indian Institute of Information Technology and Management, Gwalior (M.P.) and Department of Physics, Hindustan College of Science and Technology, Farah, Mathura (U.P.) for providing the infrastructural facilities for computational work.
### Open Access
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
### References
Baoyu L, Ding W, Qimin D, Jinlei Y (2004) Synthesis and optical study of GaP nanowires. Nanotechnology 15(12):1745–1748
Chapelle MLDDL, Han HX, Tang CC (2005) Raman scattering from GaP nanowires. Eur Phys J B 46:507–513
Gonze X, Beaken JM, Caracas R, Detraux F, Fuchs M, Rignanese GM, Sindic L, Verstraete M, Zerah G, Jollet F, Torrent M, Roy A, Mikami M, Ghosez PH, Raty JY, Allan DC (2002) First-principle computation of material properties: the ABINIT software project. Comput Mat Sci 25:478. [http://www.abinit.org](http://www.abinit.org)
Gupta R, Xiong Q, Mahan GD, Eklund PC (2003) Surface optical phonons in gallium phosphide nanowires. Nano Lett 3(12):1745–1750
Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864–B871
Karnik R, Fan R, Yue M, Li D, Yang P, Majumdar A (2005) Electrostatic control of ions and molecules in nanofluidic transistors. Nano Lett 5:943–948
Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133–A 1138
Lee MW, Hsieh HC, Lin HM, Chen CC (2003) Interband optical transitions in GaP nanowires encapsulated in GaN Nanotubes. Phys Rev B 67:161309(R)
Martin RM (2004) Electronic structure: basic theory and practical methods. Cambridge University Press, Cambridge
Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865
Sirbuly DJ, Law M, Yan HQ, Yang PD (2005) Semiconductor nanowires for subwavelength photonics integration. J. Phys. Chem. B 109(32):15190–15213
Srivastava P, Singh S (2008) Linear and second-order optical response of different GaN nanowires. Physica E 40:2742–2746
Srivastava P, Singh S, Mishra A (2011) Electronic Properties of GaP Nanowires of Different shapes. J Nanosci Nanotechnol 11:10464–10469
Troullier N, Martins JL (1991) Efficient pseudopotentials for plane-wave calculations. Phys Rev B 43:1993–2006
Wang WU, Chen C, Lin KH, Fang Y, Lieber CM (2005) Label-free detection of small-molecule-protein interactions by using nanowire nanosensors. Proc Natl Acad Sci USA 102:3208–3212
Xiong Q, Gupta R, Adu KW, Dickey EC, Lian GD, Tham D, Fischer JE, Eklund PC (2003) Raman spectroscopy and structure of crystalline gallium phosphide nanowires. J Nanosci Nanotechnol 3(4):335–339 | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3314,
1
],
[
3314,
5023,
2
],
[
5023,
9215,
3
],
[
9215,
10644,
4
],
[
10644,
15388,
5
],
[
15388,
16273,
6
]
]
} |
746b52401bb44cc17ba5eb10a76896cac50f88db | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 28974,
"total-output-tokens": 8691,
"fieldofstudy": [
"Biology",
"Medicine"
]
} | Caloric Restriction Chronically Impairs Metabolic Programming in Mice
Henriette Kirchner,1 Susanna M. Hofmann,1 Antje Fischer-Rosinsky,2 Jazzmynn Hembree,1 William Abplanalp,1 Nickki Ottaway,1 Elizabeth Donelan,1 Radha Krishna,1 Stephen C. Woods,1 Timo D. Müller,1 Joachim Spranger,2 Diego Perez-Tilve,1 Paul T. Pfuger,1 Matthias H. Tschöp,1 and Kirk M. Habegger1
Although obesity rates are rapidly rising, caloric restriction remains one of the few safe therapies. Here we tested the hypothesis that obesity-associated disorders are caused by increased adipose tissue as opposed to excess dietary lipids. Fat mass (FM) of lean C57B6 mice fed a high-fat diet (HFD; FMC mice) was “clamped” to match the FM of mice maintained on a low-fat diet (standard diet [SD] mice). FMC mice displayed improved glucose and insulin tolerance as compared with ad libitum HFD mice (P < 0.001) or SD mice (P < 0.05). These improvements were associated with fewer signs of inflammation, consistent with the less-impaired metabolism. In follow-up studies, diet-induced obese mice were food restricted for 5 weeks to achieve FM levels identical with those of age-matched SD mice. Previously, obese mice exhibited improved glucose and insulin tolerance but showed markedly increased fasting-induced hyperphagia (P < 0.001). When mice were given ad libitum access to the HFD, the hyperphagia of these mice led to accelerated body weight gain as compared with otherwise matched controls without a history of obesity. These results suggest that although caloric restriction on a HFD provides metabolic benefits, maintaining those benefits may require lifelong continuation, at least in individuals with a history of obesity.
Caloric restriction (CR) has become a popular recommendation to decrease body weight (BW) (1), achieve metabolic benefits, and potentially increase life expectancy (2–4). Although the benefits of weight loss are undeniable, the optimal method to achieve a healthy weight is the subject of continuing debate. Obesity is accompanied by many comorbidities (5), and it is widely accepted as a causal factor. A current hypothesis suggests that obesity provokes inflammation in adipose tissue (6), leading to the release of proinflammatory mediators into systemic circulation. Rodent studies suggest that consumption of a high-fat diet (HFD) leads to infiltration by T cells (7) and macrophages (8), which contributes to inflammation in adipose tissue and the development of obesity-associated diseases such as type 2 diabetes (9).
Alternative explanations for the obesity-related comorbidities are based on specific harmful effects of HFDs per se. High-fat foods induce stress in the intestinal epithelium (10) and promote inflammation by absorption of antigenic material from the gut (11,12). Furthermore, HFD feeding increases reactive oxygen species production (13) that preceded obesity (14), suggesting that like sucrose and fructose, dietary lipids may contribute to obesity-associated diseases. In the present experiments we tested the hypothesis that obesity-associated disorders are caused by increased adipose tissue, as opposed to the obesogenic diet. To dissect these possibilities, we isolated body fat mass (FM) from fat intake using a “FM clamp” mouse model (Fig. L4). In related studies, we asked whether a history of obesity affects future energy metabolism. Published reports suggest that counter-regulatory mechanisms that develop during CR lead to enhanced metabolic efficiency and rapid weight regain (15,16). We thus aimed to distinguish if this metabolic reprogramming is related to prior obesity, dietary fat intake, or having been calorically restricted (Fig. L4).
MATERIALS AND METHODS
Animals. Six- to 7-week- (FM clamp study) or 12-month-old (CR study) male, C57B6/6J mice (Jackson Laboratories) were fed a standard diet (SD; D12329; 16.4 kcal% protein; 73 kcal% carbohydrate; 10.5% kcal% fat) or a matched HFD (D12331; 16.4 kcal% protein; 25.5 kcal% carbohydrate; 58.0 kcal% fat; Research Diets, New Brunswick, NJ). Mice were single or group-housed on a 12:12-h light-dark cycle (light on from 0600 to 1800 h) at 22°C with free access to water. All studies were approved by and performed according to the guidelines of the Institutional Animal Care and Use Committee of the University of Cincinnati.
FM clamping. Mice in the SD and HFD groups had ad libitum access to food. Mice in the clamped group (FM clamped [FMC]) were fed HFD every day, 3 h after light onset. BW and food intake were measured daily with a laboratory scale (Mettler, Toledo, OH). FM and lean mass were determined every other week using noninvasive nuclear magnetic resonance technology (EchoMRI, Houston, TX). Because FM was measured every other week, allocated food portions were adjusted daily based on the daily changes in BW.
CR study. Lean (SD group), obese (HFD group), and FMC mice were generated as described above. Additionally, age-matched diet-induced obese (DIO) mice were partitioned into two CR groups, one fed SD diet and the other HFD. CR continued for 45 days, when both groups of CR mice had attained a mean FM comparable with that of the lean SD control group. All groups were then given ad libitum access to SD or HFD for the remainder of the experiment (58 days). At this time the SD mice were divided such that half remained on SD and the other half were switched to HFD.
Fasting-induced hyperphagia. All mice were fasted for 24 h on day 45 of the CR. Food was removed at 0000 h. At 0000 h the following day, mice were given free access to SD (SD and caloric restricted fed standard diet [CR-SD] groups) or HFD (HFD, FMC, and caloric restricted fed high-fat diet [CR-HFD] groups) and food intake was monitored for 24 h.
Energy expenditure and locomotor activity. Energy intake, expenditure, and home-cage activity were assessed using a combined indirect calorimetry system (TSE Systems). O2 consumption and CO2 production were measured every 45 min for a total of 120 h (including 12 h of adaptation) to determine the respiratory quotient (RQ) and energy expenditure.
Glucose and insulin tolerance tests. Intraperitoneal glucose and insulin tolerance tests were performed by injection of glucose (2 g/kg, 20% wt/vol d-glucose [Sigma] in 0.9% wt/vol saline) or human regular insulin (1 unit/kg [Lilly Humolog] in 0.9% wt/vol saline) to 6-h fasted mice. Blood samples were collected immediately before and 15, 30, 60, and 120 min after injection. Blood glucose was determined with a TheraSense Freestyle Glucometer. C-peptide was measured via radioimmunoassay (Millipore, Billerica, MA) in plasma collected at the 30-min time point of glucose tolerance test (GTT).
Plasma parameters. Leptin, insulin, ghrelin, triglyceride, and cholesterol levels in 16-h fasted mice were measured at the termination of the study. TG and cholesterol were measured by enzymatic assay (Thermo Electron, Waltham, MA). Four lipoprotein pooled samples (0.35 mL) per group were subjected to fast-performance liquid chromatography (gel filtration on two Superose 6 columns connected in series). Leptin and insulin were quantified simultaneously via multiplex assay, and ghrelin was quantified via ELISA (Millipore).
Low-density gene array. Mice were fasted for 16 h and decapitated without anesthesia, and trunk blood and tissues were collected. Tissues were frozen on dry ice and stored at −80°C. RNA was isolated using the RNeasy Lipid Mini-Kit (Qiagen) and reverse transcription PCR was performed using SuperScriptIII, DNase, and anti-RNase treatment (all Invitrogen, Carlsbad, CA). Custom-made low-density gene arrays and single-gene quantitative PCR were performed according to the manufacturer’s instructions on a 7900 real-time PCR machine (Applied Biosystems, Foster City, CA). Data were normalized to the housekeeping gene 18s and expressed as fold change.
Statistics. All data are represented as mean ± SEM. One-way or two-way ANOVA with Bonferroni’s multiple comparison post-test was performed as appropriate using GraphPad Prism version 5.0c (GraphPad Software, San Diego, CA). Statistical significance was assumed when P < 0.05.
RESULTS
To test the hypothesis that increased body FM, rather than ingestion of excess lipid, is the predominant pathogenic effect of HFD feeding, we determined the metabolic phenotype of lean and obese mice that were chronically exposed to HFD. The ad libitum HFD group developed severe DIO, as expected, while leanness in FMC mice was maintained equivalent to SD mice. This allowed for separation of the metabolic consequences of excess dietary lipids (FMC group) from the effects of increased body fat induced by excess dietary lipids (HFD ad libitum group).
**FM is dictated by caloric intake.** At study initiation all mice had identical BW (Fig. 1C). Predictably, the HFD group gained BW quickly and achieved significant DIO within 14 weeks. FM of clamped mice did not differ from SD mice (Fig. 1B). Food intake was lower in FMC mice than in SD controls, presumably because of the higher caloric density of the HFD (Fig. 1D). However, caloric intake was similar in both lean groups and appreciably lower than HFD-fed mice (Fig. 1E). These findings suggest that energy metabolism and food efficiency were not altered by exposure to the HFD per se. To test this possibility more directly, we analyzed energy expenditure.
**FM clamping normalizes energy expenditure and enhances metabolic flexibility.** Energy expenditure and locomotor activity were measured using indirect calorimetry during week 14. Consistent with prior observations (17), EE was increased ($P < 0.0001$) in the HFD group compared with the SD control group (Fig. 2A and B).
**FIG. 2. FM clamping normalizes energy expenditure.** Absolute (A) and average energy expenditure (B), RQ (C), and locomotor activity (D) of SD, HFD, and FMC mice was measured hourly. Mice from the SD and HFD group were fed with SD or HFD ad libitum. Mice from the FMC group were fed defined amounts of HFD to match FM to the SD group. All mice are male ($n = 16$ per group). All data are represented as mean ± SEM. ***$P < 0.001$.
**FIG. 3. FM clamping improves glucose tolerance and insulin sensitivity.** Glucose tolerance was assessed at week 13 via intraperitoneal GTT. After 6 h of fasting mice were injected with 2.0 g/kg glucose. FMC mice had significantly lower blood glucose excursion (A) and area under the curve (AUC; C) compared with lean SD and obese HFD mice. Insulin tolerance was assessed at week 13 via intraperitoneal insulin challenge (1 unit/kg). Insulin tolerance was significantly improved in FMC mice as compared with HFD mice when assessed by either blood glucose excursion (B) or rate of disappearance ($K_d$) over the initial 30 min (D). All data are represented as mean ± SEM. *$P < 0.05$; **$P < 0.01$; ***$P < 0.001$.
Intriguingly, EE of the FMC mice was similar to that of the SD control group, suggesting that HFD exposure per se did not compromise EE.
RQ (Fig. 2C) of the HFD group did not change markedly between the light and dark cycles (0.69 ± 0.00), implying that fat oxidation was constantly high. Conversely, the RQ of the SD group averaged 0.82 ± 0.01 over the course of the day, reflecting increased carbohydrate oxidation. The RQ of the FMC mice varied greatly between the light and dark. During the light, FMC RQ was similar to that of the HFD group, suggesting fat oxidation. At the beginning of the dark phase, the mean RQ increased considerably, reaching levels similar to those of the SD group.
Total locomotor activity (Fig. 2D) was comparable in the SD and FM-clamped groups, and both were higher than HFD mice. These data imply that body fat and/or adipose tissue–derived adipokines or other factors, rather than high proportion of fat in the HFD, may compromise both energy homeostasis and locomotor activity.
**FM clamping improves glucose and insulin tolerance.** Mice were challenged with GTT and insulin tolerance tests in week 13. Fasting blood glucose of the FM-clamped mice was slightly below all other groups, and, as anticipated, DIO mice were glucose intolerant (Fig. 3A and C). Glucose tolerance was markedly better in the FMC mice than in the HFD group. Surprisingly, glucose tolerance was also markedly improved as compared with the SD group (Fig. 3A and C). This improved glucose homeostasis was matched by enhanced insulin sensitivity in FMC mice (Fig. 3D). Analysis of the rate of disappearance in the first 30 min of the challenge revealed similar sensitivity in SD and FMC mice, which were both improved over the HFD group (Fig. 3D). Thus, consumption of HFD has beneficial effects on glucose and insulin responsiveness, when FM is constrained at a normal level.
**FM clamping prevents obesity-associated inflammation.** After 14 weeks of FM clamping, mice were killed and tissues collected to gain mechanistic insight into the beneficial metabolic effects of FM clamping. HFD mice exhibited elevated plasma leptin and insulin, but no change in ghrelin (Fig. 4A–C). Expression of key metabolic genes in skeletal muscle, hypothalamus, liver, and adipose tissue was conducted. Markers of both fatty acid and glucose transport were suppressed in the skeletal muscle of FMC mice as compared with the HFD group (Supplementary Table 1). However, two genes recently implicated in enhanced glucose transport, Nr4a3 and Ucp3, were both elevated in FMC as compared with both control groups (Supplementary Table 1). In adipose and liver, as in skeletal muscle, canonical regulators of glucose homeostasis, glucose transporter expression in...
epididymal WAT, and gluconeogenic genes of the liver were not different between groups (Supplementary Tables 2 and 3). Epididymal WAT and liver of HFD mice exhibited increased gene expression levels for tumor necrosis factor-α (TNFα), cluster of differentiation 68 (CD68), integrin αx (ITGAX), chemokine (C-C motif) ligand 2, toll-like receptor 4, glutathione S-transferase A2, and heme oxygenase 1. FM clamping dramatically prevented expression of these markers in both liver (Fig. 4D) and WAT (Fig. 4E), resulting in levels similar to those in SD mice. Additionally, hypothalamic expression of IL-6 and IKKβ were also suppressed as compared with that in HFD mice (Fig. 4F). These data suggest that DIO-associated inflammation is related to expanded FM and not dietary lipids. Furthermore, they provide additional evidence for central and peripheral inflammation as a component of diet-induced glucose intolerance.
**Post-obesity studies.** To investigate the metabolic impact of prior obesity, cohorts of DIO mice were placed on a defined CR paradigm and fed either HFD or SD until FM was reduced to that of otherwise matched SD mice. Ad libitum HFD and SD and FMC mice were maintained as controls. CR mice received 50% of calories consumed on average by the SD ad libitum group. Within 1 month mice subjected to CR lost excess BW (Fig. 5A) and FM (Fig. 5B), independent of the diet. Lean mass of previously obese mice remained significantly greater than that of the always-lean controls (Fig. 5C).
At day 44, 10 days after achieving FM levels equal to those of the SD-fed mice, all mice were subjected to a GTT and plasma lipids were analyzed. Although BW and FM were the same in all lean groups (SD, FMC, CR-SD, and CR-HFD), CR mice were most glucose tolerant as reflected by glucose excursion (Fig. 5D) and area-under-the-curve analysis (Fig. 5E). Similar to FMC mice, glucose tolerance was greatest in the CR-HFD group, indicating that dietary fat might have a beneficial effect on glucose tolerance when FM is strictly maintained. Furthermore, assessment of C-peptide 30 min after glucose challenge suggests that this enhanced tolerance occurs in the presence of normal insulin secretion (Fig. 5F). Analysis of plasma from fasted mice revealed
---
**FIG. 5. CR restores leanness independent of the diet.** A: BW of mice that were fed with SD or HFD ad libitum in comparison with calorically restricted mice on SD or HFD. The SD and HFD groups were fed ad libitum, whereas the groups CR-SD and CR-HFD were calorically restricted and fed 50% of calories (given as SD or HFD) that were consumed on average in the SD group. FMC mice were fed defined amounts of HFD to match FM to the SD group. FM (B) and lean mass (C) curves of mice fed ad libitum or that were calorically restricted are shown. D: intraperitoneal GTT conducted after 6 h of fasting at day 45 of CR. E: Area-under-the-curve (AUC) analysis of GTT. F: C-peptide secretion at 30 min after intraperitoneal glucose challenge. All mice are male (n = 10–15 per group). All data are represented as mean ± SEM. Lowercase letters above bars (A–F) denote statistically similar (P > 0.05) groups.
elevated plasma leptin and trend for increased insulin in HFD mice after 16 h fast, with similar levels in all other groups (Fig. 6A and B). A complete ablation of diet-induced hypercholesterolemia cholesterol was observed in FMC and CR mice (Fig. 6C). fast-performance liquid chromatography analysis of cholesterol identified a cholesterol profile similar to that of SD mice and greatly reduced from those of HFD mice (Fig. 6D). Furthermore, CR mice fed a HFD and FMC mice exhibited a slight increase in the LDL and HDL peaks compared with SD-fed mice. Intriguingly, when compared with SD fed mice, CR-SD mice had a marked decrease in the main HDL peak and in the shoulder, where HDL-1 and LDL elute. In addition to these effects on cholesterol, a trend for normalization of triglycerides (Fig. 6E) was observed in CR, but not FMC mice. Together these data suggest that CR after prior obesity induces beneficial effects on glucose and lipid metabolism independent of FM.
**CR induces persistent hyperphagia leading to rebound of obesity.** To test if CR disturbs metabolic programming and consequently facilitates the rebound of obesity, we measured fasting-induced hyperphagia and BW gain during ad libitum feeding. After 45 days of CR, both CR and control mice were fasted for 24 h. All mice were then given free access to SD or HFD, and food intake was monitored for 24h. SD-fed control mice consumed the least amount of calories after the fast (Fig. 7A). HFD-fed mice ate slightly, but not significantly, more than the SD control group. Caloric intake in FMC mice was significantly elevated over SD mice; yet this was not associated with expression of orexigenic signals in the hypothalamus (Fig. 4F). CR mice ate significantly more calories after food deprivation than all other groups. This effect was independent of the diet since the CR-SD group ate the same amount of calories as the CR-HFD group after refeeding.
After CR was ended, previously obese CR mice were given HFD ad libitum to characterize the effects, if any, on return to obesity. SD and FMC groups were split into two ad libitum groups each, with half allowed to consume SD and half HFD. These groups were introduced to control for feeding behavior in mice without prior obesity. SD mice maintained on the SD diet displayed relatively constant food intake and BW for the duration of the study (Fig. 7B and C). Food intake significantly increased in SD and FMC mice switched to ad libitum HFD, leading to concomitant increases in BW and FM (Fig. 7B–D). These effects, however, were intermediate to previously obese CR groups. Previously, CR HFD-fed mice increased food intake, achieving levels similar to those of obese HFD-fed mice (Fig. 7B). This exaggerated hyperphagia led to accelerated BW gain such that CR-HFD mice attained BWs and FMs similar to those of DIO mice after ~50 days of free eating (Fig. 7B–D). CR-SD mice increased food intake (Fig. 7B) and FM (Fig. 7D) in a similar manner to CR-HFD mice; however, initial BW gain was delayed (Fig. 7C). The rapid accumulation of FM was associated with a deterioration of glucose tolerance, especially in the FMC-HFD group (Fig. 8A and B). These data collectively suggest that prior obesity induces a drive to defend the BW achieved before CR, and this phenomenon is independent of diet.
**FIG. 6. CR normalizes plasma cholesterol.** Plasma leptin (A) and insulin levels (B) measured after 16-h fast at day 44 are shown. Total plasma cholesterol (C), cholesterol profile (D), and total plasma triglycerides (E) of mice that were fed with SD or HFD ad libitum in comparison with FMC or CR-SD or CR-HFD are shown. All mice are male (n = 6–10 per group). All data are represented as mean ± SEM. *P < 0.05; **P < 0.001.
DISCUSSION
To distinguish between the metabolic consequences of dietary fat intake and increased body fat, we studied three groups of age-matched, randomized male C57BL/6J mice. The first was fed ad libitum with a low-fat diet (SD), matched in protein and micronutrient composition to the HFD. The second consisted of mice that had ad libitum access to HFD, and the third (FM-clamped mice) was fed the calculated amount of HFD each day that would effectively "clamp" their FM to that of the SD group. It is noteworthy that this did not require decreasing caloric intake of FMC mice below that of the SD mice. This clamping technique revealed that BW and body composition is primarily determined by calories ingested and not by the source of calories. In the present paradigm, ingestion of a high proportion of dietary fat per se did not favor accumulation of excess body fat. Rather, DIO occurred only when excess calories were consumed, as occurred in the HFD ad libitum group.
It has been reported that as rodents become obese, total EE also increases (15,16,18). Consistent with these findings, we found that EE of DIO mice was increased and that this effect was related to the amount of body fat, i.e., exposure to HFD in the FMC group resulted in EE that was similar to SD mice. Therefore, implying that increased ingestion of fat, in and of itself, does not necessarily have adverse effects on energy homeostasis when BW, FM, and/or caloric intake are maintained at normal levels. Moreover, clamping FM to that of normal weight control mice restored metabolic flexibility. Metabolic flexibility describes the ability of an organism or tissue to adapt to substrate availability by switching between the oxidation of carbohydrates and lipids (19). As reflected by the RQ, FMC mice were able to alternate between carbohydrate and fat oxidation, whereas mice fed the HFD ad libitum mainly used fat as the primary fuel source. This fluctuation of fuel choice within the FM-clamped group was likely related to the time of feeding. Although the two control groups had access to food around the clock, FMC mice were fed only once a day, 3 h after light onset. These FMC mice typically ate their daily ration within 3 h, leaving them fasted for the remaining 21 h of the day. This pattern presumably explains why the RQ decreased during the beginning of light phase when these mice were maximally fasted.
It is noteworthy that exposure to limited amounts of HFD had no adverse effect on glucose homeostasis. Conversely, and perhaps counter-intuitively, it significantly improved glucose tolerance and insulin sensitivity. This finding suggests that in moderation dietary lipids are beneficial to glucose tolerance. It should be noted that both standard and HFD contained high amounts of sucrose. However, mice in the FMC group consumed less sucrose than SD mice because the HFD contains more fat than sucrose and the absolute caloric intake in both groups was similar. In fact, carbohydrate consumed in SD mice was about three times greater than that in FMC mice during the study period.
Carbohydrates, including sucrose, play a role in the pathogenesis of insulin resistance and are essential to
markers of inflammation (26). In contrast, mice fed HFD, containing, but further improving, ingestion of fructose-sweetened beverages stimulates hyperglycemia (20). Meta-analysis in humans (21) showed that increased consumption of sugar-sweetened beverages is strongly associated with obesity and type 2 diabetes. A proposed mechanism for the diabetes development after high-sugar consumption is pancreatic β-cell dysfunction and inflammation (22). Moreover, increased intake of fructose-sweetened beverages stimulates visceral adiposity and hepatic de novo lipogenesis (23).
To identify potential mechanisms responsible for the improved glucose homeostasis of FMC mice, we measured candidate genes in liver, skeletal muscle, hypothalamus, and white adipose tissue. Many of the expected regulators of glucose homeostasis were not differentially expressed. However, altered expression of two recently described modulators of glucose uptake, Nr4a3 and Ucp3, was identified in skeletal muscle. Intriguingly, both Nr4a3 (24) and Ucp3 (25) enhance insulin signaling, resulting in increased glucose uptake. Likewise, cytokine expression in liver was significantly increased in DIO mice. This effect is likely influenced by the amount of body fat and not the ingestion of fatty food per se since expanding body fat increases markers of inflammation (26). In contrast, mice fed HFD, but with clamped FM, had markers of inflammation comparable with that of SD mice. Therefore, a possible explanation for the preservation of glucose tolerance in FMC mice despite high-fat feeding could be the absence of inflammation. Our group has recently shown that DIO induces hypothalamic inflammation in rodents and humans after only 4 weeks exposure to HFD (27). This HFD-induced inflammation results in neuronal damage at the arcuate nucleus of the hypothalamus and possibly contributes to diabetogenesis. This hypothalamic inflammatory response to HFD is mediated by activation of Jnk (28) and the IKKβ/NF-κB pathway (29). It is noteworthy that we found that hypothalamic IKKβ expression is not upregulated in the HFD group but significantly downregulated in FMC mice. Thus, reduced activation of the hypothalamic IKKβ/NF-κB pathway could play an important role in not only maintaining, but further improving, insulin sensitivity of FMC mice compared with SD- and HFD-fed mice.
After severe CR, all mice underwent the anticipated acute period of hyperphagia relative to nonrestricted mice. However, CR mice that had previously been obese exhibited significantly greater hyperphagia than all other groups, including the FM-clamped group. This finding indicates that individuals in a postobese metabolic state are reprogrammed to favor relative overeating and rapid weight regain. The susceptibility of weight-reduced subjects to hyperphagia and regain of lost weight is well known and implicated in the obesity rebound (30). Studies in mice highlight that the magnitude of hyperphagia after CR is not proportional to the duration of restriction, indicating that hunger does not diminish during the time course of CR (31). However, in our paradigm, the degree of weight regain seems to be influenced in large part by the degree of prior obesity and not by the CR per se. The never-obese FMC mice that can be considered as mildly CR for a long period of time best depicted this effect. These mice responded with significantly less hyperphagia than mice with a history of obesity. Therefore, prior obesity, rather than CR, is likely to contribute a greater component of the drive to overeat. This finding could be explained by the relative leptin deficiency of weight-reduced previously obese mice. Substantial weight loss leads to a reduction in leptin concentrations beyond that predicted by loss of FM (32).
This drive to overeat may be directly related to the propensity for quick rebound in previously obese individuals. It is of interest, however, that prior obesity may also result in beneficial glucose metabolism. Furthermore, prior obesity also leads to changes in lipoprotein profiles that vary dependent on the diet consumed. Ad libitum consumption of a HFD after CR seems to have a beneficial effect on lipoprotein metabolism since it considerably normalizes the profile. In contrast, there was a marked reduction of HDL cholesterol levels in mice changed to the low-fat SD after CR compared with mice that had always been fed the SD. Previous studies with mice overexpressing scavenger receptor class B type I in liver demonstrated increased reverse cholesterol transport and reduced HDL cholesterol levels (33), resulting in reduction of atherosclerosis (34). Hence, consuming a low-fat diet after CR may have beneficial effects on atherogenesis independent of increased HDL. These observations in both FM-clamped and previously obese mice suggest that previously unknown benefits of mild CR, especially in the context of prior obesity. Taken together, these data suggest that CR from an obese state provides metabolic benefits, including improved glucose and lipid homeostasis. Furthermore, these benefits are equally observed when restricted on a HFD or low-fat diet. However, the data also indicate that CR (or pharmaceutical intervention) may have to be continued lifelong to prevent consequences of chronically altered metabolic programming, which may lead to an even worse state of metabolic disease.
**FIG. 8. Rebound from CR induces glucose intolerance. Intraperitoneal GTT (A) and area-under-the-curve (AUC) analysis (B) are shown. GTT was conducted after 6 h of fasting following 58 days of rebound. All mice are male (n = 6–10 per group). All data are represented as mean ± SEM. **P < 0.01.**
ACKNOWLEDGMENTS
This work was supported by National Institutes of Health Grant R01-DK-077975, Neuroendocrine Regulation of Adipocyte Metabolism (M.H.T.), and the University of Cincinnati Training Program in Neuroendocrinology of Homeostasis Grant T32-DK-059803 (K.M.H.).
M.H.T. is a consultant for Roche Pharmaceuticals and receives research funds from Roche. No other potential conflicts of interest relevant to this article were reported.
H.K. and K.M.H. were responsible for the conception, implementation, and design of the study; the analyses and interpretation of data; and drafting and critically revising the article. A.F.-R. was responsible for the implementation of the study and the analyses and interpretation of data. J.H., W.A., N.O., E.D., and R.K. were responsible for the implementation of data and drafting and critically revising the article. A.F.-R. was responsible for the implementation of the study, the analyses and interpretation of data. S.M.H. was responsible for interpretation of data and drafting and critically revising the article. A.F.-R. was responsible for the implementation of the study. S.C.W., T.D.M., J.S., D.P.-T., and P.T.P. were responsible for interpretation of data; and drafting and critically revising the article. A.F.-R. was responsible for interpretation of data and drafting and critically revising the article. A.F.-R. was responsible for the conception and design of the study, the analyses and interpretation of data. J.H., W.A., N.O., E.D., and R.K. were responsible for the implementation of data and drafting and critically revising the article. M.H.T. was responsible for the conception and design of the study, the analyses and interpretation of data. All authors approved the final version of the manuscript to be published. K.M.H. is the guarantor of this manuscript to be published. K.M.H. is the guarantor of this manuscript to be published. K.M.H. is the guarantor of this manuscript to be published.
REFERENCES
1. Tsai AG, Wadden TA. The evolution of very-low-calorie diets: an update and meta-analysis. Obesity (Silver Spring) 2006;14:1283–1293.
2. McCay CM, Crowell MP, and Maynard LA. The effect of retarded growth upon the length of the life span and upon the ultimate body size. J Nutr 1935;10:63–79.
3. Cheney KE, Liu RK, Smith GS, Leung RE, Mickey MR, Walford RL. Survival and disease patterns in C57Bl/6J mice subjected to undernutrition. Exp Gerontol 1980;15:237–258.
4. Masoro EJ. Dietary restriction-induced life extension: a broadly based biological phenomenon. Biogerontology 2006;7:153–155.
5. Guh DP, Zhang W, Bansback N, Amarsi Z, Birmingham CL, Anis AH. The incidence of co-morbidities related to obesity and overweight: a systematic review and meta-analysis. BMC Public Health 2009;9:88.
6. Tuncman G, Hirosumi J, Solinas G, Chang L, Karin M, Hotamisligil GS. Functional in vivo interactions between JNK1 and JNK2 isoforms in obese, insulin-resistant mice: essential role of dietary carbohydrate in beta cell destruction. Diabetesology 2007;10:1481–1489.
7. Malik VS, Popkin BM, Bray GA, Després JP, Willett WC, Hu FB. Sugar-sweetened beverages and risk of metabolic syndrome and type 2 diabetes: a meta-analysis. Diabetes Care 2010;33:2477–2483.
8. Schulze MB, Liu S, Rimm EB, Manson JE, Willett WC, Hu FB. Glycemic index, glycemic load, and dietary fiber intake and incidence of type 2 diabetes in young and middle-aged women. Am J Clin Nutr 2004;80:348–356.
9. Stanhope KL, Schwarz JM, Keim NL, et al. Consuming fructose-sweetened, not glucose-sweetened, beverages increases visceral adiposity and lipids and decreases insulin sensitivity in overweight/obese humans. J Clin Invest 2009;119:1322–1334.
10. Wang Y, Ghoshal S, Ward M, de Villiers W, Woodward J, Eckhardt E. Chylomicrons promote intestinal absorption and systemic dissemination of dietary antigen (ovalbumin) in mice. PLoS ONE 2009;4:8442.
11. Bournat JC, Brown CW. Mitochondrial dysfunction in obesity. Curr Opin Endocrinol Diabetes Obes 2010;17:446–452.
12. Matsuzawa-Nagata N, Takamura T, Ando H, et al. Increased oxidative stress precedes the onset of high-fat diet-induced insulin resistance and obesity. Metabolism 2008;57:1071–1077.
13. MacLean PS, Higgins JA, Johnson GC, et al. Enhanced metabolic efficiency contributes to weight regain after weight loss in obesity-prone rats. Am J Physiol Regul Integr Comp Physiol 2004;287:R1306–R1315.
14. Leibel RL, Rosenbaum MJ, Hirsch J. Changes in energy expenditure resulting from altered body weight. N Engl J Med 1995;332:621–628.
15. Felig P, Cunningham J, Levitt M, Hendler R, Nadel E. Energy expenditure in obesity in fasting and postprandial state. Am J Physiol 1983;244:E45–E51.
16. MacLean PS, Higgins JA, Johnson GC, Fleming-Elder BK, Peters JC, Hill JO. Metabolic adjustments with the development, treatment, and recovery of obesity in obesity-prone rats. Am J Physiol Regul Integr Comp Physiol 2004;287:E258–E259.
17. Arai T, Wang N, Bezouevski M, Welch C, Tall AR. Decreased atherosclerosis in heterozygous low density lipoprotein receptor-deficient mice expressing the scavenger receptor BI transgene. J Biol Chem 1999;274:2366–2371. | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
6096,
1
],
[
6096,
8710,
2
],
[
8710,
10849,
3
],
[
10849,
13607,
4
],
[
13607,
16766,
5
],
[
16766,
20513,
6
],
[
20513,
23711,
7
],
[
23711,
29412,
8
],
[
29412,
34561,
9
]
]
} |
41a669ce46c73098f0a4fa81eb1da235889014ab | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 5,
"total-fallback-pages": 0,
"total-input-tokens": 19182,
"total-output-tokens": 5919,
"fieldofstudy": [
"Physics"
]
} | Beam polarization asymmetries for the \( p(\gamma, K^+)\Lambda \) and \( p(\gamma, K^+)\Sigma^0 \) reactions at \( E_\gamma = 1.5 - 2.4 \text{ GeV} \)
R.G.T. Zegers, M. Sumihama, D.S. Ahn, J.K. Ahn, H. Akimune, Y. Asano, W.C. Chang, S. Daté, H. Ejiri, H. Fujimura, M. Fujiwara, K. Hicks, T. Hotta, K. Imai, T. Ishikawa, T. Iwata, H. Kawai, Z.Y. Kim, K. Kino, H. Kohri, N. Kumagai, S. Makino, T. Matsumura, N. Matsuoka, T. Mibe, K. Miwa, M. Miyabe, Y. Miyachi, M. Morita, N. Muramatsu, T. Nakano, M. Niiyama, N. Nomachi, T. Ooba, H. Ohkuma, D.S. Oshuev, C. Rangacharyulu, A. Sakaguchi, T. Sasaki, P.M. Shagin, Y. Shiino, H. Shimizu, Y. Sugaya, H. Toyokawa, A. Wakai, C.W. Wang, S.C. Wang, K. Yonehara, T. Yorita, M. Yoshimura, and M. Yosoi
(The LEPS collaboration)
1 Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan
2 Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
3 Advanced Science Research Center, Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-1195, Japan
4 Department of Physics, Pusan National University, Busan 609-735, Korea
5 Department of Physics, Konan University, Kobe, Hyogo 658-8501, Japan
6 Synchrotron Radiation Research Center, Japan Atomic Energy Research Institute, Mikazuki, Hyogo 679-5198, Japan
7 Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
8 Japan Synchrotron Radiation Research Institute, Mikazuki, Hyogo 679-5198, Japan
9 School of Physics, Seoul National University, Seoul, 151-747, Korea
10 Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701
11 Department of Physics, Kyoto University, Kyoto 606-8502, Japan
12 Laboratory of Nuclear Science, Tohoku University, Sendai, Miyagi 982-0826, Japan
13 Department of Physics, Yamagata University, Yamagata 990-8560, Japan
14 Department of Physics, Chiba University, Chiba 263-8522, Japan
15 Wakayama Medical University, Wakayama, Wakayama 641-8509, Japan
16 Department of Physics and Astrophysics, Nagoya University, Nagoya, Aichi 464-8602, Japan
17 Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan, Canada, S7N 5E2
18 Center for Integrated Research in Science and Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japan
19 Institute for Protein Research, Osaka University, Suita, Osaka 565-0871, Japan
(Dated: September 23, 2018)
Beam polarization asymmetries for the \( p(\gamma, K^+)\Lambda \) and \( p(\gamma, K^+)\Sigma^0 \) reactions are measured for the first time for \( E_\gamma = 1.5 - 2.4 \text{ GeV} \) and \( 0.6 < \cos(\theta_{p,\gamma}) < 1.0 \) by using linearly polarized photons at the Laser-Electron-Photon facility at SPring-8 (LEPS). The observed asymmetries are positive and gradually increase with rising photon energy. The data are not consistent with theoretical predictions based on tree-level effective Lagrangian approaches. Including the new results in the development of the models is, therefore, crucial for understanding the reaction mechanism and to test the presence of baryon resonances which are predicted in quark models but are sofar undiscovered.
PACS numbers: 14.20.Gk, 25.20.Lj, 13.60.Le, 13.30.Eg
Strangeness photoproduction is a powerful tool to obtain a deeper insight into baryon resonances. It provides additional information about the baryon resonances to that obtained from \( \pi N \) scattering and \( \pi \)-production reactions. Of special interest are nucleon resonances that have been predicted in quark models and for which no experimental evidence has been found via the \( \pi \)-induced or \( \pi \)-production reactions. Some of these resonances, referred to as ‘missing’, could couple strongly to the \( K \Lambda \) and \( K \Sigma \) channels. To better understand the problem of ‘missing’ resonances and to see whether predictions of baryon resonances can be tested, it is, therefore, very interesting to study experimentally the \( p(\gamma, K^+)\Lambda \) and \( p(\gamma, K^+)\Sigma^0 \) reactions.
Measurements of the energy dependence of the total cross section for the \( p(\gamma, K^+)\Lambda \) reaction at SAPHIR/Bonn resulted in renewed interest because of the presence of a resonance-like structure near \( W = 1900 \text{ MeV} \). Mart and Bemhold showed that this structure could be explained by introducing a \( D_{13}(1895) \) resonance for which a considerable branching into the \( K \Lambda \) channel is predicted. Measurements of the cross section at CLAS/JLAB suggest that the resonance-like structure actually consists of several components which manifest themselves at different \( K^+ \)-scattering angles.
The theoretical calculations are typically performed in a tree-level effective-Lagrangian approach. Janssen et al. showed, however, that large ambiguities arise from (i) the
choice of included resonances, (ii) coupling constants, (iii)
form factors and (iv) the treatment of the non-resonant
‘background’ [5, 7]. Great care is thus advised in
drawing definite conclusions based on the cross-section
data only. Alternative theoretical approaches in which,
for example, off-shell effects are taken into account [5],
can also describe the SAPHIR data well without inclu-
sion of ‘missing’ resonances. Moreover, coupled-channels
effects are not negligible [10]. One way to limit the free-
doms in the model calculations is to analyze results from
all photon-induced channels simultaneously [11].
For the development of the models it is of vital im-
portance to measure additional observables and improve
the quality of the cross section data. Results for the
recoil-polarization asymmetry in the $p(\gamma,K^+)\Lambda$
reaction (self-analyzing by the $\Lambda$ weak decay) are already available
from the SAPHIR data set. Extensive programs to mea-
sure cross sections and recoil polarizations are underway
at JLAB/CLAS [4] and ESRF/GRAAL [12]. Additionally,
measurements of the beam polarization asymmetry
($\Sigma$) are great assets to the database because of the high
sensitivity to the model parameters and the presence of resonances [8, 9].
This asymmetry is defined through
$\left(\frac{d\sigma}{d\Omega}\right)_{pol} = \frac{d\sigma}{d\Omega}[1 + P_{\gamma} \Sigma \cos(2\phi')]$, where
$\left(\frac{d\sigma}{d\Omega}\right)_{pol}$ is the cross section using a linearly-polarized photon beam, $d\sigma/d\Omega$
is the unpolarized cross section, $P_{\gamma}$ the degree of photon po-
larization, $\phi'$ the azimuthal angle between the photon
polarization plane and the vector normal to the
$K^+$ reaction plane. Access to this observable is most easily ob-
tained at backward-Compton scattering facilities [12, 14]
because the photon beam is easily and reliably polarized
to a high degree.
In this Letter, we present for the first time mea-
surements of the beam polarization asymmetries of the
$p(\gamma,K^+)\Lambda$ and $p(\gamma,K^+)\Sigma^0$ reactions. These data were
taken at the new SPring8/LEPS facility in Japan [14].
Photons with a maximum energy of 2.4 GeV were pro-
duced from backward Compton scattering of 351-nm
laser photons off 8-GeV electrons in the SPring-8 stor-
age ring. The photons were tagged by measuring the
scattered electron energies with a resolution $\sigma=15$ MeV.
The degree of polarization of the backscattered photon
beam was 95% at 2.4 GeV and 55% at 1.5 GeV. Half of
the data was taken with horizontally-polarized photons
and the other half with vertically-polarized photons. The
direction of the polarization was switched about every 2
hours. The typical photon flux was $10^6$/s. A 50-mm
thick-liquid-hydrogen target was used.
Charged particles were momentum-analyzed by trac-
ing their paths in a magnetic dipole field by means of a
silicon-strip vertex detector and one drift chamber posi-
tioned upstream from the dipole magnet, and two drift
chambers positioned downstream of the dipole magnet.
The upstream drift chamber consists of 6 wire planes (3
vertical planes, 2 planes at $+45^\circ$ and 1 plane at $-45^\circ$)
each of the downstream drift chambers consists of
5 wire planes (2 vertical planes, 2 planes at $+30^\circ$ and 1
plane at $-30^\circ$). Electron and positron tracks due to pair
production were largely removed at the trigger level by
means of an aerogel Čerenkov veto counter. The event
sample was further cleaned up by removing tracks with a
large track-reconstruction error (confidence level < 2%)
which were mostly due to decay-in-flight events. The
time-of-flight of each track was measured; the start sig-
nal was produced by a plastic-scintillator trigger counter
placed behind the target cell, and an array of 40 plastic
scintillators placed behind the tracking detectors pro-
vided the stop signal. The time-of-flight resolution was
about 150 ps for a typical path length of 4 m. By com-
bining time-of-flight and momentum, the mass of each
track was reconstructed with a resolution ($\sigma$) of 30 (105)
MeV/c$^2$ for a 1 (2) GeV/c kaon. A 3$\sigma$-mass cut was used
to select the positively-charged kaons, with the ad-
titional condition that 0.31 < $mass < 0.74$ GeV/c$^2$
to ensure that the $K^+$ cut does not overlap with the cuts
for the $\pi^+$ and proton. At the highest momenta ($\sim 2$
GeV/c), where the mass resolution was worst, the con-
tamination from the $\pi^+$-particles and protons amounted
to 2% (3.5%) and 2.5% (5%) for the $K^+\Lambda$ ($K^+\Sigma^0$)
production, respectively. These numbers were determined by
extrapolating the Gaussian-shaped mass distributions of
the $\pi^+$’s and protons into the $K^+$ region. $K^+$-mesons
scattered between 0° and 60° degrees in the center-of-
mass frame were detected by the LEPS detector [14].
The track-angle resolution was 2.3 mrad.
Fig. 1 shows the missing-mass spectrum obtained for
the $p(\gamma,K^+)X$ reaction. Besides $\Lambda(1116)$ and $\Sigma^0(1193)$,
additional peaks due to $\Lambda(1405)$, $\Sigma^0(1385)$ (the two are
not resolved) and $\Lambda(1520)$ are observed. A small bump
below 1 GeV/c$^2$ is due to misidentified $\pi^+$ tracks. The
missing-mass resolutions for the $\Lambda$ ($\Sigma^0$) were $\sigma = 17(16)$
and 10(9) MeV/c$^2$ at the highest and lowest momenta,
respectively. A momentum-dependent 2$\sigma$ cut was used
to select the events in each peak. The contamination of
$\Lambda$ ($\Sigma^0$) events in the $\Sigma^0$ ($\Lambda$) peak is less than 0.8%
(0.4%). In total, $7.3 \times 10^4$ $K^+\Lambda$ and $4.9 \times 10^4$ $K^+\Sigma^0$
\begin{figure}[h]
\centering
\includegraphics[width=\textwidth]{missing_mass_spectrum.png}
\caption{Missing-mass spectrum for the $p(\gamma,K^+)X$ reaction.}
\end{figure}
very nearly the same. Fig. 2 shows the measured ratio is valid because the acceptances for our data taken with the detector acceptance is not present in Eq. 1, which integrated photon yield for each polarization mode, corrected for the dead-time of the data-acquisition system and the random tagger-hit rate. The azimuthal angle \( \phi \) is measured with respect to the horizontal plane. Note that the detector acceptance is not present in Eq. 1, which is valid because the acceptances for our data taken with a horizontally and vertically-polarized photon beam are very nearly the same. Fig. 2 shows the measured ratio in the r.h.s. of Eq. 1 for the total \( K^+ \Lambda \) (a) and \( K^+ \Sigma^0 \) (b) samples. By fitting with a \( C \cos(2\phi) \) function and dividing \( C \) by \( P_\gamma \), \( \Sigma \) is obtained. When using the full data sets, the statistical errors are smaller than the systematic ones (see below).
The \( K^+ \Lambda \) and \( K^+ \Sigma^0 \) data sets were each divided into 9, 0.1-GeV wide, photon-energy bins ranging from 1.5 to 2.4 GeV. The narrow energy binning is important, since the excitation spectrum may vary rapidly due to the presence of resonances. The chosen bin-size is smaller than or comparable to the widths of the relevant baryon resonances. For each energy bin, the events were further divided according to \( K^+ \) scattering angles; 5 bins in \( \cos(\theta_{K^+}^{cm}) \) from 0.6 to 1.0, each with a width of 0.1, except for the 2 most forward bins which had a width of 0.05. For each sub-sample, the beam polarization asymmetry was determined following the above-described procedure (the reduced \( \chi^2 \) of the fits with a \( C \cos(2\phi) \) to the measured asymmetries varied from 0.4 to 2.1). Although the contamination from protons and \( \pi^+ \)'s in the \( K^+ \) sample was small, it gives rise to a non-negligible shift of the measured asymmetry for the \( K^+ \). This was corrected for by determining contamination level from the protons and \( \pi^+ \)'s and their respective asymmetries (determined by selecting \( \pi^+ \)'s and protons in the mass spectra but keeping all other selections described above; for protons the asymmetries are close to 0 and for \( \pi^+ \)'s they are positive, but in general slightly lower than for the \( K^+ \)). Since the asymmetry of the total sample is the average of the asymmetries for the \( K^+ \) events and the proton and \( \pi^+ \) contaminations, weighted by their relative contributions in each sample, the asymmetries for the \( K^+ \)-sample can be extracted. The correction ranged from 0.00 \pm 0.01 for the lowest photon energies to \(+0.03 \pm 0.02 \) at the highest photon energies.
The final results are shown in Fig. 3. The observed asymmetries are positive and increase gradually with rising photon energy. The error bars correspond to the combined statistical (ranging from 0.09 at \( E_\gamma = 1.5 \) GeV to 0.04 at \( E_\gamma = 2.4 \) GeV) and systematic errors (\( \sim 0.02 \)). The latter arise from (i) the photon-yield normalization errors (\( k \) in Eq. 1), and the uncertainties in the degree and angle of linear polarization (systematic error: 0.01), (ii) the partial loss of events in a subset of the data due to a trigger problem in case the decay proton from the \( \Lambda \) (\( \Lambda \rightarrow p\pi^- \) or \( \Sigma^0 \rightarrow \Lambda \gamma \), \( \Lambda \rightarrow p\pi^- \)) hit the trigger counter. The loss is slightly dependent on the polarization direction and the effect on the measured asymmetries was estimated by mimicking the trigger problem in the subset of the data where it did not occur (systematic error (0.01 (0.015)) for \( \Lambda \) \( \Sigma^0 \) production), (iii) contamination from events produced at the trigger counter, which is only significant at very forward \( K^+ \) scattering angles \( \cos(\theta_{K^+}^{cm}) > 0.95 \). (the systematic error is negligible for \( \Lambda \) production and 0.01 for \( \Sigma^0 \) production).
In Fig. 3 the experimental data are compared with the theoretical predictions using the MAID2000 program (dashed lines) and by Janssen et al. (solid lines). These calculations are the most up-to-date available and good examples to see model ambiguities and the sensitivity of the beam polarization asymmetry on the model assumptions. Both calculations are obtained on the basis of a tree-level effective Lagrangian model and make use of the cross-section data from SAPHIR to fix the various parameters in the models through a fitting procedure. The same \( s \)-channel resonances are taken into account, including the ‘missing’ \( D_{13}(1895) \) resonance. With the \( D_{13}(1895) \) resonance, the calculations reproduce the experimental cross sections better but also give dramatically different predictions for the beam polarization asymmetry, including a change of sign \( \frac{\pi^+}{\Lambda} \). The difference between the two sets of predictions lies in the treatment of the non-resonant background terms: Janssen et al. introduce hyperon resonances in the \( u \)-channel to counterbalance the strength produced by the Born terms in a physically relevant way. The calculations also differ in the choice for the hadronic form factor.
For the \( K^+ \Lambda \) channel, the calculations in MAID2000 over-predict the beam polarization asymmetries and those by Janssen et al. under-predict the measurements.
For the $K^+\Sigma^0$ channel, the calculations predict similar absolute values for the beam polarization asymmetries, but with opposite sign. The measurements give positive values, but the magnitude is lower than the values by Janssen et al. The discrepancy between the data and calculations does not necessarily mean that the models have fundamental shortcomings. It could merely indicate that the freedoms are too large and that fitting to cross section data only does not give sufficient boundary conditions. The photon polarization data presented here are great assets to guide the theoretical work.
For $E_\gamma > 2.0$ GeV the above-mentioned models are no longer applicable. Regge-model calculations [17], which reproduce the asymmetry at higher photon energies ($E_\gamma > 5$ GeV) well, are not applicable for energies below $\sim 2.5$ GeV since the s-channel resonances are not taken into account. The new data up to 2.4 GeV provide, therefore, another challenge for future theoretical work.
In short, we present beam polarization asymmetry data for the $p(\gamma, K^+)\Lambda$ and $p(\gamma, K^+)\Sigma^0$ reactions for $1.5 < E_\gamma < 2.4$ GeV and $0.6 < \cos(\theta_{K^+}) < 1.0$. Based on the calculations by Mart and Bennhold [5], the positive sign measured in case of the former reaction indicates the presence of a missing $D_{13}$ resonance. However, in light of the large freedoms in the models, such strong conclusions are premature. Using the new results to constrain the calculations, similar to the case for $\pi$ photoproduction at lower energy, will lead to a strongly enhanced understanding of the reaction mechanisms and are pivotal for testing the presence of missing resonances.
The authors thank the staff at SPring-8 for providing excellent experimental conditions during the long course of the experiment. This research was supported in part by the Ministry of Education, Science, Sports and Culture of Japan, the National Science Council of the Republic of China (Taiwan) and the National Science Foundation.
---
1. S. Capstick and N. Isgur, Phys. Rev. D 34, 2809 (1986).
2. S. Capstick and W. Roberts, Phys. Rev. D 49, 4570 (1994).
3. S. Capstick and W. Roberts, Phys. Rev. D 58, 074011 (1998).
4. M. Tran et al., Phys. Lett. B 445, 20 (1998).
5. T. Mart and C. Bennhold, Phys. Rev. C 61, (R)012201 (1999).
6. R. Schumacher et al., in Proceedings of the XVI Conference on Particles and Nuclei (2002), to be published.
7. S. Janssen et al., Phys. Rev. C 65, 015201 (2002), and private communication.
8. S. Janssen et al., Phys. Rev. C 66, 035202 (2002), and private communication.
9. B. Saghai, in Proceedings of the International Symposium on Hadrons and Nuclei (2001), pp. 57–66.
10. W.-T. Chiang et al., Phys. Lett. B 519, 101 (2001).
11. G. Penner and U. Mosel, Phys. Rev. C 66, 055212 (2002).
12. J. Bocquet et al., Nucl. Phys. A691, 466c (2001).
13. O. Bartalini, Phys. Lett. B 544, 113 (2002).
14. T. Nakano et al., Nucl. Phys. A684, 71c (2001).
15. T. Mart et al., MAID2000, http://www.kph.uni-mainz.de/MAID/kaon/kaonmaid.html.
16. F. Lee et al., Nucl. Phys. A695, 237 (2001).
[17] M. Guidal et al., Nucl. Phys. A627, 645 (1997). | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4814,
1
],
[
4814,
10629,
2
],
[
10629,
16077,
3
],
[
16077,
19203,
4
],
[
19203,
19255,
5
]
]
} |
133e91e91c4f7719ccbe96cb0cc4295262f34eff | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 5,
"total-fallback-pages": 0,
"total-input-tokens": 20038,
"total-output-tokens": 9118,
"fieldofstudy": [
"Medicine"
]
} | Prognostic factors and treatment effects for hepatocellular carcinoma in Child C cirrhosis
K Nouso*1, YM Ito2, K Kuwaki3, Y Kobayashi3, S Nakamura3, Y Ohashi2 and K Yamamoto3
1Department of Internal Medicine, Hiroshima City Hospital, Hiroshima, Japan; 2Department of Biostatistics, School of Public Health, The University of Tokyo, Tokyo, Japan; 3Department of Medicine and Medical Sciences, Okayama University Graduate School of Medicine, Dentistry, and Pharmaceutical Sciences, Okayama, Japan
The aim of this study is to elucidate the prognostic factors and the treatment effect on survival in hepatocellular carcinoma (HCC) patients with Child C cirrhosis. Out of 3330 newly discovered HCC patients, 157 consecutive HCC individuals with Child C cirrhosis were enrolled. The prognostic factors were examined by Cox proportional hazards regression analysis and their survival was compared by propensity score-matched analysis. Multivariate analysis revealed that high serum bilirubin (>3 mg dl⁻¹), the presence of uncontrollable ascites, and a high platelet count (>8 x 10⁹ mm⁻³), so-called background liver factors, as well as multiple tumours, large tumours (>3 cm), high alpha-fetoprotein (>400 ng ml⁻¹), and the presence of portal vein thrombus, so-called tumour factors, were factors of poor prognosis. While transcatheter arterial chemoembolisation (TACE) was a factor of good prognosis (relative risk = 0.50, 95%CI = 0.27 – 0.89, P = 0.019), local ablation therapy and transcatheter arterial chemoinfusion (TAI) were not significant prognostic factors. The survival of patients who received TACE was superior to matched patients without active treatment (P = 0.009); however, we did not observe survival benefit after local ablation therapy or TAI. These results suggested that tumour factors as well as background liver factors are prognostic factors of HCC even in patients with Child C cirrhosis, and selective use of TACE in these patients provides survival benefit.
British Journal of Cancer (2008) 98, 1161 – 1165. doi:10.1038/sj.bjc.6604282 www.bjcancer.com
Published online 18 March 2008
© 2008 Cancer Research UK
Keywords: decompensated cirrhosis; prognostic factors; hepatocellular carcinoma; therapy
Hepatocellular carcinoma (HCC) is the fifth cause of death by cancer worldwide (Parkin, 2001). Many symptomatic HCCs are diagnosed in advanced stage and cannot be treated, so the prognosis is generally poor (Wong et al, 2000; Bruix and Llovet, 2002). By the accumulation of knowledge of the risk factors and the prevalence of HCC surveillance, the proportion of HCC diagnosed in early stage and that can be treated by local ablation therapies or surgery has increased (Bolondi, 2003; Adams et al, 2004; Trevisani et al, 2004).
In spite of the early detection of HCC, many patients die of complications of severe cirrhosis without any active treatment (Ikai et al, 2007). According to the algorithms of the treatment of HCC recommended by groups in Europe and Japan (Bruix et al, 2001; Llovet, 2005; Makuuchi and Kokudo, 2006), HCC patient with Child C cirrhosis (Pugh et al, 1973) is a candidate for liver transplantation or best supportive care (BSC). However, even though HCC meets the Milan criteria, many patients do not receive liver transplantation because of the shortage of donors or advanced age (United Network for Organ Sharing, 2006). Although there is regional variability, patients diagnosed with HCC in the background of hepatitis C virus infection are usually elderly (Parkin, 2001). In Japan, the mean age of patients is 66.6 years old (Ikai et al, 2007); therefore, a large number of the patients are outside the liver transplantation criteria and receive only BSC.
Local ablation therapies and transcatheter arterial chemoembolisation (TACE) are known to be useful for HCC treatment with preserved liver function (Llovet et al, 2003). Nevertheless, these therapies for patients with Child C cirrhosis are not recommended because of reported severe adverse events. However, there is lack of knowledge on prognostic factors on the effectiveness of active treatment, except liver transplantation, in HCC patients with Child C cirrhosis (Llovet, 2005). Therefore, it is very important to identify factors influencing outcomes of cirrhotic patients affected by HCC who cannot be treated by liver transplantation.
In this study, we retrospectively examined the clinical course of HCC patients with Child C cirrhosis and analysed their prognostic factors.
PATIENTS AND METHODS
Patients
Between January 1996 and September 2006 among 3330 consecutive newly diagnosed HCC patients who were admitted to our department and affiliated hospitals, 186 individuals had Child C cirrhosis. Five patients were excluded because of a lack of clinical data, 24 were excluded because they underwent liver transplantation, and the remaining patients (n = 157) were enrolled in this
study. Informed consent was obtained from all patients for use of their clinical data. The study protocol conformed to the ethical guidelines of the World Medical Association Declaration of Helsinki, and was approved by the ethical committees of the institutes.
Diagnosis
One hundred and forty-one patients were diagnosed as having HCC by imaging modalities, such as angiography, computed tomography (CT), and magnetic resonance imaging (MRI). Diagnostic criteria for HCC via imaging was based on previous reports of hyperattenuation at the arterial phase, hypointensity at the portal phase in contrast enhanced CT (section thickness = 5–8 mm) or MRI, and tumour stain on angiography (Honda et al., 1993). The remaining 16 patients with hepatic masses who did not satisfy the above criteria underwent ultrasound (US)-guided fine-needle biopsy with histologically confirmed HCC.
Treatments
As there is no clear evidence that active treatment of HCC improves the survival of patients with Child C cirrhosis, all the patients were informed that the potential treatment benefits were unknown and the risks of the treatments were higher than in patients with Child A/B cirrhosis. We conducted local ablation therapy, TACE, or transcatheter arterial chemoinfusion (TAI) only when patients consented to undergo these interventions. Percutaneous ethanol injection therapy, radiofrequency ablation, and microwave coagulation therapy were performed in 18, 4, and 1 patients, respectively. All HCCs treated by local ablation therapy were less than 3 cm in diameter and less than three tumours, except three single large HCC with diameters between 3.0 and 3.5 cm. There are two major differences of our treatment algorithm for patients with Child C cirrhosis from that for patients with Child A/B cirrhosis. Surgical resection was not chosen and indication for local ablation therapy was stricter. When a tumour protruded from the liver surface, attached to the adjacent organs such as gall bladder, or a tumour was not confirmed well by ultrasonography, local ablation therapies were not performed. The therapies were also avoided when uncontrollable ascites was present. We included transcatheter arterial embolisation (TAE) in the group undergoing TACE, because the number of patients who received TAE was small and no clear difference in the treatment effect was reported in previous studies (Camma et al., 2002). Transcatheter arterial chemoembolisation was not chosen principally in cases of severe portal vein tumour thrombus (PVTT). Transcatheter arterial chemoembolisation and TAI were performed supraselectively in the most peripheral accessible feeding artery to avoid irreversible liver failure. When the treatment might cause immediate irreversible liver failure or severe complications, we did not perform any active treatments irrespective of the patients’ wishes, except emergency TACE for HCC rupture.
Follow-up
Biochemical liver function tests and US, dynamic CT, or MRI were performed at least every 3 months after the treatment. Re-treatment was performed depending on patients’ conditions, tumour stage and background liver function, according to the same clinical indications as for the first intervention.
Statistical analysis
The Kruskal–Wallis test was used to compare the continuous data and the χ² test was used to compare categorical data. Cox proportional hazards regression analysis was used to analyse the prognostic factors. Factors exhibiting significant values in univariate analysis and effect of the treatments were further analysed by multivariate analysis. The propensity score of choosing each treatment was calculated, followed by matching each treatment group and BSC group according to a greedy matching technique (Parsons, 2001). For calculation of the propensity score, following variables (cutoffs) were used: total bilirubin (<2, 2–3, >3, mg per dl), tumour size (<20, 20–30, >30, mm), tumour number (1, >1), PVTT (absent, present). The survival of matched patients was compared by the Kaplan–Meyer method and the differences were evaluated by the log-rank test. SAS (version 9.1.3) and JMP (version 5.0.1) software packages (SAS Institute, Cary, NC, USA) were used for analyses, and P < 0.05 was considered significant. Bonferroni correction was used for multiple comparisons of propensity score-matched analyses and P < 0.05/3 was considered significant.
RESULTS
Clinical characteristic of the patients
Twenty-three patients (14.7%) were treated by local ablation therapy, 27 (17.2%) by TACE, and 19 (12.1%) by TAI. The remaining patients (n = 88, 56.1%) did not receive any of these treatments (BSC group). One- and 3-year survival of patients was 42.6 and 14.0%, respectively.
The characteristics of all patients are reported in Table 1. There was no difference in sex and age among these groups. The positive rate of hepatitis C virus antibody was low (55.7%) in the BSC group. Background liver function (Child-Pugh score) was worse and the tumours were more advanced (tumour size, tumour number, alpha-fetoprotein (AFP), and PVTT) in the BSC group than in other groups. Eighteen patients could be re-treated by local ablation therapies, TAE, or TAI.
Risk factors for survival of HCC patients with Child C cirrhosis
Among 17 parameters and treatment modalities, high bilirubin (>3 mg dl⁻¹), the presence of uncontrollable ascites, and a high platelet count (>8 × 10⁴ mm⁻²), so-called background liver factors, as well as multiple tumour number, large tumour (>3 cm), high AFP (>400 nmol⁻¹), and the presence of PVTT, so-called tumour factors, were significant risk factors for death in univariate analysis in Table 2. Conversely, TACE and local ablation therapy were associated with better survival. As shown in Table 3, multivariate analysis revealed that all background factors and tumour factors that were significant in univariate analysis were also significant risk factors. Regarding therapies, only TACE was a significant negative risk factor for death by multivariate analysis.
Survival of patients in different therapeutic groups
One-year (3-year) survival of patients receiving local ablation therapy, TACE, TAI, and BSC was 69.1 (41.3%), 62.5 (29.8), 43.9 (12.6), and 27.7% (3.8%), respectively (P < 0.001, Figure 1). To estimate the effect of treatments, the clinical background of the patients in each group was adjusted by propensity scores, and the survival of treated groups was compared with the BSC group. Numbers of the score-matched pairs were 25, 19, and 19 for TACE vs BSC group, local ablation therapy vs BSC group, and TAI vs BSC group, respectively. One patient in the BSC group for the comparison with TACE group had a main portal vein thrombus. While survival in the TACE group was significantly better than in the BSC group ( P = 0.009, Figure 2), no differences in survival were observed between the local ablation group and BSC group ( P = 0.782, Figure 3), and between TAI group and BSC group ( P = 0.237, Figure 4).
Table 1 Clinical background of 157 patients
| TACE | TAI | Local | BSC | P-value |
|------|-----|-------|-----|---------|
| Patient number | 27 (17.2%) | 19 (12.1%) | 23 (14.7%) | 88 (56.1%) | <0.001 |
| Sex (male) | 21 (77.8%) | 15 (79.0%) | 16 (69.6%) | 64 (72.7%) | 0.085 |
| Age (years) | 66 (55–70) | 65 (60–68) | 59 (52–64) | 62 (56–70) | 0.275 |
| HCVAb (positive) | 24 (88.9%) | 15 (79.0%) | 18 (78.3%) | 49 (55.7%) | 0.003 |
| HBsAg (positive) | 2 (7.4%) | 2 (10.5%) | 4 (17.4%) | 25 (28.4%) | 0.061 |
| Total bilirubin (mg per dl) | 1.9 (1.2–2.5) | 2.4 (2.1–3.1) | 2.8 (2.1–3.4) | 3.5 (2.2–4.8) | <0.001 |
| Albumin (g per dl) | 0.81 (0.70–0.96) | 0.76 (0.66–1.10) | 0.77 (0.60–0.90) | 0.78 (0.61–1.03) | 0.593 |
| Prothrombin time (%) | 64.2 (50.0–68.9) | 61 (55.6–66.3) | 54.4 (49.4–62.0) | 54.1 (45.0–63.0) | 0.012 |
| Platelets (x 10^11 mm^-3) | 8.8 (5.7–11.6) | 7.9 (5.1–9.7) | 5.7 (4.7–7.2) | 9.4 (6.1–13.7) | 0.004 |
| Prothrombin time (%) | 64.2 (50.0–68.9) | 61 (55.6–66.3) | 54.4 (49.4–62.0) | 54.1 (45.0–63.0) | 0.012 |
| Creatinine (mg per dl) | 0.81 (0.70–0.96) | 0.76 (0.66–1.10) | 0.77 (0.60–0.90) | 0.78 (0.61–1.03) | 0.593 |
| Aspites (present) | 13 (48.2%) | 8 (42.1%) | 5 (21.7%) | 60 (68.2%) | <0.001 |
| Encephalopathy (present) | 12 (44.5%) | 9 (43.4%) | 8 (34.8%) | 40 (55.7%) | 0.811 |
| Tumour number (single) | 9 (33.3%) | 7 (36.8%) | 17 (73.9%) | 28 (31.8%) | 0.002 |
| Tumour size (mm) | 38 (23–53) | 32 (26–65) | 20 (17–29) | 51.5 (30–100) | 0.152 |
| Platelets (x 10^11 mm^-3) | 2.93 1.90–4.58 | 2.11 1.11–2.84 | 2.23 1.52–3.26 | 2.23 1.52–3.26 | <0.001 |
| AFP (ng per ml) | 32 (13–1250) | 81 (13–706) | 21 (9–106) | 188 (26–8660) | <0.001 |
| Child-Pugh score (10/11/12) | 15/11/1 | 15/11/1 | 15/11/1 | 15/11/1 | 0.004 |
Abbreviations: TACE = transcatheter arterial chemoembolisation; TAI = transcatheter arterial chemoinfusion. Other abbreviations are as listed in Table 1.
Table 2 Univariate analysis of the prognostic factors of HCC patients with Child C cirrhosis
| RR | 95% CI | P-value |
|----|-------|---------|
| Sex (male) | 1.16 | 0.78–1.78 | 0.457 |
| Age (per 10 years) | 1.11 | 0.91–1.36 | 0.264 |
| HCVAb (positive) | 0.96 | 0.65–1.44 | 0.869 |
| HBsAg (positive) | 1.21 | 0.75–1.88 | 0.404 |
| Total bilirubin (mg per dl) | 2.14 | 1.48–3.09 | <0.001 |
| Albumin (g per dl) | 1.46 | 0.94–2.21 | 0.090 |
| AST (>40 IU l^-1) | 1.04 | 0.66–1.72 | 0.843 |
| ALT (>40 IU l^-1) | 1.31 | 0.90–1.92 | 0.148 |
| Platelets (x 10^11 mm^-3) | 2.23 | 1.52–3.26 | <0.001 |
| Prothrombin time (%) | 1.24 | 0.84–1.86 | 0.275 |
| Creatinine (mg per dl) | 1.16 | 0.74–1.76 | 0.487 |
| Aspites (present) | 2.46 | 1.63–3.66 | <0.001 |
| Encephalopathy (present) | 0.98 | 0.67–1.41 | 0.926 |
| Tumour number (multiple) | 2.21 | 1.49–3.31 | <0.001 |
| Tumour size (cm) | 3.81 | 2.54–5.83 | <0.001 |
| AFP (mg per ml) | 2.49 | 1.69–3.63 | <0.001 |
| Portal invasion (present) | 3.90 | 2.64–5.76 | <0.001 |
| TACE | 0.56 | 0.33–0.91 | 0.019 |
| Local ablation | 0.42 | 0.24–0.70 | <0.001 |
| TAI | 0.97 | 0.54–1.61 | 0.915 |
Abbreviations: TACE = transcatheter arterial chemoembolisation; TAI = transcatheter arterial chemoinfusion. Other abbreviations are as listed in Tables 1 and 2.
Table 3 Multivariate analysis of the prognostic factors of HCC patients with Child C cirrhosis
| RR | 95% CI | P-value |
|----|-------|---------|
| Total bilirubin (mg per dl) | 2.94 | 1.90–4.58 | <0.001 |
| Platelets (x 10^11 mm^-3) | 1.77 | 1.11–2.84 | 0.016 |
| Aspites (present) | 1.80 | 1.14–2.87 | 0.010 |
| Tumour number (multiple) | 1.67 | 1.06–2.66 | 0.025 |
| Tumour size (cm) | 3.00 | 1.74–5.24 | <0.001 |
| AFP (mg per ml) | 1.68 | 1.05–2.67 | 0.029 |
| Portal invasion (present) | 1.77 | 1.09–2.85 | 0.019 |
| TACE | 0.50 | 0.27–0.89 | 0.019 |
| Local ablation | 1.02 | 0.51–1.96 | 0.944 |
| TAI | 0.64 | 0.33–1.16 | 0.152 |
Abbreviations are as listed in Tables 1 and 2.
DISCUSSION
The prognosis of HCC patients with Child C cirrhosis is well known to be poor; however, there is little information about the prognostic factors among patients and the effect of active treatment, except liver transplantation (Llovet, 2005). In this study, we clearly demonstrated that high total bilirubin (>3 mg dl^-1) and the presence of uncontrollable ascites, categorised as background liver factors, were independent factors for poor prognosis in HCC patients with Child C cirrhosis. In addition, tumour factors such as tumour size (>3 cm), tumour number (multiple), AFP (>400 ng ml^-1), and PVTT were also independent prognostic factors. These factors were quite similar to the reported prognostic factors for HCC, which include chronic hepatitis and Child A or B cirrhosis (Sala et al, 2005). High platelet count also correlated with poor prognosis. Platelet is known to decrease with Child C cirrhosis (Sala et al, 2005). High platelet count also correlated with poor prognosis. Platelet is known to decrease with Child C cirrhosis (Sala et al, 2005).
Hepatocellular carcinoma with Child C cirrhosis
K Nouso et al.
that the liver in patients with high platelet count is not cirrhotic and the liver function is disturbed by very advanced HCC, which can be a reason of poor prognosis. This explanation was strengthened by a result in this study. The size of HCC in patients with high platelet count was significantly larger than that in patients with low platelet count (data not shown).
The contribution of tumour factors to HCC patients with Child C cirrhosis indicated that HCC treatment might prolong survival even though the patients suffered from Child C cirrhosis. The results of multivariate analysis of the treatments and of propensity score-matched survival curves support this hypothesis. The relative risk for patients undergoing TACE was 0.50 and survival of this group was better than that of BSC ($P = 0.009$). Only two patients died within a month and had been treated by TACE because of HCC rupture (data not shown). Although TACE might be an eligible method for the treatment of HCC with Child C cirrhosis, the results do not indicate that TACE is effective in all Child C patients. Transcatheter arterial chemoembolisation was selected for patients without severe portal vein thrombus and with relatively good liver function in this analysed population. The medians of bilirubin and prothrombin time in TACE group were 1.9 mg dl$^{-1}$ and 64.2%, respectively.
While TACE showed a beneficial effect, local ablation therapy did not prolong survival. One possible reason is that the deterioration of liver function to death is much faster than tumour progression. The reported 1-year local recurrence rate of HCC in patients treated by local ablation therapy was low (2 – 18%) (Lin et al, 2005; Tateishi et al, 2006; Kim et al, 2006b), whereas the 1-year survival rate of Child C patients treated by local ablation therapy was 69.1%, indicating that many patients died without recurrence of HCC. Although no effect of local ablation therapy was observed, therapy including RFA could be used for decompensated liver cirrhosis (Kim et al, 2006a) and it is possible that it might be beneficial in special circumstances, such as when minute growth of the tumour immediately results in the occlusion of major critical vessels.
Several studies have addressed the characters of HCC with decompensated cirrhosis (Nagasue et al, 1999; Ueno et al, 2002; Toyoda et al, 2005). Ueno et al (2002) reported that high albumin, lack of oesophageal varices, small tumour, single tumour, and low AFP were survival factors for HCC patients with decompensated liver cirrhosis. The study included many Child B cirrhosis patients (over 85%); however, the results were quite similar to our data with Child C cirrhosis. Toyoda et al (2005) reported risk factors for HCC patients with Child C cirrhosis and beneficial effect of treatment; however, the study included old cases and details of the treatment were not described. Regarding therapies, BSC was recommended for the treatment of HCC with decompensated cirrhosis, except in transplantation-eligible cases, by the algorithms of HCC treatment demonstrated by groups in Europe and Japan (Bruix et al, 2001; Llovet, 2005; Makuuchi and Kokudo, 2006), while there are several reports indicating the usefulness or safety of operation, RFA, and TACE for patients with decompensated liver cirrhosis (Nagasue et al, 1999; Ueno et al, 2002; Kim et al, 2006a). Prospective randomised study is the best method to know the benefit of these therapies for HCC patients with Child C cirrhosis; however, it is ethically difficult now because no clear evidence of the beneficial effect of active treatments was reported and most of the guidelines for the treatment of HCC did not recommend these therapies except transplantation. Our study was a retrospective cohort study, the patient groups were heterogeneous and the number of patients in each arm was quite limited; however, we clearly indicates the possibility of adopting TACE for the treatment of HCC in patients with Child C cirrhosis by both multivariate Cox proportional hazard model and propensity score-matched analyses.
Recently, improvement of liver function in patients with decompensated liver cirrhosis by anti-hepatitis virus therapy such as lamivudine or adefovir dipivoxil was reported (Hiraoka et al,
2005; Takamura et al, 2007). Adoption of these anti-viral therapies can reduce patient mortality from liver failure so that the treatment effect of local ablation therapy may improve, resulting in increased candidates for active treatment of HCC with Child C cirrhosis.
In this study, we demonstrated that tumour factors as well as background liver factors were risk factors even in HCC patients with Child C cirrhosis, and that TACE can be effective in a very selected group of patients. A randomised controlled study is needed to expand the eligible criteria for active treatment.
REFERENCES
Adams PC, Arthur MJ, Boyer TD, DeLeve LD, Di Bisceglie AM, Hall M, Levin TR, Prouzenale D, Seeff L (2004) Screening in liver disease: report of an AASLD clinical workshop. Hepatol Rep 39: 1204 – 1212
Bolondi L (2003) Screening for hepatocellular carcinoma in cirrhosis. J Hepatol 39: 1076 – 1084
Bruix J, Llovet JM (2002) Prognostic prediction and treatment strategy in hepatocellular carcinoma. Hepatology 35: 519 – 524
Bruix J, Sherman M, Llovet JM, Beaugrand M, Lencioni R, Burroughs AK, Christensen E, Pagliaro L, Colombo M, Rodes J (2001) Clinical management of hepatocellular carcinoma. Conclusions of the Barcelona-2000 EASL conference. European Association for the Study of the Liver. J Hepatol 35: 421 – 430
Camma C, Schepis F, Orlando A, Albanese M, Shahied L, Trevisani F, Andreone P, Craxi A, Cottone M (2002) Transarterial chemoembolization for unresectable hepatocellular carcinoma: meta-analysis of randomized controlled trials. Radiology 224: 47 – 54
Hiraoka A, Michitaka K, Kumagawa T, Kurose K, Uhara T, Hirooka M, Yamashita Y, Kubo Y, Miyakata H, Iuchi H, Okada S, Ohmoto M, Yamamoto K, Horiike N, Onji M (2005) Efficacy of lamivudine therapy for decompensated liver cirrhosis due to hepatitis B virus with or without hepatocellular carcinoma. Oncol Rep 13: 1159 – 1163
Honda H, Ochiai K, Adachi E, Yasumori K, Hayashi T, Kawashima A, Fukuya T, Gibo M, Matsumata T, Tsumeyoshi M, Masuda K (1993) Hepatocellular carcinoma: correlation of CT, angiographic, and histopathologic findings. Radiology 189: 857 – 862
Ikai I, Arii S, Okazaki M, Okita K, Omata M, Kojima M, Takayasu K, Nakamura Y, Makuch M, Matsuyama Y, Monden M, Kudo M (2007) Report of the 17th Nationwide Follow-up Survey of Primary Liver Cancer in Japan. Hepatol Res 37: 676 – 691
Kim YK, Kim CS, Chung CH, Han YM, Lee SY, Jin GY, Lee JM (2006a) Radiofrequency ablation of hepatocellular carcinoma in patients with decompensated cirrhosis: evaluation of therapeutic efficacy and safety. AJR Am J Roentgenol 186: S261 – S268
Kim YS, Rhim H, Cho OK, Koh BH, Kim Y (2006b) Intrahepatic recurrence after percutaneous radiofrequency ablation of hepatocellular carcinoma: analysis of the pattern and risk factors. Eur J Radiol 59: 432 – 441
Lin SM, Lin CJ, Lin CC, Hsu CW, Chen YC (2005) Randomised controlled trial comparing percutaneous radiofrequency thermal ablation, percutaneous ethanol injection, and percutaneous acetic acid injection to treat hepatocellular carcinoma of 3 cm or less. Gut 54: 1151 – 1156
Llovet JM (2005) Updated treatment approach to hepatocellular carcinoma. J Gastroenterol 40: 225 – 235
Llovet JM, Burroughs A, Bruix J (2003) Hepatocellular carcinoma. Lancet 362: 1907 – 1917
Makuch M, Kokudo N (2006) Clinical practice guidelines for hepatocellular carcinoma: the first evidence based guidelines from Japan. World J Gastroenterol 12: 828 – 829
Nagasue N, Kohno H, Tachibana M, Yamanoi A, Ohmori H, El-Assal ON (1999) Prognostic factors after hepatic resection for hepatocellular carcinoma associated with Child-Turcotte class B and C cirrhosis. Ann Surg 229: 84 – 90
Parkin DM (2001) Global cancer statistics in the year 2000. Lancet Oncol 2: 533 – 543
Parsons LS, Ovation Research Group (2001) Reducing bias in a propensity score matched-pair sample using greedy matching techniques. In: Proceedings of the Twenty-Sixth Annual SAS Users Group International Conference. pp 214 – 226. Cary: SAS Institute Inc.
Pugh RN, Murray-Lyon IM, Dawson JL, Pietroni MC, Williams R (1973) Transsection of the oesophagus for bleeding oesophageal varices. Br J Surg 60: 646 – 649
Sala M, Forner A, Varela M, Bruix J (2005) Prognostic prediction in patients with hepatocellular carcinoma. Semin Liver Dis 25: 171 – 180
Takamura M, Ichida T, Ohkoshi S, Tsubata S, Osaki A, Aoyagi Y, Nomoto M, Uehara K, Terada H, Aoyagi Y (2007) Decompensated lamivudine-resistant hepatitis B virus-related cirrhosis treated successfully with adefovir dipivoxil allowing surgery for hepatocellular carcinoma. Intern Med 46: 367 – 371
Tateishi R, Shihira S, Yoshida H, Teratani T, Obi S, Yamashiki N, Akamatsu M, Kawabe T, Omata M (2006) Prediction of recurrence of hepatocellular carcinoma after curative ablation using three tumor markers. Hepatology 44: 1518 – 1527
Toyoda H, Kunuda T, Kiriyama S, Sone Y, Tanikawa M, Misaka Y, Hayashi K, Honda T, Kozuya T, Nomogaki K, Shimizu J (2005) Impact of tumor factors on the prognosis of patients with advanced cirrhosis (Child-Pugh class C) and hepatocellular carcinoma. J Gastroenterol Hepatol 20: 963 – 965
Trevisani F, Cantarini MC, Labate AM, De Notariis S, Rapaccini G, Farinati F, Del Poggio P, Di Nolfo MA, Benvegnu L, Zoli M, Borzio F, Bernardi M (2004) Surveillance for hepatocellular carcinoma in elderly Italian patients with cirrhosis: effects on cancer staging and patient survival. Am J Gastroenterol 99: 1470 – 1476
Ueno S, Tanabe G, Nukui K, Oketani M, Komoriyama Y, Hikata H, Fukukura Y, Baba Y, Imamura Y, Aoyagi T, Nomoto M, Uehara K, Terada H, Aoyagi Y (2007) Decompensated lamivudine-resistant hepatitis B virus-related cirrhosis treated successfully with adefovir dipivoxil allowing surgery for hepatocellular carcinoma. Intern Med 46: 367 – 371
We thank the following physicians for their continued dedication: Shuji Uematsu, Kunihiko Shiraga, Ryoichi Okamoto, Shota Iwadou, Yasuyuki Araki, Hiroshima City Hospital; Toshiya Osawa, Shin-ichi Fujioka, Okayama Saiseikai General Hospital; Hiroshi Ikeda, Toshihiko Kaneyoshi, Kurashiki Central Hospital; Hirohori Tanaka, Tsuyama Central Hospital; Koichi Takaguchi, Kagawa Prefectural Central Hospital; Kohsaku Sakaguchi, Fukuyama City Hospital.
ACKNOWLEDGEMENTS
We thank the following physicians for their continued dedication: Shuji Uematsu, Kunihiko Shiraga, Ryoichi Okamoto, Shota Iwadou, Yasuyuki Araki, Hiroshima City Hospital; Toshiya Osawa, Shin-ichi Fujioka, Okayama Saiseikai General Hospital; Hiroshi Ikeda, Toshihiko Kaneyoshi, Kurashiki Central Hospital; Hirohori Tanaka, Tsuyama Central Hospital; Koichi Takaguchi, Kagawa Prefectural Central Hospital; Kohsaku Sakaguchi, Fukuyama City Hospital.
Clinical Studies
© 2008 Cancer Research UK
British Journal of Cancer (2008) 98(7), 1161 – 1165 | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4909,
1
],
[
4909,
11912,
2
],
[
11912,
16899,
3
],
[
16899,
21253,
4
],
[
21253,
28068,
5
]
]
} |
9c5e9513a10d58776621f38d8baabaf5a62e4e94 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 29433,
"total-output-tokens": 10113,
"fieldofstudy": [
"Environmental Science"
]
} | Quantification of sinensetin in *Orthosiphon stamineus* from various phytogeographical zones in Indonesia
Kartini Kartini**, Rizky Eka Putri¹, Ryanto Budiono²
¹Department of Pharmaceutical Biology, Faculty of Pharmacy University of Surabaya, Surabaya, Indonesia.
²Department of Pharmaceutical Chemistry, Faculty of Pharmacy, University of Surabaya, Indonesia.
**ARTICLE INFO**
Received on: 07/07/2022
Accepted on: 23/12/2022
Available Online: 04/03/2023
Key words: Marker, *Orthosiphon stamineus*, phytogeographical, sinensetin, TLC-densitometer.
**ABSTRACT**
*Orthosiphon stamineus* is widely used as an ingredient in traditional medicine and functional food partially for its main active compound, sinensetin. Plant growth and sinensetin contents are sensitive to many variables, including phytogeographical profiles. This study sought to evaluate the quality of *O. stamineus* obtained from nine locations in Indonesia, predicated on sinensetin levels assessed using TLC-densitometry. Thin Layer Chromatography (TLC) was conducted with silica gel 60 *F*254 as the stationary phase and toluene: ethyl acetate (5:7) and a drop of formic acid for every 10 ml of that solvent mixture as the mobile phase and was analyzed without a derivatization reagent. The created method proved uncomplicated and satisfied the specificity parameters, as indicated by the identical UV spectrum shared between the sinensetin standard and sample (*λ*max = 334 nm). Also, it showed good linearity for sinensetin in the range of 14.5–87 ng/band (*r* = 0.9886). Limits of detection and limits of quantification were 9.03116 and 27.36717 ng/band, respectively. In addition, the method possessed good intra- and interday precision (marked by Relative Standard Deviations (RSDs) of 1.65%–6.47% and 4.97%) and accuracy (95.86, 120.18, and 82.44% recoveries in standard addition with three-level solutions). Of the 14 samples, sinensetin was undetected in two but found in various concentrations in the other 12 samples, from 0.0238 to 0.1533 mg/g. Using a sample from the Tawangmangu area as a reference, three groups of samples were formed: those with lower sinensetin contents (Jakarta Selatan, Lamongan, Jombang, and Sampang), higher sinensetin contents (Surabaya, Mojokerto, Kediri, and Kotabaru), and similar sinensetin contents as the reference sample (Batu, Gresik, and Madiun). The TLC-densitometry designed in this study is straightforward but satisfies the validation parameters; thus, it can be used to qualitatively and quantitatively analyze sinensetin in *O. stamineus*. Overall, *O. stamineus* in different phytogeographical zones in Indonesia has varying levels of sinensetin.
**INTRODUCTION**
*Orthosiphon stamineus* Benth. (Lamiaceae), also known as cat’s whiskers, *kumis kucing* or *misai kucing*, is among the most widely used medicinal herbs in Southeast Asian countries, including Indonesia and Malaysia (Adnyana et al., 2013; Ameer et al., 2012). In Indonesia, the plant is an important ingredient in the products “Jamu Saintifik” and “Fitofarmaka,” recognized for their efficacy in ameliorating hypertension, arthritis, and urinary stones (Indonesia Ministry of Health, 2019, 2022). Many studies have successfully discovered the bioactive compounds associated with these activities (Ashraf et al., 2018; Sarshar et al., 2017; Xu et al., 2020), namely, a variety of derivatives of phenolic acid and flavonoids (Akowuah et al., 2004; Guo et al., 2019). An example is sinensetin, a polymethoxyflavone most responsible for the biological activity of *O. stamineus* not only as an antihypertensive but also as an anticancer, anti-diabetic, antimicrobial, anti-inflamatory, vasorelaxant, and antioxidant agent (Han Jie et al., 2021; Mohamed et al., 2012; Samidurai et al., 2020; Yam et al., 2018; Wang et al., 2022).
*Orthosiphon stamineus* can grow well in different phytogeographical profiles. On the one hand, this characteristic is beneficial because it facilitates the provision of raw materials for traditional medicines for public use and industrial purposes...
in different localities. However, on the other hand, the possibility of variations in material quality can pose a disadvantage to standardized production. It accounts for the fact that the plant’s chemical constituents are sensitive to geographical origins, soil conditions, climate, harvesting process, and postharvest treatments, among others (Bensoussan et al., 2015). Therefore, because phytogeographical configurations affect the compound’s concentration, standardization of *O. stamineus* crude drugs is necessary so as to ensure uniformity of raw materials across various locations.
Herbs can be analyzed for their pharmaceutical quality through many approaches, including markers and compound fingerprints. Several fingerprint-based techniques have been applied to unveil variations in *O. stamineus* grown in different locations, such as combining TLC fingerprinting with chemometrics (Kartini et al., 2020), Fourier Transform-Infra Red (FT-IR) spectroscopy with canonical variate analysis (Rafi et al., 2015), and a virtual chemical sensor based on fast gas chromatography (Sim et al., 2003). Although these fingerprint-based systems are currently developing as they gain more attention from researchers, the conventional technique using chemical markers is still widely used by herbal pharmacopeias in many countries, including the Indonesian Herbal Pharmacopoeia. This is due to the ease of correlation with herbal dosages.
For the above reasons, TLC and High Performance Liquid Chromatography (HPLC) have been proposed to detect and measure sinensetin as a chemical marker and biological activity indicator of *O. stamineus*. This is to address the very few reports on divergent sinensetin contents in the plant samples collected from various phytogeographical zones in Indonesia. Moreover, TLC guarantees speed and simplicity, two criteria highly demanded of routine herbal quality analysis and assessment methods in pharmaceutical industries. In addition, TLC is still broadly used to analyze marker compounds in several compendia, such as the Indonesian Herbal Pharmacopoeia and the Chinese Pharmacopoeia (Shen et al., 2020). Therefore, this study aimed to evaluate the quality of *O. stamineus* obtained from 14 phytogeographical zones in Indonesia based on the concentrations of the marker compound, sinensetin, using TLC-densitometry. Here, a sample from one location, B2P2TOOT Tawangmangu (hereinafter referred to as the Tawangmangu sample), is used as a reference because the area grows *O. stamineus* for the “Jamu Saintifik” products (scientific herbal medicine) nationwide. In addition, B2P2TOOT Tawangmangu is also a service-based herbal clinical testing center to produce “Jamu Saintifik” in Indonesia.
**MATERIALS AND METHODS**
**Materials**
The chemicals used in this study included a sinensetin standard obtained from Sigma-Aldrich (USA), precoated TLC Si gel 60 F254 (20 × 20 cm), and several p.a. grade solvents from Merck KGaA (Darmstadt, Germany).
*Orthosiphon stamineus* leaves were harvested in July–September 2020 from 14 regions in Indonesia. The first eight leaves from the shoots were picked by hand, washed with running water, drained, and then dried by aeration. Afterward, the dried leaves were ground in a blender and sifted with a 45-mesh sieve. Details of the phytogeographical origins of the samples are shown in Table 1, and all samples have been verified by the Center for Information and Development of Traditional Medicines Pusat Informasi dan Pengembangan Obat Tradisional (PIPOT), the University of Surabaya, with Authentication Certificate No. 1434/D.T/I/2021.
**Extract preparation**
Approximately 1 g of *O. stamineus* leaf powder was added with 7 ml of methanol and then extracted using the ultrasound-assisted extraction method for 15 minutes at room temperature. The extract was then separated from the dregs and put into a 10 ml volumetric flask. Extraction was completed by rinsing the dregs with 3 ml of methanol and putting them into the same volumetric flask. The extract volume was then made up to 10.0 ml.
**Table 1.** Phytogeographical details of the *O. stamineus* production areas observed in the research.
| Codes | Regions | Latitude, longitude | Elevation (masl) |
|-------|------------------|---------------------------|-----------------|
| 1 | Jakarta Selatan | 6°15’25” S and 106°46’45” E | 7 |
| 2 | Surabaya | 7°16’11” S and 112°44’48” E | 7 |
| 3 | Lamongan | 7°06’25” S and 112°20’08” E | 7.7 |
| 4 | Gresik | 7°09’58” S and 113°18’07” E | <200 |
| 5 | Batu | 7°31’52” S and 112°31’12” E | 897 |
| 6 | Ngawi | 7°33’27” S and 111°17’38” E | 331 |
| 7 | Tawangmangu | 7°39’50” S and 111°08’04” E | 1,200 |
| 8 | Jombang | 7°36’52” S and 112°22’10” E | 62 |
| 9 | Sampang | 7°03’54” S and 113°15’04” E | 63 |
| 10 | Mojokerto | 7°38’37” S and 112°36’10” E | 650 |
| 11 | Madiun | 7°39’44” S and 111°36’17” E | 62 |
| 12 | Kediri | 7°46’07” S and 111°54’36” E | 78 |
| 13 | Badung | 8°35’53” S and 115°11’52” E | 350 |
| 14 | Kotabaru | 3°17’32” S and 116°13’05” E | 212 |
Standard solution preparation
Around 1.16 mg of the sinensetin standard was dissolved in sufficient methanol, then transferred to a 10 ml volumetric flask, and added with methanol to 10.0 ml. The mother solution (116 ppm) was then diluted to obtain a working solution with a concentration of 7.25 ppm.
TLC system
The *O. stamineus* leaf extract and sinensetin standard were spotted on a TLC silica gel 60 F254 plate in a 6 mm bandwidth using a CAMAG 100 µl sample syringe (Hamilton, Switzerland). Automatic spotting was conducted with a Linomat 5 TLC Applicator (CAMAG, Switzerland) in a stream of nitrogen gas. The TLC plate was then developed in a twin-through chamber (CAMAG, Switzerland), which had been saturated with the mobile phase (toluene: ethyl acetate = 5:7 and a drop of formic acid for every 10 ml of that solvent mixture) for 30 minutes. An ascending development was performed with an elution distance of 80 mm. The separation results were then documented under 254 and 366 nm UV light without derivatization reagents and then scanned using TLC Scanner 4 (CAMAG, Switzerland) with a 4 × 0.3 mm slit, data resolution of 1 nm/step, and scanning speed of 100 nm/seconds. The densitogram was then analyzed with the winCATS software.
Validation of the analytical method
Specificity study
Eight microliters of the sinensetin standard and 2 and 4 µL of the *O. stamineus* extract samples were applied to the TLC plate and then processed conforming to the TLC system designed in the current research. To ascertain the method’s specificity, the characteristics of the sinensetin in the standard and the samples were cross-compared, including Rf values, UV spectrum profiles, and λ<sub>max</sub> measured with a densitometer. The purity of the samples’ sinensetin band was confirmed by reading the UV spectrum at the beginning, apex, and end of the peak (Spangenberg et al., 2011).
Calculation of linearity, limits of detection (LOD) and quantification (LOQ)
Linearity measures the ability of an analytical procedure to obtain test results, either directly or by mathematical transformations, that correlate linearly with the amount of analyte in the sample within a particular validated range. To determine the procedure’s linearity, a series of the working solutions (2, 4, 6, 8, 10, and 12 µl) were spotted on the plate. After the plate development, the area of the sinensetin band was measured by a densitometer. The purity of the samples’ sinensetin band was confirmed by reading the UV spectrum at the beginning, apex, and end of the peak (Spangenberg et al., 2011).
Evaluation of precision
In the intraday precision testing, 6 µl of the *O. stamineus* extract was spotted repeatedly six times on one plate, while the interday precision spotting was conducted on three different plates on three successive days. Each plate was then analyzed using the TLC-densitometry designed to measure the sinensetin area. Finally, the intraday and interday precision were individually evaluated from the relative standard deviations (%RSD) calculated per plate and from the three plates (Spangenberg et al., 2011).
Evaluation of accuracy
Accuracy represents the proximity between the actual values and the test results of the method being analyzed (theoretical values). Here, accuracy was calculated as a percentage of recoveries using standard addition with multiple solutions. First, multilevel solutions (levels 1–3) were prepared by pipetting three different volumes of the standard sinensetin solutions (i.e., 80, 100, and 120 µl), and each was added with 120, 100, and 80 µl of the sample solutions. Second, to prepare unspiked samples (without the addition of the standard solutions), 120, 100, and 80 µl of the sample solutions were pipetted, and 80, 100, and 120 µl of methanol were added to each. Finally, the multilevel solutions and the unspiked samples were applied to the TLC plate, and this procedure was performed in triplicate. The plates were eluted and then analyzed using a densitometer, and the % recovery was calculated.
Measurement of the sinensetin contents of *O. stamineus*
Amounts of sinensetin in *O. stamineus* grown in 14 different phytogeographical zones in Indonesia were determined using a validated TLC system and calculated as mg/g dry weight (of the leaf).
Data analysis
The sinensetin contents, representing the 14 different phytogeographical profiles, were cross-compared using one-way ANOVA (α = 0.05). Then, a subsequent Tukey test was performed to compare the sinensetin contents of each of the 13 crude drugs against the sample harvested from Tawangmangu (reference sample). The GraphPad Prism Version 5.01 program was used to run these analyses.
RESULTS AND DISCUSSION
Organoletic properties of the crude drugs
The phytogeographical zones explored in the study are relatively diverse in elevation, that is, from 7 to 1,200 masl. However, the crude drugs obtained from the leaves were organoleptically similar, including the brownish-green color and dry and brittle characteristics (Fig. 1).
Specificity
Plant extracts contain different kinds of compounds with various physicochemical characteristics. Two or more different compounds can have similar or even identical polarity, thus appearing as one band on the TLC plate. For example, *O. stamineus* leaves contain several polymethoxy flavonoids, among which the most abundant are 3′-hydroxy-5,6,7,4′-tetramethoxyflavone and sinensetin. These compounds differ in the number and position of the methoxy groups, indicating only slightly different polarity (Hossain and Ismail, 2016).
For these reasons, specificity should be determined to ensure and guarantee that the analytical procedure measures the target compound or that the compound band appearing in the test is the target compound. Specificity was analyzed by comparing the colors and Rf values of the standard and sample bands. In addition, a similarity analysis was also conducted between the UV spectra (200–400 nm) of the standard and the sample to determine specificity.
The TLC chromatograms (Fig. 2) show a band suspected to be sinensetin in the sample bands (tracks b and c). It was a blue fluorescence band under UV light at 366 nm, with a position parallel to the sinensetin standard. Furthermore, the UV spectra of the sinensetin standard and the O. stamineus extract sample (Fig. 3) showed a similar pattern, comprising two peaks, each at maximum wavelengths of 334 and 264 nm. These spectral characteristics are typical of flavonoids in the flavone subclass. In the subsequent analysis, sinensetin in the standard and the extract samples was detected and measured at 334 nm. The selected wavelength corresponds to the one used in a previous study, that is, 338 nm (Arifianti et al., 2014). However, many chose a somewhat different wavelength, 366 nm, for the same purpose (Shehzadi et al., 2018).
Rf values corroborate the similarities shared by the sinensetin standard and samples (Table 2). Densitograms show that both had the same Rf value of 0.31 (Fig. 4). The pure presence of sinensetin in the samples was demonstrated by the values of \( r(s, m) = 0.992192 \) and \( r(m, e) = 0.997264 (>0.99) \) (Patel et al., 2019). It confirms that the suspected band is that of sinensetin and is not mixed with other compounds. From these findings, it can be inferred that the TLC method developed in this study has good specificity or is specific to detecting sinensetin levels in O. stamineus.
Linearity, the limits of detection and quantification
To determine linearity, the correlation coefficient \( (r) \) obtained from the standard curve was observed. The curve was formed using triplicate measurements \( (n = 3) \), that is, spotting different volumes of the sinensetin standard (7.25 ppm): 2, 4, 6, 8, 10, and 12 \( \mu \)l or equivalent to 14.5–87 ng/band. Based on the TLC-derived chromatogram and 2D densitogram of the standard sinensetin solution (Fig. 5), the linear regression model showed a positive linear correlation between the mass of sinensetin and the fluorescence intensity of the compound band and the peak area (Fig. 6). The \( r \)-value obtained from the model was 0.98858, meaning that the linear relationship holds for 14.5 to 87 ng/band of sinensetin for each area (Hashim et al., 2016).
LOD and LOQ, calculated from the standard curve \( (n = 3) \), were 9.03116 ng/band and 27.36717 ng/band. These values were about two times smaller than those identified in a previous study that used High Performance Thin Layer Chromatography (HPTLC) to analyze sinensetin and three other compounds in the O. stamineus leaf extract simultaneously, that is, 17.26 and 52.3 ng/spot (Hashim et al., 2016). LOD (and LOQ) indicates the smallest amount of analyte detectable (and quantifiable) by the analytical procedure used with reasonable statistical certainty. HPTLC is different from TLC as it uses a smaller particle size for the stationary phase and, consequently, produces better analytical performance, but HPTLC plates are more pricey than TLC plates (Srivastava, 2010; Zlatkis and Kaiser, 2011). The study results suggested that the developed TLC is sensitive and, thus, sufficient for evaluating sinensetin contents in O. stamineus leaves.
Precision
Precision describes the closeness of agreement between multiple sample replications and the random error in an analytical procedure. Figure 7 shows one of the chromatograms of the six samples spotted on a TLC plate used in the intraday and interday
precision testing. Table 3 provides the amounts of sinensetin read from it.
Table 3 indicates that the TLC-densitometry designed for a single sinensetin assay for *O. stamineus* has good intraday and interday precision, as shown by RSDs of 1.65%–6.47% and 4.97%, respectively. With a different precision test design, the HPTLC-densitometer in a previous study has been found to also have good intraday and interday precision for sinensetin, with RSDs of 3.76%–4.38% and 3.48%–4.24% (Shehzadi *et al.*, 2018).
Accuracy was analyzed using standard addition with multiple solutions (three levels) and unspiked samples (six spots for the TLC). The three levels produced recoveries of 95.86%, 120.18%, and 82.44% (Table 4), which correspond to previous studies that used an HPTLC-densitometer (Akowuah et al., 2006; Shehzadi et al., 2018). Because the recoveries were in the range of 80%–120%, the proposed method is therefore accurate (Riyanto, 2014).
Sinensetin levels in *O. stamineus* from various phytogeographical zones
To determine the sinensetin concentrations, each *O. stamineus* extract sample was spotted with the appropriate volume on a TLC plate and analyzed using the designed and validated procedure. TLC-derived chromatograms of the 14 samples and their sinensetin measurement results are shown in Figure 8 and Table 5. Table 5 shows that samples from the Ngawi and Badung areas contained minute sinensetin (below the LOQ). Compared with the other samples, their other metabolites were also extremely low (Fig. 8). On the contrary, the other 12 samples showed varying levels of sinensetin, ranging from 0.0238 to 0.1533 mg/g. One-way ANOVA results revealed a significant difference in the sinensetin levels of the 14 *O. stamineus* samples ($p < 0.0001$). Because this study aimed to determine the quality profile of the *O. stamineus* leaves obtained from various locations with different phytogeographic characteristics, a post hoc Tukey test was performed to statistically compare each sample with the reference sample (from the Tawangmangu area). Based on the analysis results (Fig. 9), the samples can be clustered into three groups. The group containing significantly lower sinensetin than the reference sample was comprised of the Jakarta Selatan, Lamongan, Jombang, and Sampang samples. On the contrary, the one with significantly higher sinensetin concentrations consisted of the Surabaya, Mojokerto, Kediri, and Kotabaru samples. The last group considered the Batu, Gresik, and Madiun samples as...
Table 3. Sinensetin areas ($\lambda = 334$ nm) of six $O. stamineus$ samples measured for the intraday and interday precision testing.
| Replications | Day 1 | Day 2 | Day 3 |
|--------------|-----------|-----------|-----------|
| 1 | 2,960.70 | 2,490.27 | 2,628.12 |
| 2 | 2,991.81 | 2,526.84 | 2,718.25 |
| 3 | 2,928.37 | 2,577.36 | 2,754.36 |
| 4 | 2,880.37 | 2,687.37 | 2,689.59 |
| 5 | 2,855.15 | 2,856.10 | 2,738.82 |
| 6 | 2,937.83 | 2,901.24 | 2,699.74 |
| Mean ± SD | 2,925.71 ± 50.56 | 2,673.20 ± 173.05 | 2,704.81 ± 44.57 |
| RSD (%) | 1.73 | 6.47 | 1.65 |
Intraday precision (%RSD. $n = 6$) = 1.65–6.47
Interday precision (%RSD. $n = 3$) = 4.97
Table 4. Accuracy test results of the proposed TLC method for sinensetin measurements in $O. stamineus$.
| Levels | Tracks | Areas | Total sinensetin (ng) | Measured sinensetin (ng) | Theoretical sinensetin (ng) | Recovery (%) |
|--------|--------|-------|-----------------------|--------------------------|-----------------------------|--------------|
| 1 | Unspiked samples | 1,538.20 ± 151.51 | 15.14 ± 3.04 | 16.68 ± 0.31 | 17.4 | 95.86 ± 1.75 |
| | Standard addition | 2,369.13 ± 15.21 | 31.82 ± 0.31 | 26.14 ± 0.28 | 21.75 | 120.18 ± 1.29 |
| 2 | Unspiked samples | 1,146.47 ± 82.80 | 7.28 ± 1.66 | 13.10 ± 5.32 | 21.50 | 82.44 ± 8.81 |
| | Standard addition | 2,448.87 ± 13.99 | 33.42 ± 0.28 | 21.52 ± 2.30 | 26.1 | 82.44 ± 8.81 |
| 3 | Unspiked samples | 1,436.97 ± 264.85 | 13.10 ± 5.32 | 21.52 ± 2.30 | 26.1 | 82.44 ± 8.81 |
| | Standard addition | 2,508.91 ± 114.6 | 34.62 ± 2.30 | 21.52 ± 2.30 | 26.1 | 82.44 ± 8.81 |
*Mean ± SD ($n = 3$)
Figure 8. TLC-derived chromatograms of the sinensetin standard (std) and $O. stamineus$ samples from 14 phytogeographically diverse sites (1–14) read under 254 nm (A) and 366 nm (B) UV light.
Table 5. Sinensetin levels of the $O. stamineus$ samples harvested from 14 phytogeographical zones in Indonesia.
| Sample codes | Origins of sample | Sinensetin contents (mg/g) |
|--------------|-------------------|---------------------------|
| 1 | Jakarta Selatan | 0.0238 ± 0.0013 |
| 2 | Surabaya | 0.0556 ± 0.0102 |
| 3 | Lamongan | 0.0250 ± 0.0043 |
| 4 | Gresik | 0.0485 ± 0.0045 |
| 5 | Batu | 0.0458 ± 0.0031 |
| 6 | Ngawi | * |
| 7 | Tawangmangu | 0.0394 ± 0.0073 |
| 8 | Jombang | 0.0266 ± 0.0045 |
| 9 | Sampang | 0.0255 ± 0.0033 |
| 10 | Mojokerto | 0.0564 ± 0.0086 |
| 11 | Madiun | 0.0333 ± 0.0058 |
| 12 | Kediri | 0.1533 ± 0.0097 |
| 13 | Badung | * |
| 14 | Kotabaru | 0.0523 ± 0.0073 |
*: not measurable (sinensetin level < LOQ), data were obtained from the mean ± SD of triplicate measurements ($n = 3$).
having no significantly different sinensetin contents from the reference sample.
The study results proved that the amounts of sinensetin found in *O. stamineus* are influenced by the plant’s phytogeographical origins. However, further research is required to determine whether or not the location’s elevation and other contributing variables account for such differences. The findings of this study strengthen the data of previous studies which stated that there was a diversity of agronomic characters (accumulated height gain for 8 weeks after planting; number of secondary branches and secondary branch internodes; length, width, and leaf area index; and average dry weight of stems and leaves per 4.41 m²) and the sinensetin content of *O. stamineus* from *ex situ* collections from Jawa Barat, Jawa Tengah, and Jawa Timur (Febjislami et al., 2018). These findings provide scientific evidence that justifies the essence of factoring in geographical conditions in cultivating *O. stamineus* to obtain standardized harvests with consistent sinensetin contents.
**CONCLUSION**
The TLC-densitometry designed in the study is straightforward but satisfies the validation parameters; thus, it can be used to qualitatively and quantitatively analyze sinensetin in *O. stamineus*. In addition, the study discovered that the sinensetin contents of the extracts prepared from *O. stamineus* vary across the plant’s phytogeographical zones in Indonesia. For future research, it is recommended to utilize the method for other phytogeographical locations in Indonesia and other countries.
**AUTHORS’ CONTRIBUTIONS**
Kartini Kartini conceptualized the study; Kartini Kartini and Rizky Eka Putri conducted the experiment; Kartini Kartini, Rizky Eka Putri, and Ryanto Budiono analyzed the results. All authors reviewed the manuscript.
**FINANCIAL SUPPORT**
This research was funded by the Indonesian Ministry of Education, Culture, Research and Technology with the contract number: 063 /SP-Lit/LPPM-01/KemendikbudRistek/Multi/FF/III/2022.
**CONFLICTS OF INTEREST**
The authors report no financial or any other conflicts of interest in this work.
**ETHICAL APPROVALS**
This study does not involve experiments on animals or human subjects.
**DATA AVAILABILITY**
All data generated and analyzed are included in this research article.
**PUBLISHER’S NOTE**
This journal remains neutral with regard to jurisdictional claims in published institutional affiliation.
**REFERENCES**
Adnyana IK, Setiawan F, Insanu M. From ethnopharmacology to clinical study of *Orthosiphon stamineus* Benth. studies, 2013; 1(2): 66-73.
Akowuah G, Zhari I, Norhayati I, Sadikun A, Khamshah S. Sinensetin, eupatorin, 3′-hydroxy-5, 6, 7, 4′-tetramethoxyflavone and rosmarinic acid contents and antioxidative effect of *Orthosiphon stamineus* from Malaysia. Food Chem, 2004; 87(4):559–66.
Akowuah G, Zhari I, Sadikun A, Norhayati I. HPTLC densitometric analysis of *Orthosiphon stamineus*. leaf extracts and inhibitory effect on xanthine oxidase activity. Pharm Biol, 2006; 44(1):65–70.
Ameer OZ, Salman IM, Asmawi MZ, Ibraheem ZO, Yam MF. *Orthosiphon stamineus*: traditional uses, phytochemistry, pharmacology, and toxicology. J Med Food, 2012; 15(8):678–90.
Arifianti L, Oktarina RD, Kusumawati I. Pengaruh jenis pelarut pengekstraksi terhadap kadar sinensetin dalam ekstrak daun *Orthosiphon stamineus* Benth. E-J Planta Husada, 2014; 2(1):1–4.
Ashraf K, Sultan S, Adam A. *Orthosiphon stamineus* Benth. is an outstanding food medicine: review of phytochemical and pharmacological activities. J Pharm Bioall Sci, 2018; 10(3):109.
Bensousan A, Lee S, Murray C, Bourcher S, Van Der Kooy F, Pearson JL, Liu J, Chang D, Kho O. Choosing chemical markers for quality assurance of complex herbal medicines: Development and application of the herb MaRS criteria. Clinical Pharmacology & Therapeutics, 2015; 97(6): 628-640.
Febjislami S, Melati M, Kurniawati A, Wahyu Y. Karakter agronomi dan kadar sinensetin beberapa akses tanaman kumis kucing (*Orthosiphon stamineus*). Jurnal Hortikultura Indonesia, 2018; 9(3):206–15.
Guo Z, Liang X, Xie Y. Qualitative and quantitative analysis on the chemical constituents in Orthosiphon stamineus Benth. using ultra high-performance liquid chromatography coupled with electrospray ionization tandem mass spectrometry. J Pharm Biomed Anal, 2019; 164:135–47.
Han Jie L, Jantan I, Yusoff SD, Jalil J, Husain K. Sinensetin: an insight on its pharmacological activities, mechanisms of action and toxicity. Front Pharmacol, 2021; 11:533404.
Hashim S, Beh HK, Hamil MSR, Ismail Z, Majid AMSA. High-performance thin-layer chromatography method development, validation, and simultaneous quantification of four compounds identified in standardized extracts of Orthosiphon stamineus. Pharmacogn Res, 2016; 8(4):238.
Hossain MA, Ismail Z. Quantification and enrichment of sinensetin in the leaves of Orthosiphon stamineus Benth. from different origins. Pharmacogn J, 2020; 12(1):1683–91.
Indonesia Ministry of Health. Eleven scientific herbal medicines “Jamu Saintifik”, Karanganyar, center for research and development of medicinal plants and traditional medicines (in Indonesia). Indonesia Ministry of Health, Jakarta, Indonesia, 2019.
Indonesia Ministry of Health. “Fitofarmaka” Formulary. Ministry of Health (in Indonesian). Indonesia Ministry of Health Jakarta, Indonesia, 2022.
Kartini K, Jayani NIE, Hadiyat MA, Avanti C. Thin layer chromatography fingerprinting and clustering of Orthosiphon aristatus Benth. from different origins. Pharmacogn J, 2020; 12(1):1683–91.
Mohamed EAH, Siddiqui MJA, Ang LF, Sadikun A, Chan SH, Tan SC, Asmawi MZ, Yam MF. Potent α-glucosidase and α-amylase inhibitory activities of standardized 50% ethanolic extracts and sinensetin from Orthosiphon stamineus Benth as anti-diabetic mechanism. BMC Complement Altern Med, 2012; 12(1):1–7.
Patel LJ, Raval MA, Patel SG, Patel AJ. Development and validation of stability indicating high-performance thin-layer chromatographic (HPTLC) method for quantification of asiaticoside from Centella asiatica L. and its marketed formulation. J AOAC Int, 2019; 102(4):1014–20.
Rafi M, Purwakusumah ED, Ridwan T, Barus B, Sutandi A, Darusman LK. Geographical classification of java tea (Orthosiphon stamineus) from java Island by FTIR spectroscopy combined with canonical variate analysis. Jurnal Sains dan Matematika Universitas Diponegoro, 2015; 23:25–31.
Riyanto R. Validasi & verifikasi metode Uji Deepublish. Deepublish, Yogyakarta, Indonesia.
Srivastava M. High-performance thin-layer chromatography (HPTLC). Springer Science & Business Media, Berlin, Germany, 2010.
Wang Q, Wang J, Li N, Liu J, Zhou J, Zhang P, Chen H. A systematic review of Orthosiphon stamineus Benth. in the treatment of diabetes and its complications. Molecules, 2022; 27(2):444.
Yam MF, Tan CS, Shibao R. Vasorelaxant effect of sinensetin via the NO/sGC/cGMP pathway and potassium and calcium channels. Hypertens Res, 2018; 41(10):787–97.
Zlatkis A, Kaiser REHPTLC-high performance thin-layer chromatography. Elsevier, Amsterdam, Netherlands, 2011.
Shehzadi N, Zahid F, Naheed S, Javed R, Qamar S, Sher R, Irfan Bukhari N, Ismail Z, Sadikun A. Quantification of sinensetin in extracts of Orthosiphon stamineus using high performance thin-layer chromatography. Pakistan Journal of Pharmacy, 2018; 29(1):12-19.
Shen M-R, Ye Y, Shi S-M. Development of chromatographic technologies for the quality control of Traditional Chinese Medicines in the Chinese Pharmacopoeia. J Pharm Anal., 2020; 11(2):155-62.
Sim CO, Ahmad MN, Ismail Z, Othman AR, Noor NaM, Zaihidee EM. Chemometric classification of herb–Orthosiphon stamineus according to its geographical origin using virtual chemical sensor based upon fast GC. Sensors, 2003; 3(10):458–71.
How to cite this article:
Kartini K, Putri RE, Budiono R. Quantification of sinensetin in Orthosiphon stamineus from various phytogeographical zones in Indonesia. J Appl Pharm Sci, 2023; 13(03):183-191. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4073,
1
],
[
4073,
9487,
2
],
[
9487,
15082,
3
],
[
15082,
18997,
4
],
[
18997,
19507,
5
],
[
19507,
21521,
6
],
[
21521,
24760,
7
],
[
24760,
28859,
8
],
[
28859,
32771,
9
]
]
} |
185709d3408ab635cc705b11c997799abb39406a | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 28192,
"total-output-tokens": 7692,
"fieldofstudy": [
"Biology"
]
} | Cationic Mechanosensitive Channels Mediate Trabecular Meshwork Responses to Cyclic Mechanical Stretch
Susu Chen†, Wenyan Wang†, Qilong Cao3, Shen Wu4, Ningli Wang4, Lixia Ji1* and Wei Zhu1,5*
1School of Pharmacy, Qingdao University, Qingdao, China, 2Department of Clinical Pharmacy, The Second Hospital of Traditional Chinese Medicine of Huangdao District, Qingdao, China, 3Qingdao Haier Biotech Co., Ltd., Qingdao, China, 4Beijing Institute of Ophthalmology, Beijing Tongren Hospital Eye Center, Capital Medical University, Beijing, China, 5Beijing Advanced Innovation Center for Big Data-Based Precision Medicine, Beihang University and Capital Medical University, Beijing, China
The trabecular meshwork (TM) is responsible for intraocular pressure (IOP) homeostasis in the eye. The tissue senses IOP fluctuations and dynamically adapts to the mechanical changes to either increase or decrease aqueous humor outflow. Cationic mechanosensitive channels (CMCs) have been reported to play critical roles in mediating the TM responses to mechanical forces. However, how CMCs influence TM cellular function affect aqueous humor drainage is still elusive. In this study, human TM (HTM) cells were collected from a Chinese donor and subjected to cyclically equiaxial stretching with an amplitude of 20% at 1 Hz GsMTx4, a non-selective inhibitor for CMCs, was added to investigate the proteomic changes induced by CMCs in response to mechanical stretch of HTM. Gene ontology enrichment analysis demonstrated that inhibition of CMCs significantly influenced several biochemical pathways, including store-operated calcium channel activity, microtubule cytoskeleton polarity, toll-like receptor signaling pathway, and neuron cell fate specification. Through heatmap analysis, we grouped 148 differentially expressed proteins (DEPs) into 21 clusters and focused on four specific patterns associated with Ca\(^{2+}\) homeostasis, autophagy, cell cycle, and cell fate. Our results indicated that they might be the critical downstream signals of CMCs adapting to mechanical forces and mediating AH outflow.
Keywords: trabecular meshwork, cationic mechanosensitive channels, mechanical stretching, proteomics analysis, IOP homeostasis
INTRODUCTION
The trabecular meshwork (TM), a small and complex tissue in the eye, maintains intraocular pressure (IOP) homeostasis through dynamic regulation of aqueous humor drainage (Goel et al., 2010; Acott et al., 2014; Buffault et al., 2020). Appropriate adaption of the TM to IOP fluctuations, including periodic ocular pulsation and other perturbations triggered by blinking, squeezing, rubbing, side-looking, and other activities, is extremely important for IOP homeostasis (Turner et al., 2019). Mechanical forces acting upon the TM have been reported to cause changes in autophagy (Hirt and Liton, 2017a), nitric oxide signaling (Stamer et al., 2011; Chandrawati et al., 2017), caveolin-1 signaling (Thorleifsson et al., 2010), and mechanosensitive ion channel activity.
(Tran et al., 2014; Yarishkin et al., 2019). Inappropriate adaption of the TM to the mechanical changes could potentially lead to increased resistance to aqueous humor drainage and elevated intraocular pressure (IOP), which is a strong risk factor for glaucoma (Acott et al., 2014).
Cationic mechanosensitive channels (CMCs), including transient receptor potential cation channel subfamily V member 4 (TRPV4) (Ryskamp et al., 2016), TWIK-related potassium channel-1 (TREK-1) (Carreon et al., 2017), and Piezo (Yarishkin et al., 2021; Zhu et al., 2021; Morozumi et al., 2022), have the potential to modulate calcium homeostasis, cell cytoskeleton organization, extracellular matrix (ECM) composition, and PGF2α secretion, and could therefore influence the responses of TM cells. In accordance with Yarishkin et al., we also found that GsMTx4, a non-selective inhibitor of CMCs, reduces the TM’s steady-state facility of AH outflow (Yarishkin et al., 2021; Zhu et al., 2021). However, CMC responses are very rapid and it is still not well understood how these channels act to maintain appropriate TM function in response to stretch.
Several groups have examined TM cell responses to biomechanical stretch using microarray and RNA sequencing technology. Youngblood et al. reported that mechanical stretch in the TM induces mRNA changes mainly associated with steroid biosynthesis, glycerolipid metabolism, and ECM-receptor interaction (Youngblood et al., 2020). Vittal et al. revealed that genes related to ECM modification, cytoskeletal regulation, and stress responses are notably induced in the TM by stretching (Vittal et al., 2005). However, these studies did not focus on the role of CMC signaling in TM cell stretching and furthermore did not investigate proteomic changes, which may differ from those observed at the transcriptional level.
To this end, we first investigated the proteomic changes in the TM in response to mechanical stretching through liquid chromatography with tandem mass spectrometry. We then explored CMC downstream signaling in response to stretch by blocking their function with GsMTx4.
**MATERIALS AND METHODS**
**Human Trabecular Meshwork (TM) Cell Isolation and Culture**
As previously described (Zhu et al., 2016; Yu et al., 2019; Wang et al., 2021), human TM cells of one Chinese donor (Age 54; male without any ophthalmic diseases) obtained from Beijing Tongren Hospital (Beijing, China) were isolated, seeded onto the gelatin-coated (Sigma-Aldrich, St. Louis, MO) plates (Thermo Fisher Scientific, Waltham, MA), and maintained in human-complete medium comprised of medium 199E (Gibco, Grand Island, New York), 20% fetal bovine serum (FBS; Gibco), 90 μg/ml porcine heparin (Sigma-Aldrich), 20 U/ml endothelial growth factor supplement (Sigma-Aldrich) and 1.7 mM glutamine (Sigma-Aldrich). TM cells were cultured at 37°C with 5% CO₂ and characterized at passages two to three by verifying TM biomarkers expression (Ding et al., 2014; Wang et al., 2021) and dexamethasone-inducible myocilin secretion (Yu et al., 2019; Wang et al., 2021). The use of human TM cells was approved by the ethics committee of Qingdao University and Beijing Tongren Hospital, following the use guidelines of the Medical College of Qingdao University and Beijing Tongren Hospital.
**Cyclic Mechanical Stretch**
Human TM cells (HTM) at passage three and HTM5, an immortalized cell type derived from the human TM (Pang et al., 1994), were seeded onto collagen I (Sigma-Aldrich)-coated culture plates (Flexcell International Corporation, Burlington, NC) and starved in low serum medium comprised of α-MEM (Gibco) and 1% FBS (Gibco) for 24 h. When HTM reached 80% confluency, equiaxial mechanical stretch with an amplitude of 20% at 1 Hz was cyclically applied by FlexcellFX-5000TM Tension System (Flexcell International Corporation, Burlington, NC) for 3 h. Since CMCs are sensitive to GsMTx4 (20 μM, Abcam, Cambridge, MA) was added during the stretch (Zhu et al., 2021). PBS (Gibco) was used as the vehicle control. Thus three groups of cells were collected for the proteomic analysis: control without stretch (Treatment one; T1), cyclic stretch (Treatment two; T2), and cyclic stretch with GsMTx4 treatment (Treatment three; T3).
**Protein Extraction and Quantification Analysis**
Proteins were extracted with RIPA lysis buffer (Thermo) and quantified with BCA Protein Assay Reagent Kit (Thermo). 25 μg proteins were denatured in NuPAGE-LDS sample buffer (Invitrogen, Carlsbad, CA, United States) at 95°C for 5 min and separated on 8%–17% sodium dodecyl sulfate (SDS)-acrylamide gel by electrophoresis (Stacking gel: 80 V for 40 min; Separating gel: 120 V for 120 min).
**Proteomic Analysis**
- **Reducing the Protein and Blocking Cysteine**—100 μg protein was dissolved in 100 μl triethylammonium bicarbonate (PierceTM TEAB 100 mM) and reacted with 5 μl Tris (2-carboxyethyl) phosphine (PierceTM TCEP 200 mM) at 55°C for 1 h and 5 μl PierceTM iodoacetamide (375 mM) at room temperature for 30 min. For protein precipitation, pre-chilled (-20°C) acetone (Thermo) was subsequently added. The pellet was collected through centrifugation (8,000×g, 10 min, 4°C).
- **Protein Digestion**—100 μg acetone-precipitated pellet was resuspended in 100 μl PierceTM TEAB (100 mM) and digested with trypsin (2.5 μg PierceTM trypsin for 100 μg protein) at 37°C overnight.
- **Peptide Labeling**—Tandem Mass Tag (TMT) Label Reagent was equilibrated with PierceTM anhydrous acetonitrile and reacted with the digested peptide at room temperature for 1 h. Then 8 μL 5% PierceTM hydroxyamine was added to quench the reaction.
- **C18 column separation**—The labeled peptides were dried using a vacuum centrifuge, dissolved in Solution A containing 2% PierceTM acetonitrile (vol/vol in water;
Western Blotting (WB)
40 μg protein was boiled, loaded on a 5% sodium dodecyl sulfate (SDS)-acrylamide stacking gel, separated on a 10% SDS-acrylamide gel by electrophoresis, and eventually transferred to a polyvinyl difluoride membrane (PVDF; GE Healthcare Life Sciences China, Beijing, China). After blocking in Tris-buffered Saline-Tween-20 containing 5% non-fat milk powder, incubation with diluted primary antibodies (Supplementary Table S3) followed by the corresponding secondary antibody conjugated with horseradish peroxidase (HRP; Abcam), immunoreactive bands were visualized using the enhanced chemiluminescence detection kit (Thermo) and a ChemiDoc XRS + imaging system (Bio-Rad). Band intensity was quantified using the Image Lab software (Bio-Rad) and normalized to beta-Actin (Abways Technology, ab0035, Shanghai, China). Each experiment contained four technical replicates.
Bioinformatics and Statistical Analyses
Data analysis was performed using Proteome discoverer software (version 1.4; Thermo). Proteins among different samples with fold change ≥1.50 or ≤0.66 and p values <0.05 were considered as differentially expressed proteins (DEPs) and applied for Gene Ontology (GO) enrichment analysis based on the PANTHER database, KEGG pathway enrichment analysis, and heatmap analysis. One-way ANOVA was applied to evaluate expression changes between groups.
RESULTS
Preparation of Samples for LC-MS/MS
As we previously demonstrated (Zhu et al., 2021), intracameral perfusion with GsMTx4, an inhibitor of cationic mechanosensitive channels (CMCs), leads to disturbances of conventional AH outflow. We predicted that a close relationship exists between CMCs and the TM’s biological responses to mechanical stretch. Therefore, proteomics analysis was performed to characterize this relationship by using HTM cells subjected to cyclic mechanical stretch with an amplitude of 20% at a frequency of 1 Hz for 3 h, a condition mirroring acute sustained elevation of IOP.
GsMTx4 was applied at a concentration of 20 μM to inhibit CMC function (Figure 1A). We first determined the quality of our samples through SDS-acrylamide gel electrophoresis, peptide length, and protein coverage analyses (Figures 1B–D). Peptides with lengths from 6 to 51 amino acid residues covered over 80% sequence of a protein, indicating that it is successful and sufficient for the subsequent LC-MS/MS analysis.
A Critical Role of CMCs in the TM in Response to Cyclic Stretch
We next identified those differentially expressed proteins (DEPs) with fold change ≥1.50 or ≤0.66 and p values <0.05 (T2 vs. T1: 26 up-regulated DEPs and 83 down-regulated DEPs; T3 vs. T2: 35 up-regulated DEPs and four down-regulated DEPs) for subsequent bioinformatics analyses and pathway enrichment analyses. As shown in Figure 2A, cyclic stretch induces a significant up-regulation of proteins involved in extracellular matrix organization, cytoskeleton remodeling, multicellular organismal homeostasis, and metal ion response. These findings are similar to those reported previously (Youngblood et al., 2020). In addition, changes in proteins related to aging, DNA conformation, keratinization, cell differentiation, and tissue development were also found in the TM in response to cyclic stretch. Importantly, GsMTx4 treatment significantly altered expression changes (Figure 2B) and comparison of T1 and T2 detected expression changes of proteins related to store-operated calcium channel activity, microtubule cytoskeleton polarity, and toll-like receptor three signaling pathway. Intriguingly, neuron cell fate specification was another profound change in the TM after GsMTx4 treatment (Figure 2B).
In addition to biological process enrichment analysis, we performed KEGG pathway enrichment analysis to explore how CMCs function in the TM during mechanical stretch (Figures 2C, D). Expression of proteins involved in tyrosine metabolism, DNA replication, TNF signaling, cell cycle, and cytochrome P450 pathways were significantly changed after mechanical stretch, and GsMTx4 incubation led to significant changes in hypertrophic cardiomyopathy, sulfur relay system, and circadian rhythm.
Downstream Signals Associated With CMCs in Response to Cyclic Stretch
To select the vital downstream signals of CMCs involved in HTM adapting to mechanical stretching, we subsequently grouped 148 DEPs (109 DEPs in T2 vs. T1 and 39 DEPs in T3 vs. T2) into 21 clusters (Figure 3A) and focused on four specific patterns (Figure 3B). We were particularly interested in DEPs that did not display any significant changes in response to cyclic stretching but showed a significantly increased expression after GsMTx4 treatment (Pattern 1). In Pattern 2, 3, and 4, mechanical stretching evoked a significant change in HTM, but GsMTx4 inhibited these stretch-induced changes (Figure 3B). In total 30 DEPs in Pattern 1, nine DEPs in Pattern 2, 34 DEPs in Pattern 3, and four DEPs in Pattern four were listed in Supplementary Tables S4–7 as
downstream candidates of CMCs signaling in response to cyclic mechanical stretch. Those DEPs (Table 1) that are particularly likely to maintain TM function in response to mechanical stretching include two-pore calcium channel (TPCN1), desmoglein-1 preproprotein (DSG1), glutathione S-transferase (GSTT2), chromodomain-helicase-DNA-binding protein (CHD6), transcription factor jun-B (JUNB), connective tissue growth factor (CCN2), superoxide dismutase (SOD2), cytoskeleton protein vimentin (VIM), zinc finger protein (ZFN618), ubiquitin (HACE1), AMP-activated protein kinase (PRKAB1), as well as the ECM component collagen (COL8A1).
We then verified expression changes of DSG1 and SOD2 as representative proteins for Patterns 1 and 3, respectively, by Western blot analysis. As shown in Figures 3C, D, DSG1 and SOD2 exhibited similar expression patterns as observed by LC-MS/MS (Figures 3A,B).
**DISCUSSION**
Proper adaption of the TM to cyclic mechanical stretch and other perturbations in the eye is required for maintaining AH outflow and IOP homeostasis (Ramos et al., 2009; Turner et al., 2019). Recent investigations have found that cyclic mechanical stretch at an amplitude of 10–15%, a condition mimicking physiological forces, evokes many transcriptional changes associated with ECM turnover (Shearer and Crosson, 2002; Youngblood et al., 2020), cytoskeleton remodeling, autophagy (Shim et al., 2021a), calcium...
ion sequestration (Ryskamp et al., 2016; Uchida et al., 2021), cell-cycle regulation (Wang et al., 2013), and sterol and lipid metabolism (Uchida et al., 2021). Our study confirms many of these changes at a translational level (109 DEPs of T2 vs. T1). Most of the DEPs identified are involved in aging, intermediate filament cytoskeleton organization, lipid response, and zinc and metal ions responses. Examples include hyccin (FAM), Cell Division Cycle (CDC), connective tissue growth factor (CCN), zinc finger protein (ZNF), phospholipid-transporting ATPase (ATP), and growth-regulated alpha protein (CXCL). Furthermore, in our hands cyclic mechanical stretch also causes several changes in related to rhythmic processes, cell differentiation, and developmental processes (Figure 2), providing us a new insight into the molecular effects of mechanical forces.
CMCs have been identified to play a crucial role in fast signaling during mechanotransduction in many systems (Bowman et al., 2007), including TRPV4-modulated calcium TM cell cytoskeleton (Ryskamp et al., 2016) or TREK-1-induced alternation of TM extracellular matrix composition (Carreon et al., 2017). To investigate the role of CMCs in the TM as an adaptation to cyclic mechanical stretch, GsMTx4 is an attractive tool due its highly specific inhibition of mechanosensitive channels (Gnanasambandam et al., 2017; Suchyna, 2017). Notably, GsMTx4-induced proteomic changes are not only caused by the depolarization of some types of CMCs, such as Piezo- and TRP- channels, but are also influenced by the inhibition of several mechanoenzymes (Khairallah et al., 2012; Storch et al., 2012; Gnanasambandam et al., 2017; Suchyna, 2017). In addition, some CMCs with two-pore (2P) domains have been reported to be potentiated by GsMTx4 (Gnanasambandam et al., 2017). LC-MS/MS results showed that several GsMTx4-induced DEPs during mechanical stretching are involved in store-operated calcium channel activity and microtubule cytoskeleton polarity (Figure 2). These findings hold great significance for calcium signal and cytoskeleton remodeling as CMC-related signals in response to mechanical stretch. Moreover, we also found that the toll-like receptor three signaling pathway is another CMC-mediated signaling pathway. In accordance with our findings, cyclic mechanical stretch has been reported to activate MTOR/AKT1/SMAD2/3 on primary cilia of TM cells and thus mediate autophagy (Shim et al., 2021a). These data suggest that CMCs might act as an upstream signal of the
MTOR/AKT1/SMAD2/3 pathway and autophagy. Finally, we found that several DEPs (T3 vs. T2) are involved in neuron cell fate specification, which might be a new mechanism of the TM to adapt to mechanical forces.
In addition to the pathway enrichment analysis, this study also aimed to discover key downstream DEPs of CMCs in response to cyclic mechanical stretch. In Pattern 1, complex I intermediate-associated protein 30 mitochondrial precursor (NDUFAF1) with a 6.48-fold increase (T3 vs. T2) might be one CMC-mediated downstream signal with functions in TM cell survival and IOP homeostasis. Data obtained in mice have indicated that mitochondrial abnormalities could be an early driver for the development of glaucoma (Williams et al., 2017). In Pattern 1 we also found changes in TPCN1 (6.61-fold increase T3 vs. T2) and DSG1 (6.62-fold increase T3 vs. T2), which have a significant capacity in modulating calcium homeostasis.
**FIGURE 3** | Heatmap analysis using DEPs. 148 DEPs (109 DEPs in T2 vs. T1 and 39 DEPs in T3 vs. T2) are grouped into 21 clusters (A). Four specific patterns indicating the positive roles of CMCs in this process are shown (B). The orange line indicates the average of DEPs’ expression changes in each group, while the black line denotes the expression of each DEP. (C). Western blot analysis of DSG1 as a representative of Pattern 1, SOD2 as a representative of Pattern 3 (top) and beta-Actin (bottom) in T1, T2, and T3. (D) Quantification of band intensities using Image Lab software (Bio-Rad). ****p < 0.0001 by One-way ANOVA.
TABLE 1 | Downstream candidates of CMCs in HTM adapting to mechanical stretching.
| Pattern | ProbeSetId | Gene Symbol | Gene_ID | Description | T1 | T2 | T3 |
|---------|------------|-------------|---------|-------------|------|------|------|
| Pattern 1 | NP_001933.2 | DSG1 | 1828 | desmoglein-1 preproprotein [Homo sapiens] | 1.01 | 1.01 | 6.69 |
| Pattern 1 | NP_00138275.1 | TPCN1 | 53373 | two pore calcium channel protein 1 isoform 3 [Homo sapiens] | 1.01 | 1.01 | 6.68 |
| Pattern 1 | NP_001289569.1 | GSTT2 | 2963 | glutathione S-transferase theta-2 isoform b [Homo sapiens] | 1.02 | 1.01 | 6.63 |
| Pattern 1 | NP_115597.3 | CHD6 | 84181 | chromodomain-helicase-DNA-binding protein 6 [Homo sapiens] | 1.01 | 1.01 | 6.73 |
| Pattern 2 | NP_0022200.1 | JUNB | 3726 | transcription factor jun-B [Homo sapiens] | 1.64 | 2.26 | 2.10 |
| Pattern 2 | NP_001892.1 | CCN2 | 1490 | connective tissue growth factor precursor [Homo sapiens] | 1.59 | 2.34 | 2.09 |
| Pattern 2 | NP_001198.2 | BTF3 | 689 | transcription factor BTF3 isoform B [Homo sapiens] | 1.66 | 2.26 | 2.08 |
| Pattern 2 | NP_001155046.1 | MAFF | 23764 | transcription factor MafF isoform b [Homo sapiens] | 1.66 | 2.22 | 2.12 |
| Pattern 3 | NP_0011502.1 | CXCL1 | 2919 | growth-regulated alpha protein precursor [Homo sapiens] | 2.21 | 1.69 | 2.16 |
| Pattern 3 | NP_588615.2 | ZNF618 | 114991 | zinc finger protein 618 isoform 1 [Homo sapiens] | 2.38 | 1.75 | 1.97 |
| Pattern 3 | NP_001309749.1 | SOD2 | 6648 | superoxide dismutase [Mn], mitochondrial isoform E [Homo sapiens] | 2.48 | 1.73 | 1.88 |
| Pattern 3 | NP_003371.2 | VIM | 7431 | vimentin [Homo sapiens] | 2.39 | 1.79 | 1.92 |
| Pattern 3 | NP_444513.1 | DCD | 117159 | dermcidin isoform 1 preproprotein [Homo sapiens] | 2.39 | 1.76 | 1.93 |
| Pattern 3 | NP_001264074.1 | ZBTB10 | 65986 | zinc finger and BTB domain-containing protein 10 isoform c [Homo sapiens] | 2.47 | 1.80 | 1.86 |
| Pattern 3 | NP_057613.4 | ATP8A2 | 51761 | phospholipid-transporting ATPase B isoform 1 [Homo sapiens] | 2.46 | 1.79 | 1.88 |
| Pattern 4 | NP_006244.2 | PRKAB1 | 5564 | 5'-AMP-activated protein kinase subunit beta-1 [Homo sapiens] | 2.05 | 2.41 | 1.65 |
Jablonsik et al. have demonstrated that single nucleotide polymorphisms of Cacna2d1, the subunit of alpha2/delta-1 in voltage-dependent calcium channel, are associated with intracellular Ca\textsuperscript{2+} concentration, cell contractility, cytoskeleton, and stiffness of the TM, which eventually lead to the pathogenesis of primary open-angle glaucoma (Chintalapudi et al., 2017). These findings provided significant insight into TPCN1 and DSG1 as critical downstream effectors of CMCs mediated adaptation to mechanical forces and maintenance of AH outflow. In addition, we found significant changes in the expression (T3 vs. T2) of CHD6 (6.69-fold increase; Pattern 1), JUNB (0.93-fold decrease; Pattern 2), and ZNF618 (1.13-fold increase; Pattern 3), all molecules that are associated with autophagy. As reported, the activation of autophagy is essential for mechanotransduction in the TM (Shim et al., 2021b). They might also be necessary for nitric oxide release (Hirt and Liton, 2017b), which is extremely critical in controlling outflow resistance and IOP homeostasis (Reina-Torres et al., 2021). We also identified some DEPs involved in cell cycle and cell fate specification, such as CCN2 (0.89-fold decrease; Pattern 2), ZNF618 (1.13-fold increase; Pattern 3), VIM (1.07-fold increase; Pattern 3), and PRKAB1 (0.69-fold decrease; Pattern 4). Their specific role in CMC mediated TM responses to stretch remains unclear and will be the topic of further investigation.
In summary, this study confirmed the previous transcriptomics findings of stretch-induced changes in the TM at a translational level. More importantly, we show that CMC downstream signaling influences the adaptive responses of the TM to mechanical changes. Notably, calcium signaling, cytoskeleton remodeling, autophagy, cell cycle, and cell fate are pathways involved in this CMC-mediated adaption.
DATA AVAILABILITY STATEMENT
The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: http://protemecentral.proteomexchange.org/cgi/GetDataset, PXD032288.
ETHICS STATEMENT
The studies involving human participants were reviewed and approved by ethics committee of Qingdao University and Beijing Tongren Hospital. The participants’ relatives provided their written informed consent to participate in this study.
AUTHOR CONTRIBUTIONS
WZ conceived and designed the project. WZ, SC, WW, and SW conducted the experiments and analysis. SW and QC contributed to result analysis and discussions. The manuscript was written by WZ and LJ.
FUNDING
This study was supported by the National Key Research and Development Program 2018YFA0109500, National Natural Science Foundation of China 81870653, Shandong Key Research and Development Program 2019GSF107075, and Taishan Scholar Youth Expert Program tsqn202103055.
SUPPLEMENTAL MATERIAL
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphar.2022.881286/full#supplementary-material.
Zhu, W., Gramlich, O. W., Laboissonniere, L., Jain, A., Sheffield, V. C., Trimarchi, J. M., et al. (2016). Transplantation of iPSC-Derived TM Cells Rescues Glaucoma Phenotypes In Vivo. Proc. Natl. Acad. Sci. U. S. A. 113 (25), E3492–E3500. doi:10.1073/pnas.1604153113
Zhu, W., Hou, F., Fang, J., Bahrani Fard, M. R., Liu, Y., Ren, S., et al. (2021). The Role of Piezo1 in Conventional Aqueous Humor Outflow Dynamics. iScience 24 (2), 102042. doi:10.1016/j.isci.2021.102042
Conflict of Interest: QC was employed by Qingdao Haier Biotech Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Publisher’s Note: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
Copyright © 2022 Chen, Wang, Cao, Wu, Wang, Ji and Zhu. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3008,
1
],
[
3008,
8803,
2
],
[
8803,
13802,
3
],
[
13802,
15227,
4
],
[
15227,
17759,
5
],
[
17759,
19320,
6
],
[
19320,
24592,
7
],
[
24592,
24592,
8
],
[
24592,
26194,
9
]
]
} |
9d5f6c8d6cc9e1344d28dd605bbd85dd96c33589 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 32,
"total-fallback-pages": 0,
"total-input-tokens": 59592,
"total-output-tokens": 15668,
"fieldofstudy": [
"Biology"
]
} | A novel control of human keratin expression: Cannabinoid receptor 1-mediated signaling down-regulates the expression of keratins K6 and K16 in human keratinocytes in vitro and in situ
Cannabinoid receptors (CB) are expressed throughout human skin epithelium. CB1 activation inhibits human hair growth and decreases proliferation of epidermal keratinocytes. Since psoriasis is a chronic hyperproliferative, inflammatory skin disease it is conceivable that the therapeutic modulation of CB signaling, which can inhibit both proliferation and inflammation, could win a place in future psoriasis management. Given that psoriasis is characterized by upregulation of keratins K6 and K16, we have investigated whether CB1 stimulation modulates their expression in human epidermis. Treatment of organ-cultured human skin with the CB1-specific agonist, arachidonoyl-chloro-ethanolamide (ACEA), decreased K6 and K16 staining intensity in situ. At the gene and protein levels, ACEA also decreased K6 expression of cultured HaCaT keratinocytes, which show some similarities to psoriatic keratinocytes. These effects were partly antagonized by the CB1-specific antagonist, AM251. While CB1-mediated signaling also significantly inhibited human epidermal keratinocyte proliferation in situ, as shown by K6/Ki-67-double immunofluorescence, the inhibitory effect of ACEA on K6 expression in situ was independent of its anti-proliferative effect. Given recent appreciation of the role of K6 as a functionally important protein that regulates epithelial wound healing in mice, it is conceivable that the novel CB1-mediated regulation of keratin 6/16 revealed here also is relevant to wound healing. Taken together, our results suggest that cannabinoids and their receptors constitute a novel, clinically relevant control element of human K6 and K16 expression.
Yuval Ramot\textsuperscript{1,2*}, Koji Sugawara\textsuperscript{1,3*}, Nóra Zákány\textsuperscript{1,4}, Balázs I Tóth\textsuperscript{4,5}, Tamás Bíró\textsuperscript{4} and Ralf Paus\textsuperscript{1,6}
\textsuperscript{1}Department of Dermatology, University of Luebeck, Luebeck, Germany
\textsuperscript{2}Department of Dermatology, Hadassah-Hebrew University Medical Center, Jerusalem, Israel
\textsuperscript{3}Department of Dermatology, Osaka City University Graduate School of Medicine, Osaka, Japan
\textsuperscript{4}DE-MTA “Lendület” Cellular Physiology Research Group, Department of Physiology, MHSC, RCMM, University of Debrecen, Debrecen, Hungary
\textsuperscript{5}Laboratory of Ion Channel Research and TRP Research Platform Leuven (TRPLe), Department of Cellular and Molecular Medicine, KU Leuven, Leuven, Belgium
\textsuperscript{6}Institute of Inflammation and Repair, University of Manchester, Manchester, U.K.
\textsuperscript{*These authors contributed equally}
\textbf{Short title:} CB1-mediated inhibition of keratin expression
\textbf{Corresponding author:} Professor Ralf Paus, Department of Dermatology, University of Luebeck, Ratzeburger Allee 160, D-23538, Luebeck, Germany, Tel.: 0049-451500-2543, Fax.: 0049-4512903-419, Email: [email protected]
\textit{Abbreviations:} ACEA, arachidonoyl-chloro-ethanolamide; AEA, anandamide; CB1, cannabinoid receptor 1; ECS, endocannabinoid system; HF, hair follicle; KC, keratinocyte
\textbf{Conflict of interest:} the authors state no conflict of interest.
Funding: This study was supported in part by the Daniel Turnberg United Kingdom / Middle East Travel Fellowship Scheme, administered by the Academy of Medical Sciences to Y.R.; a faculty grant from Osaka City University to K.S.; a “Lendület” grant of the Hungarian Academy of Sciences to T.B.; and a faculty grant from the University of Luebeck to R.P.
Introduction
Endocannabinoids as well as exocannabinoids (such as the active components of cannabis) are reported to control the functions of various types of cells via CB-dependent or independent manner (Kupczyk, Reich & Szepietowski 2009). The endocannabinoid system (ECS) consists of these CBs, their endogenous ligands (*i.e.* endocannabinoids, such as anandamide [AEA] and 2-arachidonoylglycerol), and enzymes responsible for endocannabinoid synthesis and degradation (Biro *et al.* 2009). In human skin, many different types of cells are now known to express functional cannabinoid receptors (CBs) (Biro *et al.* 2009; Czifra *et al.* 2012; Pucci *et al.* 2012; Roelandt *et al.* 2012; Stander *et al.* 2005; Sugawara *et al.* 2012; Telek *et al.* 2007; Toth *et al.* 2011). The ECS is increasingly appreciated as an important regulator of skin function in health and disease. Thus, the ECS has become implicated in pain (Khasabova *et al.* 2012; Walker & Hohmann 2005) and itch control (Stander, Reinhardt & Luger 2006), and the modulation of inflammation (Klein 2005) and allergy (Karsak *et al.* 2007). Additionally, it is important in skin mast cell activation and intracutaneous mast cell maturation from resident progenitors (Sugawara *et al.* 2012). Furthermore, it regulates fibrosis (Akhmetshina *et al.* 2009), sebocyte differentiation (Dobrosi *et al.* 2008) and eccrine epithelial biology (Czifra *et al.* 2012). Nevertheless, the functions of CB-mediated signaling in human keratinocytes (KCs) *in situ* are as yet poorly understood.
We have previously shown that outer root sheath KCs of human hair follicles (HFs) express CB1. CB1 stimulation by the endocannabinoid, AEA, markedly inhibited human HF growth by inhibiting hair matrix KC proliferation and inducing apoptosis, thus leading to premature HF involution (catagen development). This was reversed by the CB1-specific antagonist, AM251 (Telek *et al.* 2007). Similarly, human epidermal KC express CBs, and their differentiation is regulated *via* CB1 (Maccarrone *et al.* 2003; Paradisi *et al.* 2008). AEA also markedly suppresses human epidermal KC proliferation and induces apoptosis *via* CB1 *in*
vitro and in situ (Toth et al. 2011). This suggests that the ECS could become a useful therapeutic target in the management of chronic hyperproliferative human skin diseases, such as psoriasis (Toth et al. 2011).
However, it remains unclear whether and how CB1-mediated signaling impacts on human KC differentiation, namely on the expression of hyperproliferation-associated keratins. Psoriasis is characterized by the upregulation of keratins K6 and K16 expression within lesional epidermis (Korver et al. 2006; Mommers et al. 2000). This pair of keratins is also prominently up-regulated in the epidermis under wound healing conditions in man and mice (Moll, Divo & Langbein 2008; Paladini et al. 1996; Rotty & Coulombe 2012) and is constitutively expressed in the outer root sheath KCs of human HFs (Langbein & Schweizer 2005; Moll, Divo & Langbein 2008). Since psoriasis is a chronic inflammatory, hyperproliferative dermatosis that, in addition to its anti-proliferative properties (Telek et al. 2007; Van Dross et al. 2012), might also profit from the well-recognized anti-inflammatory properties of CB1-mediated signaling (Sugawara et al. 2012; Wilkinson & Williamson 2007), we have investigated whether CB1 stimulation modulates K6 and K16 expression in human skin. This question was made particularly interesting in view of the most recent discovery that, in murine skin, K6 is not only a wound healing-associated marker keratin, but actively down-regulates KC migration during wound repair (Rotty & Coulombe 2012).
In order to answer this question, we used the CB1-specific agonist, arachidonoyl-chloro-ethanolamide (ACEA) (Harvey et al. 2012), and checked its effect on K6 expression in situ. This was done by utilizing full thickness human skin organ culture (Lu et al. 2007) as a physiologically and clinically relevant model to study multiple aspects of human skin biology under clinically relevant conditions in vitro (Bodo et al. 2010; Knuever et al. 2012; Langan et al. 2010; Lu et al. 2007; Sugawara et al. 2012). In order to confirm the
CB1-specificity of the observed effects of ACEA, we also used the CB1-specific antagonist, AM251 (Chanda et al. 2011).
K16 serves as the type I keratin partner of K6 in the formation of intermediate filament heterodimers (Moll, Divo & Langbein 2008). It is also involved in epidermal barrier function (Grzanka et al. 2012; Thakoersing et al. 2012), and is upregulated in hyperproliferative conditions of the skin such as psoriasis (Iizuka et al. 2004) and atopic dermatitis (Grzanka et al. 2012). Therefore, we also examined the effects of ACEA on K16 expression.
HaCaT cells are a highly proliferating human KC line known to overexpress K6 (Ryle et al. 1989). Since HaCaT KCs share some other characteristics with psoriatic KCs and are often employed as surrogate “psoriatic” KCs (Balato et al. 2012; Farkas et al. 2001; George et al. 2010; Kim et al. 2011; Ronpirin & Tencomnao 2012; Saelee, Thongrakard & Tencomnao 2011), we also tested whether and how ACEA modulated K6 expression in these cells in vitro. In order to delineate whether any such effects on keratin expression resulted only indirectly from a possible down-regulation of KC proliferation by CB1 stimulation (Toth et al. 2011), double-labeling and quantitative immunohistomorphometry for both K6 and Ki-67 was performed. Finally, to investigate whether K6-expressing human KCs co-express CB1, double-immunolabeling for both antigens was employed.
**Materials and Methods**
**Human skin organ culture**
Isolated human skin samples obtained from elective plastic surgery procedures (32 pieces of skin fragments obtained by 4 mm punch biopsies from 4 individuals; 3 females and a male aged 26-74, average: 56.5; 3 skin samples were taken from the scalp and one was taken from the hip) were maintained in supplemented serum-free William’s E medium as previously
reported (Bodo et al. 2010; Knuever et al. 2012; Lu et al. 2007; Poeggeler et al. 2010). Human tissue collection and handling was performed according to Helsinki guidelines, after institutional review board ethics approval (University of Luebeck) and informed patient consent.
Skin samples were first incubated overnight to adapt to culture conditions after which the medium was replaced and vehicle or test substances were added. For human skin organ culture, skin samples were treated with ACEA (Sigma-Aldrich, Taufkirchen, Germany, 30 µM) or AM251 (Sigma-Aldrich, 1 µM), or the combination of them for 1-day after the overnight incubation (Sugawara et al. 2012). Following culturing for the time indicated, skin samples were cryoembedded and prepared for histology, immunohistochemistry/immunofluorescence and quantitative immunohistomorphometry (Ramot et al. 2010; Ramot et al. 2011; Sugawara et al. 2012). Each evaluation was performed on 2-4 sections of 2 skin fragments per each treatment group from 2-4 individuals.
**Cell culture**
Human immortalized HaCaT KCs (Boukamp et al. 1988) were cultured in DMEM (Sigma-Aldrich) supplemented with 10% fetal bovine serum (Invitrogen, Paisley, UK) and antibiotics (PAA Laboratories, Pasching, Austria). For qRT-PCR, the cells were cultured with ACEA (1 µM) for 8h.
**qRT-PCR**
qRT-PCR was performed on an ABI Prism 7000 sequence detection system (Applied Biosystems/Life Technologies, Foster City, CA, USA) using the 5’ nuclease assay as detailed
in our previous reports (Toth et al. 2011; Toth et al. 2009). Total RNA was isolated from HaCaT keratinocytes using TRIreagent (Applied Biosystems/Life Technologies, Foster City, CA, USA) and digested with recombinant RNase-free DNase-1 (Applied Biosystems) according to the manufacturer’s protocol. After isolation, one μg of total RNA was reverse-transcribed into cDNA by using High Capacity cDNA kit (Applied Biosystems) following the manufacturer’s protocol. PCR amplification was performed by using specific TaqMan primer and probes (Applied Biosystems, assay ID: Hs01699178_g1 for human K6A). As internal housekeeping gene control, transcripts of cyclophilin A (PPIA) were determined (Assay ID: Hs99999904 for human PPIA). The amount of the K6A transcripts was normalized to the control gene using the \( \Delta CT \) method.
**Immunohistochemistry**
For the detection of K6 in organ cultured human skin as well as cultured HaCaT KCs, indirect immunofluorescence staining was performed using mouse anti-human K6 antibody (Progen, Ks6.KA12) at 1:10 dilution as a primary antibody and rhodamine conjugated goat anti-mouse IgG (Jackson Immunoresearch Laboratories, West Grove, PA) at 1:200 dilution in phosphate-buffered saline (PBS) as a secondary antibody.
To study the proliferation of epidermal KCs, double-immunostaining for K6 and Ki-67 was performed. Briefly, after the staining for K6 with FITC conjugated goat anti-mouse IgG (Jackson Immunoresearch Laboratories) as a secondary antibody, sections were incubated overnight at 4°C with a mouse anti-human Ki-67 antibody (DAKO, Hamburg, Germany) at 1:20 in PBS. Sections were then washed with PBS, followed by incubation with rhodamine conjugated goat anti-mouse IgG (Jackson Immunoresearch Laboratories) (1:200 in PBS, 45 min) at room temperature.
To investigate the localization of CB1 and K6, double immunostaining was performed. For CB1 immunostaining, the highly sensitive tyramide signal amplification (TSA) technique (Perkin Elmer, Boston, MA) was applied. Cryosections were incubated overnight at 4°C with rabbit anti-CB1 (Santa Cruz, CA, USA) at 1:400 diluted in TNB (Tris, NaOH, Blocking reagent, TSA kit; Perkin-Elmer). Thereafter, the samples were labeled with goat biotinylated antibody against rabbit IgG (Jackson Immunoresearch Laboratories) at 1:200 in TNB for 45 min at room temperature. Sections were then stained with streptavidin-conjugated horseradish peroxidase (1:100, 30 min, TSA kit) and were finally incubated with rhodamine conjugated tyramide (1:50, TSA kit). The TSA method was applied according to the manufacturer’s protocol. For the second primary labeling, mouse anti-human K6 antibody (Progen) was applied at 1:20 in PBS, overnight at 4°C. After the wash with PBS, the sections were incubated with FITC conjugated goat anti-mouse IgG (Jackson Immunoresearch Laboratories) (1:200 in PBS, 45 min) at room temperature.
For K16 antigen detection, we used the LSAB (DCS, Germany) detection method (Ramot et al. 2009) using the K16-gp as primary antibody (guinea-pig, PROGEN, Heidelberg, Germany, dilution 1:1000, GP-CK16), and biotinylated goat anti-guinea pig as secondary antibody (Vector Laboratories, Burlingame, CA, USA, dilution 1:200). HistoGreen (Linaris, Wertheim-Bettingen, Germany) was used as peroxidase substrate.
For all immunostainings, the respective primary antibodies were omitted as negative controls, and morphological criteria and reproduction of the previously published intracutaneous expression patterns of the examined antigens were used as internal positive and negative controls (Moll, Divo & Langbein 2008). For all experiments, control and treated sections were stained (and later evaluated) on the same day by the same investigator. To avoid staining biases, we calculated the relative staining intensity (arbitrary intensity; 1 as control group) among treatment groups per each individual and then pooled data from all of the experiments.
High magnification images of K6/Ki67 double immunofluorescence and K6 immunofluorescence on HaCaT cells were taken by laser scanning confocal microscopy (Fluoview 300, Olympus Tokyo, Japan) running Fluoview 2.1 software (Olympus).
The staining intensity of K6 and K16 in defined reference areas was assessed by quantitative immunohistomorphometry using the ImageJ software (NIH) (Bodo et al. 2010; Ramot et al. 2010; Ramot et al. 2011). For epidermal evaluation, staining intensity was evaluated in the suprabasal cells, and for HaCaT cells, staining intensity was measured in the colonies formed. For K6 immunofluorescence intensity, skin sections from 4 different individuals were used, while K16 immunofluorescence intensity and %Ki67 were evaluated in skin sections from 2 patients. 4-6 sections per one individual (2 sections per investigated skin fragment) were used for each evaluation. Each section was evaluated in two/three different non-adjacent microscopic fields (x 200), and the mean intensity was measured, and considered as a value. Each treatment group was compared to the control group (average value), and relative change in expression was calculated. Highly comparable results were obtained from different sections from different individuals.
**Statistical Analysis**
Significance of difference between two groups was evaluated using Student's t-test for unpaired samples. For multiple comparisons, one-way analysis of variance (ANOVA) was used, followed by Bonferroni's multiple comparison test, using Prism 5.0 software (GraphPad Prism Program, GraphPad, San Diego, CA). p values <0.05 were regarded as significant. All data in the figures are expressed as mean ± SEM. *p<0.05, **p<0.01, ***p<0.001 for the indicated comparisons.
Results and Discussion
The CB1-selective agonist, ACEA, down-regulates K6 protein expression in situ
First, we asked whether the CB1-specific synthetic agonist ACEA (Pertwee et al. 2010; Sugawara et al. 2012) can modulate the expression of keratin K6 in human skin. K6 staining intensity within the epidermis of full-thickness human skin that had been organ-cultured for 24 hrs under serum-free conditions in the presence of ACEA (30 µM) or vehicle alone was assessed by quantitative immunohistomorphometry. This showed that K6 immunoreactivity (IR) was significantly reduced after ACEA treatment, compared to the vehicle control group (Fig. 1A and B).
This down-regulation was abrogated in part by the co-administration with the CB1-specific antagonist, AM251 (Pertwee et al. 2010; Sugawara et al. 2012) (Fig. 1A and B). Therefore, intraepidermal K6 protein expression in normal human skin in situ is down-regulated in a CB1-specific manner.
ACEA also down-regulates K16 protein expression in situ
Since K16 is the type I keratin partner of K6 in KCs and is thought to stabilize this keratin protein as a cytoskeletal heteropolymeric intermediate filament (Ramot et al. 2009), we next analyzed K16 IR in the epidermis of organ cultured human skin samples treated with ACEA. In line with the K6 protein expression data, K16 IR was also significantly down-regulated by ACEA in situ (Fig. 1C and D).
CB1-mediated signaling also regulates K6 expression in cultured, hyperproliferative human keratinocytes
In order to check whether the observed CB1-mediated effects on K6 regulation within intact human skin epithelium depend on intact epithelial-mesenchymal interactions between
epidermis and dermis, or are likely to reflect a direct impact of CB1 ligands on epidermal keratinocytes, we next investigated K6 expression in cultured human HaCaT KCs. This transformed human KC line is well-appreciated to constitutively express K6 and to be hyperproliferative (just like human wounded and psoriatic KC) (Balato et al. 2012; Farkas et al. 2001; George et al. 2010; Kim et al. 2011; Ronpirin & Tencomnao 2012; Ryle et al. 1989; Saelee, Thongrakard & Tencomnao 2011). K6 is expressed in hyper-proliferative cells (Weiss, Eichner & Sun 1984) and both K6 expression and basal layer epidermal KC proliferation are increased in psoriasis lesions (Donetti et al. 2012; Griffiths & Barker 2007; Korver et al. 2006; Litvinov et al. 2011; Mommers et al. 2000). HaCaT cells are known to express functional CB1 and CB2 (Leonti et al. 2010; Maccarrone et al. 2003; Paradisi et al. 2008), and this had been confirmed previously by our group, both on the gene (RT-PCR analysis) and protein levels (immunocytochemistry and western blotting techniques) (Toth et al. 2011).
Thus, being a direct target of CB1-mediated signaling, this makes these KCs not only an instructive cell culture tool for evaluating the direct, dermis-independent role of CB1-mediated signaling in the regulation of keratin expression in human KCs, but may also provide first indications as to how the observed K6 expression could relate to wound healing and/or psoriasis.
In accordance with our human skin organ culture results, ACEA (1 µM) significantly down-regulated K6 staining intensity of HaCaT cells in vitro (Fig. 2A and B). This was abrogated by the co-administration of the selective CB1 antagonist, AM251 (100 nM) (Fig. 2A and B). Unexpectedly, though, AM251 alone had a partial inhibitory effect on K6 expression, although not significant. This may be related to the fact that AM251 is an inverse agonist (Dono & Currie 2012; Fiori et al. 2011), and invites further study. The inhibitory effect of ACEA on K6 protein expression was further confirmed by quantitative RT-PCR (Fig.
Therefore, while HaCaT cells may exhibit relatively low CB expression levels, at least under our assay conditions, they showed a vigorous response to CB ligands.
**The CB1 specific agonist, ACEA significantly decreases human epidermal keratinocyte proliferation in situ**
However, the observed effects of CB1-mediated signaling on epidermal K6 expression could simply reflect the appreciated anti-proliferative effects of CB1 agonists (Casanova et al. 2003; Hermanson & Marnett 2011; Toth et al. 2011). Moreover, K6 is overexpressed in hyper-proliferative and wounded KCs (Weiss, Eichner & Sun 1984), and both K6 expression and basal KC proliferation are increased in psoriatic epidermal lesions (Donetti et al. 2012; Griffiths & Barker 2007; Korver et al. 2006; Litvinov et al. 2011; Mommers et al. 2000; Navarro, Casatorres & Jorcano 1995). Therefore, we next assessed whether CB1 stimulation by CB1 specific agonist, ACEA, could affect human KC proliferation in situ.
Just as we had seen before with the non-selective endocannabinoid, AEA (Toth et al. 2011), the CB1-specific synthetic agonist, ACEA indeed significantly decreased human epidermal KC proliferation in situ. This effect was abrogated by the CB1-specific antagonist, AM251 (assessed by quantitative Ki-67 immunomorphometry, Fig. 3A and B).
**The CB1 specific agonist, ACEA, significantly decreases K6 expression in suprabasal cells in a proliferation-independent manner**
Therefore, it needed to be dissected whether or not CB1 also reduces K6 expression in a proliferation-independent manner. This was done by selectively assessing K6 expression in non-proliferative (i.e. Ki-67-negative) epidermal KCs in situ. We found that K6 IR within non-proliferative epidermis was also reduced by ACEA (Fig. 4A and B). Furthermore, K6-expressing cells in the epidermis co-expressed CB1 in situ (Figure 4C), suggesting a
direct effect of CB1-agonists on K6-expressing human epidermal KCs \textit{in situ}. Thus, CB1 stimulation may affect K6 expression both, by reducing KC proliferation and by downregulating K6 expression directly \textit{via} CB1 in a proliferation-independent manner.
Here we provide the first evidence that CB1-mediated signaling directly regulates K6/16 expression within normal human skin. Specifically, we show that CB1 stimulation down-regulates expression of the hyper-proliferation-associated human keratins K6 \textit{in vitro} and \textit{in situ}, and inhibits human epidermal KC proliferation \textit{in situ}.
The effect of CB-mediated signaling in human KC biology remains to be fully explored. As we have also observed in isolated human skin (Fig. 4C), CB1 protein expression is detected mainly above the basal layer of the epidermis (Stander \textit{et al.} 2005), i.e. above the compartment where KC proliferation normally occurs most prominently. Wilkinson and Williamson reported that the non-selective CB agonist HU210 inhibited KC proliferation. However, this could not be blocked by either CB1 or CB2 antagonists, suggesting that cannabinoids may also inhibit human KC proliferation through a non-CB1/CB2 mechanism (Wilkinson & Williamson 2007). Nevertheless, it has been previously shown that AEA, which can interact with CB1 on human KC (Biro \textit{et al.} 2009), inhibited human KC proliferation \textit{in situ} and \textit{in vitro} (Toth \textit{et al.} 2011).
Therefore, it was important to clarify whether specific CB1 stimulation inhibits human epidermal KC proliferation \textit{in situ}. By using CB1-specific agonists and antagonists we clearly demonstrate that exclusive CB1 stimulation inhibited KC proliferation. Thus, CB1 is an important key regulator of human KC proliferation. Given the role of epidermal hyperproliferation in the pathobiology of psoriasis (Donetti \textit{et al.} 2012; Griffiths & Barker 2007; Korver \textit{et al.} 2006; Litvinov \textit{et al.} 2011; Mommers \textit{et al.} 2000; Navarro, Casatorres & Jorcano 1995), cannabimimetic agents that activate CB1, therefore, deserve consideration as a novel pharmacological strategy for treating psoriasis.
Furthermore, increased numbers of activated mast cells are often observed in and around lesional psoriatic skin, and increasing evidence suggests that mast cells are functionally important key immunocytes in the pathogenesis of psoriasis (Carvalho, Nilsson & Harvima 2010; Namazi 2005; Radosa et al. 2011; Suttle et al. 2012; Toruniowa & Jablonska 1988). Recently, we have shown that CB1 activation limits excessive mast cell activity and even inhibits mast cell maturation of resident, intracutaneous progenitors (Sugawara et al. 2012). Therefore, besides their anti-proliferative effects on human epidermal KCs, the anti-inflammatory (Richardson, Kilo & Hargreaves 1998) and mast cell-inhibitory properties of CB1 agonists in human skin (Sugawara et al. 2012) make them a particularly attractive class of agents in future psoriasis management.
It should be noted, that the constitutive level of K6 expression in organ-cultured human skin fragments is considerable higher than normal scalp skin *in vivo*. Presumably, this occurs as a response to tissue dissection and organ culture, which is well-known to elicit an immediate wound healing response in the epithelium. The latter rapidly starts to migrate over the wound edge in an attempt to enwrap the exposed skin mesenchyme (epiboly phenomenon [Stenn 1981; Brown C et al. 1991]). This constitutive up-regulation of K6 in organ-cultured normal human skin may greatly heighten the sensitivity to K6 expression-modulatory compounds, such as CB ligands, thus making skin organ culture a particularly sensitive and instructive tool for keratin research. At the same time, however, caution is advised in extrapolating from these observation made in what essentially reflects a wound healing milieu to healthy, unmanipulated human skin *in vivo*.
The current findings invite the speculation that the therapeutic downmodulation of K6 and/or K16 expression by CB1 agonists and other cannabimimetics might become exploitable for the management of other dermatoses besides psoriasis, for example pachyonychia congenita (Hickerson et al. 2011; Zhao et al. 2011) and acne (Biro et al. 2009), and could be used to
modulate KC migration-dependent reepithelialization in wound healing, similar to related findings in periodontal and intestinal wound repair (Kozono et al. 2010; Wright et al. 2005).
**Conclusion**
Our results suggest that cannabinoids and their receptors constitute a novel, clinically relevant control element of human K6 and K16 expression. Therefore, cannabimimetic agents might be relevant for the treatment of several skin conditions related to aberrant K6/K16 expression, such as psoriasis and wound healing. In addition, the skin organ culture is shown to be a clinically and physiologically relevant model system for investigating the effect of CB1 specific agonist/antagonist on human skin.
**Acknowledgements**
The authors thank Motoko Sugawara for her excellent technical assistance, and Dr. Stephan Tiede for professional advice. The generous professional support of Prof. Masamitsu Ishii and Prof. Hiromi Kobayashi, Osaka, for this work is also gratefully appreciated. Dr. Wolfgang Funk is gratefully acknowledged for harvesting human skin samples for the organ culture.
REFERENCES
Akhmetshina A, Dees C, Busch N, Beer J, Sarter K, Zwerina J, Zimmer A, Distler O, Schett G, Distler JH. 2009. The cannabinoid receptor CB2 exerts antifibrotic effects in experimental dermal fibrosis. *Arthritis and Rheumatism* 60:1129-1136.
Balato A, Lembo S, Mattii M, Schiattarella M, Marino R, De Paulis A, Balato N, Ayala F. 2012. IL-33 is secreted by psoriatic keratinocytes and induces pro-inflammatory cytokines via keratinocyte and mast cell activation. *Experimental Dermatology* 21:892-894.
Biro T, Toth BI, Hasko G, Paus R, Pacher P. 2009. The endocannabinoid system of the skin in health and disease: novel perspectives and therapeutic opportunities. *Trends in Pharmacological Sciences* 30:411-420.
Bodo E, Kany B, Gaspar E, Knuver J, Kromminga A, Ramot Y, Biro T, Tiede S, van Beek N, Poeggeler B, Meyer KC, Wenzel BE, Paus R. 2010. Thyroid-stimulating hormone, a novel, locally produced modulator of human epidermal functions, is regulated by thyrotropin-releasing hormone and thyroid hormones. *Endocrinology* 151:1633-1642.
Boukamp P, Petrussevska RT, Breitkreutz D, Hornung J, Markham A, Fusenig NE. 1988. Normal keratinization in a spontaneously immortalized aneuploid human keratinocyte cell line. *Journal of Cell Biology* 106:761-771.
Brown C, Stenn KS, Falk RJ, Woodley DT, O'Keefe EJ. 1991. Vitronectin: effects on keratinocyte motility and inhibition of collagen-induced motility. *J Invest Dermatol* 96:724-728.
Carvalho RF, Nilsson G, Harvima IT. 2010. Increased mast cell expression of PAR-2 in skin inflammatory diseases and release of IL-8 upon PAR-2 activation. *Experimental Dermatology* 19:117-122.
Casanova ML, Blazquez C, Martinez-Palacio J, Villanueva C, Fernandez-Acenero MJ, Huffman JW, Jorcano JL, Guzman M. 2003. Inhibition of skin tumor growth and angiogenesis in vivo by activation of cannabinoid receptors. *Journal of Clinical Investigation* 111:43-50.
Chanda D, Kim DK, Li T, Kim YH, Koo SH, Lee CH, Chiang JY, Choi HS. 2011. Cannabinoid receptor type 1 (CB1R) signaling regulates hepatic gluconeogenesis via induction of endoplasmic reticulum-bound transcription factor cAMP-responsive element-binding protein H (CREBH) in primary hepatocytes. *Journal of Biological Chemistry* 286:27971-27979.
Czifra G, Szollosi AG, Toth BI, Demaude J, Bouez C, Breton L, Biro T. 2012. Endocannabinoids regulate growth and survival of human eccrine sweat gland-derived epithelial cells. *Journal of Investigative Dermatology* 132:1967-1976.
Dobrosi N, Toth BI, Nagy G, Dozsa A, Geczy T, Nagy L, Zouboulis CC, Paus R, Kovacs L, Biro T. 2008. Endocannabinoids enhance lipid synthesis and apoptosis of human sebocytes via cannabinoid receptor-2-mediated signaling. *FASEB Journal* 22:3685-3695.
Donetti E, Gualerzi A, Ricceri F, Pescitelli L, Bedoni M, Prignano F. 2012. Etanercept restores a differentiated keratinocyte phenotype in psoriatic human skin: a morphological study. *Experimental Dermatology* 21:549-551.
Dono LM, Currie PJ. 2012. The cannabinoid receptor CB(1) inverse agonist AM251 potentiates the anxiogenic activity of urocortin I in the basolateral amygdala. *Neuropharmacology* 62:192-199.
Farkas A, Kemeny L, Szony BJ, Bata-Csorgo Z, Pivarcsi A, Kiss M, Szell M, Koreck A, Dobozy A. 2001. Dithranol upregulates IL-10 receptors on the cultured human keratinocyte cell line HaCaT. *Inflammation Research* 50:44-49.
Fiori JL, Sanghvi M, O'Connell MP, Krzysik-Walker SM, Moaddel R, Bernier M. 2011. The cannabinoid receptor inverse agonist AM251 regulates the expression of the EGF receptor and its ligands via destabilization of oestrogen-related receptor alpha protein. *British Journal of Pharmacology* 164:1026-1040.
George SE, Anderson RJ, Cunningham A, Donaldson M, Groundwater PW. 2010. Evaluation of a range of anti-proliferative assays for the preclinical screening of anti-psoriatic drugs: a
comparison of colorimetric and fluorimetric assays with the thymidine incorporation assay. *Assay Drug Dev Technol* 8:389-400.
Griffiths CE, Barker JN. 2007. Pathogenesis and clinical features of psoriasis. *Lancet* 370:263-271.
Grzanka A, Zebracka-Gala J, Rachowska R, Bozek A, Kowalska M, Jarzab J. 2012. The effect of pimecrolimus on expression of genes associated with skin barrier dysfunction in atopic dermatitis skin lesions. *Experimental Dermatology* 21:184-188.
Harvey BS, Ohlsson KS, Maag JL, Musgrave IF, Smid SD. 2012. Contrasting protective effects of cannabinoids against oxidative stress and amyloid-beta evoked neurotoxicity in vitro. *Neurotoxicology* 33:138-146.
Hermanson DJ, Marnett LJ. 2011. Cannabinoids, endocannabinoids, and cancer. *Cancer and Metastasis Reviews* 30:599-612.
Hickerson RP, Leachman SA, Pho LN, Gonzalez-Gonzalez E, Smith FJ, McLean WH, Contag CH, Leake D, Milstone LM, Kaspar RL. 2011. Development of quantitative molecular clinical end points for siRNA clinical trials. *Journal of Investigative Dermatology* 131:1029-1036.
Iizuka H, Takahashi H, Honma M, Ishida-Yamamoto A. 2004. Unique keratinization process in psoriasis: late differentiation markers are abolished because of the premature cell death. *Journal of Dermatology* 31:271-276.
Karsak M, Gaffal E, Date R, Wang-Eckhardt L, Rehnelt J, Petrosino S, Starowicz K, Steuder R, Schlicker E, Cravatt B, Mechoulam R, Buettner R, Werner S, Di Marzo V, Tuting T, Zimmer A. 2007. Attenuation of allergic contact dermatitis through the endocannabinoid system. *Science* 316:1494-1497.
Khasabova IA, Khasabov S, Paz J, Harding-Rose C, Simone DA, Seybold VS. 2012. Cannabinoid type-1 receptor reduces pain and neurotoxicity produced by chemotherapy. *Journal of Neuroscience* 32:7091-7101.
Kim TG, Byamba D, Wu WH, Lee MG. 2011. Statins inhibit chemotactic interaction between CCL20 and CCR6 in vitro: possible relevance to psoriasis treatment. *Experimental Dermatology* 20:855-857.
Klein TW. 2005. Cannabinoid-based drugs as anti-inflammatory therapeutics. *Nat Rev Immunol* 5:400-411.
Knuever J, Poeggeler B, Gaspar E, Klinger M, Hellwig-Burgel T, Hardenbicker C, Toth BI, Biro T, Paus R. 2012. Thyrotropin-releasing hormone controls mitochondrial biology in human epidermis. *Journal of Clinical Endocrinology and Metabolism* 97:978-986.
Korver JE, van Duijnhooven MW, Pasch MC, van Erp PE, van de Kerkhof PC. 2006. Assessment of epidermal subpopulations and proliferation in healthy skin, symptomless and lesional skin of spreading psoriasis. *British Journal of Dermatology* 155:688-694.
Kozono S, Matsuyama T, Biwasa KK, Kawahara K, Nakajima Y, Yoshimoto T, Yonamine Y, Kadomatsu H, Tancharoen S, Hashiguchi T, Noguchi K, Maruyama I. 2010. Involvement of the endocannabinoid system in periodontal healing. *Biochemical and Biophysical Research Communications* 394:928-933.
Kupczyk P, Reich A, Szepietowski JC. 2009. Cannabinoid system in the skin - a possible target for future therapies in dermatology. *Experimental Dermatology* 18:669-679.
Langan EA, Ramot Y, Hanning A, Poeggeler B, Biro T, Gaspar E, Funk W, Griffiths CE, Paus R. 2010. Thyrotropin-releasing hormone and oestrogen differentially regulate prolactin and prolactin receptor expression in female human skin and hair follicles in vitro. *British Journal of Dermatology* 162:1127-1131.
Langbein L, Schweizer J. 2005. Keratins of the human hair follicle. *International Review of Cytology* 243:1-78.
Leonti M, Casu L, Raduner S, Cottiglia F, Floris C, Altmann KH, Gertsch J. 2010. Falcarninol is a covalent cannabinoid CB1 receptor antagonist and induces pro-allergic effects in skin. *Biochemical Pharmacology* 79:1815-1826.
Litvinov IV, Bizet AA, Binamer Y, Jones DA, Sasseville D, Philip A. 2011. CD109 release from the cell surface in human keratinocytes regulates TGF-beta receptor expression, TGF-beta signalling and STAT3 activation: relevance to psoriasis. *Experimental Dermatology* 20:627-632.
Lu Z, Hasse S, Bodo E, Rose C, Funk W, Paus R. 2007. Towards the development of a simplified long-term organ culture method for human scalp skin and its appendages under serum-free conditions. *Experimental Dermatology* 16:37-44.
Maccarrone M, Di Rienzo M, Battista N, Gasperi V, Guerrieri P, Rossi A, Finazzi-Agro A. 2003. The endocannabinoid system in human keratinocytes. Evidence that anandamide inhibits epidermal differentiation through CB1 receptor-dependent inhibition of protein kinase C, activation protein-1, and transglutaminase. *Journal of Biological Chemistry* 278:33896-33903.
Moll R, Divo M, Langbein L. 2008. The human keratins: biology and pathology. *Histochemistry and Cell Biology* 129:705-733.
Mommers JM, van Rossum MM, van Erp PE, van De Kerkhof PC. 2000. Changes in keratin 6 and keratin 10 (co-)expression in lesional and symptomless skin of spreading psoriasis. *Dermatology* 201:15-20.
Namazi MR. 2005. Cannabinoids, loratadine and allopurinol as novel additions to the antipsoriatic ammunition. *Journal of the European Academy of Dermatology and Venereology* 19:319-322.
Navarro JM, Casatorres J, Jorcano JL. 1995. Elements controlling the expression and induction of the skin hyperproliferation-associated keratin K6. *Journal of Biological Chemistry* 270:21362-21367.
Paladini RD, Takahashi K, Bravo NS, Coulombe PA. 1996. Onset of re-epithelialization after skin injury correlates with a reorganization of keratin filaments in wound edge keratinocytes: defining a potential role for keratin 16. *Journal of Cell Biology* 132:381-397.
Paradisi A, Pasquariello N, Barcaroli D, Maccarrone M. 2008. Anandamide regulates keratinocyte differentiation by inducing DNA methylation in a CB1 receptor-dependent manner. *Journal of Biological Chemistry* 283:6005-6012.
Pertwee RG, Howlett AC, Abood ME, Alexander SP, Di Marzo V, Elphick MR, Greasley PJ, Hansen HS, Kunos G, Mackie K, Mechoulam R, Ross RA. 2010. International Union of Basic and Clinical Pharmacology. LXXIX. Cannabinoid receptors and their ligands: beyond CB(1) and CB(2). *Pharmacological Reviews* 62:588-631.
Poeggeler B, Knuever J, Gaspar E, Biro T, Klinger M, Bodo E, Wiesner RJ, Wenzel BE, Paus R. 2010. Thyrotropin powers human mitochondria. *FASEB Journal* 24:1525-1531.
Pucci M, Pasquariello N, Battista N, Di Tommaso M, Rapino C, Fezza F, Zuccolo M, Jourdain R, Finazzi Agro A, Breton L, Maccarrone M. 2012. Endocannabinoids stimulate human melanogenesis via type-1 cannabinoid receptor. *Journal of Biological Chemistry* 287:15466-15478.
Radosa J, Dyck W, Goerdt S, Kurzen H. 2011. The cholinergic system in guttate psoriasis with special reference to mast cells. *Experimental Dermatology* 20:677-679.
Ramot Y, Biro T, Tiede S, Toth BI, Langan EA, Sugawara K, Foitzik K, Ingber A, Goffin V, Langbein L, Paus R. 2010. Prolactin--a novel neuroendocrine regulator of human keratin expression in situ. *FASEB Journal* 24:1768-1779.
Ramot Y, Gaspar E, Dendorfer A, Langbein L, Paus R. 2009. The 'melanocyte-keratin' mystery revisited: neither normal human epidermal nor hair follicle melanocytes express keratin 16 or keratin 6 in situ. *British Journal of Dermatology* 161:933-938.
Ramot Y, Tiede S, Biro T, Abu Bakar MH, Sugawara K, Philpott MP, Harrison W, Pietila M, Paus R. 2011. Spermidine promotes human hair growth and is a novel modulator of human epithelial stem cell functions. *PLoS One* 6:e22564.
Richardson JD, Kilo S, Hargreaves KM. 1998. Cannabinoids reduce hyperalgesia and inflammation via interaction with peripheral CB1 receptors. *Pain* 75:111-119.
Roelandt T, Heughebaert C, Bredif S, Giddelo C, Baudouin C, Msika P, Roseeuw D, Uchida Y, Elias PM, Hachem JP. 2012. Cannabinoid receptors 1 and 2 oppositely regulate epidermal permeability barrier status and differentiation. *Experimental Dermatology* 21:688-693.
Ronpirin C, Tencomnao T. 2012. Effects of the antipsoriatic drug dithranol on E2A and caspase-9 gene expression in vitro. *Genet Mol Res* 11:412-420.
Rotty JD, Coulombe PA. 2012. A wound-induced keratin inhibits Src activity during keratinocyte migration and tissue repair. *Journal of Cell Biology* 197:381-389.
Ryle CM, Breitkreutz D, Stark HJ, Leigh IM, Steinert PM, Roop D, Fusenig NE. 1989. Density-dependent modulation of synthesis of keratins 1 and 10 in the human keratinocyte line HACAT and in ras-transfected tumorigenic clones. *Differentiation* 40:42-54.
Saelee C, Thongrakard V, Tencomnao T. 2011. Effects of Thai medicinal herb extracts with anti-psoriatic activity on the expression on NF-kappaB signaling biomarkers in HaCaT keratinocytes. *Molecules* 16:3908-3932.
Stander S, Reinhardt HW, Luger TA. 2006. [Topical cannabinoid agonists. An effective new possibility for treating chronic pruritus]. *Hautarzt* 57:801-807.
Stander S, Schmelz M, Metze D, Luger T, Rukwied R. 2005. Distribution of cannabinoid receptor 1 (CB1) and 2 (CB2) on sensory nerve fibers and adnexal structures in human skin. *Journal of Dermatological Science* 38:177-188.
Stenn KS. 1981. Epibolin: a protein of human plasma that supports epithelial cell movement. *Proc Natl Acad Sci USA* 78:6907-6911.
Sugawara K, Biro T, Tsuruta D, Toth BI, Kromminga A, Zakany N, Zimmer A, Funk W, Gibbs BF, Zimmer A, Paus R. 2012. Endocannabinoids limit excessive mast cell maturation and activation in human skin. *Journal of Allergy and Clinical Immunology* 129:726-738 e728.
Suttle MM, Nilsson G, Snellman E, Harvima IT. 2012. Experimentally induced psoriatic lesion associates with interleukin (IL)-6 in mast cells and appearance of dermal cells expressing IL-33 and IL-6 receptor. *Clinical and Experimental Immunology* 169:311-319.
Telek A, Biro T, Bodo E, Toth BI, Borbiro I, Kunos G, Paus R. 2007. Inhibition of human hair follicle growth by endo- and exocannabinoids. *FASEB Journal* 21:3534-3541.
Thakoersing VS, Danso MO, Mulder A, Gooris G, El Ghalbzouri A, Bouwstra JA. 2012. Nature versus nurture: does human skin maintain its stratum corneum lipid properties in vitro? *Experimental Dermatology* 21:865-870.
Toruniowa B, Jablonska S. 1988. Mast cells in the initial stages of psoriasis. *Archives for Dermatological Research. Archiv fur Dermatologische Forschung* 280:189-193.
Toth BI, Dobrosi N, Dajnoki A, Czifra G, Olah A, Szollosi AG, Juhasz I, Sugawara K, Paus R, Biro T. 2011. Endocannabinoids modulate human epidermal keratinocyte proliferation and survival via the sequential engagement of cannabinoid receptor-1 and transient receptor potential vanilloid-1. *Journal of Investigative Dermatology* 131:1095-1104.
Toth BI, Geczy T, Griger Z, Dozsa A, Seltmann H, Kovacs L, Nagy L, Zouboulis CC, Paus R, Biro T. 2009. Transient receptor potential vanilloid-1 signaling as a regulator of human sebocyte biology. *Journal of Investigative Dermatology* 129:329-339.
Van Dross R, Soliman E, Jha S, Johnson T, Mukhopadhyay S. 2012. Receptor-dependent and receptor-independent endocannabinoid signaling: A therapeutic target for regulation of cancer growth. *Life Sciences*.
Walker JM, Hohmann AG. 2005. Cannabinoid mechanisms of pain suppression. *Handb Exp Pharmacol*:509-554.
Weiss RA, Eichner R, Sun TT. 1984. Monoclonal antibody analysis of keratin expression in epidermal diseases: a 48- and 56-kdalton keratin as molecular markers for hyperproliferative keratinocytes. *Journal of Cell Biology* 98:1397-1406.
Wilkinson JD, Williamson EM. 2007. Cannabinoids inhibit human keratinocyte proliferation through a non-CB1/CB2 mechanism and have a potential therapeutic value in the treatment of psoriasis. *Journal of Dermatological Science* 45:87-92.
Wright K, Rooney N, Feeney M, Tate J, Robertson D, Welham M, Ward S. 2005. Differential expression of cannabinoid receptors in the human colon: cannabinoids promote epithelial wound healing. *Gastroenterology* 129:437-453.
Zhao Y, Gartner U, Smith FJ, McLean WH. 2011. Statins downregulate K6a promoter activity: a possible therapeutic avenue for pachyonychia congenita. *Journal of Investigative Dermatology* 131:1045-1052.
**Figure Legends**
**Figure 1. The CB1 specific agonist, ACEA significantly inhibits K6 and K16 expression in situ.** (A) Representative images of K6 immunofluorescence with organ cultured human skin treated with ACEA/AM251 (1-day). (B) Statistical analysis of K6 immunofluorescence intensity in organ cultured human skin (quantitative immunohistomorphometry, ImageJ); stimulation with ACEA (30 µM), AM251 (1 µM) or both for 1-day. n=9-22 skin
sections/group. (C) Representative images of K16 immunohistochemistry with organ cultured human skin samples with ACEA (1-day). (D) Quantitative K16 immunohistomorphometry within the epidermis of organ-cultured human skin samples after 1-day of stimulation with ACEA 30 (µM). n=4 skin sections/group. Data are expressed as mean + SEM. *p<0.05, **p<0.01.
Figure 2. The CB1 specific agonist, ACEA significantly inhibits K6 expression in cultured HaCaT cells. (A) Representative images of K6 immunofluorescence of cultured HaCaT KCs with ACEA (1 µM), AM251 (100 nM) or both for 1-day. (B) Statistical analysis of K6 immunofluorescence intensity of cultured HaCaT cells. n=6 colonies/group. (C) Statistical analysis of K6 gene expression in HaCaT cells treated with vehicle control or ACEA (1 µM) for 8h. Data are expressed as mean + SEM. *p<0.05; **p<0.01; ***p<0.001.
Figure 3. The CB1 specific agonist, ACEA significantly decreases human epidermal keratinocyte proliferation in situ. (A) Representative images of K6 (green) and Ki67 (red) double-immunofluorescence with organ cultured human skin treated with ACEA/AM251 (1-day). (B) Quantitative analysis of the percentage of Ki67+ KCs within organ cultured human epidermis. *p<0.05; ***p<0.001. n=5-12 skin sections/group.
Figure 4. The CB1 specific agonist, ACEA, significantly decreases K6 expression in suprabasal cells in a proliferation-independent manner. (A) Representative images of K6 (green) and Ki-67 (red) double immunofluorescence. Dotted rectangles indicate the reference area for quantitative immunohistomorphometry of K6 fluorescence intensity. (B) Quantitative analysis of K6 fluorescence intensity in non-proliferating (i.e. Ki67-negative) cells within human epidermis in situ. Data are expressed as mean + SEM. *p<0.05. n=5-7 skin sections/group. (C) K6 (green) and CB1 (red) double-immunofluorescence study. Yellow arrows denote double-positive KCs.
Figure 1
The CB1 specific agonist, ACEA significantly inhibits K6 and K16 expression in situ.
(A) Representative images of K6 immunofluorescence with organ cultured human skin treated with ACEA/AM251 (1-day). (B) Statistical analysis of K6 immunofluorescence intensity in organ cultured human skin (quantitative immunohistomorphometry, ImageJ); stimulation with ACEA (30 μM), AM251 (1 μM) or both for 1-day. n=9-22 skin sections/group. (C) Representative images of K16 immunohistochemistry with organ cultured human skin samples with ACEA (1-day). (D) Quantitative K16 immunohistomorphometry within the epidermis of organ-cultured human skin samples after 1-day of stimulation with ACEA 30 (μM). n=4 skin sections/group. Data are expressed as mean ± SEM. *p<0.05, **p<0.01.
A ACEA downregulates K6 expression
B K6 staining intensity in the epidermis
C ACEA downregulates K16 expression
D K16 staining intensity in the epidermis
Figure 2
The CB1 specific agonist, ACEA significantly inhibits K6 expression in cultured HaCaT cells.
(A) Representative images of K6 immunofluorescence of cultured HaCaT KCs with ACEA (1 μ M), AM251 (100 nM) or both for 1-day. (B) Statistical analysis of K6 immunofluorescence intensity of cultured HaCaT cells. n=6 colonies/group (C) Statistical analysis of K6 gene expression in HaCaT cells treated with vehicle control or ACEA (1 μ M) for 8h. Data are expressed as mean ± SEM. *p<0.05; **p<0.01; ***p<0.001.
Figure 3
The CB1 specific agonist, ACEA significantly decreases human epidermal keratinocyte proliferation in situ.
(A) Representative images of K6 (green) and Ki67 (red) double-immunofluorescence with organ cultured human skin treated with ACEA/AM251 (1-day). (B) Quantitative analysis of the percentage of Ki67+ KCs within organ cultured human epidermis. *p<0.05; ***p<0.001. n=5-12 skin sections/group.
The CB1 specific agonist, ACEA, significantly decreases K6 expression in suprabasal cells in a proliferation-independent manner.
(A) Representative images of K6 (green) and Ki-67 (red) double immunofluorescence. Dotted rectangles indicate the reference area for quantitative immunohistomorphometry of K6 fluorescence intensity. (B) Quantitative analysis of K6 fluorescence intensity in non-proliferating (i.e. Ki67-negative) cells within human epidermis in situ. Data are expressed as mean + SEM. *p<0.05. n=5-7 skin sections/group. (C) K6 (green) and CB1 (red) double-immunofluorescence study. Yellow arrows denote double-positive KCs.
A ACEA directly inhibits K6 expression
K6 expression in non-proliferating cells
B K6 fluorescence intensity in non-proliferating cells
C K6+ cells (green) co-express CB1 (red) | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
1844,
1
],
[
1844,
3383,
2
],
[
3383,
3736,
3
],
[
3736,
5918,
4
],
[
5918,
7976,
5
],
[
7976,
9806,
6
],
[
9806,
11307,
7
],
[
11307,
13118,
8
],
[
13118,
15270,
9
],
[
15270,
17025,
10
],
[
17025,
18708,
11
],
[
18708,
20776,
12
],
[
20776,
22659,
13
],
[
22659,
24877,
14
],
[
24877,
27034,
15
],
[
27034,
28123,
16
],
[
28123,
30039,
17
],
[
30039,
31995,
18
],
[
31995,
33786,
19
],
[
33786,
35701,
20
],
[
35701,
37554,
21
],
[
37554,
39560,
22
],
[
39560,
41649,
23
],
[
41649,
43587,
24
],
[
43587,
44459,
25
],
[
44459,
46382,
26
],
[
46382,
47158,
27
],
[
47158,
47319,
28
],
[
47319,
47833,
29
],
[
47833,
48241,
30
],
[
48241,
48879,
31
],
[
48879,
49060,
32
]
]
} |
913470a0bd92b8389062f57b700a89e90d8b82e7 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 10,
"total-fallback-pages": 0,
"total-input-tokens": 41615,
"total-output-tokens": 11466,
"fieldofstudy": [
"Computer Science"
]
} | Abstract
The state-of-the-art models for coreference resolution are based on independent mention pair-wise decisions. We propose a modelling approach that learns coreference at the document-level and takes global decisions. For this purpose, we model coreference links in a graph structure where the nodes are tokens in the text, and the edges represent the relationship between them. Our model predicts the graph in a non-autoregressive manner, then iteratively refines it based on previous predictions, allowing global dependencies between decisions. The experimental results show improvements over various baselines, reinforcing the hypothesis that document-level information improves conference resolution.
1 Introduction
Current state-of-the-art (SOTA) solutions for coreference resolution such as (Toshniwal et al., 2020; Xu and Choi, 2020; Wu et al., 2020) formulate the problem in an end-to-end manner where the models jointly learn to detect mentions and link coreferent mentions. The objective is to predict the antecedent of each mention-span in a document, so the model performs pair-wise decisions of all mentions. After having the model predictions, related mentions are grouped into clusters. Under this scenario, each decision (i.e., whether two mentions are related to the same entity or not) is independent. Lee et al. (2018) proposed an iterative method to update the representation of a mention with information of its probable antecedents. However, the final decisions are still made locally.
We propose a modeling approach that learns coreference at the document-level and takes global decisions. We propose to model mentions and coreference links in a graph structure where the nodes are tokens in the text, and the edges represent the relationships between them. Figures 1 and 2 show a short example taken from the CoNLL 2012 dataset (Pradhan et al., 2012) showing the graph in two perspectives. Figure 1 shows how the token nodes in a text are connected with edges drawn with arrows. We differentiate the connections between words in a coreference mention ‘mention links’, and the ones among mentions in a cluster ‘coreference links’ (see Sec. 4). Figure 2 shows the same graph in a matrix representation, where the number in a cell indicates the type of relation between the row and the column. Our model receives a document as input then predicts and iteratively refines the graph of mentions and coreference links.
We follow a similar approach to the Graph-to-Graph Transformer (G2GT) proposed in (Mohammadshahi and Henderson, 2021, 2020) for syntactic
parsing, but instead of encoding sentences, we encode documents. Our model predicts the graph in a non-autoregressive manner, then iteratively refines it based on previous predictions. This recursive process introduces global dependencies between decisions. Unlike (Mohammadshahi and Henderson, 2021), we define different structures for input and output graphs, to reflect the different roles of these graphs. To ensure that locality in the input graph reflects all the relevant relationships, the input graph encodes relations for all mention tokens. This makes the encoding process easier. To provide a unique specification of the target graph, the output only encodes a minimal set of connections. This facilitates prediction. We initialize the Transformer with pre-trained language models, either BERT (Devlin et al., 2019), or SpanBERT (Joshi et al., 2020).
Another difference with (Mohammadshahi and Henderson, 2021) is that our model predicts two levels of representation. While they predict the whole graph at each iteration, during the first iteration our model only predicts edges that identify mention-spans. This is because mention detection is a sentence-level phenomenon whose outputs are required as inputs to coreference resolution, which is a discourse-level phenomenon. But we do not organise these two tasks in a pipeline. Starting at the second iteration, the model predicts the complete graph. This allows the model to refine mention decisions given coreference decisions, and vice versa. In this way, we propose to use iterative graph refinement as an alternative to pipeline architectures for multi-level deep learning models. The iterative process finishes when there are no more changes in the graph or when a maximum number of iterations is reached.
Ideally, the whole document should be encoded at once, but in practice there is a limit on the maximum length. In order to deal with this issue, we propose two strategies: overlapping windows and reduced document. In the first strategy, we split documents into overlapping windows of the maximum allowed size $K$. The segments overlap for a length $K/2$. At decoding time, segments are input in order, and we construct the final graph by joining all graphs from different segments. In the second strategy, we use two networks. The mention-span network is the previously described overlapping model, and we use it for predicting the first graph. For the second network, we reduce the document by including only the tokens of candidate mention-spans, separated by a special token. This network refines the initial graph for the following iterations.
The experiments show improvements over the relevant baselines and state-of-the-art. They also indicate that the models reach the best solution in a maximum of three iterations. Given that we predict the graph at once for each iteration, our model’s complexity is lower than the baselines. Our contributions are the following:
- We propose a novel modeling approach to coreference resolution using a graph structure and multi-level iterative refinement.
- We propose two iterative graph refinement models that can predict the complete entity coreference structure of a document.
- We show improvements over baseline models and the relevant state-of-the-art.
2 Related Work
The first approaches to coreference resolution (CR) were rule-based systems (Lappin and Leass, 1994; Manning et al., 2014), but eventually, they were outperformed by machine learning approaches (Aone and William, 1995; McCarthy, 1995; Mitkov, 2002) due to annotated corpora’s creation. In general, there are three coreference approaches: mention-pair, entity-mention, and ranking models. Mention-pair models set coreference as a binary classification problem. The initial stage is the mention detection, where the input is raw text, and the output is the locations of each entity mention in the text. Mention detection is done as an independent task in a pipeline model (Soon et al., 2001) or as part of an end-to-end model (Lee et al., 2017). The next stage is the classification of mention pairs. At first, the best classifiers were decision trees (Soon et al., 2001; McCarthy, 1995; Aone and William, 1995), but later, neural networks became the SOTA. The final stage is reconciling the pair-wise decisions to create entity chains, usually by utilizing greedy algorithms or clustering approaches. Entity-mention models focus on maintaining single underlying entity representation for each cluster, contrast the independent pair-wise decisions of mention-pair approaches (Clark and Manning, 2015, 2016). Ranking models aim at ranking the possible antecedent of each mention instead of making binary decisions (Wiseman et al., 2016). An alternative modeling
approach is to perform clustering instead of classification (Fernandes et al., 2012).
SOTA models for CR are mostly based on Lee et al. (2017). They introduced the first end-to-end model that jointly optimizes mention detection and coreference resolution tasks. These neural network-based models also simplify the mention input representation to be word embedding vectors, instead of the traditional pipeline of different linguistic feature extraction tools such as part-of-speech (POS) tagging and dependency parsing. The following models proposed improvements over this work. Later, (Lee et al., 2018) improved the previous model by introducing higher order inference so the entity’s mention representation will get iteratively updated with the weighted average of antecedent representations, where the weights are the predictions from the model at the previous iteration. This contrasts with our approach in that we iterate over the whole coreference link graph and we perform discrete decisions at each iteration. Fei et al. (2019) use reinforcement learning to directly optimize the model on the evaluation metrics. Joshi et al. (2019) uses BERT embeddings (Devlin et al., 2019) as input. Joshi et al. (2020) introduced a new SpanBERT embedding model, which is shown to outperform BERT for the CR task. Xu and Choi (2020) showed that higher order inference has low impact on strong models such as SpanBert. Toshniwal et al. (2020) proposed a bounded memory model trained to manage limited memory by learning to forget entities. Finally, Wu et al. (2020) formulated the problem of coreference resolution as question-answering and trained a model for span prediction. This model has the advantage of being pretrained with larger data-sets from the question-answering task.
3 Baseline: Neural Coreference Resolution
Neural coreference resolution, as formulated in (Lee et al., 2017, 2018), is a mention-pair approach. It uses an exhaustive method defining mentions as any text span of any size in a document. There, a document $D$ represents a sequence of tokens of size $N$. The objective is to assign an antecedent $y_i$ to each of the $M$ text spans $m_i$ in $D$. The set of possible antecedents of the span $m_i$ is denoted as $Y(i)$. This set contains all text spans with index less than $i$, plus a null antecedent $\epsilon$, $Y(i) = \{\epsilon, m_1, ..., m_{i-1}\}$. The null antecedent is assigned when: (a) the span is not an entity mention, (b) the span is the first mention of an entity in the document. The final mention clusters are constructed greedily by grouping connected spans based on the model predictions during decoding time.
The model is trained to learn a conditional probability distribution over documents $p(y_1, ..., y_M|D)$, assuming independence among each decision of antecedent assignment $y_i$, as follows:
$$p(y_1, ..., y_M|D) = \prod_{i=1}^{M} p(y_i|D)$$
In (Lee et al., 2018), the probability distribution $p(y_i|D)$ is inferred over $T$ iterations of the model over the same input document. At each iteration $t$, the span representations are updated with the weighted average of all possible antecedents at time $t-1$ where the weights are given by the probability distribution of the model at time $t-1$. They called this model high-order coreference resolution since each mention representation considers information from its probable antecedents.
The training optimization is done using cross-entropy. Given that a mention-span $m_i$ can have more than one true antecedent, the loss considers the sum of probabilities of all true antecedents in the annotated data:
$$\log \prod_{i=1}^{M} \sum_{y_i \in Y(i) \cap C(i)} p(y_i|D)$$
where $C(i)$ indicates the cluster of mention-spans that includes $m_i$ in the annotated data. If the span does not belong to any cluster or all its antecedents have been pruned, then the span is assigned to the null cluster $C(i) = \{\epsilon\}$.
This model’s complexity is of the order $O(N^4)$, where $N$ is the document length. The complexity is computed by considering all possible text spans $M$ of the document, so $O(M) = O(N^2)$. Then, it considers all possible combinations of span-antecedents $O(M^2)$. The model prunes spans and candidate antecedents to predetermined maximum numbers in order to maintain computational efficiency.
4 Graph Modeling
We propose to model the set of coreference links of a document in a graph structure where the nodes
are tokens\(^1\) and the edges are links of different types. Given a document \(D = [x_1, ..., x_N]\) of size \(N\), the coreference graph is defined as the matrix \(G \subset \mathbb{N}^{N \times N}\) of links between tokens. Here, the relation type between two tokens, \(x_i\) and \(x_j\), is encoded with integers and is denoted as \(g_{i,j} \in \{0, 1, 2\}\). We define three relation types: (0) no link, (1) mention link, and (2) coreference link, as illustrated in Figure 2.
**Mention links** This type of link serves to identify mentions. We define mention links in two different manners depending on whether the graph is an input or output of the model for functional reasons. When the graph is an input \(G^{\text{in}}\), there is a directed link from each mention’s token to the mention head, including the head to itself. When the graph is the model’s output \(G^{\text{out}}\), there is only one directed link from the last token of the mention-span to the first token. Both encoding methods define a mention-span uniquely, even when having nested mentions; every mention has a unique start-end combination and a unique head. The model utilizes the output for prediction, so it is simpler to predict one single link, whereas, in the input, the model uses links to all tokens to provide a more direct representation of the role of every token in the mention.
**Mention heads** We simplified the head identification process by considering the first token of a mention span as the head. Although this method is naive, experiments show that this approximation works well enough in practice. However, as some spans can potentially have the same first token in case of nested mentions, we fix this issue by assigning the next token as the head if the first is already the head of any other mention.
**Coreference links** This type of link defines the relationship between a mention and each of its antecedents. We also define coreference links in two different manners depending on whether the graph is an input or output of the model. When the graph is input, there is a link from a mention head token to the head of each mention in the same cluster. When the graph is a model’s output, the mention should be connected to at least one of its antecedents. If the mention has no antecedent, or corresponds to the first mention of an entity in the text, then it is connected to a null antecedent \(c\). We use all possible connections between mentions in an entity cluster for the input so that the model receives a direct input for each coreference relationship. On the other hand, we consider that predicting at least one connection of the mention to its cluster is sufficient to specify the output graph.
The objective is to learn the conditional probability distribution \(p(G|D)\). This distribution is initially approximated by assuming independence among each relation \(g_{i,j}\) as:
\[
p(G|D) = \prod_{i=1}^{N} \prod_{j=1}^{i} p(g_{i,j}|D) \quad (3)
\]
The probability \(p(g_{i,j}|D)\) is split in two cases: one for mention links \(p_m\) and the other for coreference links \(p_c\). The mention link probability is defined as:
\[
p_m(g_{i,j}|1|D) = \sigma(W_m \cdot [h_i, h_j]) \quad (4)
\]
where \(W_m\) is a parameter matrix, and \(h_i\) and \(h_j\) are the hidden state representations of the tokens \(x_i\) and \(x_j\) respectively. This probability indicates whether there is a mention starting at position \(j\) and ending at position \(i\) of the document \(D\). The optimization is done using binary-cross-entropy loss \(\text{loss}_m\).
The coreference link probability is defined as:
\[
p_c(g_{i,j}|2|D) = \frac{\exp(W_c \cdot [h_i, h_j])}{\sum_{j' \in A(i)} \exp(W_c \cdot [h_i, h_{j'}])} \quad (5)
\]
where \(W_c\) is a parameter matrix, and \(h_i\) and \(h_j\) are the hidden state representations of the tokens \(x_i\) and \(x_j\) respectively. Similar to the baseline, we denote \(A(i)\) as the set of all candidate antecedents of \(x_i\). This set contains all mention heads with an index less than \(i\), plus a null head \(\epsilon\), \(A(i) = \{\epsilon, x_k | k < i \text{ and } x_k \in H(D)\}\), and \(H(D)\) is the set of all candidate mention heads in the document. The optimization is done with cross-entropy loss. Given that a mention-span \(m_i\) can have more than one true antecedent, the loss considers the sum of probabilities of all true antecedents in the annotated data (as in Equation (2)):
\[
\text{loss}_c = \log \prod_{i \in H(D)} \sum_{j \in Y(i) \cap \hat{C}(i)} p_c(g_{i,j}|D) \quad (6)
\]
where \(\hat{C}(i)\) indicates the annotated cluster of mention-spans that includes \(m_i\) in the annotated data. If the mention does not belong to any cluster, then the span is assigned to the null cluster.
---
\(^1\)The tokenization of the words in the document, and thus the nodes of the graph, are defined by the input format of the relevant pre-trained Transformer model.
\( \hat{C}(i) = \{ \epsilon \} \). The final loss is the sum of \( \text{loss}_m \) and \( \text{loss}_c \).
The token's hidden state representations \( \{ h_1, ..., h_N \} \) are the last hidden layer of a Transformer model. We use various pre-trained Transformer models to initialize the weight parameters, then fine-tune for the coreference task.
5 Iterative Refinement
The strong independence assumption made in Equation (3) does not reflect the real scenario and could lead to poor performance. Therefore, we use an iterative refinement approach to model interdependencies between relations, similar to G2GT (Mohammadshahi and Henderson, 2021). Under this approach, the model makes \( T \) iterations over the same document \( D \). At each iteration \( t \), the predicted coreference graph \( G_t \) is conditioned on the previously predicted one \( G_{t-1} \). The model’s conditional probability distribution is now defined as follows:
\[
\begin{align*}
p(G^t|D, G^{t-1}) &= \prod_{i=1}^{N} \prod_{j=1}^{i} p(g_{i,j}|D, G^{t-1}) \quad (7)
\end{align*}
\]
This means that the graph should be input to the Transformer model (Vaswani et al., 2017). Following (Mohammadshahi and Henderson, 2021), the graph is encoded by inputting an embedding for the type of each relation into the self-attention function of the Transformer:
\[
\begin{align*}
\text{Attention}(Q, K, V, L_k, L_v) &= \frac{\text{softmax} \left( \frac{Q \cdot (K + L_k)^{\top}}{\sqrt{d}} \right) \cdot (V + L_v)}{\text{softmax} \left( \frac{Q \cdot (K + L_k)^{\top}}{\sqrt{d}} \right) \cdot (V + L_v)} \quad (8)
\end{align*}
\]
where \( E \) is a matrix of embeddings which encode the types of links in the graph, as illustrated in Figure 2. Thus, the relationship between a pair of tokens is encoded as an embedding vector which is input when computing the attention function for that pair of tokens. \( W_k, W_v \) are weight matrices that serve to specialize \( E(G_{t-1}) \) to be either key or value vectors. The complexity of our model is of the order of \( O(N^2 \times T) \), where \( N \) is the document length, and \( T \) is the number of refinement iterations of the model.
To illustrate the iterative refinement of a graph, Figure 3 shows an example of two iterations of the model. The mention links are indicated with solid line arrows and the coreference links with dotted arrows. The initial graph matrix \( G^0 \) is full of zeros, so no connections are drawn. The first predicted graph \( G^1 \) only has mention-links because initially there were no mention heads to be connected. This graph is transformed to serve as input \( G^1 \) for the next iteration. Finally, during the second iteration, the model predicts the coreference graph \( G^2 \). The model can continue iterating for a maximum of \( T \) times.
6 Architectures
There exists in practice a maximum length for encoding a document due to limited hardware memory. In this section, we describe two strategies to manage this issue: overlapping windows and reduced document. In the experiments we also report results for a naive strategy of truncating the documents at the maximum segment length of \( K \) for both training and testing.
6.1 Overlapping Windows
Here, we split the documents into overlapping segments of the maximum size \( K \), with an overlap of \( K/2 \) tokens. The segments are encoded individually in our G2GT model. During training, each segment is treated as an independent sample. However, during decoding, the segments are decoded in
order. The subgraph corresponding to the overlapping part is input to the next segment. The union of the segmented graphs forms the final graph.
6.2 Reduced Document
This model has two parts; one to detect mentions and the other to perform coreference resolution. The mention detection is similar to the previously described model. The coreference resolution part receives a shorter version of the document as input. The complete model is described in the following:
**Mention Detection** This Transformer is non-iterative so it corresponds to the definition in Equation (3). To encode the document, we apply overlapping windows, as in the previous section. For prediction, we used the soft-target method proposed in (Miculich and Henderson, 2020). This method enables the model to increase the recall of detection. Given that the candidate mentions will be fixed for the coreference resolution part, we need to detect most of them here.
**Coreference Resolution** This part is a G2GT with iterative refinement. The input is a shorter version of the document obtained by concatenating the tokens from candidate mention-spans with a separation token in between and removing all other tokens. To maintain coherence in the document, we modify the token input representation to the sum of three vectors: (a) a token embedding, (b) an embedding of the token’s position in the original document, so we retain information of distance between mentions, and (c) the token’s contextualized representation obtained from the mention detection part where the original document is encoded. This second part predicts only coreference links, but the input graph contains both candidate mentions and coreference links. The set of candidate mentions remains the same across all iterations of this second part, but the mentions are refined in the sense that the final output only includes the mentions which are involved in the final coreference links.
Figure 4 shows an example of this architecture with one iteration over a document. The mention links are indicated with solid line arrows and the coreference links with dotted arrows. The first model predicts the graph of mention-spans \( G^\text{out} \). This graph is transformed into the input format for the next model \( G^\text{in}_0 \). Then, the second model predicts the graph of coreference \( G^\text{out}_1 \). Note that this coreference resolution model can continue iterating for \( T \) times. The final coreference graph is the output after the final iteration of the second model. The final set of mentions is only a subset of the mention candidates output by the first model, namely those mentions which participate in coreference links.
7 Experimental Setting
7.1 Dataset
We use the CoNLL 2012 corpus (Pradhan et al., 2012). It contains data from diverse domains e.g., newswire, magazines, conversations. We experiment only with the English part. Table 1 shows the statistics of the dataset; the average length per document does not exceed 500 words. We pre-process the text to extract sub-word units (Sennrich et al., 2016) with BERT tokenizer (Wu et al., 2016). We map the positional annotation of mentions from words to sub-words and retain this mapping for back transformation during evaluation.
7.2 Model configuration
We use the implementation of Wolf et al. (2019)\(^2\) of ‘BERT-base’, ‘BERT-large’ (Joshi et al., 2019) and ‘SpanBERT-large’ (Joshi et al., 2020). All hyper-parameters follow this implementation unless specified otherwise.
---
\(^2\)https://huggingface.co/transformers/
As our graphs are directed, we use only the lower 2 with a maximum segment length of $T$ (a) when a maximum number of iterations is reached, or (b) when there are no more changes in the graph, $G_t = G_{t-1}$. This criterion is for both training and testing. Our models are trained with a maximum segment length of $K = 512$ and a batch size of 1 document. We use BertAdam (Kingma and Ba, 2014; Wolf et al., 2019) optimizer with a base learning rate of $2e^{-3}$ and no warm-up.
As our graphs are directed, we use only the lower triangle of $G$ for predictions. The components of the reduced models are trained independently. The coreference resolution follows the currently described training schema. The mention detection model has no iterative refinement step and follows the training schema of the span scoring soft-target approach described in (Miculicich and Henderson, 2020), with $\rho = 0.1$.
### Training
The G2GT considers an independent loss for each different refinement iteration. There is no back-propagation between refinement iterations because the model makes discrete decisions when predicting the graph for the next refinement step. There are two stopping criteria for the refinement: (a) when a maximum number of iterations $T$ is reached, or (b) when there are no more changes in the graph, $G_t = G_{t-1}$. This criterion is for both training and testing. Our models are trained with a maximum segment length of $K = 512$ and a batch size of 1 document. We use BertAdam (Kingma and Ba, 2014; Wolf et al., 2019) optimizer with a base learning rate of $2e^{-3}$ and no warm-up.
As our graphs are directed, we use only the lower triangle of $G$ for predictions. The components of the reduced models are trained independently. The coreference resolution follows the currently described training schema. The mention detection model has no iterative refinement step and follows the training schema of the span scoring soft-target approach described in (Miculicich and Henderson, 2020), with $\rho = 0.1$.
### Evaluation
At evaluation time, we map back all sub-word units to words and reconstruct the document in CoNLL 2012 format. We use the precision, recall, and F1 score calculated in three different manners: MUC that counts the number of links between mentions, $B^3$ that counts the number of mentions, and CEAF that counts the entity clusters.
### Results Analysis
This section describes the results of various baselines and our models. First, we analyze the optimum number of refinement iterations, and then we show results using the best models.
Table 2 shows the performance of our G2GT models when varying the maximum number of refinement iterations $T$ from 2 to 5 ($T=1$ is mention detection only). The results are in terms of the F1 score of the three coreference metrics and the average. All three implementations shown in the table perform the best when using $T=4$. There is a significant decrease in performance when the graphs are not refined, $T=2$, showing the importance of modelling the interdependencies between coreference relations.
Table 3 shows the evaluation results on the test set in terms of precision (P), recall (R), and F1 score for each metric. The last column displays the average F1 of the three metrics. The first section of the table exhibits scores of different coreference resolution systems from the literature. The second section shows the result of the ‘Baseline’ (Lee et al., 2018) system described in Section 3. This model uses ELMo (Peters et al., 2018) instead of BERT to obtain word representations. Baseline
| Model | MUC P | R | F1 | MUC P | R | F1 | MUC P | R | F1 | MUC P | R | F1 | Avg. F1 |
|-------------------------------|--------|----|----|--------|----|----|--------|----|----|--------|----|----|--------|
| Clark and Manning (2015) | 76.1 | 69.4| 72.6| 65.6 | 56.0| 60.4| 59.4 | 53.0| 56.0| 63.0 |
| Wiseman et al. (2016) | 77.5 | 69.8| 73.4| 66.8 | 57.0| 61.5| 62.1 | 53.9| 57.7| 64.2 |
| Clark and Manning (2016) | 79.2 | 70.4| 74.6| 69.9 | 58.0| 63.4| 63.5 | 55.5| 59.2| 65.7 |
| Lee et al. (2017) | 78.4 | 73.4| 75.8| 68.6 | 61.8| 65.0| 62.7 | 59.0| 60.8| 67.2 |
| Fei et al. (2019) | 85.4 | 77.9| 81.4| 77.9 | 66.4| 71.7| 70.6 | 66.3| 68.4| 73.8 |
| Xu and Choi (2020) | 85.9 | 85.5| 85.7| 79.0 | 78.9| 79.0| 76.7 | 75.2| 75.9| 80.2 |
| Wu et al. (2020) | 88.6 | 87.4| 88.0| 82.4 | 82.0| 82.2| 79.9 | 78.3| 79.1| 83.1 |
| Baseline (Lee et al., 2018) | 81.4 | 79.5| 80.4| 72.2 | 69.5| 70.8| 68.2 | 67.1| 67.6| 73.0 |
| + BERT-base (Joshi et al., 2019) | 80.4 | 82.3| 81.4| 69.6 | 73.8| 71.7| 69.0 | 68.5| 68.8| 73.9 |
| + BERT-large (Joshi et al., 2019) | 84.7 | 82.4| 83.5| 76.5 | 74.0| 75.3| 74.1 | 69.8| 71.9| 76.9 |
| + SpanBERT-large (Joshi et al., 2020) | 85.8 | 84.8| 85.3| 78.3 | 77.9| 78.1| 76.4 | 74.2| 75.3| 79.6 |
| G2GT BERT-base truncated | 78.4 | 77.9| 78.1| 69.6 | 71.0| 70.3| 66.8 | 67.3| 67.0| 71.8 |
| G2GT BERT-base overlap | 81.2 | 82.8| 82.0| 69.8 | 73.6| 71.6| 69.6 | 69.3| 69.4| 74.4 |
| G2GT BERT-base reduced | 83.4 | 83.1| 83.2| 70.1 | 73.7| 71.9| 72.1 | 70.1| 71.0| 75.4 |
| G2GT BERT-large truncated | 80.1 | 79.2| 79.6| 71.3 | 71.0| 71.1| 69.1 | 68.8| 68.9| 73.2 |
| G2GT BERT-large overlap | 83.5 | 83.2| 83.3| 74.5 | 74.1| 74.3| 75.2 | 70.1| 72.6| 76.7 |
| G2GT BERT-large reduced | 84.7 | 83.1| 83.9| 76.8 | 74.0| 75.4| 75.3 | 70.1| 72.6| 77.3 |
| G2GT SpanBERT-large overlap | 85.8 | 84.9| 85.3| 78.7 | 78.0| 78.3| 76.4 | 74.5| 75.4| 79.7 |
| G2GT SpanBERT-large reduced | **85.9** | **86.0** | **85.9** | **79.3** | **79.4** | **79.3** | **76.4** | **75.9** | **76.1** | **80.5** |
Table 3: Evaluation on the test set (CoNLL 2012).
plus ‘BERT-base’, ‘BERT-large’ (Joshi et al., 2019) and ‘SpanBERT-large’ (Joshi et al., 2020) correspond to the baseline using those representations. We copy all these values from the original papers. The last section of the table presents scores of our graph-to-graph models with iterative refinement. ‘truncated’ is our model with no special treatment for document length; the documents are truncated at the maximum segment length of \( K \). ‘overlap’ and ‘reduce’ are the models described in Section 6.
As expected, pre-training with SpanBert results in better scores than with Bert, and Bert-large is better than BERT-base. Not surprisingly, ‘G2GT Bert-base truncated’ and ‘G2GT Bert-large truncated’ perform poorly in comparison to the baseline because their information is incomplete. For BERT-base, both the ‘overlap’ and ‘reduce’ models have better scores than the comparable baseline. For BERT-large and SpanBert, the ‘overlap’ model has similar scores to the baseline, but the ‘reduce’ model consistently improves over the baseline.
Overall, our G2GT ‘reduce’ method consistently shows the highest scores across all the models for each pre-trained model. Our models do not surpass SOTA (Wu et al., 2020) (shown in grey), but as mentioned before, this SOTA model is also trained on the much more abundant data from the question-answering task, and so it is not directly comparable to our model. We leave the issue of incorporating additional data into the training of our model to future work.
9 Discussion
These results support our claim that coreference resolution benefits from making global coreference decisions using document-level information. First, refinement of coreference decisions using global information about other coreference decisions clearly improves accuracy, as indicated by the improved scores for models with more than one iteration in Table 2. Second, the model which is able to combine information from the entire document, G2GT ‘reduce’, is clearly better than the model which performs the task on large windows of text and then merges the results, G2GT ‘overlap’.
One issue with our method is the necessity to iteratively pass the input through an expensive encoder model more than once. However, the number of iterations needed is small and results in significant improvement.
The length management methods would not be necessary if we had more efficient pre-trained Transformer models or larger-memory GPU hardware which could handle longer sequences. However, the computational cost of very large Transformers will always be an issue, so in general there is a need to address the issue of how to reduce the number of inputs when modelling phenomena which require large contexts, such as coreference resolution. This paper contributes towards addressing this general issue.
10 Conclusion
We proposed a G2GT model with iterative refinement for coreference resolution. For this purpose, we define a graph structure to encode coreference links contained in a document. That enables our model to predict the complete coreference graph at once. The graph is then refined in a recursive manner, iterating the model conditioned on the document and the graph prediction from the previous step. This allows global modelling of all coreference decisions using all document-level information, but it introduces computational issues for longer documents. We experimented with two methods to manage long documents and maintain computational efficiency. The first method encodes the document in overlapping segments. The second method reduces the set of tokens which are input.
The evaluation shows that both methods can outperform a comparable baseline, and that the second method has better performance than the first one and than all other comparable models. This experiment shows that global decisions and document-level information are useful to improve coreference and thus should not be ignored. It also shows that the models can benefit from increasingly powerful pre-trained language models, BERT-base (Devlin et al., 2019), BERT-large (Devlin et al., 2019), and SpanBERT (Joshi et al., 2020).
By empirically showing the benefits of making global decisions and using document-level information in coreference resolution, this work motivates further work on this topic. In addition, the model designs developed in this work provide a viable approach to addressing the related issues. Addressing the computational issues with modelling large documents in Transformers is an area of active research, and our proposed methods could be improved in future work.
References
Chinatsu Aone and Scott William. 1995. Evaluating automated and manual acquisition of anaphora resolution strategies. In 33rd Annual Meeting of the Association for Computational Linguistics, pages 122–129, Cambridge, Massachusetts, USA. Association for Computational Linguistics.
Kevin Clark and Christopher D. Manning. 2015. Entity-centric coreference resolution with model stacking. In Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 1: Long Papers), pages 1405–1415, Beijing, China. Association for Computational Linguistics.
Kevin Clark and Christopher D. Manning. 2016. Improving coreference resolution by learning entity-level distributed representations. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 643–653, Berlin, Germany. Association for Computational Linguistics.
Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. 2019. BERT: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), pages 4171–4186, Minneapolis, Minnesota. Association for Computational Linguistics.
Hongliang Fei, Xu Li, Dingcheng Li, and Ping Li. 2019. End-to-end deep reinforcement learning based coreference resolution. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 660–665, Florence, Italy. Association for Computational Linguistics.
Eraldo Fernandes, Cicero dos Santos, and Ruy Milidiú. 2012. Latent structure perceptron with feature induction for unrestricted coreference resolution. In Joint Conference on EMNLP and CoNLL - Shared Task, pages 41–48, Jeju Island, Korea. Association for Computational Linguistics.
Mandar Joshi, Danqi Chen, Yinhan Liu, Daniel S. Weld, Luke Zettlemoyer, and Omer Levy. 2020. SpanBERT: Improving pre-training by representing and predicting spans. Transactions of the Association for Computational Linguistics, 8:64–77.
Mandar Joshi, Omer Levy, Luke Zettlemoyer, and Daniel Weld. 2019. BERT for coreference resolution: Baselines and analysis. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), pages 5803–5808, Hong Kong, China. Association for Computational Linguistics.
Diederik P Kingma and Jimmy Ba. 2014. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980.
Shalom Lappin and Herbert J. Leass. 1994. An algorithm for pronominal anaphora resolution. Computational Linguistics, 20(4):535–561.
Kenton Lee, Luheng He, Mike Lewis, and Luke Zettlemoyer. 2017. End-to-end neural coreference resolution. In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing, pages 188–197, Copenaghen, Denmark. Association for Computational Linguistics.
Kenton Lee, Luheng He, and Luke Zettlemoyer. 2018. Higher-order coreference resolution with coarse-to-fine inference. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 2 (Short Papers), pages 687–692, New Orleans, Louisiana. Association for Computational Linguistics.
Christopher Manning, Mihai Surdeanu, John Bauer, Jenny Finkel, Steven Bethard, and David McClosky. 2014. The Stanford CoreNLP natural language processing toolkit. In Proceedings of 52nd Annual Meeting of the Association for Computational Linguistics: System Demonstrations, pages 55–60, Baltimore, Maryland. Association for Computational Linguistics.
JF McCarthy. 1995. Using decision trees for coreference resolution. In Proc. 14th International Joint Conf. on Artificial Intelligence (IJCAI), Quebec, Canada, Aug. 1995.
Lesly Miculicich and James Henderson. 2020. Partially-supervised mention detection. In Proceedings of the Third Workshop on Computational Models of Reference, Anaphora and Coreference, pages 91–98, Barcelona, Spain (online). Association for Computational Linguistics.
Ruslan Mitkov. 2002. Anaphora Resolution. Longman, London, UK.
Alicreza Mohammadshahi and James Henderson. 2020. Graph-to-graph transformer for transition-based dependency parsing. In Findings of the Association for Computational Linguistics: EMNLP 2020, pages 3278–3289, Online. Association for Computational Linguistics.
Alicreza Mohammadshahi and James Henderson. 2021. Recursive non-autoregressive graph-to-graph transformer for dependency parsing with iterative refinement. Transactions of the Association for Computational Linguistics, 9:120–138.
Matthew E. Peters, Mark Neumann, Mohit Iyyer, Matt Gardner, Christopher Clark, Kenton Lee, and Luke Zettlemoyer. 2018. Deep contextualized word representations. In Proceedings of the 2018 Conference of the North American Chapter of the Association for Computational Linguistics.
Sameer Pradhan, Alessandro Moschitti, Nianwen Xue, Olga Uryupina, and Yuchen Zhang. 2012. CoNLL-2012 shared task: Modeling multilingual unrestricted coreference in OntoNotes. In Joint Conference on EMNLP and CoNLL - Shared Task, pages 1–40, Jeju Island, Korea. Association for Computational Linguistics.
Rico Sennrich, Barry Haddow, and Alexandra Birch. 2016. Neural machine translation of rare words with subword units. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 1715–1725, Berlin, Germany. Association for Computational Linguistics.
Wee Meng Soon, Hwee Tou Ng, and Daniel Chung Yong Lim. 2001. A machine learning approach to coreference resolution of noun phrases. Computational Linguistics, 27(4):521–544.
Shubham Toshniwal, Sam Wiseman, Allyson Ettinger, Karen Livescu, and Kevin Gimpel. 2020. Learning to Ignore: Long Document Coreference with Bounded Memory Neural Networks. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 8519–8526, Online. Association for Computational Linguistics.
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Ł ukasz Kaiser, and Illia Polosukhin. 2017. Attention is all you need. In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems 30, pages 5998–6008. Curran Associates, Inc.
Sam Wiseman, Alexander M. Rush, and Stuart M. Shieber. 2016. Learning global features for coreference resolution. In Proceedings of the 2016 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 994–1004, San Diego, California. Association for Computational Linguistics.
Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierrick Cistac, Tim Rault, Rémi Louf, Morgan Funtowicz, et al. 2019. Huggingface’s transformers: State-of-the-art natural language processing. ArXiv, pages arXiv–1910.
Wei Wu, Fei Wang, Arianna Yuan, Fei Wu, and Jiwei Li. 2020. CorefQA: Coreference resolution as query-based span prediction. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pages 6953–6963, Online. Association for Computational Linguistics. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2586,
1
],
[
2586,
7347,
2
],
[
7347,
11792,
3
],
[
11792,
16732,
4
],
[
16732,
20261,
5
],
[
20261,
23820,
6
],
[
23820,
29759,
7
],
[
29759,
34359,
8
],
[
34359,
39489,
9
],
[
39489,
41866,
10
]
]
} |
ea83f3a1a97e7e1d67c0f9886b05b18dd80d9e97 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 18,
"total-fallback-pages": 0,
"total-input-tokens": 94299,
"total-output-tokens": 23555,
"fieldofstudy": [
"Education",
"Psychology"
]
} | Frequent Sports Dance May Serve as a Protective Factor for Depression Among College Students: A Real-World Data Analysis in China
Lirong Zhang1
Shaocong Zhao1
Wei Weng1
Qiong Lin2
Minmin Song3
Shouren Wu2
Hua Zheng4
1Department of Physical Education, Xiamen University of Technology, Xiamen, Fujian, 361024, People’s Republic of China; 2Department of Physical Education, Jimei University, Xiamen, Fujian, 361021, People’s Republic of China; 3Department of Physical Education, Fujian Agriculture and Forestry University, Fuzhou, Fujian, 350008, People’s Republic of China; 4College of Physical Education and Health Sciences, Chongqing Normal University, Chongqing, 400047, People’s Republic of China
Purpose: This study aims to investigate the role of frequent sports dance in preventing mental disorders, including anxiety and depression, among college students using real-world data, and to further analyze potential risk factors associated with anxiety and depression.
Methods: We investigated 921 college students from eight universities in China. A survey was completed by 901 students and they were included in the analysis. The anxiety score was evaluated by the Generalized Anxiety Disorder 7-item (GAD-7) scale and the depression score was evaluated by the Patient Health Questionnaire-9 (PHQ-9). Subgroup comparisons were performed among frequent sports dance students and non-frequent sports dance students.
Results: Of all the students, 9.98% had moderate-to-severe anxiety and 14.65% students suffered from moderate-to-severe depression. Compared with non-frequent sports dance students, frequent sports dance students had significantly lower depression scores (P<0.04). According to the multiple logistic regression models, when potential confounding factors were all adjusted, frequent sports dance was also significantly associated with less depression (OR=0.55, 95% CI: 0.36–0.84, P<0.01). We also found that higher college grade levels (P<0.01), non-physical education students (P<0.02), higher body mass index (P<0.02), lower exercise frequency per week (P<0.01), addiction to drinking (P=0.02), and previous diagnosis of anxiety or depression in hospital (P<0.01) were significantly associated with more anxiety; higher college grade levels (P<0.01), addiction to drinking (P<0.01), preference for eating fried food (P=0.02), soda as the main source of drinking water (P=0.01), and previous diagnosis of anxiety or depression (P=0.03) were significantly associated with more depression, while higher exercise frequency per week (P<0.01), only-child status (P<0.01), and preference for eating vegetables (P=0.02) were significantly associated with less depression.
Conclusion: Anxiety and depression are common among college students. Frequent sports dance may serve as a protective factor for preventing depression and it can be recommended for college students.
Keywords: sports dance, college student, anxiety, depression, risk factor
Introduction
Mental disorders are a significant problem among populations of college students.1 Studies have shown that up to 17–30% of college students have suffered from anxiety and 12.2–19.9% from depression.2–6 Besides, these numbers are growing over time.5 The incidence of anxiety increased from 9.3% in 2009 to 14.9% in 2015, and during the same period depression increased from 9.0% to 12.2% among college students, according to the American College Health Association National...
College Health Assessment. Anxiety and depression are students’ major risk factors for suicide. The prevalence and negative effects of anxiety and depression demonstrate the importance of prevention and creating strategies to intervene in these mental disorders among university students.
Dance sports training has been proved to significantly improve physical health outcomes. In a randomized clinical trial, jazz dance was shown to provide physical and mental benefits to university students. A meta-analysis also showed that among ordinary sports, dance was one of the most effective exercises to alleviate depressive symptoms among depressed patients. Moreover, apart from mental disorders, sports dance therapy can also be beneficial for other special populations, such as those with obesity, hypertension, elderly people with balance problems, and in Parkinson’s disease, to name just a few. However, these studies generally focused on the investigation of some special populations. Whether dance could prevent anxiety or depression among college students remains unclear. Besides, those studies had a wide range of designs with diverse quality and the method of dance therapy varied in different national and cultural contexts. Therefore, it was still difficult to draw conclusions about the positive influence of dance and sport activity on young people’s well-being. Thus, the effect of sport and dance on the young people’s well-being needs further investigation using real-world data. Besides, effective strategies for preventing anxiety and depression are not widely available among college students, mainly because of insufficient understanding of the potential risk factors for these mental disorders.
Therefore, this study aimed to investigate the role of frequent sports dance in preventing mental disorders (anxiety and depression) among college students using real-world data. We speculated that frequent sports dance is capable of serving a positive function in preventing anxiety or depression, or both of them. Besides, we further analyzed potential risk factors associated with anxiety and depression.
**Methods**
**Students**
We investigated 921 college students from eight universities in China, namely, Xiamen University of Technology, Xiamen University, JiMei University, Chengdu Sport University, Southwest Jiaotong University, Fujian Agriculture and Forestry University, Shandong Sport University, and Chongqing Normal University, via a survey. The survey was carried out online through a questionnaire; students were asked to voluntarily sign an informed consent statement using their own cell phones and completed the survey voluntarily according to their own situation. The personal information was anonymized and it was also unnecessary for participants to fill in their personal information. All data were extracted from the survey and then a database was constructed for statistical analysis. We included university students and excluded postgraduate and doctoral students. Students aged 18 years or younger were also not included. Students who were reluctant to participate in the survey were not enrolled in the study. This study was approved by the Academic Committee Board of Xiamen University of Technology (no. 202001). Formal consent was all obtained from participants. This study was conducted in accordance with the Declaration of Helsinki.
**Sample Calculation**
According to the available literature, the incidence of anxiety or depression among college students is 10–20%. We speculated that the odds ratio of frequent sports dance and the multiple correlation coefficients were both 0.6. Based on Whittemore’s formula and Monte Carlo simulations, when $\alpha=0.05$ and $1−\beta=95\%$, the sample size was 305–499 for univariate logistic regression and 477–780 for multivariate logistic regression. Altogether, the sample size should not be less than 800.
**Baseline Characteristics**
From all the patients, 30 potential risk factors were collected and analyzed, including general information, living habits, types of diet, comorbidities, and family background. In detail, these 30 risk factors were gender (female vs male), age (mean, years), college grade levels (freshmen vs sophomores vs junior vs senior vs delayed graduation), professional dancer (yes vs no), member of college sports dance team (yes vs no), physical education student (yes vs no), participant in college sports dance course (yes vs no), body mass index (BMI, kg/m$^2$) (<18.5 vs $\geq 18.5$ and <24 vs $\geq 24$ and <28 vs $\geq 28$), scholarship winner (yes vs no), scholarship level (first class vs second class vs third class vs no), sedentary time per day (hours) (<1 vs $\geq 1$ and <3 vs $\geq 3$ and <6 vs $\geq 6$), exercise frequency per week (0 vs 1–2 vs 3–4 vs $\geq 5$), study period during free time (hours) (<1 vs $\geq 1$ and <2 vs $\geq 2$ and <3 vs $\geq 3$), only-child status (yes vs no), educational background of father (primary school vs junior or high school
vs university vs graduate), educational background of mother (primary school vs junior or high school vs university vs graduate), hypertension (yes vs no), diabetes (yes vs no), addiction to smoking (yes vs no), addiction to drinking (yes vs no), preference for eating red meat (yes vs no), preference for eating vegetables (yes vs no), preference for eating fruits (yes vs no), preference for eating barbecued food (yes vs no), preference for eating fried food (yes vs no), main source of drinking water (purified water vs tea vs coffee vs soda), monthly expenses (RMB) (<1000 vs ≥1000 and <2000 vs ≥2000 and <4000 vs ≥4000), marital status (single vs dating vs married vs fertilized), previous diagnosis of anxiety or depression in hospital (yes vs no), and history of anxiety or depression in immediate family members (yes vs no). All the factors were self-reported. The only-child status was defined as having no siblings. The exercise time in the factor of exercise frequency per week was no less than 30 min per exercise. Study period during free time was defined as the time interval that participants used for self-study during free time and did not include class time.
Anxiety and Depression Evaluation
Students’ anxiety scores were evaluated by the Generalized Anxiety Disorder 7-item (GAD-7) scale and depression score were evaluated by the Patient Health Questionnaire-9 (PHQ-9). According to the literature, GAD-7 and PHQ-9 are effective and useful tools to investigate the anxious and depressive status of young people and college students. The classifications were as follows: students with a GAD-7 of 15 points or more were considered as having severe anxious status; a GAD-7 of 10–14 points was moderate anxiety; a GAD-7 of 5–9 points was mild anxiety; and a GAD-7 of 4 points or less was no anxiety. Regarding the PHQ-9, a score of 15 points or more was severe depression; a score of 10–14 points was moderate depression; a score of 5–9 points was mild depression; and a score of 4 points or less was no depression.
Subgroup Analysis
Subgroup comparisons were performed among frequent sports dance students and non-frequent sports dance students. Frequent sports dance students were defined as those who were members of a college sports dance team. In this team, regular dance practices took place four times a week (90 min/practice) each semester. Non-frequent sports dance students included participants in college sports dance courses and ordinary college students. Ordinary college students were those who did not participate in both college sports dance teams and college sports dance courses. Students who participated in sports dance courses were required to attend courses once a week (90 min/practice). All students had voluntarily chosen dance courses or took part in dance teams to practice dance skills, including waltz, tango, foxtrot, quickstep, and Latin. According to students’ feedback and expectations, the dance practice’s content, dance costume, intensity, and length of time had changed over time. Generally, each session began with a 15 min warm-up. Then, a muscular and psychological relaxation exercise was performed for 10 min. Dance practice was lasted for 55 min. Dances training in the class was mainly done working in pairs. But at the beginning of semester, students who were not familiar with the dance training would train individually and then work with their partners as a team. During the period of dance practice, students were encouraged to examine their creativity, physical well-being, and expression of emotions. Besides, at the end of each session, students were encouraged to describe and express their true experiences and emotions for 10 min.
Logistic Regression Analysis
The above-mentioned 30 potential risk factors were used to predict anxiety and depression in college students. Simple and multiple logistic regression models were used to screen these potential risk factors for anxiety and depression. Significant factors evaluated using the multiple logistic regression models were considered as the independent risk or protective factors.
Effectiveness Evaluation of Significant Risk Factors
The effectiveness of the significant risk factors was also evaluated by receiver operating characteristic (ROC) curves, correct classification rates, sensitivity, specificity, false-positive rates, false negative rates, and goodness-of-fit tests. An ROC value of more than 0.8 indicates an excellent prediction model, an ROC value of 0.7–0.8 means a good prediction model, and an ROC value of less than 0.7 represents an acceptable prediction model. For the goodness-of-fit test, a P-value of more than 0.05 indicates good calibration ability of the prediction model.
Statistical Analysis
All analyses were performed with SAS 9.2 statistical software. Comparisons between two continuous variables were made using the t-test or the Wilcoxon rank sum
test. Differences among the categorical variables between groups were analyzed using the chi-squared test, the continuous corrected chi-squared test, or Fisher’s exact test. The simple and multiple logistic regression models were used to screen potential risk factors predicting mental disorders. A P-value of less than 0.05 was considered statistically significant (two-sided tests).
Results
Students’ Baseline Characteristics
Of all the enrolled students, the mean±SD age was 19.40±2.08 years, with 56.38% female and 43.62% male students. The majority of students were freshmen (45.39%). There were 5.66% professional dancers, 11.65% members of college sports dance teams, 26.08% physical education students, and 29.86% participants in college sports dance courses. Most participants were non-scholarship winners (75.69%), had a sedentary time of 1–3 hours per day (34.18%), exercised once or twice per week (44.40%), and studied for 1–2 hours during their free time (39.62%). Table 1 shows the detail basic demographic information of all included college students.
Subgroup Analysis
Compared with non-frequent sports dance students, frequent sports dance students significantly had more females (P<0.04), higher age (P<0.01), higher college grade levels (P<0.01), more professional dancers (P<0.01), more scholarship winners (P<0.01), higher parental educational levels (P=0.02 and P=0.03), more students preferring to eat fruit (P=0.04), and lower depression score (P=0.04) (Table 2). Further, the non-frequent sports dance students were classified into two groups: participants in college sports dance courses and ordinary college students. When the three groups were compared together, similar results were obtained (Table 3). This confirmed that frequent sports dance students had the lowest depression score (P=0.06).
Risk Factors for Anxiety
According to multiple logistic regression models, college grade levels (OR=1.43, 95% CI: 1.21–1.68, P<0.01), physical education students (OR=0.66, 95% CI: 0.46–0.94, P=0.02), BMI (OR=1.18, 95% CI: 1.02–1.36, P=0.02), exercise frequency per week (OR=0.78, 95% CI: 0.66–0.93, P<0.01), addiction to drinking (OR=2.19, 95% CI: 1.14–4.21, P=0.02), and previous diagnosis of anxiety or depression in hospital (OR=3.58, 95% CI: 1.56–8.24, P<0.01) were significant, while other characteristics were not significant (Table 4). Namely, higher college grade levels, higher BMI values, addiction to drinking, and previous diagnosis of anxiety or depression were independent risk factors for anxiety, while being a physical education student and higher exercise frequency per week were independent protective factors for anxiety.
Risk Factors for Depression
Based on the multiple logistic regression models, college grade levels (OR=1.35, 95% CI: 1.15–1.59, P<0.01), member of college sports dance team (OR=0.55, 95% CI: 0.36–0.84, P<0.01), exercise frequency per week (OR=0.75, 95% CI: 0.65–0.87, P<0.01), only-child status (OR=0.68, 95% CI: 0.52–0.88, P<0.01), addiction to drinking (OR=2.59, 95% CI: 1.35–5.00, P<0.01), preference for eating vegetables (OR=0.68, 95% CI: 0.49–0.95, P<0.02), preference for eating fried food (OR=1.39, 95% CI: 1.06–1.83, P=0.02), main source of drinking water (OR=1.28, 95% CI: 1.05–1.55, P=0.01), and previous diagnosis of anxiety or depression in hospital (OR=2.54, 95% CI: 1.11–5.81, P=0.03) were significantly associated with depression (Table 5). That is to say, higher college grade levels, addiction to drinking, preference for eating fried food, main source of drinking water (soda), and previous diagnosis of anxiety or depression were independent risk factors for depression, while member of college sports dance team, higher exercise frequency per week, only-child status, and preference for eating vegetables were independent protective factors for depression.
Effectiveness Evaluation of Significant Risk Factors
Figure 1 shows the ROC curves and C values of all six significant characteristics for anxiety. College grade levels had the highest C value, up to 0.65, followed by exercise frequency per week (0.61). When all six significant characteristics were combined, the C value was 0.77 and the correct classification rate was 94.5%, with a sensitivity of 28.0% and a specificity of 96.3% (Table 6). Figure 2 shows the ROC curves and C values of all six significant characteristics for depression. Exercise frequency per week showed the highest C value (0.65). The P-values obtained from the goodness-of-fit test were all above 0.05 in both the anxiety and depression models.
## Table 1 Baseline Characteristics
| Characteristics | Students (n=901) |
|---------------------------------------------|-------------------------------------|
| **Gender** | |
| Female | 56.38% (508/901) |
| Male | 43.62% (393/901) |
| **Age (mean, years)** | 19.40±2.08 |
| **College grade level** | |
| Freshman | 45.39% (409/901) |
| Sophomore | 39.18% (353/901) |
| Junior | 12.99% (117/901) |
| Senior | 2.00% (18/901) |
| Delayed graduation | 0.44% (4/901) |
| **Professional dancer** | |
| Yes | 5.66% (51/901) |
| No | 94.34% (850/901) |
| **Member of college sports dance team** | |
| Yes | 11.65% (105/901) |
| No | 88.35% (796/901) |
| **Physical education student** | |
| Yes | 26.08% (235/901) |
| No | 73.92% (666/901) |
| **Participant in college sports dance course** | |
| Yes | 29.86% (269/901) |
| No | 70.14% (632/901) |
| **BMI (kg/m²)** | |
| <18.5 | 18.53% (167/901) |
| 18.5–24 | 57.27% (516/901) |
| 24–28 | 9.21% (83/901) |
| ≥28 | 14.98% (135/901) |
| **Scholarship winner** | |
| Yes | 24.31% (219/901) |
| No | 75.69% (682/901) |
| **Scholarship level** | |
| First class | 6.10% (55/901) |
| Second class | 9.21% (83/901) |
| Third class | 8.99% (81/901) |
| No | 75.69% (682/901) |
| **Sedentary time per day (hours)** | |
| <1 | 20.98% (189/901) |
| 1–3 | 34.18% (308/901) |
| 3–6 | 33.19% (299/901) |
| ≥6 | 11.65% (105/901) |
| **Exercise frequency per week** | |
| 0 | 6.10% (55/901) |
| 1–2 | 44.40% (400/901) |
| 3–4 | 27.86% (251/901) |
| ≥5 | 21.64% (195/901) |
(Continued)
| Characteristics | Students (n=901) |
|-----------------------------------------------------|-----------------|
| Study period during free time (hours) | |
| 0 | 1.55% (14/901) |
| <1 | 23.75% (214/901)|
| 1–2 | 39.62% (357/901)|
| 2–3 | 19.09% (172/901)|
| ≥3 | 15.98% (144/901)|
| Only-child status | |
| Yes | 41.07% (370/901)|
| No | 58.93% (531/901)|
| Educational background of father | |
| Primary school | 19.98% (180/901)|
| Junior or high school | 56.38% (508/901)|
| University | 21.86% (197/901)|
| Graduate | 1.78% (16/901) |
| Educational background of mother | |
| Primary school | 30.41% (274/901)|
| Junior or high school | 50.72% (457/901)|
| University | 17.54% (158/901)|
| Graduate | 1.33% (12/901) |
| Hypertension | |
| Yes | 1.11% (10/901) |
| No | 98.89% (891/901)|
| Diabetes | |
| Yes | 0.22% (2/901) |
| No | 99.78% (899/901)|
| Addiction to smoking | |
| Yes | 4.11% (37/901) |
| No | 95.89% (864/901)|
| Addiction to drinking | |
| Yes | 3.77% (34/901) |
| No | 96.23% (867/901)|
| Preference for eating red meat | |
| Yes | 84.46% (761/901)|
| No | 15.54% (140/901)|
| Preference for eating vegetables | |
| Yes | 82.02% (739/901)|
| No | 17.98% (162/901)|
| Preference for eating fruits | |
| Yes | 73.58% (663/901)|
| No | 26.42% (238/901)|
| Preference for eating barbecued food | |
| Yes | 34.41% (310/901)|
| No | 65.59% (591/901)|
(Continued)
Discussion
This study found that anxiety and depression were common among college students, after analyzing 901 students in China. Of all the participating students, 9.98% had moderate-to-severe anxiety and 14.65% suffered from moderate-to-severe depression. In other studies, 17.0–30% of college students suffered from anxiety and 12.2–19.9% had depression. The incidence of anxiety and depression varies among university students mainly because of the different evaluation tools and heterogeneity of populations. This study also demonstrated that frequent sports dance students had significantly lower depression scores than non-frequent sports dance students. According to the multiple logistic regression models, frequent sports dance also maintained significance for depression after adjusting for other potential risk factors. Thus, we concluded that frequent sports dance can serve as a protective factor for preventing depression. In a clinical trial conducted by Akandere and Demir in 2011,
Table 2 Comparisons of Characteristics Between Frequent Dance and Non-Frequent Dance Students
| Characteristics | Frequent Dance Students* (n=105) | Non-Frequent Dance Students** (n=796) | P |
|------------------------------|----------------------------------|--------------------------------------|-------|
| Gender | | | |
| Female | 65.71% (69/105) | 55.15% (439/796) | 0.04 |
| Male | 34.29% (36/105) | 44.85% (357/796) | |
| Age (mean, years) | 20.27±3.31 | 19.29±1.84 | <0.01 |
| College grade level | | | |
| Freshman | 24.76% (26/105) | 48.12% (383/796) | <0.01 |
| Sophomore | 40.00% (42/105) | 39.07% (311/796) | |
| Junior | 22.86% (24/105) | 11.68% (93/796) | |
| Senior | 11.43% (12/105) | 0.75% (6/796) | |
| Delayed graduation | 0.95% (1/105) | 0.38% (3/796) | |
| Professional dancer | | | <0.01 |
| Yes | 16.19% (17/105) | 4.27% (34/796) | |
| No | 83.81% (88/105) | 95.73% (762/796) | |
| Physical education student | | | 0.08 |
| Yes | 19.05% (20/105) | 27.01% (215/796) | |
| No | 80.95% (85/105) | 72.99% (581/796) | |
| BMI (kg/m²) | | | 0.31 |
| <18.5 | 23.81% (25/105) | 17.84% (142/796) | |
| 18.5–24 | 57.14% (60/105) | 57.29% (456/796) | |
| 24–28 | 5.71% (6/105) | 9.67% (77/796) | |
| ≥28 | 13.33% (14/105) | 15.20% (121/796) | |
| Scholarship winner | | | <0.01 |
| Yes | 35.24% (37/105) | 22.86% (182/796) | |
| No | 64.76% (68/105) | 77.14% (614/796) | |
| Scholarship level | | | <0.01 |
| First class | 13.33% (14/105) | 5.15% (41/796) | |
| Second class | 16.19% (17/105) | 8.29% (66/796) | |
| Third class | 5.71% (6/105) | 9.42% (75/796) | |
| No | 64.76% (68/105) | 77.14% (614/796) | |
| Sedentary time per day (hours)| | | 0.95 |
| <1 | 22.86% (24/105) | 20.73% (165/796) | |
| 1–3 | 34.29% (36/105) | 34.17% (272/796) | |
| 3–6 | 32.38% (34/105) | 33.29% (265/796) | |
| ≥6 | 10.48% (11/105) | 11.81% (94/796) | |
| Exercise frequency per week | | | 0.17 |
| 0 | 3.81% (4/105) | 6.41% (51/796) | |
| 1–2 | 37.14% (39/105) | 45.35% (361/796) | |
| 3–4 | 35.24% (37/105) | 26.88% (214/796) | |
| ≥5 | 23.81% (25/105) | 21.36% (170/796) | |
(Continued)
Table 2 (Continued).
| Characteristics | Frequent Dance Students* (n=105) | Non-Frequent Dance Students** (n=796) | P |
|----------------------------------------|----------------------------------|--------------------------------------|------------|
| **Study period during free time (hours)** | | | |
| 0 | 1.90% (2/105) | 1.51% (12/796) | 0.09 |
| <1 | 13.33% (14/105) | 25.13% (200/796) | |
| 1–2 | 43.81% (46/105) | 39.07% (311/796) | |
| 2–3 | 20.00% (21/105) | 18.97% (151/796) | |
| ≥3 | 20.95% (22/105) | 15.33% (122/796) | |
| **Only-child status** | | | 0.41 |
| Yes | 44.76% (47/105) | 40.58% (323/796) | |
| No | 55.24% (58/105) | 59.42% (473/796) | |
| **Educational background of father** | | | 0.02 |
| Primary school | 10.48% (11/105) | 21.23% (169/796) | |
| Junior or high school | 56.19% (59/105) | 56.41% (449/796) | |
| University | 30.48% (32/105) | 20.73% (165/796) | |
| Graduate | 2.86% (3/105) | 1.63% (13/796) | |
| **Educational background of mother** | | | 0.03 |
| Primary school | 19.05% (20/105) | 31.91% (254/796) | |
| Junior or high school | 56.19% (59/105) | 50.00% (398/796) | |
| University | 21.90% (23/105) | 16.96% (135/796) | |
| Graduate | 2.86% (3/105) | 1.13% (9/796) | |
| **Hypertension** | | | 1.00*** |
| Yes | 0.95% (1/105) | 1.13% (9/796) | |
| No | 99.05% (104/105) | 98.87% (787/796) | |
| **Diabetes** | | | 1.00*** |
| Yes | 0.00% (0/105) | 0.25% (2/796) | |
| No | 100.00% (105/105) | 99.75% (794/796) | |
| **Addiction to smoking** | | | 1.00# |
| Yes | 3.81% (4/105) | 4.15% (33/796) | |
| No | 96.19% (101/105) | 95.85% (763/796) | |
| **Addiction to drinking** | | | 1.00# |
| Yes | 3.81% (4/105) | 3.77% (30/796) | |
| No | 96.19% (101/105) | 96.23% (766/796) | |
| **Preference for eating red meat** | | | 0.93 |
| Yes | 84.76% (89/105) | 84.42% (672/796) | |
| No | 15.24% (16/105) | 15.58% (124/796) | |
| **Preference for eating vegetables** | | | 0.76 |
| Yes | 80.95% (85/105) | 82.16% (654/796) | |
| No | 19.05% (20/105) | 17.84% (142/796) | |
| **Preference for eating fruits** | | | 0.04 |
| Yes | 81.90% (86/105) | 72.49% (577/796) | |
| No | 18.10% (19/105) | 27.51% (219/796) | |
| **Preference for eating barbecued food**| | | 0.98 |
| Yes | 34.29% (36/105) | 34.42% (274/796) | |
| No | 65.71% (69/105) | 65.58% (522/796) | |
(Continued)
Table 2 (Continued).
| Characteristics | Frequent Dance Students* | Non-Frequent Dance Students** | P |
|------------------------------------------------------|-----------------------------------|-----------------------------------|-------|
| | (n=105) | (n=796) | |
| Preference for eating fried food | | | |
| Yes | 34.29% (36/105) | 33.04% (263/796) | 0.80 |
| No | 65.71% (69/105) | 66.96% (533/796) | |
| Main source of drinking water | | | |
| Purified water | 90.48% (95/105) | 89.57% (713/796) | 0.82 |
| Tea | 4.76% (5/105) | 5.65% (45/796) | |
| Coffee | 0.95% (1/105) | 0.38% (3/796) | |
| Soda | 3.81% (4/105) | 4.40% (35/796) | |
| Monthly expenses (RMB) | | | 0.14 |
| <1000 | 7.62% (8/105) | 12.94% (103/796) | |
| 1000–2000 | 73.33% (77/105) | 74.37% (592/796) | |
| 2000–4000 | 17.14% (18/105) | 10.68% (85/796) | |
| ≥4000 | 1.90% (2/105) | 2.01% (16/796) | |
| Marital status | | | 0.65 |
| Single | 76.19% (80/105) | 79.02% (629/796) | |
| Dating | 22.86% (24/105) | 20.10% (160/796) | |
| Married | 0.95% (1/105) | 0.38% (3/796) | |
| Fertilized | 0.00% (0/105) | 0.50% (4/796) | |
| Previous diagnosis of anxiety or depression in hospital| | | 0.82 |
| Yes | 1.90% (2/105) | 2.26% (18/796) | |
| No | 98.10% (103/105) | 97.74% (778/796) | |
| Anxiety or depression history of immediate family members| | | 0.50 |
| Yes | 2.86% (3/105) | 1.88% (15/796) | |
| No | 97.14% (102/105) | 98.12% (781/796) | |
| Anxiety (GAD-7) (mean) | 3.92 | 4.40 | 0.36 |
| Depression (PHQ-9) (mean) | 4.40 | 5.63 | 0.04 |
Notes: *Frequent sports dance students were members of college sports dance team; **Non-frequent sports dance students included two groups: participants in college sports dance course and ordinary college students; ***P-value was obtained from Fisher’s exact test; #P-value was obtained from the continuous corrected chi-squared test. Abbreviations: BMI, body mass index; GAD, Generalized Anxiety Disorder; RMB, Renminbi (#); PHQ, Patient Health Questionnaire.
participants (120 healthy college students ranging from 20 to 24 years of age) were randomly classified into a dance training group (n=60) and a control group (n=60), and a dance training program was performed on 3 days a week for 12 weeks in the dance training group. The results showed that dance positively alleviated the depression levels in university students. More recently, Hellem et al. evaluated the effect of OULA, a dance fitness program, on depression in 53 women who had been diagnosed with major or persistent depressive disorders, and concluded that this was a useful intervention to decrease depression and anxiety severity. Our study was the first to analyze and confirm the effect of sports dance on mental disorders using real-world data in a series of 901 Chinese university students. In this real-world situation, all students voluntarily chose dance courses or took part in dance teams to practice dance skills, including waltz, tango, foxtrot, quickstep, and Latin. Students who participated in dance courses attended courses once a week, while members of dance teams practiced dance four times a week. There were also many students who did not attend any dance courses. According to our survey, 11.65% (105/901) were members of college sports dance teams, 21.09% (190/901)
Table 3 Comparison of Characteristics Between Different Sports Dance Groups in College Students
| Characteristics | Frequent Dance Students* (n=105) | Participants in College Sports Dance Course (n=190) | Ordinary College Students (n=606) | P |
|---------------------------|---------------------------------|----------------------------------------------------|----------------------------------|-------|
| Gender | | | | <0.01 |
| Female | 65.71% (69/105) | 66.84% (127/190) | 51.49% (312/606) | |
| Male | 34.29% (36/105) | 33.16% (63/190) | 48.51% (294/606) | |
| Age (mean, years) | 20.27±3.31 | 19.47±3.16 | 19.23±1.14 | <0.01 |
| College grade level | | | | <0.01 |
| Freshman | 24.76% (26/105) | 47.37% (90/190) | 48.35% (293/606) | |
| Sophomore | 40.00% (42/105) | 44.21% (84/190) | 37.46% (227/606) | |
| Junior | 22.86% (24/105) | 6.32% (12/190) | 13.37% (81/606) | |
| Senior | 11.43% (12/105) | 2.11% (4/190) | 0.33% (2/606) | |
| Delayed graduation | 0.95% (1/105) | 0.00% (0/190) | 0.50% (3/606) | |
| Professional dancer | | | | <0.01 |
| Yes | 16.19% (17/105) | 8.95% (17/190) | 2.81% (17/606) | |
| No | 83.81% (88/105) | 91.05% (173/190) | 97.19% (589/606) | |
| Physical education student| | | | <0.01 |
| Yes | 19.05% (20/105) | 9.47% (18/190) | 32.51% (197/606) | |
| No | 80.95% (85/105) | 90.53% (172/190) | 67.49% (409/606) | |
| BMI (kg/m²) | | | | <0.01 |
| <18.5 | 23.81% (25/105) | 29.47% (56/190) | 14.19% (86/606) | |
| 18.5–24 | 57.14% (60/105) | 54.21% (103/190) | 58.25% (353/606) | |
| 24–28 | 5.71% (6/105) | 7.37% (14/190) | 10.40% (63/606) | |
| ≥28 | 13.33% (14/105) | 8.95% (17/190) | 17.16% (104/606) | |
| Scholarship winner | | | | |
| Yes | 35.24% (37/105) | 22.11% (42/190) | 23.10% (140/606) | 0.02 |
| No | 64.76% (68/105) | 77.89% (148/190) | 76.90% (466/606) | |
| Scholarship level | | | | <0.01 |
| First class | 13.33% (14/105) | 4.21% (8/190) | 5.45% (33/606) | |
| Second class | 16.19% (17/105) | 7.89% (15/190) | 8.42% (51/606) | |
| Third class | 5.71% (6/105) | 10.00% (19/190) | 9.24% (56/606) | |
| No | 64.76% (68/105) | 77.89% (148/190) | 76.90% (466/606) | |
| Sedentary time per day (hours) | | | | |
| <1 | 22.86% (24/105) | 20.53% (39/190) | 20.79% (126/606) | 0.45 |
| 1–3 | 34.29% (36/105) | 27.89% (53/190) | 36.14% (219/606) | |
| 3–6 | 32.38% (34/105) | 38.95% (74/190) | 31.52% (191/606) | |
| ≥6 | 10.48% (11/105) | 12.63% (24/190) | 11.55% (70/606) | |
| Exercise frequency per week | | | | |
| 0 | 3.81% (4/105) | 3.16% (6/190) | 7.43% (45/606) | 0.02 |
| 1–2 | 37.14% (39/105) | 52.11% (99/190) | 43.23% (262/606) | |
| 3–4 | 35.24% (37/105) | 28.95% (55/190) | 26.24% (159/606) | |
| ≥5 | 23.81% (25/105) | 15.79% (30/190) | 23.10% (140/606) | |
(Continued)
Table 3 (Continued).
| Characteristics | Frequent Dance Students* (n=105) | Participants in College Sports Dance Course (n=190) | Ordinary College Students (n=606) | P |
|-------------------------------------|----------------------------------|-----------------------------------------------|---------------------------------|-------|
| Study period during free time (hours)| | | | <0.01 |
| 0 | 1.90% (2/105) | 1.58% (3/190) | 1.49% (9/606) | |
| <1 | 13.33% (14/105) | 18.95% (36/190) | 27.06% (164/606) | |
| 1–2 | 43.81% (46/105) | 35.79% (68/190) | 40.10% (243/606) | |
| 2–3 | 20.00% (21/105) | 21.58% (41/190) | 18.15% (110/606) | |
| ≥3 | 20.95% (22/105) | 22.11% (42/190) | 13.20% (80/606) | |
| Only-child status | | | | 0.13 |
| Yes | 44.76% (47/105) | 46.32% (88/190) | 38.78% (235/606) | |
| No | 55.24% (58/105) | 53.68% (102/190) | 61.22% (371/606) | |
| Educational background of father | | | | <0.01 |
| Primary school | 10.48% (11/105) | 15.26% (29/190) | 23.10% (140/606) | |
| Junior or high school | 56.19% (59/105) | 54.74% (104/190) | 56.93% (345/606) | |
| University | 30.48% (32/105) | 26.84% (51/190) | 18.81% (114/606) | |
| Graduate | 2.86% (3/105) | 3.16% (6/190) | 1.16% (7/606) | |
| Educational background of mother | | | | <0.01 |
| Primary school | 19.05% (20/105) | 25.26% (48/190) | 33.99% (206/606) | |
| Junior or high school | 56.19% (59/105) | 47.89% (91/190) | 50.66% (307/606) | |
| University | 21.90% (23/105) | 24.74% (47/190) | 14.52% (88/606) | |
| Graduate | 2.86% (3/105) | 2.11% (4/190) | 0.83% (5/606) | |
| Hypertension | | | | 0.23 |
| Yes | 0.95% (1/105) | 0.00% (0/190) | 1.49% (9/606) | |
| No | 99.05% (104/105) | 100.00% (190/190) | 98.51% (597/606) | |
| Diabetes | | | | 0.61 |
| Yes | 0.00% (0/105) | 0.00% (0/190) | 0.33% (2/606) | |
| No | 100.00% (105/105) | 100.00% (190/190) | 99.67% (604/606) | |
| Addiction to smoking | | | | 0.26 |
| Yes | 3.81% (4/105) | 2.11% (4/190) | 4.79% (29/606) | |
| No | 96.19% (101/105) | 97.89% (186/190) | 95.21% (577/606) | |
| Addiction to drinking | | | | 0.64 |
| Yes | 3.81% (4/105) | 2.63% (5/190) | 4.13% (25/606) | |
| No | 96.19% (101/105) | 97.37% (185/190) | 95.87% (581/606) | |
| Preference for eating red meat | | | | 0.34 |
| Yes | 84.76% (89/105) | 81.05% (154/190) | 85.48% (518/606) | |
| No | 15.24% (16/105) | 18.95% (36/190) | 14.52% (88/606) | |
| Preference for eating vegetables | | | | 0.15 |
| Yes | 80.95% (85/105) | 86.84% (165/190) | 80.69% (489/606) | |
| No | 19.05% (20/105) | 13.16% (25/190) | 19.31% (117/606) | |
| Preference for eating fruits | | | | <0.01 |
| Yes | 81.90% (86/105) | 81.05% (154/190) | 69.80% (423/606) | |
| No | 18.10% (19/105) | 18.95% (36/190) | 30.20% (183/606) | |
| Preference for eating barbecued food| | | | 0.41 |
| Yes | 34.29% (36/105) | 38.42% (73/190) | 33.17% (201/606) | |
| No | 65.71% (69/105) | 61.58% (117/190) | 66.83% (405/606) | |
were participants in college sports dance courses, and 67.26% (606/901) ordinary college students did not attend any dance courses.
Furthermore, this study also found that higher college grade levels, addiction to drinking, preference for eating fried food, main source of drinking water (soda), and previous diagnosis of anxiety or depression were independent risk factors for depression, while higher exercise frequency per week, only-child status, and preference for eating vegetables were independent protective factors for depression. In other studies, some personal factors or detrimental behaviors, including Arab ethnicity,23 female gender,23,24 poor relationship with peers,23 higher year of study,23 poor academic performance,23 poor diet,25 lack of sports,25 sleep problems,25,26 alcohol abuse,27 non-compliance with doctor’s prescription,25 and maladaptive coping behavior,28 were found to be associated with depression. The above-mentioned studies enrolled a variety of populations, including medical students,23 adolescents,24 healthy people,25 second-year college students,26 first-year female college students,27 and Dutch service members.28 Our study supplemented the current and available literature. The results of our study may shed further light on strategies for preventing or alleviating depression, such as
Table 3 (Continued).
| Characteristics | Frequent Dance Students* (n=105) | Participants in College Sports Dance Course (n=190) | Ordinary College Students (n=606) | P |
|----------------------------------------|---------------------------------|----------------------------------------------------|---------------------------------|-----|
| Preference for eating fried food | | | | |
| Yes | 34.29% (36/105) | 34.74% (66/190) | 32.51% (197/606) | 0.82|
| No | 65.71% (69/105) | 65.26% (124/190) | 67.49% (409/606) | |
| Main source of drinking water | | | | |
| Purified water | 90.48% (95/105) | 87.37% (166/190) | 90.26% (547/606) | 0.90|
| Tea | 4.76% (5/105) | 6.84% (13/190) | 5.28% (32/606) | |
| Coffee | 0.95% (1/105) | 0.53% (1/190) | 0.33% (2/606) | |
| Soda | 3.81% (4/105) | 5.26% (10/190) | 4.13% (25/606) | |
| Monthly expenses (RMB) | | | | |
| <1000 | 7.62% (8/105) | 12.11% (23/190) | 13.20% (80/606) | 0.21|
| 1000–2000 | 73.33% (77/105) | 71.58% (136/190) | 75.25% (456/606) | |
| 2000–4000 | 17.14% (18/105) | 13.68% (26/190) | 9.74% (59/606) | |
| ≥4000 | 1.90% (2/105) | 2.63% (5/190) | 1.82% (11/606) | |
| Marital status | | | | |
| Single | 76.19% (80/105) | 81.58% (155/190) | 78.22% (474/606) | 0.45|
| Dating | 22.86% (24/105) | 16.84% (32/190) | 21.12% (128/606) | |
| Married | 0.95% (1/105) | 1.05% (2/190) | 0.17% (1/606) | |
| Fertilized | 0.00% (0/105) | 0.53% (1/190) | 0.50% (3/606) | |
| Previous diagnosis of anxiety or depression in hospital | | | | |
| Yes | 1.90% (2/105) | 4.21% (8/190) | 1.65% (10/606) | 0.11|
| No | 98.10% (103/105) | 95.79% (182/190) | 98.35% (596/606) | |
| Anxiety or depression history of immediate family members | | | | |
| Yes | 2.86% (3/105) | 1.58% (3/190) | 1.98% (12/606) | 0.75|
| No | 97.14% (102/105) | 98.42% (187/190) | 98.02% (594/606) | |
| Anxiety (GAD-7) (mean) | 3.92 | 4.50 | 4.37 | 0.32|
| Depression (PHQ-9) (mean) | 4.40 | 5.83 | 5.57 | 0.06|
Notes: *Frequent sports dance students were members of college sports dance team, and non-frequent sports dance students included two groups: participants in college sports dance course and ordinary college students.
Abbreviations: BMI, body mass index; RMB, Renminbi (%); GAD, Generalized Anxiety Disorder; PHQ, Patient Health Questionnaire.
Table 4: Simple and Multiple Logistic Regression Analysis of Characteristics for Anxiety in University Students in China
| Characteristics | Simple Logistic Regression | Multiple Logistic Regression |
|--------------------------------------|---------------------------|-----------------------------|
| | OR (95% CI) | P | OR (95% CI) | P |
| Gender | 1.42 (1.10–1.84) | <0.01 | NS | |
| Age (years) | 1.09 (1.03–1.16) | <0.01 | NS | |
| College grade level | 1.42 (1.21–1.67) | <0.01 | 1.43 (1.21–1.68) | <0.01 |
| Professional dancer | 0.66 (0.37–1.18) | 0.16 | NS | |
| Member of college sports dance team | 0.91 (0.61–1.35) | 0.63 | NS | |
| Physical education student | 0.56 (0.42–0.76) | <0.01 | 0.66 (0.46–0.94) | 0.02 |
| Participant in college sports dance course | 1.05 (0.80–1.39) | 0.71 | NS | |
| BMI (kg/m²) | 1.12 (0.98–1.29) | 0.10 | 1.18 (1.02–1.36) | 0.02 |
| Scholarship winner | 1.16 (0.86–1.56) | 0.33 | NS | |
| Scholarship level | 1.04 (0.91–1.18) | 0.59 | NS | |
| Sedentary time per day (hours) | 1.19 (1.04–1.36) | 0.01 | NS | |
| Exercise frequency per week | 0.71 (0.61–0.82) | <0.01 | 0.78 (0.66–0.93) | <0.01 |
| Study period during free time (hours)| 1.00 (0.89–1.13) | 0.98 | NS | |
| Only-child status | 0.83 (0.64–1.07) | 0.15 | NS | |
| Educational background of father | 1.08 (0.90–1.30) | 0.40 | NS | |
| Educational background of mother | 0.92 (0.77–1.10) | 0.36 | NS | |
| Hypertension | 1.75 (0.54–5.65) | 0.35 | NS | |
| Diabetes | 1.0 (0.07–14.93) | 1.00 | NS | |
| Addiction to smoking | 1.51 (0.81–2.82) | 0.20 | NS | |
| Addiction to drinking | 2.46 (1.30–4.68) | <0.01 | 2.19 (1.14–4.21) | 0.02 |
| Preference for eating red meat | 0.96 (0.68–1.37) | 0.83 | NS | |
| Preference for eating vegetables | 0.71 (0.51–0.98) | 0.04 | NS | |
| Preference for eating fruits | 1.10 (0.82–1.46) | 0.54 | NS | |
| Preference for eating barbecued food | 1.26 (0.97–1.65) | 0.08 | NS | |
| Preference for eating fried food | 1.23 (0.94–1.61) | 0.14 | NS | |
| Main source of drinking water | 1.18 (0.98–1.43) | 0.08 | NS | |
| Monthly expenses (RMB) | 1.12 (0.90–1.41) | 0.31 | NS | |
| Marital status | 1.15 (0.87–1.51) | 0.33 | NS | |
| Previous diagnosis of anxiety or depression in hospital | 4.15 (1.82–9.47) | <0.01 | 3.58 (1.56–8.24) | <0.01 |
| Anxiety or depression history of immediate family members | 1.35 (0.56–3.29) | 0.51 | NS | |
Abbreviations: BMI, body mass index; RMB, Renminbi (¥); OR, odds ratio; CI, confidence interval; NS, not significant.
| Characteristics | Simple Logistic Regression | Multiple Logistic Regression |
|---------------------------------------------|----------------------------|------------------------------|
| | OR (95% CI) | P | OR (95% CI) | P |
| Gender | 1.20 (0.93–1.54) | 0.16 | NS |
| Age (years) | 1.08 (1.02–1.14) | 0.01 | NS |
| College grade level | 1.33 (1.14–1.56) | <0.01 | 1.35 (1.15–1.59) | <0.01 |
| Professional dancer | 0.61 (0.35–1.08) | 0.09 | NS |
| Member of college sports dance team | 0.65 (0.44–0.98) | 0.04 | 0.55 (0.36–0.84) | <0.01 |
| Physical education student | 0.64 (0.48–0.86) | 0.003 | NS |
| Participant in college sports dance course | 0.99 (0.76–1.30) | 0.97 | NS |
| BMI | 1.14 (0.99–1.30) | 0.06 | NS |
| Scholarship winner | 1.06 (0.79–1.41) | 0.69 | NS |
| Scholarship level | 0.99 (0.87–1.12) | 0.88 | NS |
| Sedentary time per day (hours) | 1.13 (0.99–1.29) | 0.06 | NS |
| Exercise frequency per week | 0.72 (0.63–0.84) | <0.01 | 0.75 (0.65–0.87) | <0.01 |
| Study period during free time (hours) | 0.92 (0.81–1.04) | 0.16 | NS |
| Only-child status | 0.72 (0.56–0.93) | 0.01 | 0.68 (0.52–0.88) | <0.01 |
| Educational background of father | 0.96 (0.80–1.15) | 0.66 | NS |
| Educational background of mother | 0.87 (0.73–1.04) | 0.12 | NS |
| Hypertension | 1.77 (0.56–5.61) | 0.33 | NS |
| Diabetes | 0.76 (0.05–11.35) | 0.84 | NS |
| Addiction to smoking | 1.79 (0.97–3.28) | 0.06 | NS |
| Addiction to drinking | 3.67 (1.95–6.90) | <0.01 | 2.59 (1.35–5.00) | <0.01 |
| Preference for eating red meat | 0.91 (0.65–1.28) | 0.59 | NS |
| Preference for eating vegetables | 0.55 (0.40–0.76) | <0.01 | 0.68 (0.49–0.95) | 0.02 |
| Preference for eating fruits | 1.01 (0.76–1.34) | 0.95 | NS |
| Preference for eating barbecued food | 1.44 (1.11–1.87) | 0.006 | NS |
| Preference for eating fried food | 1.49 (1.15–1.94) | 0.003 | 1.39 (1.06–1.83) | 0.02 |
| Main source of drinking water | 1.43 (1.19–1.72) | <0.01 | 1.28 (1.05–1.55) | 0.01 |
| Monthly expenses (RMB) | 1.02 (0.82–1.28) | 0.83 | NS |
| Marital status | 1.16 (0.89–1.51) | 0.29 | NS |
| Previous diagnosis of anxiety or depression in hospital | 2.73 (1.21–6.15) | 0.02 | 2.54 (1.11–5.81) | 0.03 |
| Anxiety or depression history of immediate family members | 1.67 (0.70–3.96) | 0.25 | NS |
**Abbreviations:** BMI, body mass index; RMB, Renminbi (¥); OR, odds ratio; CI, confidence interval; NS, not significant.
ROC Curves for Comparisons
**Figure 1** ROC curves for significant factors associated with anxiety. Of the significant factors, x3 indicates college grade levels, x6 indicates physical education student, x8 indicates body mass index, x12 indicates exercise frequency per week, x20 indicates addiction to drinking, and x29 indicates previous diagnosis of anxiety or depression in hospital.
Abstinence from drinking, healthy diet (eating less fried food, drinking less soda, and eating more vegetables), exercising more frequently, and appropriate treatment of previous anxiety or depression. Regarding risk factors for anxiety, we found that higher college grade levels, higher BMI values, addiction to drinking, and previous diagnosis of anxiety or depression were independent risk factors for anxiety, while being a physical education student and higher exercise frequency per week were independent protective factors for anxiety. Accordingly, management of weight, stopping drinking, treatment of previous anxiety or depression, and exercising more frequently may facilitate the prevention and treatment of anxiety among college students. Other studies also pointed out that female gender, poor body image, year of study, and poor academic performance were associated with increased anxiety symptoms. The current study found that the demands for preventing and intervening in mental disorders were high in college students. Overall, 9.98% students had moderate-to-severe anxiety and 14.65% students suffered from moderate-to-severe depression, according to our survey. Therefore, there is an urgent need to make necessary strategies available to help college students to prevent and handle anxiety and depression, such as participating in sports dance teams, having a healthy diet, exercising more frequently, management of weight, and appropriate treatment of previous anxiety or depression. In this study, we concluded that frequent dance positively alleviated the depression levels in university students. The reasons behind this may be that frequent sports dancers had more chance to be exposed to the active environment during dance practice, and physical well-being obtained from the exercise may also improve mental health.
However, this study has some limitations. First, since this is a study based on a survey, the evidence level of the study was not superior to the grade in clinical trials, as the clinical trials usually have a clinical evidence level of IV. Self-reported data was also a limitation in the study since participants may not be able to recall some essential information. Nonetheless, our study was the first to analyze the effect of dance on mental disorders using real-world data. Second, the reliability and validity of the data were not evaluated. However, we used standardized scales to evaluate the anxiety and depression status. Still, a large sample was needed for the investigation.
In conclusion, anxiety and depression are common among college students. Frequent sports dance may serve as a protective factor for preventing depression. Besides, lower college grade levels, being a physical education student, lower BMI, higher exercise frequency per week, only-child status, and preference for eating vegetables were independent protective factors for mental disorders. Conversely, addiction to drinking, preference for eating fried food, soda water served as the main drinking water,
| Models | ROC values | CCR | Sensitivity | Specificity | False-Positive Rate | False-Negative Rate | Goodness-of-Fit Test |
|----------|------------|------|-------------|-------------|---------------------|---------------------|----------------------|
| Anxiety | 0.77 | 94.5%| 28.0% | 96.3% | 82.1% | 2.1% | 0.99 |
| Depression | 0.75 | 88.0%| 13.2% | 92.7% | 89.9% | 5.5% | 0.62 |
**Table 6** Evaluation of Models Including All Significant Characteristics
**Abbreviations:** ROC, receiver operating characteristics; CCR, correct classification rate.
Figure 2 ROC curves for significant factors associated with depression. Of the significant factors, x3 indicates college grade levels, x5 indicates member of college sports dance team, x12 indicates exercise frequency per week, x14 indicates only-child status, x20 indicates addiction to drinking, x22 indicates preference for eating vegetables, x25 indicates preference for eating fried food, x26 indicates main source of drinking water, and x29 indicates previous diagnosis of anxiety or depression in hospital.
and previous diagnosis of anxiety or depression were independent risk factor for mental disorders.
Funding
This study was funded by the Fujian young teacher education research project (no. JAS170328).
Disclosure
The authors declare that they have no conflicts of interest.
References
1. Auerbach RP, Alonso J, Axinn WG, et al. Mental disorders among college students in the World Health Organization World Mental Health Surveys. Psychol Med. 2016;46(14):2955–2970. doi:10.1017/S0033291716001165
2. Beiter R, Nash R, McCrady M, et al. The prevalence and correlates of depression, anxiety, and stress in a sample of college students. J Affect Disord. 2015;173:90–96. doi:10.1016/j.jad.2014.10.054
3. Fortney JC, Curran GM, Hunt JB, et al. Prevalence of probable mental disorders and help-seeking behaviors among veteran and non-veteran community college students. Gen Hosp Psychiatry. 2016;38:99–104. doi:10.1016/j.genhosppsych.2015.09.007
4. Ghrouz AK, Noohu MM, Dihshad Manzar M, Warren Spence D, BaHammam AS, Pandi-Perumal SR. Physical activity and sleep quality in relation to mental health among college students. Sleep Breath. 2019;23(2):627–634. doi:10.1007/s11325-019-01780-z
5. Oswalt SB, Lederer AM, Chestnut-Stiech K, Day C, Halbritter A, Ortiz D. Trends in college students’ mental health diagnoses and utilization of services, 2009–2015. J Am Coll Health. 2020;68(1):41–51. doi:10.1080/07448481.2018.1515748
6. Eisenberg D, Gollust SE, Golberstein E, Hefner JL. Prevalence and correlates of depression, anxiety, and suicidality among university students. Am J Orthopsychiatry. 2007;77(4):534–542. doi:10.1037/0002-9432.77.4.534
7. Lew B, Huen J, Yu P, et al. Associations between depression, anxiety, stress, hopelessness, subjective well-being, coping styles and suicide in Chinese university students. PLoS One. 2019;14(7):e0217372. doi:10.1371/journal.pone.0217372
8. Fong Yan A, Cobley S, Chan C, et al. The effectiveness of dance interventions on physical health outcomes compared to other forms of physical activity: a systematic Review and meta-analysis. Sports Med. 2018;48(4):933–951. doi:10.1007/s40279-017-0853-5
9. Wang Z, An G, Zhang W, Yang G. The effect of jazz dance on physical and mental health of students with different physical fitness. J Sports Med Phys Fitness. 2019;59(5):880–885. doi:10.23736/ S0022-4707.18.08025-8
10. Guo S, Liu F, Shen J, Wei M, Yang Y. Comparative efficacy of seven exercise interventions for symptoms of depression in college students: a network meta-analysis. Medicine (Baltimore). 2020;99(47):e23058. doi:10.1097/MD.0000000000023058
11. Allet L, Muller-Pingeot S, Punt I, et al. Dance therapy combined with patient education improves quality of life of persons with obesity: a pilot feasibility study for a randomised controlled trial. Obes Res Clin Pract. 2017;11(1):79–87. doi:10.1016/j.orcp.2016.03.005
12. Conceicao LS, Neto MG, Do Amaral MA, Martins-Filho PR, Oliveira Carvalho V. Effect of dance therapy on blood pressure and exercise capacity of individuals with hypertension: a systematic review and meta-analysis. Int J Cardiol. 2016;220:553–557. doi:10.1016/j.ijcard.2016.06.182
13. Filar-Mierzwka K, Dlugosz M, Marchewka A, Dabrowski Z, Poznanska A. The effect of dance therapy on the balance of women over 60 years of age: the influence of dance therapy for the elderly. J Women Aging. 2017;29(4):348–355. doi:10.1080/08952841.2016.1194689
14. de Natale ER, Paulus KS, Aiello E, et al. Dance therapy improves motor and cognitive functions in patients with Parkinson’s disease. NeuroRehabilitation. 2017;40(1):141–144. doi:10.3233/NRE-161399
15. Koch SC, Riege RFF, Tisborn K, Biondo J, Martin L, Beelmann A. Effects of dance movement therapy and dance on health-related psychological outcomes. A meta-analysis update. Front Psychol. 2019;10:1806. doi:10.3389/fpsyg.2019.01806
16. Mansfield L, Kay T, Meads C, et al. Sport and dance interventions for healthy young people (15–24 years) to promote subjective well-being: a systematic review. BJM Open. 2018;8(7):e020959. doi:10.1136/bmjopen-2017-020959
17. Hsieh FY. Sample size tables for logistic regression. Stat Med. 1989;8(7):795–802. doi:10.1002/sim.4780080704
18. Borghero F, Martinez V, Zitko P, Vohringer PA, Cavada G, Rojas G. Screening depressive episodes in adolescents. Validation of the Patient Health Questionnaire-9 (PHQ-9). Rev Med Chil. 2018;146(4):479–486. Spanish. doi:10.4067/s0034-98722018000400479
19. Lowe B, Decker O, Muller S, et al. Validation and standardization of the Generalized Anxiety Disorder Screener (GAD-7) in the general population. Med Care. 2008;46(3):266–274. doi:10.1097/MLR.0b013e318160d093
20. Bartolo A, Monteiro S, Pereira A. Factor structure and construct validity of the Generalized Anxiety Disorder 7-item (GAD-7) among Portuguese college students. Cad Saude Publica. 2017;33(9):e00212716. doi:10.1590/0102-311x00212716
21. Akandere M, Demir B. The effect of dance over depression. Coll Antropol. 2019;43(1):31–40. doi:10.1007/s40596-017-0733-1
22. Hellem T, Sung YH, Ferguson H, Hildreth L. The emotional dance with depression: a longitudinal investigation of OULA(R) for depression in women. J Bodyw Mov Ther. 2020;24(4):413–422. doi:10.1016/j.jbmt.2020.05.007
23. Mahroon ZA, Borgan SM, Kamel C, Maddison W, Royston M, Donnellan C. Factors associated with depression and anxiety symptoms among medical students in Bahrain. Acad Psychiatry. 2018;42(1):31–40. doi:10.1007/s40596-017-0733-1
24. Crockett MA, Martinez V, Jimenez-Molina A. Subthreshold depression in adolescence: gender differences in prevalence, clinical features, and associated factors. J Affect Disord. 2020;272:269–276. doi:10.1016/j.jad.2020.03.111
25. Doom JR, Haefeli GJ. Teasing apart the effects of cognition, stress, and depression on health. Am J Health Behav. 2013;37(5):610–619. doi:10.5993/AJHB.37.5.4
26. Wallace DD, Boynton MH, Lytle LA. Multilevel analysis exploring the links between stress, depression, and sleep problems among two-year college students. J Am Coll Health. 2017;65(3):187–196. doi:10.1080/07448481.2016.1269111
27. Rosenthal SR, Clark MA, Marshall BDL, et al. Alcohol consequences, not quantity, predict major depression onset among first-year female college students. Addict Behav. 2018;85:70–76. doi:10.1016/j.addbeh.2018.05.021
28. de Kruijf LGM, Moussault ORM, Plat MJ, Hoencamp R, van der Wurff P. Coping strategies of Dutch servicemembers after deployment. Mil Med Res. 2019;6(1):9. doi:10.1186/s40779-019-0199-4
29. Gao W, Ping S, Liu X. Gender differences in depression, anxiety, and stress among college students: a longitudinal study from China. J Affect Disord. 2020;263:292–300. doi:10.1016/j.jad.2019.11.121 | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3451,
1
],
[
3451,
8463,
2
],
[
8463,
13383,
3
],
[
13383,
17960,
4
],
[
17960,
22056,
5
],
[
22056,
25402,
6
],
[
25402,
26402,
7
],
[
26402,
31227,
8
],
[
31227,
37117,
9
],
[
37117,
42879,
10
],
[
42879,
49501,
11
],
[
49501,
56926,
12
],
[
56926,
63390,
13
],
[
63390,
66669,
14
],
[
66669,
71602,
15
],
[
71602,
75751,
16
],
[
75751,
80710,
17
],
[
80710,
82969,
18
]
]
} |
3e7f8756ea1d3be195d258b1deccc9c761bcc3eb | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 23,
"total-fallback-pages": 0,
"total-input-tokens": 70998,
"total-output-tokens": 24868,
"fieldofstudy": [
"Biology"
]
} | Sleep Loss Causes Dysfunction in Murine Extraorbital Lacrimal Glands
Shenzhen Huang, Hongli Si, Jiangman Liu, Di Qi, Xiaoting Pei, Dingli Lu, Sen Zou, and Zhijie Li
Henan Eye Institute, Henan Eye Hospital, Henan Provincial People’s Hospital, People’s Hospital of Henan University, People’s Hospital of Zhengzhou University, Zhengzhou, China
Correspondence: Zhijie Li, Henan Eye Institute, Henan Provincial People’s Hospital, Zhengzhou 450003, China; [email protected], [email protected].
Received: February 3, 2022
Accepted: May 31, 2022
Published: June 22, 2022
Citation: Huang S, Si H, Liu J, et al. Sleep loss causes dysfunction in murine extraorbital lacrimal glands. Invest Ophthalmol Vis Sci. 2022;63(6):19. https://doi.org/10.1167/iovs.63.6.19
Purpose. Sleep loss markedly affects the structure and function of the lacrimal gland and may cause ocular surface disease as a common public health problem. This study aims to investigate the circadian disturbance caused by sleep loss leading to dysfunction of extraorbital lacrimal glands (ELGs).
Methods. A mouse sleep deprivation (SD) model for sleep loss studies was built in C57BL/6J male mice. After four weeks, the ELGs were collected at three-hour intervals during a 24-hour period. The Jonckheere-Terpstra-Kendall algorithm was used to determine the composition, phase, and rhythmicity of transcriptomic profiles in ELGs. Furthermore, we compared the non-sleep-deprived and SD-treated mouse ELG (i) reactive oxygen species (ROS) by fluorescein staining, (ii) DNA damage by immunostaining for γ-H2Ax, and (iii) circadian migration of immune cells by immunostaining for CD4, CD8, γδ-TCR, CD64, and CX3CR1. Finally, we also evaluated (i) the locomotor activity and core body temperature rhythm of mice and (ii) the mass, cell size, and tear secretion of the ELGs.
Results. SD dramatically altered the composition and phase-associated functional enrichment of the circadian transcriptome, immune cell trafficking, metabolism, cell differentiation, and neural secretory activities of mouse ELGs. Additionally, SD caused the ROS accumulation and consequent DNA damage in the ELGs, and the ELG dysfunction caused by SD was irreversible.
Conclusions. SD damages the structure, function, and diurnal oscillations of ELGs. These results highlight comprehensive characterization of insufficient sleep–affected ELG circadian transcriptome that may provide a new therapeutic approach to counteract the effects of SD on ELG function.
Keywords: sleep loss, circadian transcriptome, reactive oxygen species, extraorbital lacrimal glands
Sufficient sleep is an indispensable part of human life to maintain good health. In modern society, sleep deprivation (SD) and its complications caused by various factors have become a growing public health problem. Chronic SD of less than seven hours per day is associated with a variety of diseases such as obesity, diabetes, hypertension, heart disease, and stroke. Sleep deficiency also increases the risk of ocular diseases, such as macular degeneration and glaucoma. The latest studies on the influence of SD on lacrimal gland secretion show that poor sleep in human and experimental animal models is accompanied by reduced lacrimal gland secretion of varying degrees, changes in the structure of the lacrimal glands, and the occurrence of dry eye disease. Although these expand our understanding of the association between sleep quality and lacrimal gland function, little known is known about the mechanisms by which disruptions in the sleep-wake cycle affect the physiological rhythms of the lacrimal gland. Because of the daily cycles of light on earth, mammals have evolved a robust rhythm in the physiological functions of their organs and tissues. In a steady state, this rhythm is mainly regulated by the retino-hypothalamic tract. As a circadian pacemaker, the suprachiasmatic nuclei (SCN), a tiny region in the hypothalamus of the brain, sets the timing of rhythms of various peripheral organs by regulating neuronal activity, body temperature, and hormonal signals and then completes its daily physiological functions through the coordination mechanism of these organs. The lacrimal glands maintain the health of the ocular surface by secreting an aqueous layer in the tear film of the eye together with many important chemicals, peptides, and proteins to lubricate and protect the ocular surface. Similar to other glands, its secretion process is closely controlled by the body’s circadian rhythm, including tear volume, physical properties, and chemical composition. Any factor that interferes with the circadian rhythm of the extraorbital lacrimal glands (ELGs), such as jet lag, hyperglycemia,
high fructose intake,33 and aging,34 can affect its normal physiological function. In severe cases, it may even cause dry eye disease.16 Normally, sleep occurs in synchrony with endogenous circadian rhythms.35,36 Disruptions of the circadian rhythm influence the sleep-wake cycle, whereas interrupting the sleep-wake cycle also affects endogenous circadian rhythms. Several studies have shown that mistimed sleep has a profound effect on the rhythm of gene expression in central and peripheral tissues.37,38 For example, sleep restriction reduces the transcription of circadian clock genes in the brain by about 80% and severely affects the transcriptome of the mouse liver.38 Insufficient sleep reduces circadian clock gene transcription in the human blood from 8.8% to 6.9%.39 As mentioned earlier, ELGs have a robust circadian rhythm as well25,31,32. Accumulated evidence shows sleep disturbance can cause different degrees of damage to the structure and function of ELGs dependent on the time and degree of disturbance.16 For example, lack of sleep quickly leads to increase of tear film osmotic pressure, shortened tear film breakup time, and decreased tear secretion.33,34 This may lead to dry eye disease in healthy people.33,16,40 Despite these, the mechanisms behind the sleep-wake cycle interference that reshapes the circadian rhythm of ELGs have not been directly explored.
Circadian rhythms are relevant to almost all physiological functions in mammals.31 Circadian rhythm disturbance causes disruptions in body functions through complex mechanisms and increases the risk of certain diseases.21,42 Substantial evidence suggests that normal circadian rhythms are closely linked to the oxidative stress–antioxidant defense system.43,44 When normal circadian rhythms are disturbed (either genetically45 or environmentally altered46–48), this results in the accumulation of reactive species induced by oxidative stress, which severely interferes with normal immune,49 metabolic,50 and neuroendocrine functions.49 A recent study confirmed that reduced sleep duration can cause accumulation of reactive oxygen species (ROS) in the gut and increase the incidence of death.31 Importantly, a recent study has shown that ROS accumulation is involved in various pathological changes in the lacrimal gland and its physiological secretion of tears.32 Given the damaging potential of ROS, it is valuable to explore the reversible or irreversible consequences of SD-induced lacrimal gland dysfunction by evaluating ROS levels and tear secretion.
To address this question, we sought to verify two complementary hypotheses by using an SD mouse model: (1) whether SD impairs the ELG function by accumulating ROS and disrupting the metabolic, immune, and neural functions; and (2) whether SD-induced ELG dysfunction is reversible or irreversible impairments. This study highlights the interplay between sleep, circadian rhythm, and lacrimal gland secretory function and provides a new perspective for understanding how SD impairs the physiological function of lacrimal gland that may trigger ocular surface disease.
**Materials and Methods**
**Overall Experimental and Analysis Workflow**
As depicted in Supplementary Figure S1, we present an overall experimental and analysis workflow of ELGs for sleep-deprived (SD) and non-sleep-deprived (non-SD) C57BL/6J mice. In this experimental model, we focus on the effect of SD on C57BL/6J mice by using phenotype profiling and transcriptional profiling. The phenotype profiling includes mouse habits (locomotor activity, core body temperature, body weight, water intake, and pellet intake) and basic physiological characteristics of ELGs (secretion, mass, cell size, and immune cell trafficking) for the SD-treated and non-SD-treated C57BL/6J mice (Supplementary Figs. S1A, S1B, S1D). At the end of the experiment, we collected the mouse ELGs every three hours according to the zeitgeber time (ZT) and used high-throughput RNA sequencing (RNA-Seq) to obtain the diurnal transcriptome data of the ELGs in an LD cycle (Supplementary Figs. S1A–C). To discover the pattern behind the massive transcriptome data, we used the Jonckheere-Terpstra-Kendall (JTK) cycling algorithm to analyze the changes in circadian rhythm genes of mouse ELGs between the SD-treated and non-SD-treated C57BL/6J mice. Further transcriptional profiling was performed, which includes Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway analysis, function interaction networks, time series clustering analysis, and functional annotation with phase set enhanced analysis (PSEA) (Supplementary Fig. S1E). The four-week treatment of mice under normal conditions after four weeks of SD (Supplementary Fig. S1F) was also performed by us. Locomotor activity, core body temperature, body weight, tear secretion, ELG mass, and ROS were collected (Supplementary Figs. S1G, S1H).
**Animals and SD Protocol**
All animal experiments were implemented in compliance with the guideline set by the ARVO Statement for the Use of Animals in Ophthalmic and Vision Research, and were approved by the Henan Province People’s Hospital Institutional Animal Care and Use Committee. Wild-type C57BL/6J male mice (six to eight weeks of age; Nanjing University Model Animal Institute, Nanjing, China) and CX3CR-1GFP mice (six to eight weeks of age; Jackson Laboratory, Bar Harbor, ME, USA) were housed in light-tight circadian chambers and had free access to food and water under an LD cycle (lights on at 07:00 a.m. and lights off at 07:00 p.m.). The mice were housed in SD devices under an LD cycle as previously described.33,35,36 After two weeks of acclimatization, the mice were divided into four groups including the non-SD group, the SD group, a forced-recovery-in-normal-sleep condition (SD-FR-NSC) mouse model for four weeks after the four weeks of SD, and a normal-sleep-condition (SD-NSC) mouse model for four weeks after the four weeks of SD. For the SD group, the sweep bar worked every 1.5 minutes during the light cycle (ZT0–12) for four weeks. For SD-FR-NSC group, the sweep bar worked every 1.5 minutes during the light cycle (ZT0–12) for the first four weeks and sweep bar worked every 1.5 minutes during the dark cycle (ZT12–24) for the last four weeks. For the SD-NSC group, the sweep bar ran every 1.5 minutes during the light cycle (ZT0–12) for the first four weeks, and the sweep bar shut off automatically during the light cycle (ZT0–12) for the last four weeks.
**Behavioral Activity Monitoring and Analysis**
Locomotor activity and core body temperature were monitored by using telemetry system (model ER-4000 E-Mitter; Mini Mitter, Sunriver, OR, USA) as previously described.35–37 After the mouse was anesthetized, the miniature transmitter (ER-4000 E-Mitter) was surgically implanted into the
abdomen of the mouse. The radio-telemetry receiver (ER-4000 receivers) was used to collect telemetry signals to monitor the locomotor activity in five-minute bins and core body temperature in 20-minute bins.
Tear Secretion Measurement
The tear volume secreted by C57BL/6J male mice was assayed as previously reported. Briefly, mice were lightly anesthetized and injected intraorbitally with pilocarpine hydrochloride (4.5 mg/kg in saline solution, HY-B0726; MedChemExpress, Monmouth Junction, NJ, USA). To obtain the tear volume of mice, phenol red thread (Cat. no. 30059010; Tianjin Jingming New Technological Development Co., Ltd., Tianjin, China) in the inner canthus of the eye for 20 seconds was used at ZT0, ZT6, ZT12, and ZT18. The red length of the phenol red thread infiltrated by tear fluid in the non-SD group, the SD group, SD-FR-NSC group, and SD-NSC group was recorded and analyzed.
ELGs Immunohistochemistry and Quantitative Analysis
The bilateral ELGs and intestinal tract, including small intestine and large intestine, of the non-SD group, SD group, SD-FR-NSC group, and SD-NSC group were immediately stored in 4% paraformaldehyde for immunohistochemical investigations. The immunohistochemistry of ELGs was performed as previously reported. Briefly, after dewaxing, antigen retrieval, blocking endogenous peroxidase, and serum blocking, the paraffin sections of the ELGs were incubated with anti-β-catenin antibody (Cat. no. GB11015; Servicebio Company, Wuhan, China), anti-CD4 antibody (Cat. no. 25229s; Cell Signaling Technology, Inc., Danvers, MA, USA), anti-CD8 antibody (Cat. no. 98941s; Cell Signaling Technology, Inc.), anti-Ki67 antibody (Cat. no. GB111141; Servicebio Company, Beijing, China), anti-CD64 antibody (Cat. no. ab140779; Abcam, Cambridge, MA, USA), anti-γδ T antibody (Cat. no. 555178; RD Systems, Minneapolis, MN, USA), anti-γ-H2A.X antibody (Cat. no. 7631T; Cell Signaling Technology, Inc.), anti-nitrotyrosine antibody (Cat. no. MAB3248; RD Systems), and anti-beta III tubulin monoclonal antibody (Cat. no. GB12139; Servicebio Company). Then, ELG sections were placed in PBS (pH 7.4, Cat. no. G0002; Servicebio Company) and washed 3 times for 5 minutes. After ELGs sections were dried slightly, a secondary antibody corresponding to the primary antibody was dropped into the circle to cover the tissue and was incubated at room temperature for 50 minutes. The antibody was dropped into the circle to cover the tissue slightly, a secondary antibody corresponding to the primary antibody was added into sections and incubated for 5 minutes each time. Then DAPI staining solution (Cat. no. G1012; Servicebio Company) was added into sections and incubated for 10 minutes at room temperature in the dark. After the sections were slightly dried, they were mounted with anti-fade mounting medium (Cat. no. G1401; Servicebio Company) and washed three times for 5 minutes each time. Then ImageJ (version 1.42q; National Institutes of Health) was used to examine and image the ELGs, ortho-fluorescent microscopy (NIKON ECLIPSE C1; Nikon Inc., Melville, NY, USA) with slide scanner (NIKON DS-U3; Nikon Inc.) was used, and quantification was performed using ImageJ (version 1.42q; National Institutes of Health).
Tissue Collection, RNA Extraction and RNA-Seq
Euthanasia of animals was implemented by using cervical dislocation to obtain the mouse ELGs. All ELG samples were collected in the same two-week period in July 2020 (n = 3 per sampling time point every three hours). The bilateral ELGs were immediately stored in liquid nitrogen for total RNA extraction by using Trizol reagent (Invitrogen Inc., Carlsbad, CA, USA). According to the Trizol RNA extraction protocol, the total RNA from two ELGs of the same mouse was extracted using the RNAeasy spin column kit (Qiagen, Hilden, Germany) and qualified and quantified using Nano Drop and Agilent 2100 bioanalyzer (Thermo Fisher Scientific, Waltham, MA, USA).
High throughput mRNA sequencing was performed according to our previous reports. Briefly, the extracted mRNA was purified by using oligo(dT)-attached magnetic beads and fragmented into small pieces. The first-strand cDNA and second-strand cDNA were synthesized sequentially by using random hexamer-primed reverse transcription with installed A-Tailing Mix and RNA index adapters to end repair. To get the final library, the splint oligo sequence was adopted to denature and circularize the double-stranded PCR products of cDNA fragments by using PCR amplification. Then, the mRNA library construction was carried out on the BGIsq500 platform (BGI Group, Shenzhen, China). The sequencing data of mRNA library was filtered by using SOAPnuke (version 1.5.2, https://github.com/BGI-flexlab/SOAPnuke). The clean reads were mapped to the reference genome and reference coding gene set by using HISAT2 (version 1.4.2, http://www.ccb.jhu.edu/software/hisat/index.shtml) and Bowtie2 (version 2.2.5, http://bowtiebio.sourceforge.net/%20Bowtie2%20/end-ex.shtml), respectively.
Analysis of Rhythmic Gene Expression
To seek the 24-hour cycling rhythmic genes from ELGs transcriptome of the non-SD group and SD group, we used the JTK_CYCLE algorithm as we previously described. Briefly, the expression genes from ZT0, ZT3, ZT6, ZT9, ZT12, ZT15, ZT18, and ZT21 (n = 3) were imported into the JTK_CYCLE algorithm on R software package. The period, phase, amplitude, and adjusted P value of the ELGs transcriptome were calculated by using JTK_CYCLE. According to our previous research, we defined the rhythm gene with expression ≥0.1 and adjusted P < 0.05, nonrhythmic
genes with expression $\geq 0.1$ and adjusted $P \geq 0.05$, and low-expressed genes with expression $< 0.1$ over the 24-hour period, respectively.
**Functional Annotation With KEGG and PSEA**
To observe changes of phenotype in non-SD group and SD group, functional enrichment analysis with KEGG (https://www.kegg.jp/) of annotated rhythmic genes were performed by Phyper (https://en.wikipedia.org/wiki/Hypergeometric_distribution). The terms and pathways with $Q$ value $< 0.05$ were defined as significant levels. Phase distribution of circadian pathways over the 24-hour period were calculated using the PSEA version 1.1 tool as previously described.\(^62,63\) KEGG gene sets (c2.cp.kegg.v6.2.symbols.gmt) was used and downloaded from the Molecular Signatures Database.\(^64\) Each significant pathway was set as Kuiper $Q < 0.05$.
**Time-Series Clustering Analysis**
To reveal data sets of structures in rhythmic gene expression, the soft clustering tools using the fuzzy c-means algorithm on R software package was adopted.\(^55,66\) The tool is an R package termed Mfuzz and can be found at http://itb1.biologie.hu-berlin.de/~futschik/software/R/ Mfuzz/index.html. In this study, the number of clusters in the non-SD and SD treated rhythmic genes was set as 4 and core threshold was set as 0.7 in the R package.
**Protein-Protein Association Networks**
To disclose the interaction between genes and genes involved in metabolic genes, immune genes, and neural genes, protein-protein association networks (PPANs) functional enrichment analysis was determined using the STRING database (version 11.0, https://string-db.org/).\(^67\) The interaction sources were set as experiments and databases, meaning of network edges were set as confidence, minimum required interaction score was set as highest confidence (0.900), clustering method was set as kmeans clustering, and the number of clusters was set as 4.
**Transcription Factor Enrichment Analysis**
To predict which transcription factors (TFs) regulated genes associated with ROS, immunity, metabolism, cell differentiation, and neural activity, we used the ChIP-X Enrichment Analysis 3 (ChEA3) tool.\(^68\) The integration method of Mean-Rank and Fisher's exact test $P$ value is used to rank the TFs and display the top 10 TFs.
**Statistics and Software**
All data are shown as mean $\pm$ standard error of the mean (SEM). GraphPad Prism software (Version 8.1.0; San Diego, CA, USA) and IBM SPSS Statistics software (Version 23.0; IBM Corp, Armonk, NY, USA) were used to present the bar charts, graphs, line charts, and data analysis. The Rayleigh vectors, phase-period distribution, and phase distribution with KEGG pathway of the oscillating genes were analyzed using Oriana software (Version 4.01; Kovach Computing Services, Pentraeth, Wales, UK) and phase set enrichment analysis algorithm.\(^69\) To visualize complex data, the heatmaps were created in R package (64-bit, version 3.5.3).
Data were analyzed by using the Student $t$-test or one-way ANOVA, followed by the Bonferroni correction for multiple testing. Statistical significance was set at $P < 0.05$.
**Results**
**SD Altered Animal General and Circadian Behavior**
To assess the effect of SD on animal general behaviors of C57BL/6J mice, we collected the change curves of pellet intake, water intake, and body weight in SD-treated mouse model for four weeks. As shown in Figures 1A through 1F, the pellet intake, water intake, and body weight of C57BL/6J mice continue to increase over time in the non-SD group and SD group. After four weeks of SD, the pellet consumption (Fig. 1A) and body weight (Fig. 1E) of SD-treated mice were significantly lower than those in the non-SD-treated mice. However, the water consumption (Fig. 1C) of SD-treated mice was significantly greater than that of non-SD-treated mice. In the normal rhythmic state, mice consume most of their food during the nighttime (ZT12–24) and only a small amount during the daytime.\(^69,70\) As Figure 1 shows, the SD treatment significantly reduced nighttime (ZT12–24) pellet intake (Fig. 1B) but increased daytime (ZT0–12) water intake (Fig. 1D).
To record animal circadian behavior, we collected the locomotor activity of the non-SD-treated and SD-treated mouse models in a light-dark (LD) cycle continuously for four weeks. As shown in Figure 1G, the locomotor activity of the non-SD-treated mice in the dark cycle is greater than in the light cycle as previously reported.\(^31,32\) However, the locomotor activity of SD-treated mice has an opposite rhythm: greater in the light cycle than in the dark cycle (Fig. 1H). To further visualize and compare the effects of SD on the locomotor activity and core body temperature rhythm of mice, we presented the data at day 28 of non-SD-treated and SD-treated mice in an LD cycle (Figs. 1I–L). As shown in Figures 1I to 1L, the locomotor activity and core body temperature of the non-SD group in the dark cycle is greater than that in the light cycle as previously reported,\(^31\) which show a normal circadian rhythm change, that is, the core body temperature of the mouse model increases with locomotor activity. However, locomotor activity of the SD group in the light cycle is significantly greater than that in the dark cycle (Figs. 1G–I), the core body temperature of the SD group in the dark cycle is significantly greater than that in the light cycle (Figs. 1K, 1L), which show an abnormal circadian rhythm change, that is, the core body temperature of the mouse not increases with locomotor activity (Figs. 1I–L). Collectively, these results demonstrate that SD dramatically changed the animal behavior.
**SD Comprehensively Alters the Rhythmic Transcriptome in ELG**
To analyze the effects of SD on circadian transcriptomic profiles in murine ELGs, we investigated the expression of cycling transcripts in ELGs collected at eight time points at three-hour intervals. To analyze the transcripts, the JTK_CYCLE algorithm was adopted according to previous reports.\(^31,32,34,60\) This identified 2624 (16.03%) and 2989 (18.26%) circadian transcripts (Supplementary Figs. S2A, S2B) from a total of 16,373 ELG transcripts in SD-treated mice and non-SD treated mice, respectively (Fig. 2A). As
FIGURE 1. SD treatment altered the general biological and circadian rhythmic behavior of mice. (A) The change curve of pellet intake in SD-treated mice after four weeks. *P < 0.05, **P < 0.01. (B) The change curve of body weight in SD-treated mice after four weeks. *P < 0.05, **P < 0.01, NS, statistically nonsignificant. (C) The change curve of water intake in SD-treated mice after four weeks. *P < 0.05, **P < 0.01. (D) The change curve of water intake in SD-treated mice after four weeks in an LD cycle was recorded. *P < 0.05, **P < 0.01. (E) The change curve of core body temperature in SD-treated mice after four weeks. *P < 0.05, ***P < 0.001. (F) The locomotor activity of non-SD-treated and SD-treated mice in an LD cycle were recorded continuously for four weeks. (G,H) The locomotor activity of non-SD-treated and SD-treated mice in the light and dark cycle were further analyzed at day 28. The gray shading indicates dark cycles. (I) The core body temperature of non-SD-treated and SD-treated mice in an LD cycle were recorded at day 28 (non-SD-treated mouse: F = 6.330, P < 0.001; SD-treated mouse: F = 57.432, P < 0.001). The gray shading indicates dark cycles. (J) The core body temperature of non-SD-treated and SD-treated mice in the light and dark cycle were further analyzed at day 28. *P < 0.05, ***P < 0.001, ***P < 0.001, &&&P < 0.001.
shown in Figure 2A, the numbers of rhythmic genes shared in the non-SD group and SD group are 950 (20.40%); the numbers of rhythmic genes unique to the non-SD group and SD group were 2039 (43.70%) and 1674 (35.90%), respectively. The heatmap shows the ELGs rhythmic genes with significantly different expression patterns between the non-SD group (Fig. 2B) the and SD group (Fig. 2C).
To investigate the loss of rhythm genes in the non-SD group, we calculated the shared genes between nonrhythmic genes and low-expressed genes in the SD group and the rhythm genes in the non-SD group. As shown in Figure 2D, the overlapping numbers of nonrhythmic genes and low-expressed genes in the SD group and the rhythm genes in the non-SD group are 2028 (13.80%) and 11 (0.10%), respectively. To investigate the sources of rhythm genes in the SD group, we calculated the shared genes between nonrhythmic genes and low-expressed genes in the non-SD group and the rhythm genes in the SD group. As shown in Supplementary Figure S2E, the overlapping numbers of nonrhythmic genes and low-expressed genes in the non-SD group and the rhythm genes in the SD group are 1671 (11.70%) and 3 (0.10%), respectively.
To further assess the effect of rhythmically transcribed genes in ELG, the Oriana software was be used to analyze the phase, period, and Rayleigh vector of the oscillating rhythmic genes unique to the non-SD group and SD group and those shared between the non-SD group and SD group. The rose diagram showing the phase of 2989 rhythmic genes of non-SD group was mainly distributed in the light cycle (ZT0–ZT10), with a mean vector (μ) of 06:12 and a length of mean vector (r) of 0.61 (Supplementary Fig. S2C). However, the rose diagram showing the phase of 2624 rhythmic genes of the SD group was mainly distributed in the juncture of the light-dark cycle (ZT7–ZT17), with a mean vector (μ) of 12:07 and a length of mean vector (r) of 0.53 (Supplementary Fig. S2D). The rose diagram showing the phase of 2039 rhythmic genes unique to the non-SD group was mainly distributed in the light cycle (ZT0–ZT9), with a mean
FIGURE 2. Changes of rhythmic transcriptome of ELGs between the non-SD group and SD group. (A) The Venn diagram showing the comparison of rhythmic transcriptome of ELGs between the non-SD group and the SD group. (B) Heatmap showing the expression changes of rhythmic genes unique to the non-SD group (left) and SD group (right) arranged in a specific order according to the non-SD group in a 24-hour cycle. The expression range of genes were normalized to ±2. (C) Heatmap showing the expression changes of rhythmic genes unique to the SD group (left) and non-SD group (right) arranged in a specific order according to the SD group in a 24-hour cycle. The expression range of genes were normalized to ±2. (D) Venn diagram revealing the comparison of transcriptomes of ELGs between the rhythmic genes in the non-SD group (cyan), non-rhythmic genes in the non-SD group (pink), and low expression genes in the non-SD group (light orange). (E) Phase analysis of oscillating rhythmic genes unique to the non-SD group (left) and the SD group (right). Gray shades indicate dark cycles, and white indicate light cycles. (F) Phase analysis of oscillating rhythmic genes shared between the non-SD group (left) and the SD group (right). Gray shades indicate dark cycles, and white indicate light cycles. (G) The histograms show phase distribution of oscillating rhythmic genes unique to the non-SD group (left) and SD group (right). The normal curves were shown as black.
vector (μ) of 0.52 and a length of mean vector (r) of 0.62 (Fig. 2E, left). However, the rose diagram showing the phase of 1674 rhythmic genes unique to the SD group was mainly distributed in the juncture of the light-dark cycle (ZT9–ZT16.5), with a mean vector (μ) of 12:59 and a length of mean vector (r) of 0.62 (Fig. 2E, right). Analogously, the rose diagram shows the different distribution of the phase (ZT6–ZT12 vs. ZT17.5–ZT13.5), mean vector (μ, 07:34 vs. 10:01), and mean vector (r, 0.52 vs. 0.47) for 950 rhythmic genes shared in the non-SD group (Fig. 2F, left) and the SD group (Fig. 2E, right).
To further explore the effect of SD on the rhythmic genes of ELGs, we analyzed the phase distribution of the non-SD group and SD group. As shown in Supplementary Figure S2F, the mean values of the phase distribution for rhythmic genes of the non-SD group and SD group are 7.46 and 11.49, respectively. Analogously, the histogram shows the different mean values of phase distribution (6.47 vs. 12.25) for rhythmic genes unique to the non-SD group (Fig. 2G, left) and unique to the SD group (Fig. 2G, right); and the histogram shows the different mean values of phase distribution (8.66 vs. 9.66) for rhythmic genes shared in the non-SD group (Fig. 2H, left) and unique to the SD group (Fig. 2H, right).
Meanwhile, we investigated whether the phase was shifted by SD. Among the 950 rhythmic genes shared in the non-SD group and SD group, the phase shifts were further compared. Compared with the non-SD group, only 260 (27.37%) rhythmic genes have no phase shift, and 690 (72.63%) rhythm genes of the SD group have phase shift (Fig. 2I, left). Further analysis revealed that there are 148 (21.45%) rhythm genes in the SD group with advanced phase and 542 (78.55%) rhythmic genes in the SD group with delayed phase (Fig. 2I, right). Collectively, these data suggest that SD globally alters the circadian transcriptional profiling in ELGs.
**SD Reprograms the KEGG and Phase-Set Enriched Pathways in ELGs**
To recognize the changes of transcriptomic profiling, the Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway enrichment analysis was adopted by using the rhythmic genes unique to the non-SD group and SD group, and shared between the non-SD group and SD group. The results are shown in Figures 3A, 3C, and 3D and Supplementary Tables S1 through S3, respectively. There is no KEGG pathway in the SD group as in the non-SD group (Figs. 3A, 3C). Two enriched KEGG pathways of oscillating rhythmic genes unique to the SD group and shared between the non-SD and SD group, which are metabolic pathways and pathways for biosynthesis of secondary metabolites (Figs. 3C, 3D), were found. Therefore these results suggest that the SD reprograms normal circadian pathways in mouse ELGs.
To investigate the biologically related gene sets association with temporally coordinated expression, the PSEA was used. As shown in Figure 3B, phase distribution of the enriched circadian pathways of oscillating rhythmic genes unique to the non-SD group are increased in the light phase (ZT1.5 to ZT9). However, the phase distribution of enriched circadian pathways of oscillating rhythmic genes unique to SD group are increased in the junction of the light-dark phase (ZT9 to ZT15) (Fig. 3E). For the rhythmic genes unique to the non-SD group, the enriched circadian pathways can be divided into six categories: cellular processes, environmental information processing, genetic information processing, human diseases, metabolism, and organismal systems (Fig. 3B). For the rhythmic genes unique to the SD group, the enriched circadian pathways can be divided into six categories as well: (1) cellular processes: lysosome (non-SD group vs. SD group, ZT5.95 vs. ZT10.58), peroxisome (ZT6.76 vs. ZT11.16), regulation of actin cytoskeleton (ZT6.30 vs. ZT12.41), adherens junction (ZT6.56 vs. ZT12.44), endocytosis (ZT5.20 vs. ZT12.64), cell cycle (ZT5.23 vs. ZT13.48), and focal adhesion (ZT5.50 vs. ZT13.48); (2) environmental information processing: cytokine-cytokine receptor interaction (ZT5.62 vs. ZT12.65), calcium signaling pathway (ZT6.04 vs. ZT12.71), JAK stat signaling pathway (ZT4.85 vs. ZT13.50), WNT signaling pathway (ZT6.16 vs. ZT13.99), and MAPK signaling pathway (ZT5.53 vs. ZT14.49); (3) genetic information processing: proteasome, spliceosome, and ribosome (ZT7.28 vs. ZT15.61); (4) human diseases: small cell lung cancer (ZT5.45 vs. ZT12.64), pathways in cancer (ZT5.05 vs. ZT13.51), Alzheimers disease (ZT7.05 vs. ZT13.74), Huntington’s disease (ZT6.94 vs. ZT13.90), and Parkinson’s disease (ZT7.24 vs. ZT13.97); (5) metabolism: valine, leucine, and isoleucine degradation, lysine degradation, propanoate metabolism, pyruvate metabolism, purine metabolism (ZT6.46 vs. ZT11.98), pyrimidine metabolism, glycolysis/gluconeogenesis, and oxidative phosphorylation (ZT8.11 vs. ZT13.08); (6) organic systems: insulin signaling pathway (ZT6.51 vs. ZT11.27), GnRH signaling pathway (ZT6.17 vs. ZT12.12), PPAR signaling pathway, neurotrophin signaling pathway (ZT6.71 vs. ZT12.68), cardiac muscle contraction, leukocyte transendothelial migration (ZT5.56 vs. ZT13.99), and axon guidance (ZT6.69 vs. ZT14.25) (Fig. 3E). These results demonstrated that SD alters the biological pathways of ELGs in both KEGG and PSEA level.
**SD Alters the Cluster-Dependent Transcriptomic Map and Rhythmic Transcript-Associated KEGG in ELGs**
To discriminate the difference of structural features for large gene expression datasets affected by SD, the cluster-dependent transcriptomic map was presented by using soft Mfuzz in R package. Four different oscillation clusters of rhythmic genes were discovered over a 24-hour cycle in the non-SD (Fig. 3F-I, left) and SD group (Fig. 3J-M, left). For cluster 1 (non-SD group vs. SD group, ZT5.84 vs. ZT5.37 enriched rhythmic genes), the peaks were located at different ZT times (ZT1-ZT4 vs. ZT5-ZT11), and the troughs were located at different ZT times (ZT12-ZT18 vs. ZT15-ZT21). For cluster 2 (non-SD group vs. SD group, ZT5.35 vs. ZT14.16 enriched rhythmic genes), the peaks were located at a similar ZT time (ZT6-ZT12 vs. none), and the troughs were located at different ZT times (ZT15-ZT21 vs. ZT9-ZT15). For cluster 3 (non-SD group vs. SD group, ZT5.38 vs. ZT6.46 enriched rhythmic genes),
**Figure 3.** KEGG pathways and phase distribution of circadian pathways identify dynamic patterns of transcriptomic activity over 24 hours and KEGG pathways for the non-SD group and SD group. (A, C, D) Top 10 enriched KEGG pathways of oscillating rhythmic genes unique to the non-SD group (A), SD group (C), and shared between the non-SD and SD group (D). The dot size as shown in the figure shows the boundary for $Q < 0.05$. (B, E) Phase distribution of enriched circadian pathways ($Q < 0.05$) of oscillating rhythmic genes unique to the non-SD group (Panel B) and SD group (Panel E). The red dotted line on the inner circle and outside circle represent the oscillating rhythmic genes and phase distribution of KEGG pathways, respectively. The gray shading indicates dark cycles. (F–M) The distributions of temporal genes unique to the non-SD (F–I, left) and SD group of ELGs (J–M, left). The lines indicate the dynamic patterns used to show the expression of gene over an LD cycle, with the expression range normalized to ±2. Gray shading indicates dark cycles. The top 10 significant KEGG pathways of rhythmic genes in cluster 1-4 unique to the non-SD (F–I, right) and SD group (J–M, right) with $P < 0.05$ were shown.
Sleep Loss Reprograms ELG Circadian Transcriptome
SD Does Not Elicit Core Clock Desynchrony
To determine the influence of SD on the expression pattern of core clock genes in the ELGs, transcript levels of the 12 canonical core clock genes, including *NR1D1* (also known as REV-ERBa), *NR1D2* (also known as REV-ERBβ), *CLOCK*, *PER1*, *PER2*, *PER3*, *Arntl* (also known as *Bmal1*), *CRY1*, *CRY2*, *NPAS2*, *RORA*, and *RORC* were determined using three biological RNA-Seq data sets for mouse ELGs at every three-hour intervals for 24 hours. On SD treatment for four weeks, the expression patterns of core clock genes in ELGs were basically kept similar to the non-SD-treated ELGs despite some variation in temporal expression profiles (Fig. 4). Thus we concluded that interruption of sleep-wake cycle does not elicit core clock desynchrony in ELGs.
SD Triggers DNA Damage Response by the Accumulation of ROS in ELGs
To study the effect of SD on the expression of ROS-related genes in mouse ELGs, we first visualized the changes in the expression of the non-SD group and the SD group during an LD cycle by using a heatmap. As shown in Figure 5A, the expression of ROS-related genes regulated by SD is obviously different from the non-SD group according to the same sequence of genes. Next, to investigate the levels of oxidative stress in ELGs caused by SD, the marker for ROS, dihydroethidium, and the marker for protein nitration, nitrotyrosine, were used for immunostaining. As shown in Figure 5B, the level of ROS shows circadian oscillation peaking at ZT18 in non-SD-treated mouse ELGs. However, the SD-treated mice show disordered circadian oscillation and a higher amount of ROS compared with the non-SD group (Figs. 5C, 5D). Accumulation of ROS in the gut was also observed as previously reported (Supplementary Fig. S3). And then, to further study the levels of ROS in the SD-treated ELGs with daily oscillation peaking at ZT0 (Figs. 5H–J). Finally, to predict which TFs regulated ROS-related transcripts, the ChEA3 tool was used. As Supplementary Figure S4A shows, the top 10 TFs were enriched in the SD-treated ELGs, that is, MTF1, SPI1, IRF8, TFE3, IRF5, STAT5β, FLI1, TET2, NFE2, and ELF4, respectively. Therefore these results demonstrate that SD triggers DNA damage response by the accumulation of ROS in ELGs.
SD Alters the Rhythmicity of Mass, Cell Size and Differentiation in ELGs
SD has been proven to accelerate neuronal autophagy and apoptosis, corneal epithelial apoptosis, and neuropeptide-associated apoptosis in the hippocampus. To verify whether SD will adversely affect cell differentiation in the lacrimal gland, we evaluated the mass, cell size, cell cycle, cell growth, cell proliferation, apoptosis, and cell senescence of mouse ELGs through the measurement of their transcriptome composition expression levels and immunohistochemical methods. As previously reported, our data indicated that the mouse ELG mass adjusted per body weight exhibits diurnal changes using covariance analysis (AWT). However, as shown in Figures 7A and 7B, the AWT in SD-treated ELGs significantly decreased at five timepoints and the peak shifted six hours in advance. Consistent with this, the overall longitudinal histological view of the SD-treated ELGs were shorter in size at ZT18 compared with that of non-SD-treated ELGs (Fig. 7C).
To understand the cause of the reduction in lacrimal gland mass and volume caused by SD treatment, we calculated the alteration in lacrimal gland cell size over a 24-hour cycle using immunohistochemistry as we previously performed functional enrichment analysis using KEGG of annotated DEGs and obtained 21 significantly enriched KEGG pathways (Supplementary Table S4). The significantly enriched top 10 KEGG pathways are shown in Figure 6R, and the PPANs were visualized by using STRING database to disclose the relevance of immune-related genes in mouse ELGs. Three functional clusters can be found (Clusters 1–3) and the significantly enriched KEGG pathways associated with immune-related genes are presented (Fig. 6S). Finally, to predict which TFs regulated immunity-related transcripts, the ChEA3 tool was used. As Supplementary Figure S4B shows, the top 10 TFs were enriched in the SD-treated ELGs, that is, PLSCR1, BATF2, RELB, IRF7, STAT2, NFKB2, STAT3, CEBPB, BATF3, and TRAFD1, respectively. Collectively, these results demonstrate that the SD dramatically changed the immunologic processes.
Sleep Loss Reprograms ELG Circadian Transcriptome
FIGURE 4. The expression profiles and phase distribution of core clock genes in an LD cycle for the non-SD and SD group. The temporal expression profiles and phase distribution of twelve core clock genes that includes *Arntl* (non-SD-treated ELGs: $F = 43.268, P < 0.001$; SD-treated ELGs: $F = 112.159, P < 0.001$), *Clock* (non-SD-treated ELGs: $F = 8.204, P < 0.001$; SD-treated ELGs: $F = 21.278, P < 0.001$), *Cry1* (non-SD-treated ELGs: $F = 3.624, P < 0.05$; SD-treated ELGs: $F = 8.204, P < 0.001$), *Cry2* (non-SD-treated ELGs: $F = 21.278, P < 0.001$; SD-treated ELGs: $F = 12.598, P < 0.001$), *Npas2* (non-SD-treated ELGs: $F = 25.537, P < 0.001$; SD-treated ELGs: $F = 10.182, P < 0.001$), *Per1* (non-SD-treated ELGs: $F = 9.647, P < 0.001$; SD-treated ELGs: $F = 13.495, P < 0.001$), *Per2* (non-SD-treated ELGs: $F = 4.146, P < 0.001$; SD-treated ELGs: $F = 6.687, P < 0.001$), *Per3* (non-SD-treated ELGs: $F = 34.644, P < 0.001$; SD-treated ELGs: $F = 41.468, P < 0.001$), *Rora* (non-SD-treated ELGs: $F = 58.984, P < 0.001$; SD-treated ELGs: $F = 32.901, P < 0.001$; SD-treated ELGs: $F = 98.103, P < 0.001$). Cyan line represents the non-SD group and red line represents the SD group. Gray shading indicates dark cycles. *P* < 0.05, **P** < 0.01, ***P*** < 0.001.
The results showed that the circadian rhythmicity of cell size in SD-treated ELGs basically disappeared compared to a significant diurnal change of the mean cell size in the non-SD-treated ELG (Figs. 7D, 7E).
Next, to explore the molecular basis of these changes, we investigated the transcripts related to cell cycle, cell growth, cell proliferation, apoptosis, and cell senescence of ELGs using GSEA and heatmap analysis. The GSEA result showed...
FIGURE 5. Accumulation of reactive oxygen species triggered by SD between the non-SD group and SD group in mouse ELGs. (A) Heatmaps of diurnal expression for reactive oxygen-related genes between the non-SD group and SD group in mouse ELGs. The expression levels of reactive oxygen-related genes were obtained from RNA-Seq and expression range was normalized to ±3. (B) Representative images of ROS levels are shown in the ZT0, ZT6, ZT12, and ZT18 after SD between the non-SD group and SD group in mouse ELGs. Scale bar: 50 μm.
that the cell cycle pathway was significantly enriched in ELGs (Figs. 7G, 7H). Compared with the non-SD group, the transcriptional profiling of cell cycle (Fig. 7I), cell growth (Fig. 7J), cell proliferation (Fig. 7K), apoptosis (Fig. 7L), and cell senescence (Fig. 7M) within 24 has been completely changed in SD-treated ELGs. To predict which TFs regulated cell-differentiation-related transcripts, the ChEA3 tool was used, and the top 10 TFs were enriched in the SD-treated ELGs (Supplementary Figs. S4C–F). It is evident that nine shared TFs—that is, FOXM1, CENPA, DNM1T1, E2F1, E2F7, MYBL2, PA2G4, ZNF367, and ZNF695—may regulate cell-cycle, cell-growth, cell-proliferation, and cell-apoptosis transcripts. Finally, to evaluate cell proliferation using levels of Ki67, SD-treated ELGs changed their diurnal oscillation pattern of Ki67, peaking at different ZT and were shown to have higher expression levels compared to the non-SD-treated ELGs (Figs. 7N-Ω). Collectively, SD changes the circadian oscillation of cell differentiation in ELGs.
SD Reprograms the Composition of Metabolism-Related Transcriptome in ELGs
Circadian rhythms are intertwined with metabolic processes. To investigate whether circadian rhythm disturbance is accompanied by SD, we compared the differential expression of metabolism-related genes and their enrichment pathways between the non-SD and SD groups. As shown in Figure 7R, the expression pattern of metabolism-related genes was significantly altered in SD-treated mice compared with non-SD-treated mice. Gene enrichment analysis revealed 78 significantly enriched KEGG pathways (Supplementary Table S5). The top 10 KEGG pathways in SD-treated ELG were shown in Figure 7S. The interplay network of these metabolism-related genes was further visualized through protein-protein association networks based on STRING database. As shown in Figure 7T, four metabolism-related functional clusters were identified (clusters 1–4). Finally, to predict which TFs regulated metabolism-related transcripts, the ChEA3 tool was used. As Supplementary Figure S4H shows, the top 10 TFs were enriched in the SD-treated ELGs, that is, MYPOP, MYT1L, CAMTA1, SNAPC5, SCR71, HMGN3, THYN1, KCNP5, RORB, and ARNT2, respectively. In summary, these results suggest that SD significantly alters the metabolic processes of ELGs.
SD Alters the Murine ELG Transcriptome Profile of Neural Activity-Related Genes
As previously reported, the circadian disruption has an adverse effect on nerve-controlled response in mouse ELGs. To investigate how SD-associated circadian disruption affects the neural activities in mouse ELGs, a secretion response experiment was performed using cholinergic agonist pilocarpine as previously reported. As Figures 8A to 8C show, tear secretion of the non-SD group exhibited circadian oscillation peaking at ZT18 as our previous report. However, SD-treated mice showed disordered circadian oscillation and a lower volume of tear secretion compared with the non-SD group (Figs. 8B, 8C).
To further identify the molecular signature of SD-associated influence on tear secretion, we identified the alteration of neural activity-related transcriptome profile in SD-treated ELGs over the LD cycle. The heatmap shows that there were 15 down-regulated and 135 up-regulated genes in SD-treated ELGs compared with non-SD-treated ELGs (Fig. 8D). All the significantly enriched KEGG pathways based on these neural activity-related genes were presented in Figure 8E. To further reveal an interaction network of neural-related genes, the PPANs were visualized based on the abovementioned genes. Four distinct clusters were displayed by the Kmeans clustering method (Fig. 8F).
Moreover, GSEA analysis showed that neurotrophin signaling pathway was significantly enriched in ELGs (Figs. 8G, 8H). Finally, we quantified nerve density in ELGs using fluorescein isothiocyanate–conjugated anti-mouse beta III tubulin monoclonal antibody. The results showed that the nerve density of SD-treated ELG was significantly reduced compared with non-SD-treated mice (Figs. 8I, 8J). Finally, to predict which TFs regulated metabolism-related transcripts, the ChEA3 tool was used. As Supplementary Figure S4H shows, the top 10 TFs were enriched in the SD-treated ELGs, that is, MYPOP, MYT1L, CAMTA1, SNAPC5, SCR71, HMGN3, THYN1, KCNP5, RORB, and ARNT2, respectively. Therefore, these results demonstrate that SD dramatically alters the nerve innervation, interacting networks of neural-associated genes, and secretory response of mouse ELGs.
SD Causes Irreversible Impairment of ELG Function Accompanied by General and Circadian Behavior
To determine whether locomotor activity, core temperature, ELG mass, and tear secretion is reversible or irreversible impairment after SD, the SD-treated mice were kept in cages for four weeks under the normal sleep conditions (SD-NSC) to obtain sufficient sleep and forced recovery in normal sleep condition (SD-FR-NSC) to rapid reversal of sleep-wake cycle. As Figure 9A shows, the weight of SD-FR-NSC-treated mice did not exhibit a statistically significant change compared with that of non-SD mice; however, the weight of SD-FR-NSC-treated mice exhibited a significant increase compared with that of non-SD mice. The ELG mass was also collected. The AWT of SD-NSC and SD-FR-NSC significantly increased and exhibited differ-
FIGURE 6. The effect of SD on the immune-related cell and genes in mouse ELGs. (A) Diurnal oscillations of the relative abundance of CD4⁺ cells by using immunohistochemistry in the ELGs for the non-SD group and SD group at six-hour intervals (non-SD-treated mice: $F = 8.312$, $p < 0.05$).
ent oscillating rhythms compared with the non-SD group (Figs. 9B, 9C).
To further evaluate whether the damage of SD to lacrimal gland function is reversible or irreversible, we further tested the amount of tear secretion. As shown in Figures 9D and 9E, compared with the SD group, the amount of tear secretion in the SD-NSC and SD-FR-NSC groups were significantly increased, but it did not return to a normal circadian rhythm. The locomotor activity and core body temperature of SD-NSC and SD-FR-NSC were also collected and visualized, which are significantly improved compared with SD mice, but did not return to normal levels (Figs. 9F-I).
To further elucidate the mechanism of lasting adverse effect of lacrimal secretion function after SD following four weeks of spontaneous recovery or forced recovery in normal sleep conditions, we examined the level of ROS in mouse ELGs. The ROS of the SD-NSC and SD-FR-NSC groups present a different oscillating rhythm compared with the non-SD group and SD group, but the average ROS levels are lower than SD and it did not return to a normal circadian rhythm (Figs. 9J-L). Collectively, these results show that the SD causes irreversible impairment in the secretory function of the lacrimal gland, at least for the short term.
**DISCUSSION**
Clinical studies have shown that quality of sleep is strongly associated with the prevalence of dry eye.87–91 However, its incidence exhibits some bias depending on the population, region, study size, and accompanying patient mental status (e.g., during the COVID19 epidemic).17,80–84 For example, studies from Europe and Japan have shown that up to 45% of participants with dry eye reported poor sleep quality.13,81 In addition, people suffering from sleep disorders (such as sleep apnea) and who engage in shift work have a higher prevalence of dry eye than other populations.17,82 However, a direct link between these two conditions has not been well established at the cellular and molecular levels. In this study, using a mouse model of chronic SD, we found that SD causes severe disturbances in the circadian rhythm of the lacrimal gland, both at the transcriptomic level and at the physiological level. In addition, we found that SD causes accumulation of oxidative stress products in the lacrimal gland and DNA damage. Importantly, the disturbance of lacrimal gland secretion caused by SD are irreversible.
**SD Changes the Rhythm Oscillation of ELGs**
The circadian clock system consists of a central circadian clock and a peripheral circadian clock. Although SCN are considered the central or master clock, peripheral tissues also have circadian rhythm genes.85,86 Our previous studies show that the ELGs, as a peripheral tissue, also has circadian rhythm gene oscillations under the SCN control and is reprogramed by overnutrition caused by high fructose intake.35 hyperglycemia caused by streptozotocin,32 as well as changes in light cycle phase.34 In this study, we reveal that (1) SD significantly reduced ELG mass, and significantly changed the circadian oscillation pattern of ELG mass, which is consistent with the circadian oscillation pattern of the change in liver mass by the LD cycle16; (2) the rhythm genes of ELGs in mice after four weeks of SD were reduced, which is consistent with that of human blood cells after suffering from sleep interruption17,27–30; (3) the phase of unique rhythm genes in the SD group was delayed by about seven days compared with the non-SD group; and (4) SD induces the rhythm genes of ELGs to show a cluster-dependent transcriptomic map and rhythmic transcript-associated KEGG pathway in ELGs. All these changes explain the adverse effects of SD on the transcriptional level of lacrimal function.
FIGURE 7. The variation of cell differentiation-related genes and metabolism-related genes between the non-SD group and SD group in mouse ELGs. (A) The diurnal changes of mouse AWT of non-SD-treated and SD-treated mouse models in the LD cycle were recorded at day 28. The gray shading indicates dark cycles (non-SD-treated ELGs: $F = 3.520$, $P < 0.05$; SD-treated ELGs: $F = 1.501$, $P > 0.05$), **$P < 0.01$, ***$P < 0.001$. (B) The changes of mouse AWT of non-SD-treated and SD-treated mice in an LD cycle were recorded at day 28. ***$P < 0.001$. (C) Overall longitudinal view of the murine lacrimal glands from the non-SD group and SD group at ZT18. Scale bar: 500 μm. (D) The circadian oscillating pattern of ELG cell size for the non-SD group and SD group in the LD cycle (non-SD-treated mice: $F = 19.983$, $P < 0.001$; SD-treated mice: $F = 2.125$, $P > 0.05$). **$P < 0.01$, ***$P < 0.001$. (E) The average cell size of ELG cell size for the non-SD group and SD group in the LD cycle. ***$P < 0.001$. (F) The representative immunohistochemical images of ELG cell size for the non-SD group and SD group at ZT18. Scale bar: 20 μm. (G, H) The enriched cell cycle-related KEGG pathways and heatmap were created by GSEA in the non-SD group and SD group. (I-M) Heatmaps of diurnal expression for cell cycle (I), cell growth (J), cell proliferation (K), cell apoptosis (L), cell senescence-related genes (M) between the non-SD group and SD group in mouse ELGs. The expression levels of cell cycle-related genes were obtained from RNA-Seq and expression range of DEGs was normalized to ±3. (N) Diurnal oscillations of the relative abundance of Ki67$^+$ cells by using immunohistochemistry in the ELGs for the non-SD group and SD group at six-hour intervals (non-SD-treated mice: $F = 2.535$, $P > 0.05$; SD-treated mice: $F = 6.062$, $P < 0.01$). Each time point shows the median and SEM. *$P < 0.05$, ***$P < 0.001$. (O) Average relative abundance of Ki67$^+$ cells of ELGs from the non-SD group and SD group. ***$P < 0.001$. (P-Q) Representative immunohistochemistry images (Ki67$^+$ cells) of mouse ELGs at ZT6 from the non-SD group and SD group. The sectional view of ELG structure from the non-SD group (P) and SD group (Q). Scale bar: 50 μm. (R) Heatmaps of diurnal expression for metabolism-related genes between the non-SD group and SD group in mouse ELGs. The expression levels of metabolism-related genes were obtained from RNA-Seq and expression range of DEGs was normalized to ±3. (S) The top 10 KEGG pathways enriched histogram of metabolism-related genes with $Q < 0.05$ were displayed. (T) The PPANs and functional clusters (Clusters 1–4) with relevant KEGG pathway of metabolism-related genes between the non-SD group and SD group in mouse ELGs ($Q < 0.001$).
睡眠剥夺重新编程ELG昼夜节律转录组
图8. 本研究比较了非SD组和SD组小鼠ELG中与神经相关的基因的变异情况。图(A)展示了泪液分泌测试的示意图。图(B)显示了非SD组和SD组小鼠在LD周期中的泪液分泌情况。***P < 0.001。
图(C)比较了非SD组和SD组在LD周期中的平均泪液分泌。
图(D)展示了非SD组和SD组在LD周期中的神经相关基因的昼夜表达模式。这些神经相关基因的表达水平由RNA-Seq获得，并在DEGs表达范围的基础上归一化到±3。
图(E)显示了显著富集的KEGG通路中与神经相关的基因。
图(F)和图(H)显示了非SD组和SD组小鼠ELGs中与神经相关的KEGG通路。
典型图示：非SD组和SD组小鼠ELGs中beta III tubulin（红）神经纤维的代表性图像。图示中，神经纤维的平均相对丰度在非SD组和SD组小鼠ELGs中，**P < 0.05。
FIGURE 9. The irreversible impairments in general and circadian behavior and ELG function of SD-treated mice. (A) Changes in body weight of non-SD, SD, SD-NSC and SD-FR-NSC groups. non-SD vs. SD, *P < 0.05, **P < 0.01, ***P < 0.001; non-SD vs. SD-NSC, P < 0.05, **P < 0.01, ***P < 0.001; non-SD vs. SD-FR-NSC, P < 0.05, **P < 0.01, ***P < 0.001; SD vs. SD-NSC, #P < 0.05, ##P < 0.01, ###P < 0.001. NS indicated not statistically significant. (B) The diurnal changes of mouse AWT of non-SD, SD, SD-NSC and SD-FR-NSC in the LD cycle were recorded. The gray shading indicates dark cycles (non-SD: F = 3.520, P < 0.05; SD: F = 1.501, P > 0.05; SD-NSC: F = 1.682, P > 0.05; SD-FR-NSC: F = 1.134, P > 0.05). (C) The changes of mouse AWT of non-SD, SD, SD-NSC and SD-FR-NSC in an LD cycle were recorded. (D) The tear secretion of non-SD, SD, SD-NSC and SD-FR-NSC in an LD cycle were recorded. The gray shading indicates dark cycles (non-SD: F = 17.660, P < 0.001; SD: F = 3.096, P = 0.05; SD-NSC: F = 0.106, P > 0.05; SD-FR-NSC: F = 2.263, P > 0.05). (E) Comparison of average tear secretion of non-SD, SD, SD-NSC and SD-FR-NSC in an LD cycle were recorded. (F) The locomotor activity of non-SD, SD, SD-NSC and SD-FR-NSC in an 12h/12h LD cycle were recorded. (G) The core body temperature of non-SD, SD, SD-NSC and SD-FR-NSC in an LD cycle were recorded. (H) The locomotor activity of non-SD, SD, SD-NSC and SD-FR-NSC in the light and dark cycle were further analyzed. (I) The core body temperature of non-SD, SD, SD-NSC and SD-FR-NSC in the light and dark cycle were further analyzed. (J) Quantification of ROS levels in ELGs from non-SD, SD, SD-NSC and SD-FR-NSC at six-hour intervals (non-SD: F = 10.079, P < 0.001; SD: F = 0.442, P > 0.05; SD-NSC: F = 0.442, P > 0.05; SD-FR-NSC: F = 2.893, P > 0.05). Each time point shows the median and SEM of biological samples. (K) Average quantification of ROS levels in ELGs from non-SD, SD, SD-NSC and SD-FR-NSC. (L) Representative images of ROS levels of non-SD, SD, SD-NSC and SD-FR-NSC are shown in the ZT0, ZT6, ZT12, and ZT18 in mouse ELGs. Scale bar: 50 μm.
SD Leads to a Chronic Inflammatory Response in ELGs
Effective and adequate sleep time is intimately linked to the maintenance of a normal immune system. Disruption of the normal sleep-wake cycle will initiate dysregulation of the immune system. It has been found that SD interferes with the normal migratory pattern of certain immune cells in a bone marrow-circulation-peripheral tissue pattern by affecting the expression of certain adhesion molecules, chemokines, and their corresponding receptors on the vascular endothelium. The cumulative results of this chronic process can trigger the development of certain organ-specific, systemic diseases associated with immune dysfunction. Our previous studies have shown that a jet-lag model induced by altering the light cycle significantly alters the pattern of recruitment of immune cells to the lacrimal gland and dramatically alters the immune-related circadian transcriptome. Ultimately, a chronic sub-inflammatory state of the lacrimal gland is invoked. In line with this, similar results were obtained in the present study disrupting the normal sleep-wake cycle. Thus our data further highlight the close association between normal circadian rhythms and the local immune niche of the lacrimal gland.
SD Weakens Secretion Activity of ELGs Under Nervous System Control
Although insufficient sleep or interference with normal sleep can reduce the secretion of tears in humans and experimental animals, change the composition of tears, and even lead to dry eye disease, the underlying mechanism is not completely clear. The secretory activity of the lacrimal gland is closely controlled by the nervous system, especially the parasympathetic nerve branch of autonomic nerves. We first performed an enrichment analysis, including KEGG and GSEA, of neural-related differentiation genes expression and found that neurotrophin signaling-related pathways were activated. Neurotrophins control many aspects of survival, development, and function of neurons in both the peripheral and the central nervous systems. SD can cause changes and even damage in the structure of the central and peripheral nerves. Therefore we compared ELG nerve density of the non-SD group and SD group. Our findings show that the nerve density of the ELGs in the SD group decreased significantly compared with the non-SD group. Neural activity mainly depends on changes in the quality and quantity of synapses formed in the surface of nerve endings and target cells. The synaptic size, strength, potentiation, transcriptome, and proteome of the nervous system have significant daily rhythm and dynamically change with sleep with synapses larger after waking up and smaller after sleep.
We found that compared with non-SD treated ELGs, different types of synaptic signaling pathways in SD-treated ELGs have undergone significant changes, especially dopaminergic synapse and cholinergic synapses. This is consistent with findings of abnormal synapses in the central nervous system after SD. In summary, all these abnormal activities of structures, circadian rhythms, and neural-related transcriptomes may be one of the main reasons for the significant decrease in ELG secretory activity caused by SD in this study. However, further studies on the molecular mechanisms of SD-altered ELG circadian dysfunction is needed.
SD Strengthens the Metabolism of ELGs
Circadian rhythm and metabolism have a bidirectional effect. Any change in circadian activities may rewrite the metabolic process. For example, BMAL1 knockout, Per2 knockout, and Cry1/Cry2 double knockout mice are prone to obesity and metabolic syndrome. The circadian rhythm disorder caused by SD has been confirmed to be closely related to the occurrence and development of metabolic diseases. After SD in healthy men, the levels of various metabolites in the blood have been shown to have a significant increase. SD causes significant changes in protein-related genes and free amino acids of tear secretion. Similarly, in this study, we found disorders in the expression of metabolism-related genes in SD-treated ELGs. The main feature is that expression levels, KEGG enrichment pathways, and PPANs of all metabolism-related genes have undergone major changes. The significance and mechanism of SD leading to disorders of metabolism in the ELGs need to be further studied.
SD Damages the Morphology and Structure of ELGs
SD can cause changes in the morphology and structure of many organs or tissues through changes in hormone levels, which may cause atrophy in organs such as the ventral prostate, muscle, spleen, and brain. Consistent with these studies, mouse ELGs suffering from SD in this study experienced a significant reduction in mass, volume, and cell size. Further analysis of transcripts related to cell cycle, growth, proliferation, senescence, and apoptosis of ELGs showed that the expression of transcripts related to these pathways was significantly increased in SD-treated mice compared with the non-SD group. The results of immunohistochemistry showed that SD changed the circadian rhythm of Ki67 expression in ELGs and significantly increased its expression, which was consistent with the increase in transcripts related to cell proliferation in ELGs. The significance and mechanism of SD leading to disorders of morphology and structure through cell differentiation in ELGs need to be further studied.
SD Does Not Affect the Core Clock System
So far, existing data suggest that the core circadian clock network in cells is a relatively stable system. In general, if the retino-hypothalamic tract system is not disturbed, the core clock machine remains stable, whether reversing the timing of feeding under metabolic stress or in the context of aging. This study further confirmed the conclusion that the core clock system is a relatively stable system by using the model that interferes with sleep but does not change the light cycle. In contrast, rhythmic clock genes or clock-controlled genes are sensitive to different environmental alterations such as nutritional challenges. Therefore further exploration of the mechanisms by which SD causes the decoupling of the core clock and the expression of downstream CCGs would be of potential therapeutic value in addressing abnormalities in lacrimal gland structure and function caused by SD.
**SD-Induced Dysfunction of ELGs Is Linked to ROS and Oxidative Stress**
In mammals, there is balance between oxidative stress and the antioxidant defense system. When this system is out of balance, it causes damage to proteins, lipids, and DNA of cells. Excessive and prolonged oxidative stress can cause diseases as atherosclerosis, Alzheimer’s disease, Parkinson’s disease, cancer, and even death. Similarly, several recent studies have shown that oxidative stress is also involved in the pathophysiological processes of the lacrimal gland, such as aging and various inflammatory responses, which ultimately manifest as a decrease in lacrimal gland secretory function. The present study found that SD and its disturbance of the circadian rhythm of ELGs were accompanied by the accumulation of oxidative products in the lacrimal gland. Furthermore, four weeks of treatment under normal sleep conditions did not significantly reduce ROS accumulation in the lacrimal glands of SD-treated mice, and lacrimal gland secretion did not return to normal levels. Although a small number of studies have shown a close correlation between the circadian system and the oxidative stress-antioxidative stress system, it is worthwhile to further explore how SD-triggered circadian rhythm disturbances contribute to the oxidative stress in the lacrimal gland and its impairment. One possibility is that an internal time lag is created during the decoupling between the core clock and the downstream CCGs, leading to oxidative stress. This deserves further exploration.
**Study Limitation**
This study faces certain limitations. First, there are different degrees of confounding effects in the study that depended on the time, intensity, and method of SD implementation.
---
*Figure 10.* Graphical summary of SD-triggered ocular surface diseases. (This figure was created using the Servier Medical ART: SMART (smart.servier.com) according to a Creative Commons Attribution 3.0.)
This study was limited to observing adverse changes in the mouse ELG after four weeks of SD treatment. Second, this study used a nocturnal animal mouse model, whereas humans belong to the diurnal population. The opposite circadian oscillation pattern is noteworthy for the interpretation of certain data. Third, bioinformatics analysis in this study was limited to the transcriptome level. Fourth, in this study, we observed only the effect of SD on ELG function in mice and did not examine the effect of SD on corneal homeostasis, especially with respect to the corneal nerve and sensation. With prolonged corneal exposure or reduced blink reflexes of the eyelids, SD may also reduce corneal sensitivity through local inflammation-mediated effects or systemic effects in the cornea. This altered sensitivity may affect the secretory function of the lacrimal gland through the lacrimation reflex. Future studies could address this problem by implementing tarsorrhaphy and/or nonvisual means of sleep deprivation. Finally, a multi-omics study would likely provide more comprehensive information on the effects of SD in lacrimal gland function.
Summary
In conclusion, we demonstrated that SD can cause lacrimal gland dysfunction by accumulating ROS and disrupting the metabolic, immune, and neural functions, in terms of changes in the circadian transcriptome and lacrimal gland structure. These impairments hold clinical relevance, particularly in contexts in which chronic insufficient sleep is prevalent, especially in populations such as emergency service personnel, medical professionals, and new parents. In addition, we found that the above pathological changes caused by SD were irreversible (Fig. 10). These data present a comprehensive platform for future research to explore potential therapeutic strategies to alleviate abnormalities in the physiological state of the ocular surface caused by chronic insufficient sleep.
Acknowledgments
Supported by the Basic Science Project of Henan Eye Institute/Henan Eye Hospital (grant number 2JJCZD001), the National Natural Science Foundation of China (grant numbers 82101089, 82171014, and 81770962), the Basic Science Project for Youth of Henan Eye Institute/Henan Eye Hospital (grant number 20JQSN003), the Key R&D and Promotion Special Program of Henan Province (grant numbers 21210231011 and 222102310120), the Henan Provincial Medical Science and Technology Research Joint Co-construction Project (grant number LHGJ20200064), the Doctoral Research and Development Foundation of Henan Provincial People’s Hospital (grant number ZC20190146).
Disclosure: S. Huang, None; H. Si, None; J. Liu, None; D. Qi, None; X. Pei, None; B. Lu, None; S. Zou, None; Z. Li, None
References
1. Irwin MR. Why sleep is important for health: a psychoneuroimmunological perspective. Annu Rev Psychol. 2015;66:143–172.
2. Siegel JM. Do all animals sleep? Trends Neurosci. 2008;31:208–213.
3. Ford ES, Cunningham TJ, Croft JB. Trends in self-reported sleep duration among US adults from 1985 to 2012. Sleep. 2015;38:829–832.
4. Watson NF, Badr MS, Belenky G, et al. Joint consensus statement of the American academy of sleep medicine and sleep research society on the recommended amount of sleep for a healthy adult: methodology and discussion. Sleep. 2015;38:1161–1183.
5. Knutson KL, Van Cauter E. Associations between sleep loss and increased risk of obesity and diabetes. Ann N Y Acad Sci. 2008;1129:287–304.
6. Hung HC, Yang YC, Ou HY, et al. The association between self-reported sleep quality and overweight in a Chinese population. Obesity (Silver Spring). 2013;21:486–492.
7. Shan Z, Ma H, Xie M, et al. Sleep duration and risk of type 2 diabetes: a meta-analysis of prospective studies. Diabetes Care. 2015;38:529–537.
8. Dutil C, Chaput JP. Inadequate sleep as a contributor to type 2 diabetes in children and adolescents. Nutr Diabetes. 2017;7:e266.
9. Mansukhani MP, Covassin N, Somers VK. Apneic sleep, insufficient sleep, and hypertension. Hypertension. 2019;73:744–756.
10. Kecklind G, Axelsson J. Health consequences of shift work and insufficient sleep. Bmj. 2016;355:i5210.
11. Grandner MA, Chakravorty S, Perlis ML, et al. Habitual sleep duration associated with self-reported and objectively determined cardiometabolic risk factors. Sleep Med. 2014;15:42–50.
12. Jike M, Itani O, Watanabe N, et al. Long sleep duration and health outcomes: A systematic review, meta-analysis and meta-regression. Sleep Med Rev. 2018;39:25–56.
13. Magno MS, Utheim TP, Snieder H, et al. The relationship between dry eye and sleep quality. Ocul Surf. 2021;20:13–19.
14. Khurana RN, Porco TC, Claman DM, et al. Increasing sleep duration is associated with geographic atrophy and age-related macular degeneration. Retina. 2016;36:255–258.
15. Ido T, Tomita G, Kitazawa Y. Diurnal variation of intraocular pressure of normal-tension glaucoma. Influence of sleep and arousal. Ophthamology. 1991;98:296–300.
16. Li S, Ning K, Zhou J, et al. Sleep deprivation disrupts the lacrimal system and induces dry eye disease. Exp Mol Med. 2018;50:e451.
17. Karaca I, Yagci A, Palamar M, et al. Ocular surface assessment and morphological alterations in meibomian glands with meibography in obstructive sleep apnea Syndrome. Ocul Surf. 2019;17:771–776.
18. Takahashi JS. Transcriptional architecture of the mammalian circadian clock. Nat Rev Genet. 2017;18:164–179.
19. Reppert SM, Weaver DR. Molecular analysis of mammalian circadian rhythms. Annu Rev Physiol. 2001;63:647–676.
20. Hastings MH, Maywood ES, Brancaccio M. Generation of circadian rhythms in the suprachiasmatic nucleus. Nat Rev Neurosci. 2018;19:453–469.
21. Colwell CS. Linking neural activity and molecular oscillations in the SCN. Nat Rev Neurosci. 2011;12:553–569.
22. Ralph MR, Foster RG, Davis FC, et al. Transplanted suprachiasmatic nucleus determines circadian period. Science. 1990;247:975–978.
23. Son GH, Chung S, Kim K. The adrenal peripheral clock: glucocorticoid and the circadian timing system. Front Neuroendocrinol. 2011;32:451–465.
24. Zheng L, Seon YJ, McGrath J, et al. Clock genes show circadian rhythms in salivary glands. J Dent Res. 2012;91:783–788.
25. Vu CHV, Kawashima M, Nakamura W, et al. Circadian clock regulates tear secretion in the lacrimal gland. Exp Eye Res. 2021;206:108524.
26. Romano A, Peisich A, Madjarov B. The circadian rhythm of lacrimal secretion and its parameters, determined in a group of healthy individuals, and its potential diagnostic and therapeutic significance. Adv Exp Med Biol. 1994;350:93–97.
27. Srivivasa S, Chan C, Jones L. Apparent time-dependent differences in inferior tear meniscus height in human subjects with mild dry eye symptoms. Clin Exp Optom. 2007;90:345–350.
28. Benjamin WJ, Hill RM. Human tears: osmotic characteristics. Invest Ophthalmol Vis Sci. 1983;24:1624–1626.
29. Benito MJ, González-García MJ, Tesón M, et al. Intra- and inter-day variation of cytokines and chemokines in tears of healthy subjects. Exp Eye Res. 2014;120:43–49.
30. Huth SW, Miller MJ, Leopold IH. Calcium and protein in tears: diurnal variation. Arch Ophthalmol. 1981;99:1628–1633.
31. Huang S, Jiao X, Lu D, et al. Light cycle phase advance as a model for jet lag reprograms the circadian rhythms of murine extraorbital lacrimal glands. Ocul Surf. 2021;20:95–114.
32. Jiao X, Lu D, Pei X, et al. Type 1 diabetes mellitus impairs diurnal oscillations in murine extraorbital lacrimal glands. Ocul Surf. 2020;18:438–452.
33. Lu D, Lin C, Jiao X, et al. Short-term high fructose intake reprograms the transcriptional clock rhythm of the murine extraorbital lacrimal gland. Invest Ophthalmol Vis Sci. 2019;60:2038–2048.
34. Jiao X, Pei X, Lu D, et al. Microbial reconstitution improves aging-driven lacrimal gland circadian dysfunction. Am J Pathol. 2021;191:2091–2116.
35. Musiek ES, Holtzman DM. Mechanisms linking circadian clocks, sleep, and neurodegeneration. Science. 2016;354:1004–1008.
36. Sanchez REA, Kalume F, de la Iglesia HO. Sleep timing and aging-driven lacrimal gland circadian dysfunction. Ocul Surf. 2021;18:438–452.
37. Archer SN, Oster H. How sleep and wakefulness influence circadian rhythmicity: effects of insufficient and mistimed sleep on the animal and human transcriptome. J Sleep Res. 2015;24:476–493.
38. Maret S, Dorsa R, Gurcel L, et al. Homer 1a is a core brain molecular correlate of sleep loss. Proc Natl Acad Sci USA. 2007;104:20090–20095.
39. Möhr-Levet CS, Archer SN, Bucca G, et al. Effects of insufficient sleep on circadian rhythmicity and expression amplitude of the human blood transcriptome. Proc Natl Acad Sci USA. 2013;110:E1132–E1141.
40. Haneya A, Sawada N, Uchino M, et al. Relationship between unhealthy sleep status and dry eye symptoms in a Japanese population: The JPHC-NEXT study. Ocul Surf. 2021;21:306–312.
41. Logan RW, McClung CA. Rhythms of life: circadian disruption and brain disorders across the lifespan. Nat Rev Neurosci. 2019;20:49–65.
42. Takahashi JS, Hong HK, Ko CH, et al. The genetics of mammalian circadian order and disorder: implications for physiology and disease. Nat Rev Genet. 2008;9:764–775.
43. Edgar RS, Green EW, Zhao Y, et al. Peroxiredoxins are conserved markers of circadian rhythms. Nature. 2012;485:459–464.
44. O’Neill JS, Reddy AB. Circadian clocks in human red blood cells. Nature. 2011;469:498–503.
45. Kondratov RV, Kondratova AA, Gorbacheva VY, et al. Early aging and age-related pathologies in mice deficient in BMAL1, the core component of the circadian clock. Genes Dev. 2006;20:1868–1873.
46. Sharifi-Rad M, Anil Kumar NV, Zucca P, et al. Lifestyle, oxidative stress, and antioxidants: back and forth in the pathophysiology of chronic diseases. Front Physiol. 2020;11:694.
47. Buyukhatipoglu H, Kirhan I, Vural M, et al. Oxidative stress increased in healthcare workers working 24-hour on-call shifts. Am J Med Sci. 2010;340:462–467.
48. Sharifian A, Farahani S, Pasalar P, et al. Shift work as an oxidative stressor. J Circadian Rhythms. 2005;3:15.
49. Faraut B, Bayon V, Léger D. Neuroendocrine, immune and oxidative stress in shift workers. Sleep Med Rev. 2013;17:433–444.
50. Nikel P, Fuhrer T, Chavarria M, et al. Reconfiguration of metabolic fluxes in Pseudomonas putida as a response to sub-lethal oxidative stress. ISME J. 2021;15:1751–1766.
51. Vaccaro A, Kaplan Dor Y, Nambara K, et al. Sleep loss can cause death through accumulation of reactive oxygen species in the gut. Cell. 2020;181:1307–1328.e1315.
52. de Souza RG, Yu Z, Hernandez H, et al. Modulation of oxidative stress and inflammation in the aged lacrimal gland. Am J Pathol. 2021;191:294–308.
53. McAlpine CS, Kiss MG, Rattik S, et al. Sleep modulates haematopoiesis and protects against atherosclerosis. Nature. 2019;566:383–387.
54. Xie J, Zhao ZZ, Li P, et al. Senkyunolide I protects against sepsis-associated encephalopathy by attenuating sleep deprivation in a murine model of cecal ligation and puncture. Oxid Med Cell Longev. 2021;2021:6647258.
55. Harkin A, O’Donnell JM, Kelly JP. A study of VitalView for behavioural and physiological monitoring in laboratory rats. Physiol Behav. 2002;77:65–77.
56. Yamaguchi Y, Suzuki T, Mizoro Y, et al. Mice genetically deficient in vasopressin V1a and V1b receptors are resistant to jet lag. Science. 2013;342:85–90.
57. Kato AS, Burris KD, Gardinier KM, et al. Forebrain-selective AMPA-receptor antagonism guided by TARP γ-8 as an antiepileptic mechanism. Nat Med. 2016;22:1496–1501.
58. Doyle ME, Boggs I, Attia R, et al. Autoimmune dacryoadenitis of NOD/LtJ mice and its subsequent effects on tear protein composition. Am J Pathol. 2007;171:1224–1236.
59. Jiao X, Wu M, Lu D, et al. Transcriptional profiling of daily patterns of mRNA expression in the C57BL/6j mouse cornea. Curr Eye Res. 2019;44:1054–1066.
60. Hughes ME, Hogensen JB, Kornacker K. JTK_CYCLE: an efficient nonparametric algorithm for detecting rhythmic components in genome-scale data sets. J Biol Rhythms. 2010;25:372–380.
61. Dyr KA, Lutter D, Artati A, et al. Atlas of circadian metabolism reveals system-wide coordination and communication between clocks. Cell. 2018;174:1571–1585.e1511.
62. Mure LS, Le HD, Benegiamo G, et al. Diurnal transcriptome atlas of a primate across major neural and peripheral tissues. Science. 2018;359:eaao3188.
63. Zhang R, Pottelezhnikov AA, Hogensen JB, et al. Discovering biology in periodic data through phase set enrichment analysis (PSEA). J Biol Rhythms. 2016;31:244–257.
64. Subramanian A, Tamayo P, Mootha VK, et al. Gene set enrichment analysis: a knowledge-based approach for interpreting genome-wide expression profiles. Proc Natl Acad Sci USA. 2005;102:15545–15550.
65. Kumar L, EF M, Muzu: a software package for soft clustering of microarray data. Bioinformation. 2007;2:5–7.
66. Futschik ME, Carlisle B. Noise-robust soft clustering of gene expression time-course data. J Bioinform Comput Biol. 2005;3:965–988.
67. Szklarczyk D, Gable AL, Lyon D, et al. STRING v11: protein–protein association networks with increased coverage,
Sleep Loss Reprograms ELG Circadian Transcriptome
supporting functional discovery in genome-wide experimental datasets. *Nucleic Acids Res.* 2019;47:D607–D615.
68. Keenan AB, Torre D, Lachmann A, et al. ChEA3: transcription factor enrichment analysis by orthogonal omics integration. *Nucleic Acids Res.* 2019;47:W212–W224.
69. Mendoza J, Graff C, Dardente H, et al. Feeding cues alter clock gene oscillations and photic responses in the suprachiasmatic nuclei of mice exposed to a light/dark cycle. *J Neurosci.* 2005;25:1514–1522.
70. Mathew D, Zhou P, Pywell CM, et al. Ablation of the ID2 gene results in altered circadian feeding behavior, and sex-specific enhancement of insulin sensitivity and elevated glucose uptake in skeletal muscle and brown adipose tissue. *PloS One.* 2013;8:e73064.
71. Lake CM, Holsclaw JK, Bellendir SP, et al. Relationship between unhealthy sleep status and dry eye symptoms in Singapore Malays and Indians. *Invest Ophthalmol Vis Sci.* 2018;59:Des143–Des150.
72. Nguyen KD, Fentress SJ, Qiu Y, et al. Circadian gene Bmal1 regulates diurnal oscillations of Ly6C(hi) inflammatory monocytes. *Science.* 2013;341:1483–1488.
73. Casanova-Acebes M, Pitaval C, Weiss LA, et al. Rhythmic modulation of the hematopoietic niche through neutrophil clearance. *Cell.* 2013;153:1025–1035.
74. Cao Y, Li Q, Liu L, et al. Modafinil protects hippocampal neurons by suppressing excessive autophagy and apoptosis in mice with sleep deprivation. *Br J Pharmacol.* 2019;176:1282–1297.
75. Xie G, Huang X, Li H, et al. Caffeine-related effects on cognitive performance: Roles of apoptosis in rat hippocampus following sleep deprivation. *Biochim Biophys Res Commun.* 2021;534:632–638.
76. Bass J, Takahashi JS. Circadian integration of metabolism and energetics. *Science.* 2010;330:1349–1354.
77. Alexandre C, Latremoliere A, Ferreira A, et al. Decreased alertness due to sleep loss increases pain sensitivity in mice. *Nat Med.* 2017;23:768–774.
78. Stapleton F, Alves M, Bunya YV, et al. TFOS DEWS II Epidemiology Report. *Ocul Surf.* 2017;15:334–365.
79. Ayaki M, Tsubota K, Kawashima M, et al. Sleep Disorders are a Prevalent and Serious Comorbidity in Dry Eye. *Invest Ophthalmol Vis Sci.* 2018;59:e1053–e1063.
80. Yu X, Guo H, Liu X, et al. Dry eye and sleep quality: a large community-based study in Hangzhou. *Sleep.* 2019;42.
81. Kawashima M, Uchino M, Yokoi N, et al. The association of Yu X, Guo H, Liu X, et al. Dry eye and sleep quality: a large community-based study in Hangzhou. *Sleep.* 2019;42.
82. Casanova-Acebes M, Pitaval C, Weiss LA, et al. Rhythmic modulation of the hematopoietic niche through neutrophil clearance. *Cell.* 2013;153:1025–1035.
83. Hanyuda A, Sawada N, Uchino M, et al. Relationship between unhealthy sleep status and dry eye symptoms in a Japanese population: the JP Hear NEX Study. *Ocul Surf.* 2021;21:306–312.
84. Badhan IJ, Petris RJ, Makara M, et al. Impact of the COVID-19 pandemic on eye strain and dry eye symptoms. *Ocul Surf.* 2021;22:38–46.
85. Mohawk JA, Green CB, Takahashi JS. Central and peripheral circadian clocks in mammals. *Ann Rev Neurosci.* 2012;35:445–462.
86. Sinturel F, Gerber A, Mauvoisin D, et al. Diurnal oscillations in liver mass and cell size accompany ribosome assembly cycles. *Cell.* 2017;169:651–663.e614.
87. Archer SN, Laing EE, Möller-Levet CS, et al. Mistimed sleep disrupts circadian regulation of the human transcriptome. *Proc Natl Acad Sci USA.* 2014;111:E682–E691.
88. Besedovsky L, Lange T, Haack M. The sleep-immune crosstalk in health and disease. *Physiol Rev.* 2019;99:1325–1380.
89. Dengler V, Westphalen K, Koeppen M. Disruption of circadian rhythms and sleep in critical illness and its impact on innate immunity. *Curr Pharm Des.* 2015;21:3460–3476.
90. He W, Holtkamp S, Hergenhahn SM, et al. Circadian expression of migratory factors establishes lineage-specific signatures that guide the homing of leukocyte subsets to tissues. *Immunity.* 2018;49:1175–1190.e1177.
91. Lee YB, Koh JW, Hyon JY, et al. Sleep deprivation reduces tear secretion and impairs the tear film. *Invest Ophthalmol Vis Sci.* 2014;55:3525–3531.
92. Darra DA. Neural regulation of lacrimal gland secretory processes: relevance in dry eye diseases. *Prog Retin Eye Res.* 2009;28:155–177.
93. Jin K, Imada T, Hisamura R, et al. Identification of lacrimal gland postganglionic innervation and its regulation of tear secretion. *Am J Pathol.* 2020;190:1068–1079.
94. Huang CT, Chiang RP, Chen CL, et al. Sleep deprivation aggravates median nerve injury-induced neuropathic pain and enhances microglial activation by suppressing melatonin secretion. *Sleep.* 2014;37:1513–1523.
95. Dai XJ, Jiang J, Zhang Z, et al. Plasticity and susceptibility of brain morphometry alterations to insufficient sleep. *Front Psychiatry.* 2018;9:266.
96. Spano GM, Banninng SW, Marshall W, et al. Sleep deprivation by exposure to novel objects increases synapse density and axon-spine interface in the hippocampal CAI region of adolescent mice. *J Neurosci.* 2019;39:6613–6625.
97. Noya SB, Colameo D, Brüning F, et al. The forebrain synaptic transcriptome is organized by clocks but its proteome is driven by sleep. *Science.* 2019;366:eav2642.
98. Asher G, Sassone-Corsi P. Time for food: the intimate interplay between nutrition, metabolism, and the circadian clock. *Cell.* 2015;161:84–92.
108. Damiola F, Le Minh N, Preitner N, et al. Restricted feeding uncouples circadian oscillators in peripheral tissues from the central pacemaker in the suprachiasmatic nucleus. *Genes Dev.* 2000;14:2950–2961.
109. Eckel-Mahan KL, Patel VR, de Mateo S, et al. Reprogramming of the circadian clock by nutritional challenge. *Cell.* 2013;155:1464–1478.
110. Sato S, Solanas G, Peixoto FO, et al. Circadian Reprogramming in the Liver Identifies Metabolic Pathways of Aging. *Cell.* 2017;170:664–677.e611.
111. Sies H. Oxidative stress: oxidants and antioxidants. *Exp Physiol.* 1997;82:291–295.
112. Hardeland R, Coto-Montes A, Poeggeler B. Circadian rhythms, oxidative stress, and antioxidative defense mechanisms. *Chronobiol Int.* 2003;20:921–962.
113. Belmonte C, Nichols JJ, Cox SM, et al. TFOS DEWS II pain and sensation report. *Ocul Surf.* 2017;15:404–437.
114. Acosta MC, Peral A, Luna C, et al. Tear secretion induced by selective stimulation of corneal and conjunctival sensory nerve fibers. *Invest Ophthalmol Vis Sci.* 2004;45:2335–2336.
**APPENDIX A: SUPPLEMENTARY DATA**
All data needed to evaluate the conclusions in the paper are present in the paper and/or the supplementary materials including Supplementary Tables S1 through S5 and Supplementary Figures S1 through S4. Additional data related to this article are available through NCBI’s BioProject database under accession PRJNA798106. | 2025-03-06T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
4715,
1
],
[
4715,
11531,
2
],
[
11531,
17137,
3
],
[
17137,
23395,
4
],
[
23395,
26864,
5
],
[
26864,
28324,
6
],
[
28324,
34652,
7
],
[
34652,
35877,
8
],
[
35877,
40337,
9
],
[
40337,
42125,
10
],
[
42125,
42653,
11
],
[
42653,
48032,
12
],
[
48032,
48322,
13
],
[
48322,
52064,
14
],
[
52064,
54841,
15
],
[
54841,
55239,
16
],
[
55239,
57341,
17
],
[
57341,
63689,
18
],
[
63689,
65658,
19
],
[
65658,
71962,
20
],
[
71962,
78704,
21
],
[
78704,
84060,
22
],
[
84060,
85471,
23
]
]
} |
0ae589174a71ede39cc02288d69126b52e80b6d4 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 30,
"total-fallback-pages": 0,
"total-input-tokens": 162989,
"total-output-tokens": 39896,
"fieldofstudy": [
"Mathematics"
]
} | Ordered random walks$^*$
Peter Eichelsbacher$^†$ Wolfgang König$^‡$
Abstract
We construct the conditional version of $k$ independent and identically distributed random walks on $\mathbb{R}$ given that they stay in strict order at all times. This is a generalisation of so-called non-colliding or non-intersecting random walks, the discrete variant of Dyson’s Brownian motions, which have been considered yet only for nearest-neighbor walks on the lattice. Our only assumptions are moment conditions on the steps and the validity of the local central limit theorem. The conditional process is constructed as a Doob $h$-transform with some positive regular function $V$ that is strongly related with the Vandermonde determinant and reduces to that function for simple random walk. Furthermore, we prove an invariance principle, i.e., a functional limit theorem towards Dyson’s Brownian motions, the continuous analogue.
Key words: Dyson’s Brownian motions, Vandermonde determinant, Doob $h$-transform, non-colliding random walks, non-intersecting random processes, fluctuation theory.
AMS 2000 Subject Classification: Primary 60G50, 60F17.
Submitted to EJP on June 21, 2007, final version accepted April 24, 2008.
$^*$Both authors have been supported by Deutsche Forschungsgemeinschaft via SFB/TR 12.
$^†$Ruhr-Universität Bochum, Fakultät für Mathematik, NA3/68, D-44780 Bochum, Germany, [email protected]
$^‡$Universität Leipzig, Mathematisches Institut, Augustusplatz 10/11, D-04109 Leipzig, Germany, [email protected]
1 Introduction and main result
1.1 Dyson’s Brownian motions and non-colliding processes.
In 1962, F. Dyson [Dy62] made a beautiful observation. He looked at a process version of the famous Gaussian Unitary Ensemble (GUE), a matrix-valued diffusion known as Hermitian Brownian motion. He was interested in the process of the vectors of the eigenvalues of that matrix process. It turned out that this process admits a concise description: it is in distribution equal to a family of standard Brownian motions, conditional on having never any collision of the particles. More explicitly, it is the conditional distribution of $k$ independent standard Brownian motions $B_1, \ldots, B_k$ on $\mathbb{R}$ given that the $k$-dimensional Brownian motion $B = (B_1, \ldots, B_k)$ never leaves the Weyl chamber,
$$W = \{ x \in \mathbb{R}^k : x_1 < x_2 < x_3 < \cdots < x_k \}.$$
(1.1)
In other words, $B$ is conditioned on the event $\{ T = \infty \}$, where
$$T = \inf \{ t \in [0, \infty) : B(t) \notin W \}$$
(1.2)
is the first time of a collision of the particles. The definition of the conditional process needs some care, since the event $\{ T = \infty \}$ has zero probability. As usual in such cases, it is defined via a Doob $h$-transform with some suitable harmonic function $h : W \to (0, \infty)$. It turned out that a suitable choice for $h$ (in fact, the only one, up to constant multiples) is the Vandermonde determinant $\Delta : \mathbb{R}^k \to \mathbb{R}$ given by
$$\Delta(x) = \prod_{1 \leq i < j \leq k} (x_j - x_i) = \det \begin{bmatrix} x_j^{i-1} \end{bmatrix}_{i,j=1,\ldots,k}, \quad x = (x_1, \ldots, x_k) \in \mathbb{R}^k.$$
(1.3)
More precisely, $h = \Delta : W \to (0, \infty)$ is a positive harmonic function for the generator $\frac{1}{2} \sum_{i=1}^n \partial_i^2$ of $B = (B_1, \ldots, B_k)$ on $W$, and $\Delta(B(t))$ is integrable for any $t > 0$ under any starting measure of the motions. Hence we may consider the Doob $h$-transform of $B$ on $W$ with $h = \Delta$. The transformed process is called Dyson’s Brownian motions. It is known since long that this transformed process is identical to the limiting conditional process given $\{ T > t \}$ as $t \to \infty$. Therefore, the process is also called non-colliding Brownian motions.
For some decades after this discovery, it was quiet about non-colliding random processes, but the interest renewed in the 1990ies, and it has become an active research area and is being studied for a couple of reasons. M.-F. Bru [Br91] studied another interesting matrix-valued stochastic process whose eigenvalue process admits a nice description in terms of non-colliding random processes, the Wishart processes, which are based on squared Bessel processes in place of Brownian motions. These processes and some few more were studied in [KO01]. Non-colliding Brownian motions on the circle were investigated in [HW96], asymptotic questions about Brownian motions in a Weyl chamber in [Gr99], and a systematic study of a large class of physically relevant matrix-valued processes and their eigenvalue processes is carried out in [KT04].
Certainly, also the time-discrete version has been studied, more precisely, families of $k$ i.i.d. discrete random walks, conditional on never leaving $W$. It is important for the present paper to note that so far only random walks have been considered that have the following continuity property: at the first time of a violation of the strict ordering, there are two components of
the walk that are at the same site (and produce therefore a collision). In other words, leaving \( W \) is only possible via a step into the boundary \( \partial W \) of \( W \). This property is shared by nearest-neighbor random walks on the lattice \( \mathbb{Z}^k \), started in \( (2\mathbb{Z})^k \cap W \) (in which case the walkers cannot jump over each other) and by walks that have only steps in \( \{0,1\}^k \) or by imposing similar rules. Obviously, this continuity property makes the analysis much easier, but heavily restricts the choice of the step distribution. For walks having this property, the event of never leaving \( W \) (i.e., of being strictly ordered at any time) is identical to being non-colliding, hence the term non-colliding random walks became popular, but also vicious walkers, non-intersecting paths and non-intersecting walks. We consider the latter two terms misleading since it is the graphs that are non-intersecting, more precisely the graph of the polygon line that interpolates between discrete time units. Non-intersecting paths played an important role in the proof of Johansson's beautiful analysis \([Jo00, Jo02]\) of the corner-growth model (which is equivalent to directed first-passage percolation). These works naturally raise the interesting question how far the connections between the corner-growth model and non-intersecting paths reach; they are yet known only for rather restricted waiting-time distributions respectively step distributions. Further relationships to other models, like the Arctic circle, are investigated in \([Jo02]\). Recently \([BS06]\), a random matrix central limit behavior was obtained for the rescaled versions of many non-intersecting random walks with an essentially general step distribution. The non-intersecting property was required only up to a fixed time. Furthermore, also applications in the study of series of queues in tandem were found and analysed; see the survey article \([OC03]\).
Especially in recent years, more and more connections have been found between non-colliding random processes and various models, some of which have not yet been fully understood. A number of explicit examples have been worked out, and the class of random processes whose non-colliding version could be rigorously established and characterized, is growing. It is now known how to construct and describe these conditional versions for a couple of examples of random walks, among which the binomial random walk, the multinomial walk, and the (continuous-time) Poisson random walk \([KOR02]\), and birth and death processes and the Yule process \([Do05, Ch. 6]\). In all these explicit examples, it fortunately turned out that the Vandermonde determinant, \( \Delta \), is a positive regular function for the generator of the family of the random walks, and the Doob \( h \)-transform with \( h = \Delta \) could explicitly be calculated. A survey on non-colliding random walks appears in \([K05, Ch. 4]\).
However, to the best of our knowledge, the theory of non-colliding random processes still consists of a list of explicit, instructive and important examples, but the general picture is still lacking. In particular, the precise class of random walks for whose generator the Vandermonde determinant is a positive regular function, is widely unknown yet, and it is also yet unknown what function in general replaces \( \Delta \) in the construction, if it can be carried out.
The present paper reveals the general mechanism of constructing from a tuple of \( k \) i.i.d. random walks on \( \mathbb{R} \) the conditional version that never leaves \( W \), i.e., whose components stay in strict order at any time. Only the finiteness of some sufficiently high moments of the walker's steps and the validity of the local central limit theorem will be assumed. We will identify a positive harmonic function in terms of which we will construct the version that never leaves \( W \). Furthermore, we will also consider the asymptotic behavior of the conditional walk and prove an invariance principle, i.e., the convergence of the properly rescaled process towards the continuous version, Dyson's Brownian motions. We consider the results of this paper as a universal approach to non-intersecting paths, which opens up a possibility to attack in future also related
models like the corner-growth model in a universal manner.
Since a general random walk makes jumps of various sizes, the term non-colliding is misleading, and the term non-intersecting refers to the graphs instead of the walks. We prefer to replace these terms by ordered random walks, for obvious reasons. General non-colliding random walks in the strict sense seem to represent an exciting and open research topic that may be inspired from other topics than processes of random matrices and will presumably not have much to do with Dyson’s Brownian motions.
1.2 Ordered random walks
For $k \in \mathbb{N}$, let $X_1, \ldots, X_k$ be $k$ independent copies of a random walk, $X_i = (X_i(n))_{n \in \mathbb{N}_0}$, on $\mathbb{R}$. Then $X = (X_1, \ldots, X_k)$ is a random walk on $\mathbb{R}^k$ with i.i.d. components. Our goal is to construct a conditional version of $X$, given that the $k$ components stay in a fixed order for all times. That is, we want to condition $X$ on never leaving the Weyl chamber $W$ in (1.1). Another way to formulate this is to condition on the event $\{\tau = \infty\}$, where
$$\tau = \inf\{n \in \mathbb{N}_0 : X(n) \notin W\}$$
is the first time that some component reaches or overtakes another one. Some care is needed in defining the conditional process, since the event $\{\tau = \infty\}$ has zero probability. We shall construct this process as a Doob $h$-transform and show that it coincides with the limiting conditional process given $\{\tau > n\}$ as $n \to \infty$.
Let $S \subset \mathbb{R}$ denote the state space of the random walk $X_1$ when started at 0. Let $\mathbb{P}$ denote the underlying probability measure. For $x \in \mathbb{R}^k$, we write $\mathbb{P}_x$ when the process $X = (X(n))_{n \in \mathbb{N}_0}$ starts at $X(0) = x$, and we denote by $\mathbb{E}_x$ the corresponding expectation. A function $h : W \cap S^k \to (0, \infty)$ is called a positive regular function with respect to the restriction of the transition kernel of $X$ to $W \cap S^k$ if
$$\mathbb{E}_x[h(X(1)) \mathbb{1}_{\{\tau > 1\}}] = h(x), \quad x \in W \cap S^k.$$ (1.5)
In this case, we may define the Doob $h$-transform of the process $X$ via the $n$-step transition probabilities
$$\widehat{\mathbb{P}}_x^{(h)}(X(n) \in dy) = \mathbb{P}_x(\tau > n; X(n) \in dy) \frac{h(y)}{h(x)}, \quad x, y \in W \cap S^k, n \in \mathbb{N}. \quad (1.6)$$
The regularity and positivity of $h$ guarantee that the right hand side of (1.6) is a probability measure on $W$ in $dy$. The state space of the Doob $h$-transform is equal to $W \cap (S^k - x)$ when started at $x$. A priori, the existence and uniqueness of such positive regular function is far from clear, and also the question if the corresponding Doob transform has anything to do with the conditional version given $\{\tau > n\}$ in the limit as $n \to \infty$.
In the present paper, we present a positive regular function $V$ such that the Doob $h$-transform with $h = V$ turns out to be the conditional version of $X$ given never exiting $W$. Under the latter process, we understand (in the case of its existence) the limiting process $X$ given $\{\tau > n\}$ as $n \to \infty$. Furthermore, we analyse the decay of the probability of the event $\{\tau > n\}$ and give a limit theorem for the rescaled path’s endpoint, $n^{-1/2}X(n)$, conditioned on this event. Another main goal is the analysis of the conditional process at large times. We show that the rescaled conditional process $(n^{-1/2}X(|tn|))_{t \geq 0}$ converges towards Dyson’s Brownian motions.
Now we state the precise assumptions on the walk. We want to work with a random walk that lies in the normal domain of attraction of Brownian motion. Without loss of generality we therefore put the
**Centering Assumption.** The walk’s steps have mean zero and variance one.
We distinguish the two cases of a lattice walk and a non-lattice walk. The following assumption will enable us to apply a local central limit theorem, which will be an important tool in our proofs.
**Regularity Assumption.** Either the support of the walk, \(\{X_1(n): n \in \mathbb{N}_0\}\), under \(\mathbb{P}_0\), is contained in the lattice \(\alpha \mathbb{Z}\) for some maximal \(\alpha \in (0, \infty)\), or the distribution of \(X_1(N)\) possesses a bounded density for some \(N \in \mathbb{N}\).
The walk’s state space, \(S\), is equal to \(\alpha \mathbb{Z}\) in the first case, the lattice case, and it is equal to \(\mathbb{R}\) in the second case, the non-lattice case.
Now we introduce the main object of the paper, the positive regular function \(h = V\) we will be working with. Define \(V: W \cap S^k \to \mathbb{R}\) by
\[
V(x) = \Delta(x) - \mathbb{E}_x[\Delta(X(\tau))], \quad x \in W \cap S^k.
\]
(1.7)
Actually, it is a priori not clear at all under what assumptions \(V\) is well-defined, i.e., under what assumptions \(\Delta(X(\tau))\) is integrable under \(\mathbb{P}_x\) for any \(x \in W\). This question is trivially answered in the affirmative for walks that have the above mentioned continuity property, which may be also formulated by saying that \(\mathbb{P}_x(X(\tau) \in \partial W) = 1\). This property depends on the initial site \(x \in W\) (e.g. simple random walk in \(\mathbb{Z}^k\) starting in \((2\mathbb{Z})^k\) has this property, but not when it starts in the site \((1,2,\ldots,k)\), say). All examples of walks considered in the literature so far (see Section 1.1) have this property. If the walk has this property, then \(X(\tau)\) has some equal components, \(\mathbb{P}_x\)-a.s., and therefore the Vandermonde determinant \(\Delta(X(\tau))\) equals zero, \(\mathbb{P}_x\)-a.s., which shows that \(V(x) = \Delta(x)\).
However, in the general case considered in the present paper, the integrability of \(\Delta(X(\tau))\) seems subtle, and we succeeded in proving the integrability only under some moment condition on the steps and the local central limit theorem.
**Theorem 1.1.** Assume that the random walk \(X\) satisfies the Centering Assumption and the Regularity Assumption. Then, there is a \(\mu = \mu_k > 0\), depending only on \(k\), such that, if the \(\mu\)-th moment of the walk’s steps is finite, the following hold.
(i) For any \(x \in W\), the random variable \(\Delta(X(\tau))\) is integrable under \(\mathbb{P}_x\).
(ii) The function \(V\) defined in (1.7) is a positive regular function with respect to the restriction of the transition kernel to \(W \cap S^k\), and \(V(X(n))\) is integrable with respect to \(\mathbb{P}_x\) for any \(x \in W\) and any \(n \in \mathbb{N}\).
(iii) The Doob \(h\)-transform of \(X\) on \(W \cap S^k\) with \(h = V\) is equal to the distributional limit of the conditional process given \(\{\tau > n\}\) as \(n \to \infty\).
(iv) For any \( x \in W \), the distribution of \( n^{-\frac{1}{2}}X(n) \) under \( \mathbb{P}_x(\cdot \mid \tau > n) \) converges towards the distribution on \( W \) with density \( y \mapsto \frac{1}{2\pi}e^{-\frac{1}{2}|y|^2}\Delta(y) \) (with \( Z_1 \) the norming constant). Moreover,
\[
\lim_{n \to \infty} n^{\frac{k-1}{2}}\mathbb{P}_x(\tau > n) = KV(x), \quad \text{where} \ K = \int_W \frac{e^{-\frac{1}{2}|y|^2}}{(2\pi)^{k/2}}\Delta(y) \, dy \prod_{l=0}^{k-1} \frac{1}{H^l}, \quad (1.8)
\]
(v) For any \( M > 0 \), uniformly in \( x \in W \) satisfying \( |x| \leq M \), \( \lim_{n \to \infty} n^{-\frac{1}{2}(k-1)}V(\sqrt{n}x) = \Delta(x) \).
(vi) For any \( x \in W \), the distribution of \( n^{-\frac{1}{2}}X(n) \) under \( \tilde{\mathbb{P}}_x^{(v)} \) converges towards the distribution on \( W \) with density \( y \mapsto \frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}|y|^2}\Delta(y)^2 \), the Hermite ensemble (with \( Z_2 \) the norming constant). More generally, the distribution of the process \( (n^{-\frac{1}{2}}X(\lfloor nt \rfloor))_{t \in [0,\infty)} \) under the transformed probabilities, i.e., under \( \tilde{\mathbb{P}}_x^{(v)} \sqrt{n}x \) for any \( x \in W \), converges towards Dyson’s Brownian motions started at \( x \).
The proof of Theorem 1.1 is distributed over a couple of propositions and lemmas. More precisely, (i) is contained in Proposition 3.1, (ii) in Lemma 4.4, (iii) in Lemma 4.6, (iv) in Corollary 3.8, (v) in Lemma 4.3 and (vi) in Lemma 4.7. An explicit formula for the transition probabilities of the transformed process appears in (4.81) below.
The only role of the Regularity Assumption is to establish the expansion in the local central limit theorem in (3.29) below, under a sufficient moment condition. Hence, all conclusions of Theorem 1.1 hold under (3.29) instead of the Regularity Assumption.
Our main tool in the proof of Theorem 1.1 is an extension of the well-known Karlin-McGregor formula to arbitrary random walks on \( \mathbb{R}^k \) with i.i.d. step distributions. Furthermore, we use Hölder’s inequality (this is why we lose control on the minimal integrability assumption), the local central limit theorem and Donsker’s invariance principle. Another helpful fact, proved in [KOR02], is that the process \( (\Delta(X(n)))_{n \in \mathbb{N}} \) is a martingale, provided that \( \Delta(X(n)) \) is integrable for any \( n \in \mathbb{N} \).
The special case \( k = 2 \) includes the well-known and much-studied question of conditioning a single path to be positive at all times (by consideration of the difference of the two walks). In fluctuation theory, one studies the question of conditioning a walk \( S = (S_n)_{n \in \mathbb{N}_0} \) on \( \mathbb{R} \) on not leaving \( [0,\infty) \), i.e., on the event \( \{\tilde{\tau} = \infty\} \), where \( \tilde{\tau} = \inf\{n \in \mathbb{N} : S_n < 0\} \). Here it is known that there is a positive regular function for the restriction of the transition kernel to \( [0,\infty) \). In case that the first moment of the step distribution is finite, this function is given as
\[
\tilde{V}(x) = \frac{x - \mathbb{E}_x[S_{\tilde{\tau}}]}{\mathbb{E}_0[-S_{\tilde{\tau}}]}, \quad x \in [0,\infty).
\]
This formula is analogous to (1.7), but note that \( V \) is defined in the interior of \( W \) only, and it is actually not clear how to extend it to \( \bar{W} \) in general. For \( x \in (0,\infty) \), one has \( \tilde{\tau} = \inf\{n \in \mathbb{N}_0 : S_n < 0\} \) under \( \mathbb{P}_x \), and in the case that the steps have a density, \( \tilde{\tau} \) is identical to our \( \tau \) if \( S = X_2 - X_1 \) in the case \( k = 2 \). In this case, we have \( \mathbb{E}_0[-S_{\tilde{\tau}}]\tilde{V}(x) = V(0,x) \) for \( x \in (0,\infty) \). The case \( k = 2 \) was considered in [BD94]. The standard proof of existence and representations for \( \tilde{V} \) uses fluctuation theory and the Sparre-Andersen identity, see [F71. Chapter XII and XVIII],
e.g. Instead, we use rough moment estimates and Hölder’s inequality in the present paper and therefore lose control on minimal integrability assumptions.
The problem remains open under what minimal assumptions the assertions of Theorem 1.1 remain true and what a positive regular function for the restriction to \( W \) could look like in the case of less integrability of the steps. Further future work will be devoted to the study of the system of \( k \) ordered walks in the limit \( k \to \infty \), from which we hope to deduce interesting and universal variants of Wigner’s semicircle law.
The remainder of this paper is devoted to the proof of Theorem 1.1. In Section 2, we present our main tool, a generalisation of the well-known Karlin-McGregor formula, a determinantal formula for the marginal distribution before the first time of a violation of the strict ordering. In Section 3 we prove that \( \Delta(X(\tau)) \) is integrable under \( \mathbb{P}_x \) for any \( x \in W \), a fact which establishes that \( V(x) \) is well-defined. Finally, in Section 4 we prove a couple of properties of \( V \), in particular its positivity (a fact which is crucial to define the transformed process) and the functional limit theorem towards Dyson’s Brownian motions.
2 A generalized Karlin-McGregor formula
An important tool for handling the distribution of the process \( X \) on the event \( \{ \tau > n \} \) is the well-known Karlin-McGregor formula [KM59] for the transition probabilities before a violation of the strict ordering of the components. This is an explicit formula for the distribution of \( X(n) \) on \( \{ \tau > n \} \) for a variety of stochastic processes including nearest-neighbor random walks on \( \mathbb{Z}^k \) and Brownian motion. In the standard Brownian motion case, this formula reads
\[
P_x(T > t; B(t) \in dy) = \det \left( \mathbb{P}_{x_i}(B_1(t) \in dy_j) \right)_{i,j=1,...,k}, \quad t > 0, x, y \in W,
\]
where the \( k \) motions start from \( x \) under \( \mathbb{P}_x \) (recall (1.1) and (1.2)). The proof is based on the continuity of the paths and on the reflection principle: if the two motions \( B_i \) and \( B_j \) meet each other at time \( T = s \in (0,t) \), then the paths \( (B_j(r))_{r \in [s,t]} \) and \( (B_i(r))_{r \in [s,t]} \) are interchanged, and we obtain motions that arrive at \( y_j \) and \( y_i \) rather than at \( y_i \) and \( y_j \). A clever enumeration shows that (2.9) holds. For this method to work it is crucial that the two motions \( B_i \) and \( B_j \) are located at the same site at time \( T \). The same argument applies to many other processes including discrete-time walks on the lattice \( \mathbb{Z}^k \) that have the continuity property discussed prior to Theorem 1.1, i.e., \( \mathbb{P}_x(X(\tau) \in \partial W) = 1 \). Since the proof of the Karlin-McGregor formula also involves a reflection argument, it is valid only for walks on \( \mathbb{Z}^k \) whose step distribution is i.i.d.
In the present paper, we overcome the continuity restriction, and we work with \( (k \) copies of) an arbitrary walk on the real line. We succeed in finding an analogue of the formula in (2.9), which we present now. Introduce the signed measure
\[
\mathcal{D}_n(x, dy) = \det \left( \mathbb{P}_{x_i}(X_1(n) \in dy_j) \right)_{i,j=1,...,k},
\]
\[
= \sum_{\sigma \in \mathfrak{S}_k} \text{sign}(\sigma) \prod_{i=1}^k \mathbb{P}_{x_{\sigma(i)}}(X_1(n) \in dy_i), \quad x = (x_1, \ldots, x_k), y = (y_1, \ldots, y_k),
\]
where \( \mathfrak{S}_k \) denotes the set of permutations of \( 1, 2, \ldots, k \).
The following is a generalization of (2.9) to general random walks on the real line. We use the notation of Section 1.2 but no assumptions on drift or moments are made, nor on existence of densities.
**Proposition 2.1** (Generalized Karlin-McGregor formula). Let \((X(n))_{n \in \mathbb{N}_0}\) be an arbitrary random walk on \(\mathbb{R}^k\) with i.i.d. components. Then the following hold.
(i) For any \(n \in \mathbb{N}\) and any \(x, y \in W\),
\[
\mathbb{P}_x(\tau > n; X(n) \in dy) = D_n(x, dy) - \mathbb{E}_x \left[ \mathbb{I}_{\{\tau \leq n\}} D_{n-\tau}(X(\tau), dy) \right]. \tag{2.11}
\]
(ii) Define \(\psi: \mathbb{R}^k \setminus W \to \mathbb{R}^k\) by
\[
\psi(y) = (y_j - y_i)(e_j - e_i), \quad \text{where } (i, j) \in \{1, \ldots, k\}^2 \text{ minimal satisfying } i < j \text{ and } y_i > y_j. \tag{2.12}
\]
Here \(e_i\) is the \(i\)-th canonical unit vector in \(\mathbb{R}^k\), and ‘minimal’ refers to alphabetical ordering.
Then, for any \(l, n \in \mathbb{N}\) satisfying \(l \leq n\) and any \(x, y \in W\),
\[
- \mathbb{E}_x \left[ \mathbb{I}_{\{\tau = l\}} D_{n-l}(X(l), dy) \right] = \mathbb{E}_x \left[ \mathbb{I}_{\{\tau = l\}} D_{n-l}(X(l), d(y + \psi(X(l)))) \right]. \tag{2.13}
\]
It is the assertion in (i) which we will be using in the present paper; no reflection argument is involved. The assertion in (ii) uses the reflection argument and is stated for completeness only.
In the special case of walks on \(\mathbb{Z}\) that enjoy the above mentioned continuity property, \(\mathbb{P}_x(X(\tau) \in \partial W) = 1\), the second term on the right of (2.11) vanishes identically since the vector \(X(\tau)\) has two identical components, and therefore the determinant vanishes.
An extension of Proposition 2.1 may be formulated for arbitrary Markov chains on \(\mathbb{R}^k\) that satisfy the strong Markov property; the assertion in (ii) additionally needs exchangeability of the step distribution. However, the analogue of \(D_n\) does not in general admit a determinantal representation.
**Proof of Proposition 2.1.** We write \(y_\sigma = (y_{\sigma(1)}, \ldots, y_{\sigma(k)})\). Using (2.10), we have
\[
\mathbb{P}_x(\tau > n; X(n) \in dy) - D_n(x, dy)
= \sum_{\sigma \in \mathbb{S}_k} \text{sign}(\sigma) \left[ \mathbb{P}_x(\tau > n; X(n) \in dy_\sigma) - \mathbb{P}_x(X(n) \in dy_\sigma) \right]
= - \sum_{\sigma \in \mathbb{S}_k} \text{sign}(\sigma) \mathbb{P}_x(\tau \leq n; X(n) \in dy_\sigma), \tag{2.14}
\]
since all the summands \(\mathbb{P}_x(\tau > n; X(n) \in dy_\sigma)\) are equal to zero with the exception of the one for \(\sigma = \text{id}\). Apply the strong Markov property to the summands on the right hand side of (2.14) at time \(\tau\), to obtain
\[
\mathbb{P}_x(\tau \leq n; X(n) \in dy_\sigma) = \sum_{m=1}^n \int_{\mathbb{R}^k \setminus W} \mathbb{P}_x(\tau = m; X(m) \in dz) \mathbb{P}_z(X(n - m) \in dy_\sigma). \tag{2.15}
\]
Substitute this in (2.14), we obtain
\[
\text{right side of (2.14)} = - \sum_{m=1}^{n} \int_{\mathbb{R}^k \setminus W} \mathbb{P}_x(\tau = m; X(m) \in dz) \sum_{\sigma \in \mathcal{S}_k} \text{sign}(\sigma) \mathbb{P}_x(X(n-m) \in dy_{\sigma})
\]
\[
= - \sum_{m=1}^{n} \int_{\mathbb{R}^k \setminus W} \mathbb{P}_x(\tau = m; X(m) \in dz) \text{det} \left( \left[ \mathbb{P}_{\sigma_i}(X_1(n-m) \in dy_j) \right]_{i,j=1,\ldots,k} \right)
\]
\[
= - \sum_{m=1}^{n} \mathbb{E}_x \left[ 1_{\{\tau=m\}} \mathcal{D}_{n-m}(X(m), dy) \right].
\]
This shows that (i) holds. In order to show (ii), we use the reflection argument of [KM59]. Fix \( l \in \{0, 1, \ldots, n\} \) and a continuous bounded function \( f: \mathbb{R}^k \rightarrow \mathbb{R} \), then it is sufficient to show
\[
- \sum_{\sigma \in \mathcal{S}_k} \text{sign}(\sigma) \mathbb{E}_x \left[ 1_{\{\tau=l\}} \mathcal{E}_{X(l)} \left[ f(X_{\sigma}(n-l)) \right] \right] = \sum_{\sigma \in \mathcal{S}_k} \text{sign}(\sigma) \mathbb{E}_x \left[ 1_{\{\tau=l\}} \mathcal{E}_{y} \left[ f(X_{\sigma}(n-l)+\psi(y)) \right] \right] \bigg|_{y=X(l)}.
\]
This is done as follows. Given a transposition \( \lambda = (i, j) \) satisfying \( i < j \), let \( \tau_{\lambda} = \inf\{n \in \mathbb{N} : X_i(n) \geq X_j(n)\} \) be the first time at which the \( i \)-th and the \( j \)-th component of the walk are not in strict order anymore. On the event \( \{\tau = l\} \), there is a minimal transposition \( \lambda^* \) such that \( \tau = \tau_{\lambda^*} \). On the event \( \{\tau = l, \lambda^* = (i, j)\} \), abbreviating \( y = X(l) \), in the inner expectation we reflect the path \( (y = X_{\sigma}(0), X_{\sigma}(1), \ldots, X_{\sigma}(n-l)) \) in the \( i-j \)-plane around the main diagonal (i.e., we interchange all the steps of the \( i \)-th component with the ones of the \( j \)-th component), and we obtain a path that terminates after \( n-l \) steps at \( X_{\sigma_{\lambda^*}}(n-l) + \psi(y) \). Obviously, the reflection is measure-preserving, and therefore we have
\[
\mathbb{E}_y \left[ f(X_{\sigma}(n-l)) \right] = \mathbb{E}_y \left[ f(X_{\sigma_{\lambda^*}}(n-l) + \psi(y)) \right], \quad \text{a.s. on } \{\tau = l, \lambda^* = (i, j)\}, \text{ where } y = X(l).
\]
Hence, denoting the set of transpositions by \( T_k \), we have
\[
- \sum_{\sigma \in \mathcal{S}_k} \text{sign}(\sigma) \mathbb{E}_x \left[ 1_{\{\tau=l\}} \mathcal{E}_{X(l)} \left[ f(X_{\sigma}(n-l)) \right] \right] = \sum_{\lambda \in T_k} \sum_{\sigma \in \mathcal{S}_k} \text{sign}(\sigma \circ \lambda) \mathbb{E}_x \left[ 1_{\{\tau=l, \lambda^* = (i, j)\}} \mathcal{E}_{y} \left[ f(X_{\sigma_{\lambda^*}}(n-l) + \psi(y)) \right] \right] \bigg|_{y=X(l)}.
\]
Now substitute \( \sigma \circ \lambda \), interchange the two sums and carry out the sum on \( \lambda \), to see that the right hand side is equal to the right hand side of (2.17).
\[ \square \]
3 Existence of \( V(x) \)
In this section, we assume that \( (X(n))_{n \in \mathbb{N}_0} \) is a random walk satisfying the assumptions of Theorem 1.1. Furthermore, we fix \( x \in W \). We prove that \( V(x) \) in (1.7) is well-defined. This is equivalent to showing the integrability of \( \Delta(X(\tau)) \) under \( \mathbb{P}_x \). This turns out to be technically nasty and to require a couple of careful estimates. The proof of the integrability of \( \Delta(X(\tau)) \) will be split into a number of lemmas. In Section 3.1, we explain the subtlety of the problem and
reduce the proof of the integrability of $\Delta(X(\tau))$ to the control of the tails of $\tau$. In Section 3.2 we provide a version of a higher-order local central limit theorem for later use. Our main strategy is explained in Section 3.3 where we also formulate and prove the main steps of the proof. Finally, in Section 3.4 we finish the proof of the integrability of $\Delta(X(\tau))$.
### 3.1 Integrability of $\Delta(X(\tau))$ and the tails of $\tau$.
The reason that the proof of integrability of $\Delta(X(\tau))$ is subtle comes from the following heuristic observation. We want to show that the series
$$\sum_{n \in \mathbb{N}} \mathbb{E}_x[|\Delta(X(\tau))| \mathbb{1}_{\{\tau = n\}}]$$
converges. Since we shall prove that $\mathbb{P}_x(\tau > n) \asymp n^{-\frac{k}{4}(k-1)}$, one can conjecture (but we actually do not prove that) that the event $\{\tau = n\}$ should have probability of order $n^{-\frac{k}{4}(k-1)-1}$. On this event, $|X(\tau)|$ is of order $|X(n)| \approx \sqrt{n}$, according to the central limit theorem. Therefore also all the differences $|X_i(n) - X_j(n)|$ with $1 \leq i < j \leq k$ should be of that order, with one exception: at time $\tau = n$, there is a random pair of indices $i^*, j^*$ such that $X_{i^*}(n)$ and $X_{j^*}(n)$ are close together, since the $i^*$-th and $j^*$-th walk just crossed each other. Hence, $|\Delta(X(\tau))|$ should be of order $n^{-\frac{1}{2}} \prod_{1 \leq i < j \leq k} \sqrt{n} = n^{\frac{k}{2}(k-1)-\frac{1}{2}}$, where the first term accounts for that random pair $i^*, j^*$. Hence, in the expectation in (3.18), there is a subtle extinction between two terms. However, that term should be of order $n^{-\frac{3}{2}}$ and therefore summable.
The next lemma shows that, for proving the finiteness of the series in (3.18), it will be crucial to control the tails of $\tau$.
**Lemma 3.1.** Assume that the $\mu$-th moment of the steps is finite, for some $\mu > (k-1)(\frac{k}{2}(k-1) + 2)$. Then there are $r \in (0, \frac{k}{4}(k-1) - 1)$ for the case $k > 2$ and $r \in (0, \frac{1}{2})$ for $k = 2$ and $\lambda \in (0,1)$ such that, for any set $M \subset W$ that is bounded away from zero, there is $C > 0$ such that
$$\mathbb{E}_x[|\Delta(X(\tau))| \mathbb{1}_{\{\tau \leq n\}}] \leq C|x|^{(1+a)\frac{k}{4}(k-1)} + C\left(\sum_{l=|x|^{2(1+a)}}^n \tau^r \mathbb{P}_x(\tau > l)\right)^\lambda, \quad n \in \mathbb{N}, x \in M, a \geq 0.$$
(3.19)
Using (3.19) for $a = 0$ and using some obvious estimates, we also have that for any compact set $M \subset W$, there is $C > 0$ such that
$$\mathbb{E}_x[|\Delta(X(\tau))| \mathbb{1}_{\{\tau \leq n\}}] \leq C + C\left(\sum_{l=1}^n \tau^r \mathbb{P}_x(\tau > l)\right)^\lambda, \quad n \in \mathbb{N}, x \in M.$$
(3.20)
We will use (3.20) later in the present section and (3.19) turns out to be crucial in the proof of Lemma 4.3 below.
**Proof.** For $l \in \mathbb{N}$, let $Y_i(l)$ be the $l$-th step of the $i$-th walk, hence, $X_i(n) = x_i + \sum_{l=1}^n Y_i(l)$, $\mathbb{P}_x$-almost surely, and all the random variables $Y_i(l)$ with $i \in \{1, \ldots, k\}$ and $l \in \mathbb{N}$ are i.i.d. with $\mathbb{E}[|Y_i(l)|^\mu] < \infty$.
1316
We split the expectation on the left hand side of (3.19) into the events \( \{ \tau \leq |x|^{2(1+\alpha)} \} \) and \( \{ |x|^{2(1+\alpha)} < \tau \leq n \} \). On the first event, we basically use that \( |X(\tau)| \leq O(|x|^{1+\alpha}) \). Indeed, abbreviating \( S_i(l) = Y_i(1) + \cdots + Y_i(l) \), we obtain
\[
E_x[|\Delta(X(\tau))|1_{|x|^{2(1+\alpha)} \leq \tau \leq |x|^{2(1+\alpha)}}] \leq \sum_{l \leq |x|^{2(1+\alpha)}} E_x \left[ \prod_{i \leq j} |x_i - x_j + S_i(l) - S_j(l)|1_{\tau = l} \right] \\
\leq E_x \left[ \prod_{i \leq j} \left( |x_i - x_j| + \max_{l \leq |x|^{2(1+\alpha)}} |S_i(l) - S_j(l)| \right) \right]. \tag{3.21}
\]
Under our moment assumption, the expectation of \( \prod_{(i,j) \in A} \max_{l \leq |x|^{2(1+\alpha)}} |S_i(l) - S_j(l)| \) is at most of order \( |x|^{|A|^{(1+\alpha)}} \), for any \( A \subset \{(i,j) \in \{1, \ldots, k\}^2 : i < j\} \), as is seen using Hölder’s inequality and Doob’s \( L^p \)-inequality with \( p = |A| \), since \( (S_i(l) - S_j(l))_{l \in \mathbb{N}_0} \) is a martingale. This explains the first term on the right hand side of (3.19), for any \( k \geq 2 \).
Now we turn to the expectation on the event \( \{|x|^{2(1+\alpha)} < \tau \leq n\} \). First we consider \( k > 2 \). Define, for \( m = 1, \ldots, k - 1 \),
\[
\tau_m = \inf \{ n \in \mathbb{N}_0 : X_m(n) \geq X_{m+1}(n) \}, \tag{3.22}
\]
the first time at which the \( m \)-th and the \((m+1)\)-st component violate the strict ordering. Hence, \( \tau = \inf_{m=1,\ldots,k-1} \tau_m \). On \( \{ \tau = m \} \), we have
\[
0 \leq X_m(\tau_m) - X_{m+1}(\tau_m) \leq Y_m(l) - Y_{m+1}(l). \tag{3.23}
\]
We use Hölder’s inequality twice as follows. Fix \( p, q > 1 \) satisfying \( \frac{1}{p} + \frac{1}{q} = 1 \). For any \( \xi > 0 \), we have (abbreviating \( \Upsilon_{m,l} = Y_m(l) - Y_{m+1}(l) \)),
\[
E_x[|\Delta(X(\tau))|1_{|x|^{2(1+\alpha)} < \tau = \tau_m \leq n}] \\
\leq E_x \left[ \sum_{l \leq |x|^{2(1+\alpha)}} \left( \int \left( \frac{(1+\xi)_{(\frac{k-1}{k} - 1) + \xi}}{l^{\frac{1}{k} + \xi}} \prod_{(i,j) \neq (m,m+1)} \frac{|X_i(l) - X_j(l)|}{l^{\frac{1}{k} + \xi}} \right) \right)^{1/p} \right] \\
\leq E_x \left[ \left( \sum_{l \leq |x|^{2(1+\alpha)}} |\Upsilon_{m,l}|^q \prod_{(i,j) \neq (m,m+1)} \left| \frac{X_i(l) - X_j(l)}{l^{\frac{1}{k} + \xi}} \right|^q \right)^{1/q} \right] \\
\leq E_x \left[ \left( \sum_{l \leq |x|^{2(1+\alpha)}} \int \left( \frac{(1+\xi)_{(\frac{k-1}{k} - 1) + \xi}}{l^{\frac{1}{k} + \xi}} \prod_{(i,j) \neq (m,m+1)} \left| \frac{X_i(l) - X_j(l)}{l^{\frac{1}{k} + \xi}} \right|^q \right) \right]^{1/p} \right] \\
\times E_x \left[ \left( \sum_{l \leq |x|^{2(1+\alpha)}} l^{-(\frac{1}{k} - 1) - q\xi} \prod_{(i,j) \neq (m,m+1)} \left| \frac{X_i(l) - X_j(l)}{l^{\frac{1}{k} + \xi}} \right|^q \right) \right]^{1/q}. \tag{3.24}
\]
We put \( r = p(\frac{k}{2} - 1) - 1 \) and \( \lambda = 1/p \) and choose \( \xi \) so small and \( p \) so close to one that \( r < \frac{k}{4}(k-1) - 1 \) and \( q\xi(\frac{k}{2}(k-1) - 1) > 1 \). When we pick \( \xi = (\frac{k}{2}(k-1) - 1)^{-1}(\frac{k}{2}(k-1) + 2)^{-1} \), then this is achieved by any choice of \( q > (\xi(\frac{k}{2}(k-1) - 1))^{-1} = \frac{k}{2}(k-1) + 2 \). According to our integrability assumption, we can pick \( q \) such that the \((k-1)q\)-th moment of the steps of
the random walk is finite. Note that $|Y_{m,l}|\prod_{i,j\neq (m,m+1)} |X_i(l) - X_j(l)|l^{-\frac{1}{2}}$ can be estimated against a sum of products of the form
$$|Y_\gamma(l)|\prod_{i=1}^k \left(\frac{|X_i(l)|}{\sqrt{l}}\right)^{\beta_i}, \quad \text{for some } \gamma \in \{1, \ldots, k\} \text{ and } \beta_1, \ldots, \beta_k \in \mathbb{N}_0,$$
with $\beta_1 + \cdots + \beta_k = \frac{k}{2}(k-1) - 1$; moreover $\beta_i \leq k - 1$ for every $i$ and $\beta_\gamma \leq k - 2$. We use $C$ to denote a generic positive constant, not depending on $x$, nor on $l$, possibly changing its value from appearance to appearance. According to our moment assumption, for any $i \in \{1, \ldots, k\}$, $l \in \mathbb{N}$ and any $\beta \in (0, k - 1)$, we have
$$\mathbb{E}_x\left[\left(\frac{|X_i(l)|}{\sqrt{l}}\right)^{\beta q}\right] \leq C + C \left(\frac{|x|}{\sqrt{l}}\right)^{\beta q} \quad \text{and} \quad \mathbb{E}_x\left[\left(\frac{|X_i(l)|}{\sqrt{l}}\right)^{\beta q} |Y_i(l)|^q\right] \leq C + C \left(\frac{|x|}{\sqrt{l}}\right)^{\beta q}, \quad (3.25)$$
where in the second relation we assumed that $\beta \leq k - 2$. On our set of summation on $l$, both upper bounds are bounded by $(C + |x|^{-a})^{\beta q}$ and may therefore be estimated against $C$, since $|x|$ is bounded away from zero for $x \in M$. Hence, the term on the last line of $(3.24)$ is bounded, since the sum over $l^{-\xi q}l^{\frac{k}{2}(k-1)-1}$ converges.
The first term of the right hand side of $(3.24)$ can be estimated as follows.
$$\mathbb{E}_x\left[\tau^{p(\frac{1}{2}(k-1)-1)(\frac{1}{2}+\xi)} I_{\{|x|^{2(1+a)}<\tau\leq n\}}\right]^{1/p} \leq C |x|^{1+\frac{2}{(1+a)}(k-1)} + C \left(\int_{|x|^{2(1+a)}}^n dt \mathbb{P}_x(\tau > t)\right)^{1/p} \leq C |x|^{1+\frac{2}{(1+a)}(k-1)} + C \left(\sum_{l=\lceil|x|^{2(1+a)}\rceil}^n l^{\xi p} \mathbb{P}_x(\tau > l)\right)^{1/p} .$$
Now put $\lambda = 1/p$. From this estimate, the assertion follows for any $k > 2$. When $k = 2$ things are actually much simpler. Again using Hölder’s inequality twice, we have
$$\mathbb{E}_x[|X_2(\tau) - X_1(\tau)|I_{\{|x|^{2(1+a)}<\tau\leq n\}}] \leq \mathbb{E}_x\left[\tau^{p(\frac{1}{2}+\xi)} I_{\{|x|^{2(1+a)}<\tau\leq n\}}\right]^{1/p} \times \mathbb{E}_x\left[\sum_{l=\lceil|x|^{2(1+a)}\rceil}^n l^{-q\xi} \frac{|Y_1(l) - Y_2(l)|^q}{\sqrt{l}}\right]^{1/q} . \quad (3.26)$$
Now we put $r = p(\frac{1}{2}+\xi) - 1$ and choose $\xi$ so small and $p$ so close to one that $r < \frac{1}{2}$ and $q\xi > 1$. Now the estimate $(3.19)$ is derived in a similar way as for $k > 2$. \qed
We remark that upper estimates for $\mathbb{E}_x[|\Delta(X(\tau))|I_{\{\tau=n\}}]$ in terms of $\mathbb{P}_x(\tau=n)$ are relatively easy to derive, but not sufficient for our purposes, since the techniques we develop in Section 3.3 below do not give sufficient control on the asymptotics of $\mathbb{P}_x(\tau=n)$. However, they are good enough to control the ones of $\mathbb{P}_x(\tau > n)$. 1318
3.2 Local expansions.
In this section we state, for future reference, one of our main tools, the expansion in the local central limit theorem, see [Pe75, Ch. VII, Par. 3]. We are under the Centering and the Regularity Assumptions. Recall that, in the lattice case, the maximal span of the walk is \( \alpha \), and in the non-lattice case that, for some \( N \in \mathbb{N} \), the density \( p_N \) is bounded. We define, for \( n \geq N \),
\[
p_n(x) = \begin{cases} \mathbb{P}_0(X_1(n) = x), & \text{in the lattice case,} \\ \frac{\mathbb{P}_0(X_1(n) \in dx)}{dx}, & \text{in the non-lattice case.} \end{cases}
\]
(3.27)
In the lattice case, the numbers \( p_n(x) \) sum up to one over the lattice \( S = \alpha \mathbb{Z} \), and in the non-lattice case, \( p_n \) is a probability density on \( S = \mathbb{R} \). Then we have
**Lemma 3.2** (Local CLT expansion). Assume that the Centering and the Regularity Assumptions hold and that the \( \mu \)-th moment of the step distribution is finite for some integer \( \mu \geq 2 \). Then
\[
\sqrt{n}p_n(x\sqrt{n}) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}} (1 + o(1)) + \frac{o(n^{1-\frac{\mu}{2}})}{1 + |x|^\mu}, \quad \text{uniformly for } x \in \frac{1}{\sqrt{n}}S.
\]
(3.28)
**Proof.** [Pe75, Thms. VII.16 resp. VII.17] state that
\[
\sqrt{n}p_n(x\sqrt{n}) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}} (1 + \sum_{\nu=1}^{\mu-2} \tilde{q}_{\nu}(x) + o(n^{1-\frac{\mu}{2}})) \quad \text{uniformly for } x \in \frac{1}{\sqrt{n}}S,
\]
(3.29)
where \( \tilde{q}_\nu \) are polynomials of order \( \leq 3\nu \) whose coefficients depend on the first cumulants of the step distribution only. The term \( e^{-\frac{x^2}{2}} \sum_{\nu=1}^{\mu-2} \tilde{q}_\nu(x) \) is either equal to \( e^{-\frac{x^2}{2}} o(1) \) (if \( |x| \leq o(n^{\frac{1}{2}}) \)) or it is \( o(n^{1-\frac{\mu}{2}}) \) (if \( |x| \geq n^{\frac{1}{4}} \), say). Hence, (3.28) follows. \( \square \)
We are going to rephrase an integrated version of the Karlin-McGregor formula of Proposition 2.1 in terms of \( p_n \). This will be the starting point of our proofs. For notational convenience, we will put \( N = 1 \) in the non-lattice case (it is easy, but notationally nasty, to adapt the proofs to other values of \( N \)). We introduce a rescaled version of the measure \( D_l(x,dy) \). For \( x = (x_1, \ldots, x_k) \in W \cap S^k \) and \( l \in \mathbb{N} \), introduce
\[
D_l^{(n)}(x,y) = \det \left[ \sqrt{n}p_l(y_i\sqrt{n} - x_j) \right]_{i,j=1,\ldots,k} = \sum_{\sigma \in S_k} \text{sign}(\sigma) \prod_{i=1}^{k} \left( \sqrt{n}p_l(y_i\sqrt{n} - x_{\sigma(i)}) \right), \quad y = (y_1, \ldots, y_k) \in W.
\]
(3.30)
In the non-lattice case, the map \( y \mapsto D_l^{(n)}(x,y) \) is a density of the measure that is obtained from \( D_l(x,dy) \) as the image measure under the map \( y \mapsto y/\sqrt{n} \). In the lattice case, it is equal to that measure; note that it is zero outside the lattice \( \frac{1}{\sqrt{n}}S^k \).
Then we may rephrase Proposition 2.1 as follows.
**Lemma 3.3.** For any continuous and bounded function \( f : \mathbb{R}^k \cap W \to \mathbb{R} \),
\[
\mathbb{E}_x \left[ f \left( n^{-\frac{1}{2}} X(n) \right) 1_{(\tau > n)} \right] = \begin{cases} \int_{W} \left[ D_l^{(n)}(x,y) - \mathbb{E}_x \left[ 1_{(\tau \leq n)}D_{n-\tau}^{(n)}(X(\tau),y) \right] \right] f(y) \, dy & \text{in the non-lattice case,} \\ \sum_{y \in W \cap \frac{1}{\sqrt{n}}S} \left[ D_l^{(n)}(x,y) - \mathbb{E}_x \left[ 1_{(\tau \leq n)}D_{n-\tau}^{(n)}(X(\tau),y) \right] \right] f(y) & \text{in the lattice case.} \end{cases}
\]
(3.31)
Proof. This is a reformulation of (2.11) using (3.30).
3.3 Our main strategy.
We are going to explain how we will prove the integrability of $\Delta(X(\tau))$ under $P_x$. As is seen from Lemma 3.1 our main task is to give good bounds for $P_n$ of the divergent scale function $n^{-\frac{k}{2}(k-1)}$ (where some error of some small positive power of $n$ would not spoil the proof). In order to do that, we use the Karlin-McGregor formula of Proposition 2.1 more precisely, the formula in (3.31).
We shall need a cutting argument for large values of $y$ in (3.31). To do this, we fix a slowly divergent scale function $n^\eta$ (with some small $\eta > 0$) and cut the integral in (3.31) into the area where $|y| \leq n^\eta$ and the remainder. The remainder is small, according to some moment estimate. On the set where $|y| \leq n^\eta$, we derive uniform convergence of the integrand, using appropriate expansions in the local central limit theorem and an expansion in the determinant. The second term in the integrand in (3.31), which is $E_x[1_{\{\tau \leq n\}}D_{n^{-\tau}}^<(X(\tau), y)]$, will have to be split into the three parts where
$$
\tau \leq t_n, \quad t_n < \tau \leq n - s_n, \quad n - s_n < \tau \leq n,
$$
where $t_n, s_n \to \infty$ are auxiliary sequences such that $n/t_n$ and $s_n/\sqrt{n}$ are small positive powers of $n$, say. The necessity for such a split is the application of the local central limit theorem inside the expectation: it is possible only for values $\tau \leq n - s_n$, and it gives asymptotically correct values only for $\tau \leq t_n$. We will eventually show that the first part gives the main contribution, and the two other parts are small remainder terms.
The reason that we have to work with a local central theorem (in fact, even with an expansion to sufficient deepness) is the following. After application of the approximation, there will be an extinction of terms in the determinant. As a result, the main term will turn out to be of order $n^{-\frac{k}{2}(k-1)}$. Hence, we need an error term of the size $o(n^{-\frac{k}{2}(k-1)})$ in the central limit regime, and this precision can be achieved only via an expansion of a local theorem. Sufficient moment conditions will imply that the contribution from outside the central limit region is also of the size $o(n^{-\frac{k}{2}(k-1)})$.
Let us now turn to the details. We first turn to the analysis of the main term of the integrand on the right of (3.31), where $\{\tau \leq n\}$ is replaced by $\{\tau \leq t_n\}$. We need the function
$$
V_n(x) = \Delta(x) - E_x[\Delta(X(\tau)) 1_{\{\tau \leq n\}}], \quad n \in \mathbb{N}, \ x \in \mathbb{R}^k.
$$
Under the assumption that the steps have finite $(k-1)$-st moment (which we will in particular impose), it is clear that $V_n(x)$ is well-defined. It is also relatively easy to show that $V_n$ is positive:
**Lemma 3.4.** For any $n \in \mathbb{N}$ and $x \in W$, $V_n(x) > 0$.
**Proof.** We recall the fact that $(\Delta(X(n)))_n$ is a martingale under $P_x$ for any $x \in W$, see [KOR02, Th. 2.1]. Hence, by the Optional Sampling Theorem we obtain
$$
V_n(x) = \Delta(x) - E_x[\Delta(X(\tau)) 1_{\{\tau \leq n\}}]
= E_x[\Delta(X(n))] - E_x[\Delta(X(n)) 1_{\{\tau \leq n\}}]
= E_x[\Delta(X(n)) 1_{\{\tau > n\}}],
$$
and this is obviously positive.
Lemma 3.5. Assume that the \( \mu \)-th moment of the steps is finite for some \( \mu \geq k - 1 \). Fix small parameters \( \eta, \xi > 0 \) satisfying \( 8 \eta < \xi \). We put \( t_n = n^{1-\xi} \). Then, for any \( x, y \in W \cap \frac{1}{\sqrt{n}} S^k \), uniformly for \( |x| = o(\sqrt{n}) \) and \( |y| = o(n^{\eta}) \), as \( n \to \infty \),
\[
D_n^{(n)}(x, y) = \mathbb{E}_x \left[ \mathbb{1}_{\{t \leq t_n\}} D_n^{(n)}(X(\tau), y) \right] \\
= \prod_{l=0}^{k-1} \frac{1}{l!} e^{-\frac{1}{2} |y|^2} \Delta(y) \left( 1 + o(1) \right) + O(n^{1-\mu(\eta + \xi^{1/4})}).
\]
Proof. According to (3.28), we have, uniformly in \( x, y \in \mathbb{R}^k \cap \frac{1}{\sqrt{n}} S^k \),
\[
D_n^{(n)}(x, y) = (2\pi)^{-\frac{k}{2}} \det \left[ (e^{-\frac{1}{2}(y_j - x_i)^2})_{i,j=1,\ldots,k} \right] \left( 1 + o(1) \right) + o(1) + o(n^{1-\frac{\mu}{2}})
\]
\[
= \frac{e^{-\frac{1}{2}|y|^2}}{(2\pi)^{k/2}} e^{-\frac{1}{2\sqrt{n}}|x|^2} \det \left[ (e^{-\frac{1}{2}|y|^2})_{i,j=1,\ldots,k} \right] \left( 1 + o(1) \right) + o(n^{1-\frac{\mu}{2}}).
\]
In order to evaluate the last determinant, we write, for \( |x| |y| = o(\sqrt{n}) \),
\[
e^{-\frac{1}{2}|y|^2} = \sum_{l=1}^{k} \frac{x_i^{l-1}}{(l-1)!} \frac{y_j^{l-1}}{\sqrt{n}} \det \left[ \frac{x_i^{l-1}}{(l-1)!} \right] \left( 1 + o(1) \right)
\]
and use the determinant multiplication theorem. This gives, with \( K' = \prod_{l=0}^{k-1} (l)!^{-1} \), if \( |x| |y| = o(\sqrt{n}) \),
\[
\det \left[ (e^{-\frac{1}{2}|y|^2})_{i,j=1,\ldots,k} \right] = \det \left[ \left( \frac{x_i^{l-1}}{(l-1)!} \right)_{i,l=1,\ldots,k} \right] \det \left[ \left( \frac{y_j^{l-1}}{\sqrt{n}} \right)_{j,l=1,\ldots,k} \right] \left( 1 + o(1) \right)
\]
\[
= K' \Delta(x) n^{-\frac{k}{2}(k-1)} \Delta(y) \left( 1 + o(1) \right).
\]
Substituting (3.36) in (3.33), we obtain
\[
D_n^{(n)}(x, y) = K' n^{-\frac{k}{2}(k-1)} \Delta(x) e^{-\frac{1}{2}|y|^2} \Delta(y) \left( 1 + o(1) \right) + o(n^{1-\frac{\mu}{2}}), \quad \text{for } |x| |y| = o(\sqrt{n}).
\]
In order to handle the second term on the left of (3.33) we have to distinguish if \( |X(\tau)| \) is large or not. For this purpose, fix \( m_n = n^{1-\xi^{1/2}} \), and split
\[
\mathbb{E}_x \left[ \mathbb{1}_{\{t \leq t_n\}} D_n^{(n)}(X(\tau), y) \right] \\
= \mathbb{E}_x \left[ \mathbb{1}_{\{t \leq t_n\}} \mathbb{1}_{\{|X(\tau)| \leq n^{\eta} \sqrt{m_n}\}} D_n^{(n)}(X(\tau), y) \right] + \mathbb{E}_x \left[ \mathbb{1}_{\{t \leq t_n\}} \mathbb{1}_{\{|X(\tau)| > n^{\eta} \sqrt{m_n}\}} D_n^{(n)}(X(\tau), y) \right].
\]
Let us estimate the second term. From now we use \( C \) to denote a generic positive constant, depending only on \( k \) or the step distribution. Observe from (3.29) and (3.30) that
\[
|D_n^{(n)}(x, y)| \leq C \left( \frac{n}{2} \right)^{\frac{k}{2}}, \quad n, l \in \mathbb{N}, x, y \in W \cap \frac{1}{\sqrt{n}} S^k.
\]
Lemma 3.6. Consider the non-lattice case. Assume that the formulation for the lattice case and its proof are analogous, and are left to the reader. For notational convenience, we assume that
\[ \mu \] for some \( a \) generic positive constant, depending only on the step distribution or on \( k \), possibly changing its value from appearance to appearance.
Hence, on \( \{ \tau \leq t_n \} \), \( D_{n-t}^{(n)}(X(\tau), y) \) is uniformly bounded in \( n \) and \( y \), since \( t_n = o(n) \) and therefore \( \frac{t_n}{n} \) is bounded. Using the boundedness of \( D_{n-t}^{(n)}(X(\tau), y) \), the Markov inequality and (3.25), we obtain, for all \( x, y \in W \cap \frac{1}{\sqrt{n}} S^k \) satisfying \( |x| = o(\sqrt{n}) \), as \( n \to \infty \),
\[
\mathbb{E}_x \left[ \mathbb{I}_{\{\tau \leq t_n\}} \mathbb{I}_{\{|X(\tau)| > n^{\eta} \sqrt{m_n}\}} D_{n-t}^{(n)}(X(\tau), y) \right] \\
\leq C \sum_{l=1}^{t_n} \mathbb{P}_x(\tau = l, |X(l)| > n^{\eta} \sqrt{m_n}) \leq C t_n \sup_{l=1}^{t_n} \mathbb{P}_x(|X(l)| > n^{\eta} \sqrt{m_n}) \\
\leq C t_n \sup_{l=1}^{t_n} \mathbb{E}_x[|X(l)||^{\mu}] n^{-\eta \mu} n^{-\mu/2} \leq O(\mu(t_n/m_n)^{\mu/2} n^{-\eta \mu}) \\
\leq O(n^{1-\mu(\eta + \xi_1/4)}).
\]
The first term in (3.38) can be handled in the same way as in (3.37). Indeed, for \( x, y \in W \cap \frac{1}{\sqrt{n}} S^k \) satisfying \( |x| = o(\sqrt{n}) \) and \( |y| = o(n^{\eta}) \),
\[
\mathbb{E}_x \left[ \mathbb{I}_{\{\tau \leq t_n\}} \mathbb{I}_{\{|X(\tau)| \leq n^{\eta} \sqrt{m_n}\}} D_{n-t}^{(n)}(X(\tau), y) \right] = \sum_{l=0}^{k-1} \frac{1}{l!} n^{-\frac{k}{2}(k-1)} \mathbb{E}_x \left[ \mathbb{I}_{\{\tau \leq t_n\}} e^{-\frac{1}{2} l |X(\tau)|^2} \mathbb{I}_{\{|X(\tau)| \leq n^{\eta} \sqrt{m_n}\}} \Delta(X(\tau)) \right] e^{-\frac{1}{2} |y|^2} (2\pi)^{k/2} \Delta(y) (1 + o(1)) + o(n^{1-\frac{k}{2}})
\]
\[ = \prod_{l=0}^{k-1} \frac{1}{l!} n^{-\frac{k}{2}(k-1)} \mathbb{E}_x \left[ \mathbb{I}_{\{\tau \leq t_n\}} \Delta(X(\tau)) \right] e^{-\frac{1}{2} |y|^2} (2\pi)^{k/2} \Delta(y) (1 + o(1)) + o(n^{1-\frac{k}{2}}). \tag{3.41} \]
The first step uses that (3.37) is applicable for \( x = X(\tau) \) because \( \frac{(n-x)}{n} \to 1 \), since \( |X(\tau)| |y| = o(n^{2\eta} \sqrt{m_n}) = o(n^{1/2 + 2\eta}) = o(\sqrt{n}) \); recall that we assumed that \( 8\eta < \xi_1 \). The second step in (3.41) is derived in a similar way as in (3.40), using also that, on the event \( \{ |X(\tau)| \leq n^{\eta} \sqrt{m_n} \} \), we have \( |X(\tau)|^2/n \leq n^{\eta} \sqrt{m_n}/n \to 0 \), according to the choice of \( m_n \) and \( 8\eta < \xi_1 \).
Now substitute (3.41) and (3.40) in (3.38) and this and (3.37) on the left side of (3.33) to finish the proof.
Now we examine the part where \( t_n \leq \tau \leq n - s_n \). We restrict to the non-lattice case; the formulation for the lattice case and its proof are analogous, and are left to the reader.
Lemma 3.6. Consider the non-lattice case. Assume that the \( \mu \)-th moment of the steps is finite for some \( \mu > k - 1 \). Fix small parameters \( \eta, \varepsilon, \xi_1, \xi_2 > 0 \) such that \( \xi_2 > \varepsilon + \eta \). We put \( t_n = n^{1-\xi_1} \) and \( s_n = n^{1+\xi_2} \). Then, for any \( x \in W \), uniformly for \( |x| = o(\sqrt{n}) \), as \( n \to \infty \),
\[
\int_W \mathbb{I}_{\{|y| \leq n^\eta\}} \left[ \mathbb{E}_x \left[ \mathbb{I}_{\{t_n \leq \tau \leq n - s_n\}} D_{n-t}^{(n)}(X(\tau), y) \right] \right] dy \\
\leq O(n^{\varepsilon + \eta - \xi_2}) \mathbb{P}_x(\tau \geq t_n) + o(n^{1 - \mu(\eta + \xi_2) + O(n^{1-\xi_1}) + O(n^{1-\varepsilon\mu})}. \tag{3.42}
\]
Proof. For notational convenience, we assume that \( t_n \) and \( s_n \) are integers. We will use \( C > 0 \) as a generic positive constant, depending only on the step distribution or on \( k \), possibly changing its value from appearance to appearance.
Similarly to \((3.38)\), in the expectation on the left of \((3.42)\), we distinguish if \(|X(\tau)|\) is larger than \(n^y\sqrt{m_n}\) or not, where this time we pick \(m_n = n^{1+\xi/2}\). Furthermore, we recall the stopping time \(\tau_m\) from \((3.22)\) and sum on all values of \(m\) and distinguish if \(|X_m(\tau) - X_{m+1}(\tau)|\) is smaller than \(n^\xi\) or not. Furthermore, we sum on all values of \(\tau\). Recalling also \((3.39)\), we estimate the integrand on the left side of \((3.42)\) as
\[
\left| E_x \left[ \mathbb{1}_{\{t_n \leq \tau \leq n-s_n\}} D_{n-l}^{(n)}(X(\tau), y) \right] \right| \leq Z_{n}^{(1)}(y) + Z_{n}^{(2)}(y) + Z_{n}^{(3)}(y),
\]
where
\[
Z_{n}^{(1)}(y) = \sum_{l=t_n}^{n-s_n} E_x \left[ \mathbb{1}_{\{\tau = l\}} \mathbb{1}_{\{|X(l)| > n^\eta \sqrt{m_n}\}} \right] D_{n-l}^{(n)}(X(l), y)
\]
\[
Z_{n}^{(2)}(y) = \sum_{l=t_n}^{n-s_n} \sum_{m=1}^{k-1} E_x \left[ \mathbb{1}_{\{\tau = \tau_m = l\}} \mathbb{1}_{\{|X_m(l) - X_{m+1}(l)| > n^\xi\}} \right] D_{n-l}^{(n)}(X(l), y)
\]
\[
Z_{n}^{(3)}(y) = \sum_{l=t_n}^{n-s_n} \sum_{m=1}^{k-1} E_x \left[ \mathbb{1}_{\{\tau = \tau_m = l\}} \mathbb{1}_{\{|X(l)| \leq n^\eta \sqrt{m_n}\}} \mathbb{1}_{\{|X_m(l) - X_{m+1}(l)| \leq n^\xi\}} \right] D_{n-l}^{(n)}(X(l), y)
\]
Let us estimate the integral over \(Z_{n}^{(1)}\). Observe that the measure with density \(y \mapsto |D_{n-l}^{(n)}(x, y)|\) has bounded total mass:
\[
\int_W dy |D_{n-l}^{(n)}(x, y)| \leq k^l \left( \int \sqrt{m_n} dz \right)^k \leq k^l, \quad 0 \leq l \leq n, x \in W.
\]
Using this and the Markov inequality, we obtain, for \(|x| = o(\sqrt{n}) = o(\sqrt{n - s_n})\), as \(n \to \infty\),
\[
\int_W dy Z_{n}^{(1)}(y) \leq C \sum_{l=t_n}^{n-s_n} n^{s_n} \mathbb{P}_x(|X(l)| > n^\eta \sqrt{m_n}) \leq C \sum_{l=t_n}^{n-s_n} E_x[|X(l)|^\mu] n^{-\eta \mu} m_n^{-\mu/2}
\]
\[
\leq C n (n/m_n)^{\mu/2} n^{-\eta \mu} \leq O(n^{1-\mu(\eta+\xi/4)}).
\]
In a similar way, we estimate the integral over \(Z_{n}^{(2)}\). Recall that, on the event \(\{\tau = l = \tau_m\}\), we may use \((3.23)\), \((3.47)\) and then the Markov inequality, to obtain
\[
\int_W dy Z_{n}^{(2)}(y) \leq C \sum_{l=t_n}^{n-s_n} \sum_{m=1}^{k-1} \mathbb{P}_x(|Y_{m+1}(l) - Y_m(l)| > n^\xi) \leq C n n^{-\xi} \leq O(n^{1-\xi}).
\]
Hence, \((3.48)\) and \((3.49)\) yield the two latter error terms on the right hand side of \((3.42)\).
We turn to an estimate of \(Z_{n}^{(3)}(y)\). For \(t_n \leq l \leq n-s_n\), on the event \(\{\tau = l\} \cap \{|X(l)| \leq n^\eta \sqrt{m_n}\}\), we use the local central limit theorem in \((3.28)\) to obtain
\[
D_{n-l}^{(n)}(X(l), y)
\]
\[
= \text{det} \left[ \left( \sqrt{\eta} \sqrt{m_n} - X_i(l) \right)_{i,j=1,\ldots,k} \right]
\]
\[
= \left( \frac{n}{n-l} \right) \frac{\pi^{k/2}}{2^{k/2}} \frac{n^{k\xi}}{(2\pi)^{k/2}} \det \left[ \left( e^{-1/2|y|^2} \frac{n}{m_n} \right)_{i,j=1,\ldots,k} \right] \left( 1 + o(1) \right) + o(n-l)^{1-\mu/2}.
\]
Abbreviate $a = X(l)\sqrt{n}/(n - l)$, then the determinant may be written
$$\det \left[ (e^{a_{ij}})_{i,j=1,\ldots,k} \right] = \sum_{1 \leq i < j \leq k} \left( 1 - e^{-(a_m - a_{m+1})|y_i - y_j|} \right) \sum_{\sigma \in \mathfrak{S}_k} \text{sign}(\sigma) \prod_{p=1}^{k} e^{a_{\sigma(p)} y_p}.$$ \hspace{1cm} (3.51)
Observe that the exponent $(a_m - a_{m+1})(y_i - y_j)$ asymptotically vanishes on the event \{ $|X_m(l) - X_{m+1}(l)| \leq n^\varepsilon$ \}, since on \{ $|y| \leq n^\eta$ \} we obtain
$$|a_m - a_{m+1}| |y_i - y_j| \leq n^{\varepsilon + \eta} \frac{\sqrt{n}}{n - l} \leq n^{\varepsilon + \eta + \frac{1}{2}} \frac{1}{s_n} = n^{\varepsilon + \eta - \xi_2} = o(1),$$ \hspace{1cm} (3.52)
since $\xi_2 > \varepsilon + \eta$. Hence, we may use that $|1 - e^x| \leq \mathcal{O}(|x|)$ as $x \to 0$, and obtain from (3.51) that
$$\left| \det \left[ (e^{y_i X(l)\sqrt{n}/n})_{i,j=1,\ldots,k} \right] \right| \leq \mathcal{O}(n^{\eta + \varepsilon - \xi_2}) \sum_{\sigma \in \mathfrak{S}_k} \prod_{i=1}^{k} e^{X_{\sigma(i)}(l)/\sqrt{n}/n - y_i}.$$ \hspace{1cm} (3.53)
Using this in (3.50) and this in (3.46), we arrive at
$$Z_n^{(3)}(y) \leq \mathcal{O}(n^{\eta + \varepsilon - \xi_2}) \sum_{l=t_n}^{n-s_n} \left( \frac{n}{n - l} \right)^{\frac{k}{2}} \sum_{\sigma \in \mathfrak{S}_k} \mathbb{E}_x \left[ \mathbb{I}_{\{\tau = t\}} e^{-\frac{1}{2} |X_{\sigma}(l)/\sqrt{n}/n - y|^2 \frac{n}{n - l}} \right] + o\left( s_n^{1-\mu/2} \right).$$
Now we integrate over $y$ and use Fubini’s theorem:
$$\int_W \mathbb{I}_{\{|y| \leq n^\eta\}} Z_n^{(3)}(y) \, dy$$
$$\leq \mathcal{O}(n^{\eta + \varepsilon - \xi_2}) \sum_{l=t_n}^{n-s_n} \sum_{\sigma \in \mathfrak{S}_k} \mathbb{E}_x \left[ \mathbb{I}_{\{\tau = t\}} \int_{\mathbb{R}^k} e^{-\frac{1}{2} |X_{\sigma}(l)/\sqrt{n}/n - y|^2 \frac{n}{n - l}} \left( \frac{n}{n - l} \right)^{\frac{k}{2}} \, dy \right] + o\left( n^{\frac{1}{2} - \frac{\mu}{2} + \eta k + \xi_2} \right)$$
$$\leq \mathcal{O}(n^{\varepsilon + \eta - \xi_2}) \sum_{l=t_n}^{n-s_n} \mathbb{P}_x(\tau = t) + o\left( n^{\frac{1}{2} - \frac{\mu}{2} + \eta k + \xi_2} \right)$$
$$\leq \mathcal{O}(n^{\varepsilon + \eta - \xi_2}) \mathbb{P}_x(\tau \geq t_n) + o\left( n^{\frac{1}{2} - \frac{\mu}{2} + \eta k + \xi_2} \right).$$
Substituting this in (3.43) and combining with (3.48) and (3.49), we arrive at (3.42). \hfill \Box
### 3.4 Proof of integrability of $\Delta(X(\tau))$.
Now we collect the preceding and prove the integrability of $\Delta(X(\tau))$ under $\mathbb{P}_x$ for any $x$:
**Proposition 3.7 (Integrability of $\Delta(X(\tau))$).** There is $\mu_k$, depending only on $k$, such that, if the $\mu_k$-th moment of the steps is finite, for any $x \in W$, the variable $\Delta(X(\tau))$ is integrable under $\mathbb{P}_x$. Moreover, uniformly in $x \in W$ on compacts,
$$\lim_{n \to \infty} n^{k(1 - \frac{1}{k})} \mathbb{P}_x \left( \tau > n; \frac{1}{\sqrt{n}} X(n) \in dy \right) = \prod_{l=1}^{k-1} \frac{1}{l!} V(x) e^{-\frac{1}{2} |y|^2} \mathcal{D} \left( \frac{y}{(2\pi)^{k/2}} \right) \, dy,$$ \hspace{1cm} (3.54)
in the sense of weak convergence of distributions on $W$.
1324
Before we give the proof, we state some conclusions:
**Corollary 3.8** (Tails of τ and limit theorem before violation of ordering). Assume that the \( \mu_k \)-th moment of the steps is finite, with \( \mu_k \) as in Proposition 3.7. Then
\[
\lim_{n \to \infty} n^{\frac{k}{2}(k-1)} \mathbb{P}_x(\tau > n) = K V(x), \quad \text{where } K = \prod_{l=1}^{k-1} \frac{1}{l!} \int_{W} \frac{e^{-\frac{1}{2} |y|^2}}{(2\pi)^{k/2}} \Delta(y) \, dy. \tag{3.55}
\]
Furthermore, the distribution of \( n^{-\frac{1}{2}} X(n) \) under \( \mathbb{P}_x(\cdot \mid \tau > n) \) converges towards the distribution on \( W \) with density \( y \mapsto \frac{1}{Z_1} e^{-\frac{1}{2} |y|^2} \Delta(y) \), where \( Z_1 \) is the normalisation.
Note that we *a priori* do not know yet whether or not \( V \) is positive. However, its nonnegativity is now clear, which we want to state explicitly:
**Corollary 3.9** (Nonnegativity of \( V \)). For any \( x \in W \), the number \( V(x) \) defined in (1.7) is well-defined and nonnegative.
This follows either from the asymptotics in Proposition 3.7 or from the fact that \( V_n \) is positive (see Lemma 3.4), in combination with \( V(x) = \lim_{n \to \infty} V_n(x) \) via Lebesgue’s theorem.
**Proof of Proposition 3.7** Fix some continuous and bounded function \( f : W \to \mathbb{R} \). We abbreviate
\[
a_n(f) = n^{\frac{k}{2}(k-1)} \mathbb{E}_x \left[ f\left(n^{-\frac{1}{2}} X(n)\right) \mathbb{1}_{\{\tau > n\}} \right] \quad \text{and} \quad a_n = a_n(\mathbb{1}) \quad \text{and} \quad A_n = \max\{a_1, \ldots, a_n\}.
\]
Our first step, see (3.65), is to derive an expansion for \( a_n(f) \) in terms of \( K(f)V_n(x) \) with some suitable \( K(f) \in (0, \infty) \) and error terms depending on \( A_n \) and \( \mathbb{P}_x(n - s_n \leq \tau \leq n) \). Specialising to \( f = \mathbb{1} \) and using an upper bound for \( V_n(x) \) derived from Lemma 3.1, we obtain a recursive upper bound for \( a_n \) in terms of \( A_n \) and \( a_{n-s_n} - a_{n} \). This estimate directly implies that \( (A_n)_{n \in \mathbb{N}} \) is bounded, hence also \( (a_n)_{n \in \mathbb{N}} \) is bounded. Via Lemma 3.1, this directly implies the integrability of \( \Delta(X(\tau)) \), i.e., we know that \( V(x) \) is well-defined, and \( V(x) = \lim_{n \to \infty} V_n(x) \). Using this again in (3.65) for \( f = \mathbb{1} \), we further obtain that \( a_n \) converges towards \( K V(x) \), where \( K \) is defined in (3.55). Using this in (3.65) for arbitrary \( f \), we derive the assertions in (3.54) and finish the proof.
As in Lemmas 3.5 and 3.6 we pick small parameters \( \varepsilon, \eta, \xi_1, \xi_2 > 0 \), and we put \( t_n = n^{1-\xi_1} \) and \( s_n = n^{\frac{1}{2}+\xi_2} \). Now we require that
\[
8\eta < \xi_1 \quad \text{and} \quad \xi_2 > \varepsilon + \eta + \xi_1 \frac{k}{4}(k-1), \tag{3.56}
\]
and we pick \( \mu \) so large that
\[
\mu > (k-1)\left(\frac{k}{2}(k-1)+2\right) \quad \text{and} \quad \frac{k}{4}(k-1) + \max \left\{ -\mu\eta, \frac{1}{2} - \frac{\mu}{4} + \eta k + \xi_2, 1 - \mu(\eta + \xi_1/4), 1 - \varepsilon \mu \right\} < 0. \tag{3.57}
\]
In the following, we will restrict ourselves to the non-lattice case. The necessary changes for the lattice cases are only notational. We use \( C \) to denote a generic positive constant that is uniform in \( n \) and uniform in \( x \) on compacts and may change its value from appearance to appearance. All
following limiting assertions hold for $x \in W$ uniformly on compacts. We begin with multiplying (3.31) with $n \frac{k}{4}(k-1)$ and distinguishing the events $\{|X_n| \geq n^{\frac{k}{10}+\eta}\}$ and its complement. This gives
$$a_n(f) = n^\frac{k}{4}(k-1) \mathbb{E}_x \left[ f \left( n^{-\frac{1}{2}} X(n) \right) \mathbb{I}_{\{\tau > n\}} \mathbb{I}_{\{n^{-1/2}|X(n)| \geq n^\eta\}} \right]$$
$$+ n^\frac{k}{4}(k-1) \int_W \mathbb{I}_{\{|y| \leq n^\eta\}} \left[ I_n(y) + II_n(y) + III_n(y) \right] f(y) \, dy,$$
where
$$I_n(y) = D^{(n)}_n(x, y) - \mathbb{E}_x \left[ \mathbb{I}_{\{\tau \leq n\}} D^{(n)}_n(X(\tau), y) \right],$$
$$II_n(y) = -\mathbb{E}_x \left[ \mathbb{I}_{\{n+1 \leq \tau \leq n+s\}} D^{(n)}_n(X(\tau), y) \right],$$
$$III_n(y) = -\mathbb{E}_x \left[ \mathbb{I}_{\{n-s+1 \leq \tau \leq n\}} D^{(n)}_n(X(\tau), y) \right].$$
We use the Markov inequality for the first term on the right hand side of (3.58), which gives
$$n^\frac{k}{4}(k-1) \left| \mathbb{E}_x \left[ f \left( n^{-\frac{1}{2}} X(n) \right) \mathbb{I}_{\{\tau > n\}} \mathbb{I}_{\{n^{-1/2}|X(n)| \geq n^\eta\}} \right] \right|$$
$$\leq n^\frac{k}{4}(k-1) \| f \|_\infty \mathbb{P}_x \left( n^{-1/2}|X(n)| \geq n^\eta \right) \leq C n^\frac{k}{4}(k-1)n^{-\mu}$$
$$\leq O(n^\frac{k}{4}(k-1)-\mu) = o(1),$$
since $\frac{k}{4}(k-1) - \mu < 0$ by (3.57). Hence,
$$a_n(f) = o(1) + \int_W \mathbb{I}_{\{|y| \leq n^\eta\}} n^\frac{k}{4}(k-1) \left[ I_n(y) + II_n(y) + III_n(y) \right] f(y) \, dy,$$
Now we use (3.33) for $I_n(y)$, (3.42) for $II_n(y)$ and (3.47) for $III_n(y)$. This gives
$$a_n(f) = o(1) + \prod_{l=0}^{k-1} \int_W \mathbb{I}_{\{|y| \leq n^\eta\}} e^{-\frac{1}{2}|y|^2} \mathbb{P}_x \left( \tau \leq n \right) f(y) \, dy V_{t_n}(x) (1 + o(1))$$
$$+ n^\frac{k}{4}(k-1) O(n^{\frac{1}{4}+\eta-\xi}) + n^\frac{k}{4}(k-1) O(n^{1-\mu})$$
$$+ n^\frac{k}{4}(k-1) \left( o(n^{\frac{1}{4}+\eta-\xi}) + O(n^{1-\mu}) \right).$$
Use that $\lim_{n \to \infty} (n/t_n)^{\frac{k}{4}(k-1)} n^{\frac{1}{4}+\eta-\xi} = 0$ (see (3.56)) to write the first term in the second line of (3.64) as $o(1) a_{t_n}$. Using our assumptions on $\mu$ in (3.57), the third line of (3.64) is $o(1)$. Therefore, we have from (3.64)
$$a_n(f) = K(f) V_{t_n}(x) (1 + o(1)) + o(1) (1 + o(1)) a_{t_n} + n^\frac{k}{4}(k-1) O(\mathbb{P}_x(n - s_n \leq \tau \leq n)).$$
where
$$K(f) = \prod_{l=1}^{k-1} \frac{1}{l!} \int_W \mathbb{P}_x \left( \tau > l \right) f(y).$$
In order to estimate $V_{t_n}(x)$, we use Lemma 3.1 (more precisely, (3.20)) and obtain, for some $\lambda \in (0, 1)$ and $r \in (0, \frac{1}{2}(k-1) - 1)$,
$$|V_{t_n}(x)| \leq |\Delta(x)| + C + C \left( \sum_{l=1}^{t_n} l^r \mathbb{P}_x(\tau > l) \right)^\lambda \leq C + C \left( \sum_{l=1}^{t_n} l^{r+\frac{k}{4}(k-1)} a_l \right) \leq C + C A_n^\lambda,$$
1326
since the sum over \( p^{-\frac{1}{4}(k-1)} \) converges. Remark, that \( \mu \) is chosen so large that (3.57) holds, therefore Lemma 3.1 can be applied. We therefore obtain from (3.65), specialised to \( f = \mathbb{I} \),
\[
a_n \leq C + CA_n + C(a_n-s_n(1 + a(1)) - a_n),
\]
(3.67)
where we used \( n^{\frac{k}{4}(k-1)} P_x(n - s_n \leq \tau \leq n) = a_{n-s_n}(n/(n-s_n))^{\frac{k}{4}(k-1)} - a_n \) and where we recalled that \( s_n = o(n) \) and therefore \( n^{\frac{k}{4}(k-1)} = (n-s_n)^{\frac{k}{4}(k-1)}(1 + o(1)) \).
Solving this recursive bound for \( a_n \), we obtain the estimate
\[
a_n \leq C + \frac{C}{C+1} A_n^\lambda + \frac{o(1)}{C+1} A_n + \frac{C + o(1)}{C+1} a_{n-s_n} \leq C + \frac{C}{C+1} A_n^\lambda + \frac{C + o(1)}{C+1} A_n.
\]
(3.68)
Since the right hand side is increasing in \( n \), we also have this upper bound for \( A_n \) instead of \( a_n \). Now it is clear that \( (A_n)_{n \in \mathbb{N}} \) is a bounded sequence, i.e., \( \limsup_{n \to \infty} n^{\frac{k}{4}(k-1)} P_x(\tau > n) < \infty \). From Lemma 3.1 (more precisely, from (3.20)) we see that \( V(x) \) is well-defined, and \( \lim_{n \to \infty} V_n(x) = V(x) \) by Lebesgue’s theorem.
Now, we prove that \( \lim_{n \to \infty} a_n = KV(x) \), where \( K = K(1) \) is defined in (3.55). We start from (3.65) with \( f = \mathbb{I} \), which now reads
\[
a_n = KV(x)(1 + o(1)) + o(1) + O(a_{n-s_n}(1 + o(1)) - a_n), \quad n \to \infty,
\]
(3.69)
where we recall that \( a_{n-s_n}(1 + o(1)) - a_n \geq 0 \). Hence,
\[
a_n \leq \frac{KV(x)}{1+C}(1 + o(1)) + \frac{C + o(1)}{1+C} a_{n-s_n}.
\]
Consider \( \overline{a} = \limsup_{n \to \infty} a_n \) and note that \( \limsup_{n \to \infty} a_{n-s_n} \leq \overline{a} \). Hence, we obtain that \( \overline{a} \leq KV(x) \). In the same way, we derive from (3.69) that \( a = \liminf_{n \to \infty} a_n \) satisfies \( a \geq KV(x) \). This shows that \( \lim_{n \to \infty} a_n \) exists and is equal to \( KV(x) \).
Now we go back to (3.65) with an arbitrary continuous and bounded function \( f \), which now reads
\[
a_n(f) = K(f)V(x)(1 + o(1)) + o(1) + n^{\frac{k}{4}(k-1)} O(P_x(n - s_n \leq \tau \leq n))
= K(f)V(x)(1 + o(1)) + o(1) + O(|a_{n-s_n} - a_n|)
= K(f)V(x)(1 + o(1)) + o(1).
\]
This implies that (3.54) holds and finishes the proof of Proposition 3.7.
4 Properties of \( V \), and convergence towards Dyson’s Brownian motions
In this section we prove a couple of properties of the function \( V \) established in Proposition 3.7 like integrability properties, regularity, positivity and behavior at infinity. Furthermore, we introduce the Doob \( h \)-transform with \( h = V \) and show that it is equal to a family of \( k \) independent random walks, conditioned to be ordered at any time, and we prove an invariance principle towards Dyson’s Brownian motions.
In Section 3 we saw that establishing the existence of $V(x)$ requires a detailed analysis of the asymptotics of $P_x(\tau > n; n^{-\frac{1}{2}} X(n) \in dy)$ on the scale $n^{-\frac{1}{2}(k-1)}$. In the present section, we will see that the proof of many properties of $V$, in particular its asymptotics at infinity and its positivity, requires a good control of the asymptotics of $P_x\sqrt{\pi}(\tau > l; l^{-\frac{1}{2}} X(l) \in dy)$ for $l/n$ bounded away from zero.
Recall the notation of Section 1.1 in particular that a tuple of $k$ Brownian motions starts in $x \in \mathbb{R}^k$ under $P_x$, and their collision time, $T$, in (1.2).
**Lemma 4.1.** For any $t > 0$ and any $x \in W$,
$$
\lim_{n \to \infty} P_x\sqrt{\pi}(\tau > tn; n^{-\frac{1}{2}} X([tn]) \in dy) = P_x(T > t; B(t) \in dy) \quad \text{weakly.}
$$
**Proof.** This follows from Donsker’s invariance principle. Indeed, the vector $B^{(n)} = (B^{(n)}_1, \ldots, B^{(n)}_k)$ of the processes $B^{(n)}_i(s) = n^{-\frac{1}{2}} X_i([sn])$ converges towards a Brownian motion $B$ on $\mathbb{R}^k$ starting at $x$. Consider the set $A = \{f: [0, t] \to W: f$ is continuous, then $P_x(B \in \partial A) = 0 \}$ for any $x \in W$. Hence, $P_x\sqrt{\pi}(\tau > tn) = P_x\sqrt{\pi}(B^{(n)} \in A)$ converges towards $P_x(B \in A) = P_x(T > t)$. The extension of this statement to (4.70) is straightforward. □
The following estimate is analogous to Lemma 3.1.
**Lemma 4.2.** Assume that the $\mu$-th moment of the steps is finite, for some $\mu > (k-1)(\frac{k}{2}(k-1)+2)$. Then there are $\varepsilon > 0$, $r \in (0, \frac{k}{4}(k-1)-1)$ for $k > 2$ and $r \in (0, \frac{1}{12})$ for $k = 2$ and $\lambda \in (0, 1)$ such that, for any $M > 0$, there is $C_M > 0$ such that, for any $x \in W$ satisfying $|x| \leq M$,
$$
\mathbb{E}^n P_x\sqrt{\pi}\left[|\Delta(X(\tau))| \mathbf{1}_{\{\tau > Rn\}}\right] \leq C_M(Rn)^{-\varepsilon} \left(\sum_{l \in \mathbb{N}} l^r P_x\sqrt{\pi}(\tau > l)\right)^{\frac{\lambda}{p}}, \quad R > 1, n \in \mathbb{N}.
$$
**Proof.** Recall the notation of $\tau_m$ in (3.22) and the estimate in (3.23). In the same way as in the proof of Lemma 3.1 (see in particular (3.24)), we obtain the estimate, for any $m \in \{1, \ldots, k-1\}$,
$$
\mathbb{E}^n P_x\sqrt{\pi}\left[|\Delta(X(\tau))| \mathbf{1}_{\{\tau = \tau_m > Rn\}}\right] \leq \mathbb{E}^n P_x\sqrt{\pi}\left[\tau^{\frac{k}{2}(k-1)-1}(\frac{\lambda}{2} + \varepsilon) \mathbf{1}_{\{\tau > Rn\}}\right]^{1/p} \times \left(\sum_{l \geq Rn} l^{-q\xi[\frac{k}{2}(k-1)-1]} \mathbb{E}^n P_x\left[|Y_{m,l}|^q \prod_{(i,j) \neq (m,m+1)} \frac{|X_i(l) - X_j(l)|^q}{\sqrt{l}}\right]\right)^{1/q},
$$
where we pick for $k > 2$ again $\xi = (\frac{k}{2}(k-1)-1)^{-1}(\frac{k}{2}(k-1)+2)^{-1}$ and any $q > (\xi[\frac{k}{2}(k-1)-1])^{-1} = \frac{k}{2}(k-1)+2$; and $p$ is determined by $1 = \frac{1}{p} + \frac{1}{q}$.
In a similar way as in the proof of Lemma 3.1, one sees that the expectation in the second line of (4.71) is bounded in $n$ and $x \in W$ satisfying $|x| \leq M$, since $l/n$ is bounded away from zero in the sum. Hence, the second line is not larger than
$$
C_M \left(\sum_{l \geq Rn} l^{-q\xi[\frac{k}{2}(k-1)-1]}\right)^{1/q} \leq C_M(Rn)^{\frac{k}{2} - \frac{\xi[\frac{k}{2}(k-1)-1]}{q}},
$$
for some $C_M > 0$, not depending on $n$ nor on $R$ nor on $x$, as long as $x \in W$ and $|x| \leq M$. Note that the exponent $-\varepsilon = \frac{1}{q} - \xi[\frac{k}{2}(k-1)-1]$ is negative.
Let us turn to the other term on the right side of (4.71). We abbreviate \( r = p\left[\frac{k}{2}(k-1) - 1\right] + \xi \) and know that \( r + 1 < \frac{k}{4}(k-1) \). Then we have
\[
E_{\sqrt{m}x}\left[\tau^{p\left[\frac{k}{2}(k-1) - 1\right] + \xi} \mathbb{1}_{\left\{ \tau \geq Rm \right\}}\right]^{1/p} \leq E_{\sqrt{m}x}\left[\tau^{r+1}\right]^{1/p} \leq C\left(\sum_{l \in \mathbb{N}} l^{p} \mathbb{P}_{\sqrt{m}x}(\tau > l)\right)^{1/p},
\]
(4.72)
for some \( C > 0 \) that does not depend on \( n \), nor on \( x \) or \( R \). Now put \( \lambda = 1/p \).
From now on we assume that a sufficiently high moment of the walk’s steps is finite, in accordance with Proposition 3.7, see (3.57).
Lemma 4.3 (Asymptotic relation between \( V \) and \( \Delta \)). Assume that the \( \mu_k \)-th moment of the steps is finite, with \( \mu_k \) as in Proposition 3.7. For any \( M > 0 \), uniformly for \( x \in W \) satisfying \( |x| \leq M \),
\[
\lim_{n \to \infty} n^{-\frac{k}{2}(k-1)} V(\sqrt{m}x) = \Delta(x).
\]
(4.73)
**Proof.** For notational reasons, we write \( m \) instead of \( n \). As is seen from (1.7), it suffices to show that \( \lim_{m \to \infty} m^{-\frac{k}{2}(k-1)} E_{\sqrt{m}x}[|\Delta(X(\tau))|] = 0 \), uniformly for \( x \in W \) satisfying \( |x| \leq M \). With some large \( R > 0 \), we split this expectation into \( \{ \tau \leq Rm \} \) and \( \{ \tau > Rm \} \). For the first term, we are going to use Donsker’s invariance principle. Indeed, under where \( C > 0 \), some \( M \) satisfies \( |x| \leq M \). From now on we assume that a sufficiently high moment of the walk’s steps is finite, in accordance with Proposition 3.7.
\[
\text{Lemma 4.3 (Asymptotic relation between } V \text{ and } \Delta). \text{ Assume that the } \mu_k \text{-th moment of the steps is finite, with } \mu_k \text{ as in Proposition 3.7. For any } M > 0, \text{ uniformly for } x \in W \text{ satisfying } |x| \leq M,
\[
\lim_{n \to \infty} n^{-\frac{k}{2}(k-1)} V(\sqrt{m}x) = \Delta(x).
\]
(4.73)
**Proof.** For notational reasons, we write \( m \) instead of \( n \). As is seen from (1.7), it suffices to show that \( \lim_{m \to \infty} m^{-\frac{k}{2}(k-1)} E_{\sqrt{m}x}[|\Delta(X(\tau))|] = 0 \), uniformly for \( x \in W \) satisfying \( |x| \leq M \). With some large \( R > 0 \), we split this expectation into \( \{ \tau \leq Rm \} \) and \( \{ \tau > Rm \} \). For the first term, we are going to use Donsker’s invariance principle. Indeed, under \( \mathbb{P}_{\sqrt{m}x} \), the vector \( B^{(m)} = (B_1^{(m)}, \ldots, B_k^{(m)}) \) of the processes \( B^{(m)}(t) = m^{-\frac{k}{2}} X_i(\lfloor tm \rfloor) \) converges towards a Brownian motion \( B \) on \( \mathbb{R}^k \) starting at \( x \). Hence, for any \( R > 0 \), the random variable \( Z_m = m^{-\frac{k}{2}(k-1)} \Delta(X(\tau)) \mathbb{1}_{\{\tau \leq Rm\}} \) converges weakly towards \( \Delta(B(T)) \mathbb{1}_{\{T \leq R\}} \), which is equal to zero by continuity. We now show that \( (Z_m)_{m \in \mathbb{N}} \) is uniformly integrable, from which it follows that \( \lim_{m \to \infty} E_{\sqrt{m}x}[Z_m] = 0 \). (It is not difficult to see that this convergence is uniform for \( x \in W \) satisfying \( |x| \leq M \).) To show the uniform integrability, pick some \( p > 1 \) sufficiently close to one and estimate (using the notation introduced at the beginning of the proof of Lemma 3.1)
\[
E_{\sqrt{m}x}[|Z_m|^p] \leq C m^{-p\frac{k}{2}(k-1)} \sum_{l = 1}^{[Rm]} E_{\sqrt{m}x}\left[ \prod_{1 \leq i < j \leq k} \left( |x_i \sqrt{m} - x_j \sqrt{m}|^p + |S_i(l) - S_j(l)|^p \right) \mathbb{1}_{\{\tau = l\}} \right]
\]
\[
\leq C + C m^{-p\frac{k}{2}(k-1)} \mathbb{E}\left[ \prod_{1 \leq i < j \leq k} \max_{1 \leq l \leq Rm} |S_i(l) - S_j(l)|^p \right],
\]
where \( C > 0 \) denotes a generic positive constant, not depending on \( m \). Now the same argument as the one below (3.21) applies (if \( p \) is sufficiently close to one) to show that the right hand side is bounded. Hence, \( (Z_m)_{m \in \mathbb{N}} \) is uniformly integrable.
The main difficulty is to show that \( \lim_{m \to \infty} m^{-\frac{k}{2}(k-1)} E_{\sqrt{m}x}[|\Delta(X(\tau))| \mathbb{1}_{\{\tau > Rm\}}] \) vanishes as \( R \to \infty \), uniformly for \( x \in W \) satisfying \( |x| \leq M \). According to Lemma 4.2 we only have to show that, for \( r \in (0, \frac{k}{4}(k-1) - 1) \) and \( \lambda \in (0, 1) \) as in Lemma 4.2
\[
\lim_{m \to \infty} m^{-\frac{k}{2}(k-1)} \left( \sum_{n \in \mathbb{N}} n^{r} \mathbb{P}_{\sqrt{m}x}(\tau > n) \right)^{\lambda} < \infty,
\]
(4.74)
uniformly for \( x \in W \) satisfying \( |x| \leq M \). For this, it suffices to find, for any sufficiently small \( \gamma > 0 \) (only depending on \( r \) and \( k \)), some \( C > 0 \) such that
\[
\mathbb{P}_{\sqrt{m}x}(\tau > n) \leq C \left( \frac{m^{1/\lambda}}{n} \right)^{\frac{1}{4}(k-1)}, \quad \text{if } m = o(n^{1-\gamma}),
\]
(4.75)
uniformly for $x \in W$ satisfying $|x| \leq M$.
The proof of (4.75) uses parts of the proof of Proposition 3.7. We again restrict ourselves to the non-lattice case. We use $C$ as a generic positive constant that is uniform in $m$, $n$ and $x$ in the ranges considered. As in the proof of Proposition 3.7, we pick small parameters $\eta, \varepsilon, \xi_1, \xi_2 > 0$ satisfying $8\eta < \xi_1$ and $\xi_2 > \varepsilon + \eta + \xi_1 \frac{k}{2} (k - 1)$. We assume that the $\mu$-th steps of the walk are finite, where $\mu$ is so large that (3.57) holds. Abbreiate $a_{m,n} = \mathbb{P}_{\sqrt{m}x}(\tau > n)(n/m^{1/\lambda})^{\frac{k}{2} (k - 1)}$ for $m, n \in \mathbb{N}$. For any $n \in \mathbb{N}$, we pick $m_n \leq o(n^{1-\gamma})$ maximal for $m \mapsto a_{m,n}$, and we put $A_n = \max \{a_{m_1,1}, \ldots, a_{m_n,n}\}$. Then our goal is to prove that $(A_n)_{n \in \mathbb{N}}$ is bounded. The index $m_n$, and hence also $A_n$, depends on $x$, but our estimates will be uniform in $x \in W$ satisfying $|x| \leq M$.
We split into the event $\{|X(n)| \leq n^{\frac{1}{2} + \eta}\}$ and the remainder. For the first term, we also use Lemma 3.3 with $f = 1$. This gives
$$\mathbb{P}_{\sqrt{m}x}(\tau > n) \leq \mathbb{P}_{\sqrt{m}x}(|X(n)| > n^{\frac{1}{2} + \eta})$$
$$+ \int_W dy \mathbb{1}_{|y| \leq n^\eta} \left[D_{n}^{(m)}(\sqrt{m}x, y) - \mathbb{E}_{\sqrt{m}x}[\mathbb{1}_{|y| \leq n} D_{n}^{(m)}(X(\tau), y)]\right].$$
Since in particular $m_n = o(n)$, the first term, $\mathbb{P}_{\sqrt{m}x}(|X(n)| > n^{\frac{1}{2} + \eta})$, can be estimated via Markov inequality against $Cn^{-\mu}$ using (3.25). If we choose $\mu$ such that $-\mu + \frac{k}{4} (k - 1) < 0$ (which is fulfilled under the moment condition in Proposition 3.7 see (3.57)), we obtain the bound $\mathbb{P}_{\sqrt{m}x}(|X(n)| > n^{\frac{1}{2} + \eta}) \leq Cn^{-\frac{k}{4} (k - 1)} \leq C(m_n^{1/\lambda}/n)^{\frac{k}{2} (k - 1)}$. Let us turn to the second line of (4.76).
As in the proof of Proposition 3.7, we split the expectation in the second line of (4.76) into the parts where $\tau \leq t_n$, $t_n \leq \tau \leq n - s_n$, and $n - s_n \leq \tau \leq n$, where $t_n = n^{1-\xi_1}$ and $s_n = n^{\frac{1}{2} + \xi_2}$. We want to apply Lemma 3.5 to the first part (together with the term $D_{n}^{(m)}(\sqrt{m}x, y)$) and Lemma 3.6 to the second, i.e., we replace $x$ by $\sqrt{m}x$ in that lemmas. Lemma 3.6 immediately applies since $\sqrt{m}x = o(\sqrt{n})$, and Lemma 3.5 applies if we assume that $\gamma > \xi_1$ to ensure that $\sqrt{m}x = o(\sqrt{t_n})$, which we do henceforth. Furthermore, for the last term we use (3.47) and obtain, as in (3.64):
$$\mathbb{P}_{\sqrt{m}x}(\tau > n) \leq Cn^{-\frac{k}{4} (k - 1)} \int_W \mathbb{1}_{|y| \leq n^\eta} \frac{e^{-\frac{1}{2} |y|^2}}{(2\pi)^{1/2}} \Delta(y) dy V_{t_n}(\sqrt{m}x)$$
$$+ O(n^{\varepsilon+\eta-\xi_2}) \mathbb{P}_{\sqrt{m}x}(\tau \geq t_n) + C\mathbb{P}_{\sqrt{m}x}(n - s_n \leq \tau \leq n)$$
$$+ o(n^{\frac{1}{2} + \frac{\eta}{4}+nk+\xi_2}) + O((n^{-\mu} + \xi_{1}/4)) + O(n^{1-\varepsilon\mu}) + C(m_n^{1/\lambda}/n)^{\frac{k}{2} (k - 1)}.$$
Since $\mu$ satisfies (3.57), the last line is not larger than $C(m_n^{1/\lambda}/n)^{\frac{k}{2} (k - 1)}$. Hence, we obtain
$$a_{m,n} \leq Cm_n^{-\frac{k}{4} (k - 1)} V_{t_n}(\sqrt{m}x) + Cn^{\varepsilon+\eta-\xi_2}(n/t_n)^{\frac{k}{2} (k - 1)} a_{m,n,t_n}$$
$$+ C\left(a_{m,n, n-s_n}(n/(n-s_n))^{\frac{k}{2} (k - 1)} - a_{m,n,n}\right) + C.$$
Note that the factor $n^{\varepsilon+\eta-\xi_2}(n/t_n)^{\frac{k}{2} (k - 1)} = n^{\varepsilon+n-\xi_2+n\xi_{1}/4}$ is $o(1)$ by our requirement that the exponent is negative. We use Lemma 3.1 to estimate, for $r \in (0, \frac{k}{4} (k - 1) - 1)$, $\lambda \in (0, 1)$
and \( a \geq \gamma \) as in that lemma,
\[
V_n(\sqrt{m_n}x) \leq \Delta(\sqrt{m_n}x) + C m_n^{(1+a)\frac{k}{2}(k-1)} + C \left( \sum_{t=\lfloor m_n^{1+a} \rfloor}^{t_n} t^r P_{\sqrt{m_n}x}(\tau > t) \right)^\lambda
\]
\[
\leq C m_n^{(1+a)\frac{k}{2}(k-1)} + C m_n^{(1+a)\frac{k}{2}(k-1)} \left( \sum_{t=\lfloor m_n^{1+a} \rfloor}^{t_n} t^{-\frac{k}{2}(k-1)} a_{m_n,t} \right)^\lambda
\]
\[
\leq C m_n^{(1+a)\frac{k}{2}(k-1)} + C m_n^{(1+a)\frac{k}{2}(k-1)} a_{n}^\lambda.
\]
Remark that to bound \( a_{m_n,t} \) by \( A_n \) one needs to know that \( m_n \leq o(t^{1-\gamma}) \) i.e. \( m_n \leq o(m_n^{(1+a)(1-\gamma)}) \); therefore one must choose \( a > \gamma \). Substituting this in (4.78) and solving for \( a_{m_n,n} \), we obtain
\[
a_{m_n,n} \leq C + C m_n^{(1+a-\frac{1}{2})\frac{k}{2}(k-1)} + C m_n^{(1+a-\frac{1}{2})\frac{k}{2}(k-1)} A_n^\lambda + o(1) a_{m_n,n} + \frac{C+o(1)}{C+1} a_{m_n,n-s_n},
\]
(4.79)
Now pick \( a > 0 \) small enough such that the second term on the right hand side is \( \leq C \) and such that the third is \( \leq A_n^\lambda \). Recall that \( m_n \) satisfies \( a_{m_n,n} = \max_{m \leq o(n^{1-\gamma})} a_{m,n} \). Picking \( \xi > 0 \) even smaller, we can assume that \( m_n = o(t^{1-\gamma}) \), hence \( a_{m_n,n} \leq a_{m_n,n} \leq A_n \leq A_n \). Similarly, \( a_{m_n,n-s_n} \leq A_n \). Hence, we obtain
\[
a_{m_n,n} \leq C + A_n^\lambda + \frac{C+o(1)}{C+1} A_n.
\]
Since the right hand side is increasing in \( n \), we also obtain this estimate for \( A_n \) instead of \( a_{m_n,n} \). From this, it follows that \( (A_n)_{n \in \mathbb{N}} \) is bounded. This finishes the proof.
In the following lemma, we see in particular that \( V \) does not increase much faster than \( \Delta \) on \( W \) at infinity. In particular, we can prove some integrability property of \( V \), its regularity and its positivity. Recall that the \( \mu \)-th moment of the steps is assumed finite for some sufficiently large \( \mu \), properly chosen in accordance with Proposition 3.7.
**Lemma 4.4** (Bounds on \( V \), integrability, regularity and positivity). Assume that the \( \mu_k \)-th moment of the steps is finite, with \( \mu_k \) as in Proposition 3.7.
(i) There is a constant \( C > 0 \) such that \( V(x) \leq \Delta(x) + |x|^\frac{k}{2}(k-1) + C \) for any \( x \in W \).
(ii) Fix \( \nu > 0 \), then \( E_x[V(X(n))^{\nu} I_{\{\tau>n\}}] \) is finite for any \( n \in \mathbb{N} \) and \( x \in W \).
(iii) \( V \) is regular for the restriction of the transition kernel to \( W \).
(iv) \( V \) is positive on \( W \).
**Proof.** (i) According to Lemma 3.3 there is \( N_0 \in \mathbb{N} \) such that, for any \( n \in \mathbb{N} \) satisfying \( n \geq N_0 \) and for any \( x \in W \) satisfying \( |x| \leq 1 \),
\[
V(x\sqrt{n}) \leq n^\frac{k}{2}(k-1) \lceil \Delta(x) + 1 \rceil.
\]
1331
Now let $x \in W$ be arbitrary. If $|x| \geq N_0 + 1$, then the above implies that
\[
V(x) = V\left(\frac{x}{\sqrt{|x|^2}} \sqrt{|x|^2}\right) \leq \lceil |x|^2 \rceil \frac{1}{2}(k-1) \Delta\left(\frac{x}{\sqrt{|x|^2}}\right) + 1 \leq \Delta(x) + (|x| + 1)^{\frac{k}{2}+1}.
\]
It suffices to show that $V$ is bounded on bounded subsets of $W$. It is clear that the map $x \mapsto E_x[\Delta(X(n))]1_{\{\tau \leq 2\}}$ is bounded on bounded subsets of $W$. Use Lemma 4.2 with $R = 2$ and $n = 1$ to estimate, for $x$ in some bounded subset of $W$,
\[
E_x[\Delta(X(\tau))1_{\{\tau > 2\}}] \leq C E_x[\tau^{r+1}]^\lambda,
\]
see (4.2). It is clear that the map $t \mapsto E_{tx}[\tau^{r+1}]$ is increasing, since, for $t_1 < t_2$, the random variable $\tau$ is stochastically smaller under $\mathbb{P}_{tx}$ than under $\mathbb{P}_{t_2x}$. In the proof of Lemma 4.3 (see (4.4)) it is in particular shown that $x \mapsto E_{tx}[\tau^{r+1}]$ is bounded on bounded subsets of $W$ if $t$ is sufficiently large. This ends the proof of (i).
(ii) By (i), we have, for any $\nu > 0$,
\[
E_x[V(X(n))^\nu 1_{\{\tau > n\}}] \leq E_x[|\Delta(X(n))|^{\nu}] + E_x[|X(n)|^{\nu + \frac{k}{2}(k-1)}] + C.
\]
Since $\Delta$ is a polynomial of degree $k-1$ in any $x_i$ and by independence of the components, the right hand side is finite as soon as both $\nu (k-1)$ and $\nu + \frac{k}{2}(k-1)$ do not exceed $\mu$. Since we assumed that $k \geq 2$, this is true as soon as $\nu \leq \frac{\mu}{2(k-1)}$.
(iii) We recall from [KOR02, Th. 2.1] that the process $(\Delta(X(n)))_{n \in \mathbb{N}}$ is a martingale under $\mathbb{P}_x$ for any $x \in \mathbb{R}^k$. In particular, $E_x[\Delta(X(n))] = \Delta(x)$ for any $n \in \mathbb{N}$ and any $x \in \mathbb{R}^k$. The regularity of $V$ is shown as follows. For any $x \in W$,
\[
E_x[1_{\{\tau > 1\}}V(X(1))] = E_x[1_{\{\tau > 1\}}\Delta(X(1))] - E_x[1_{\{\tau > 1\}}\Delta(X(\tau))]
\]
\[
= E_x[1_{\{\tau > 1\}}\Delta(X(1))] - E_x[1_{\{\tau > 1\}}\Delta(X(\tau))]
\]
\[
= E_x[1_{\{\tau > 1\}}\Delta(X(1))] - E_x[\Delta(X(\tau))] + E_x[\Delta(X(\tau))1_{\{\tau \leq 1\}}]
\]
\[
= E_x[\Delta(X(1))] - E_x[\Delta(X(\tau))] + E_x[\Delta(X(\tau))1_{\{\tau \leq 1\}} - \Delta(X(1))1_{\{\tau \leq 1\}}]
\]
\[
= V(x),
\]
where the second equality follows from the strong Markov property at time 1.
(iv) Recall that $Y(n) = X(n) - X(n-1) \in \mathbb{R}^k$ is the step vector of the random walk at time $n$. Certainly, $Y(1)$ lies in $\overline{W}$ with positive probability. From the Centering Assumption it follows that $Y_1(1)$ is not constant almost surely. Therefore, the vector $v = E[Y(1) \mid Y(1) \in \overline{W}]$ lies in $W$, since, for any $i = 2, \ldots, k$, we have $v_i - v_{i-1} = E[Y_i(1) - Y_{i-1}(1) \mid Y_i(1) - Y_{i-1}(1) \geq 0]$, and $Y_i(1) - Y_{i-1}(1)$ is positive with positive probability on $\{Y_i(1) - Y_{i-1}(1) \geq 0\}$.
Let $A$ be a closed neighborhood of $v$ that is contained in $W$. Hence, for any sufficiently large $m \in \mathbb{N}$, we have that
\[
P_x(\tau > m, X(m) \in mA) \geq P_x(Y(1), \ldots, Y(m) \in W)P_x\left(1_mX(m) \in A \mid Y(1), \ldots, Y(m) \in \overline{W}\right) > 0,
\]
since the first term is positive for any $m$, and the last one converges to one, according to the weak law of large numbers. According to Lemma 4.3 for any sufficiently large $n \in \mathbb{N}$ and for
any $y \in A$, $V(\sqrt{m}y) \geq \frac{1}{2}m^{-\frac{k}{2}(k-1)}\inf_A \Delta$. In particular, $\inf_{y \in mA} V(y) > 0$ for any sufficiently large $m$.
Now recall from Corollary 3.9 that $V \geq 0$ and iterate the regularity equation for $V$ to the effect that
\[
V(x) = E_x[V(X(m))\mathbb{1}_{\{\tau > m\}}] \geq \inf_{mA} E_x[V(X(m))\mathbb{1}_{\{X(m) \in mA\}}\mathbb{1}_{\{\tau > m\}}] \\
\geq \inf_{mA} V \mathbb{P}_x(X(m) \in mA, \tau > m) > 0.
\]
Hence, $V(x)$ is positive. \qed
**Remark 4.5** ($(V_n)_{n \in \mathbb{N}_0}$ as an iterating sequence). A modification of the calculation in (4.80) shows that $E_x[\mathbb{1}_{\{\tau > 1\}}V_n(X(1))] = V_{n+1}(x)$ for any $x \in W$ and $n \in \mathbb{N}$. Furthermore, it is clear that $V_0 = \Delta$. In other words, we can see the sequence $(V_n)_{n \in \mathbb{N}_0}$ as the iterating sequence for the iterated application of the expectation before the first violation of the ordering, starting with initial function $\Delta$. ◦
Now that we know that $V: W \to (0, \infty)$ is a positive regular function for the restriction of the transition kernel to $W$, we can finally define the Doob $h$-transform of $X$ on $W \cap S^k$ with $h = V$. Recalling (2.10), its transition probabilities are given by
\[
\widehat{\mathbb{P}}_x^{(V)}(X(n) \in dy) = \mathbb{P}_x(\tau > n; X(n) \in dy) \frac{V(y)}{V(x)} = \left[D_n(x, dy) - E_x[\mathbb{1}_{\{\tau \leq n\}}D_{n-\tau}(X(\tau), dy)]\right] \frac{V(y)}{V(x)}, \quad n \in \mathbb{N}, x, y \in W.
\]
The measure on the right hand side is indeed a probability measure in $dy$ on $W$, since, by Lemma 3.1(ii) it has finite mass on $W$, and by Lemma 3.1(iii) its mass is even equal to one.
Now we can show that the transformed process deserves the name ‘$k$ random walks conditioned on being strictly ordered for ever’.
**Lemma 4.6** (Conditional interpretation). Assume that the $\mu_k$-th moment of the steps is finite, with $\mu_k$ as in Proposition 3.7. The conditional distribution of the process $(X(n))_{n \in \mathbb{N}_0}$ given \{$\tau > m$\} converges, as $m \to \infty$, to the Doob $h$-transform of $(X(n))_{n \in \mathbb{N}_0}$ with $h = V$, i.e., for any $x \in W$ and $n \in \mathbb{N}$,
\[
\lim_{m \to \infty} \mathbb{P}_x(X(n) \in dy \mid \tau > m) = \mathbb{P}_x^{(V)}(X(n) \in dy), \quad \text{weakly.} \quad (4.82)
\]
**Proof.** Using the definition of the conditional probability and the Markov property at time $n$, we see that, for any $n, m \in \mathbb{N}$ satisfying $n < m$,
\[
\mathbb{P}_x(X(n) \in dy \mid \tau > m) = \frac{\mathbb{P}_x(\tau > n; X(n) \in dy)m^{\frac{1}{2}(k-1)}\mathbb{P}_y(\tau > m-n)}{m^{\frac{1}{2}(k-1)}\mathbb{P}_x(\tau > m)}.
\]
According to (3.55), the last term in the numerator converges towards $KV(y)$, and the denominator converges towards $KV(x)$ as $m \to \infty$. Compare to the first line of (4.81) to see that this finishes the proof.
1333
Recall that Dyson’s Brownian motions is the Doob $h$-transform of a standard Brownian motion on $W$ with $h$ equal to the restriction of the Vandermonde determinant $\Delta$ to $W$. Recall that $\widehat{\mathbb{P}}_x^{(V)}$ is the Doob $h$-transform with $h = V$ of the random walk $X$ on $W \cap S^k$. The Brownian motion $B = (B_1, \ldots, B_k)$ on $\mathbb{R}^k$ starts from $x \in W$ under $\mathbb{P}_x$, and $\mathbb{E}_x$ denotes the corresponding expectation. Denote by $P_x^{(\Delta)}(B(t) \in dy)$ the Doob $h$-transform with $h = \Delta$ of the Brownian motion $B$ on $\mathbb{R}^k$, e.g.
$$P_x^{(\Delta)}(B(t) \in dy) = \mathbb{P}_x(T > t; B(t) \in dy) \frac{\Delta(y)}{\Delta(x)}, \quad x \in W, t > 0.$$
**Lemma 4.7** (Convergence towards Dyson’s Brownian motions). Assume that the $\mu_k$-th moment of the steps is finite, for $\mu_k$ as in Proposition [3.7]. Then, under $\widehat{\mathbb{P}}_x^{(V)}$ the process $B^{(n)} = (n^{-\frac{1}{2}}X([tn]))_{t \in [0, \infty)}$ weakly converges, as $n \to \infty$, towards Dyson’s Brownian motions started at $x$. More precisely, the sequence $(B^{(n)})_{n \in \mathbb{N}}$ is tight, and, for any $x \in W$, and any $t > 0$,
$$\lim_{n \to \infty} \widehat{\mathbb{P}}_x^{(V)} \left( \frac{1}{\sqrt{n}} X([tn]) \in dy \right) = P_x^{(\Delta)}(B(t) \in dy), \quad \text{weakly.} \quad (4.83)$$
**Proof.** Using (4.81) and Lemmas 4.1 and 4.3 we see that, for any $t > 0$, as $n \to \infty$,
$$\widehat{\mathbb{P}}_x^{(V)} \left( \frac{1}{\sqrt{n}} X([tn]) \in dy \right) = \mathbb{P}_x^{(V)} \left( \tau > [tn]; \frac{1}{\sqrt{n}} X([tn]) \in dy \right) \frac{V(\sqrt{n} y)}{V(\sqrt{n} x)} \quad \to \quad \mathbb{P}_x(T > t; B(t) \in dy) \frac{\Delta(y)}{\Delta(x)} = P_x^{(\Delta)}(B(t) \in dy). \quad (4.84)$$
This shows that (4.83) holds.
Now we show the tightness. According to the Kolmogorov-Chentsov criterion, it suffices to find, for any $S > 0$, constants $\alpha, \beta, C > 0$ such that
$$\mathbb{E}_x^{(V)}[|B^{(n)}(t) - B^{(n)}(s)|^\alpha] \leq C|t - s|^{1+\beta}, \quad \alpha, \beta, C > 0, \quad s, t \in [0, S], n \in \mathbb{N}. \quad (4.85)$$
This is done as follows. We pick some $\alpha \in (2, 4)$. Fix $0 \leq s < t \leq S$. First note that using the Markov property we obtain
$$\mathbb{E}_x^{(V)}[|B^{(n)}(t) - B^{(n)}(s)|^\alpha] \leq \int_W \int_W |z_1 - z_2|^\alpha \mathbb{P}_x^{(V)} \left( \tau > [sn]; \frac{X([sn])}{\sqrt{n}} \in dz_1 \right) \times \mathbb{P}_x^{(V)} \left( \tau > [tn] - [sn]; \frac{X([tn] - [sn])}{\sqrt{n}} \in dz_2 \right) \frac{V(\sqrt{n} y)}{V(x \sqrt{n})} \quad \leq \int_W \int_W |z_1 - z_2|^\alpha \mathbb{P}_x^{(V)} \left( \frac{X([sn])}{\sqrt{n}} \in dz_1 \right) \mathbb{P}_x^{(V)} \left( \frac{X([tn] - [sn])}{\sqrt{n}} \in dz_2 \right) \frac{V(\sqrt{n} y)}{V(x \sqrt{n})}. \quad (4.86)$$
We use $C$ as a generic positive constant, not depending on $s, t$ (as long as $0 \leq s < t \leq S$) nor on $n$, nor on $z_1$ or $z_2$. By Lemma 4.3 $1/V(x \sqrt{n}) \leq Cn^{-\frac{k}{2}(k-1)}$, uniformly in $x$ on compact subsets.
of $W$. From Lemma 4.4(i), we know that there is a polynomial $P: \mathbb{R}^k \to \mathbb{R}$ of degree $\leq \frac{k}{2}(k-1)$ such that $V(z_2\sqrt{n}) \leq |P(z_2)|n^{\frac{k}{2}(k-1)}$ for any $n \in \mathbb{N}$ and $z_2 \in W$. Hence,
$$E_x^{(V)}\left[|B^{(n)}(t) - B^{(n)}(s)|^\alpha\right] \leq CE_x^{\sqrt{n}}\left[|B^{(n)}(t) - B^{(n)}(s)|^\alpha|P(B^{(n)}(t))|\right].$$
Now we use Hölder’s inequality with $p = 4/\alpha$ and $q = 4/(4 - \alpha)$, to obtain
$$E_x^{(V)}\left[|B^{(n)}(t) - B^{(n)}(s)|^\alpha\right] \leq CE_x^{\sqrt{n}}\left[|B^{(n)}(t) - B^{(n)}(s)|^{4/4}E_x^{\sqrt{n}}\left[|P(B^{(n)}(t))|^{4/(4-\alpha)}\right]^{1-\alpha/4}\right].$$
It is known that the first expectation $E_x^{\sqrt{n}}\left[|B^{(n)}(t) - B^{(n)}(s)|^{4}\right]$ on the right hand side can be estimated against $C|t - s|^2$. Furthermore, the second expectation is bounded in $n \in \mathbb{N}$ and $t \in [0,1]$ as soon as the $(\frac{k}{2}(k-1))^4$-th moment of the steps is finite, i.e., as soon as $\frac{k}{2}(k-1)^4 \leq \mu_k$. Choosing $\alpha$ sufficiently close to 2, this is satisfied, by our assumption that $\mu_k > k(k-1)$. For this choice of $\alpha$ we obtain
$$E_x^{(V)}\left[|B^{(n)}(t) - B^{(n)}(s)|^\alpha\right] \leq C|t - s|^\alpha/2,$$
which shows that (4.85) holds with $\beta = \alpha/2 - 1 > 0$. \hfill \ensuremath{\Box}
References
[Ba00] J. Baik, Random vicious walks and random matrices, *Comm. Pure Appl. Math.* 53, 1385–1410 (2000). MR1773413
[BS06] J. Baik and T. Suidan, Random matrix central limit theorems for non-intersecting random walks, *Ann. Probab.* 35, no. 5, 1807–1834 (2007). MR2349576
[BD94] J. Bertoin and R. A. Doney, On conditioning a random walk to stay nonnegative, *Ann. Probab.* 22:4, 2152–2167 (1994). MR1331218
[BJ02] P. Bougerol and T. Jeulin, Paths in Weyl chambers and random matrices, *Probab. Theory Related Fields* 124:4, 517–543 (2002). MR1942321
[Br91] M.-F. Bru, Wishart processes, *J. Theoret. Probab.* 3:4, 725–751 (1991). MR1132135
[Do05] Y. Doumerc, Matrices aléatoires, processus stochastiques et groupes de r´eflexions, PhD thesis, Universit´e Toulouse (2005).
[Dy62] F.J. Dyson, A Brownian-motion model for the eigenvalues of a random matrix, *J. Math. Phys.* 3, 1191–1198 (1962). MR0148397
[F71] W. Feller, *An Introduction to Probability Theory and its Applications*, Vol. 2, John Wiley and Sons, New York, 2nd edition (1971). MR0270403
[Gr99] D. Grabiner, Brownian motion in a Weyl chamber, non-colliding particles, and random matrices, *Ann. Inst. H. Poincaré Probab. Statist.* **35**:2, 177–204 (1999). MR1678525
[HW96] D. Hobson and W. Werner, Non-colliding Brownian motion on the circle, *Bull. Math. Soc.* **28**, 643–650 (1996). MR1405497
[Jo00] K. Johansson, Shape fluctuations and random matrices, *Commun. Math. Phys.* **209**, 437–476 (2000). MR1737991
[Jo02] K. Johansson, Non-intersecting paths, random tilings and random matrices, *Probab. Theory Related Fields***123**:2, 225–280 (2002). MR1900323
[KM59] S.P. Karlin and G. McGregor, Coincidence probabilities, *Pacif. J. Math.* **9**, 1141–1164 (1959). MR0114248
[KT02] M. Katori and H. Tanemura, Scaling limit of vicious walks and two-matrix model, *Phys. Rev. E.* **66** 011105 (2002).
[KT03] M. Katori and H. Tanemura, Non-colliding Brownian motions and Harish-Chandra formula, *Elec. Commun. Prob.* **8**, Paper No. 13 (2003). MR2042750
[KT04] M. Katori and H. Tanemura, Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems, *J. Math. Phys.* **45**, 3058–3085 (2004). MR2077500
[KNT04] M. Katori, T. Nagao and H. Tanemura, Infinite systems of non-colliding Brownian particles, *Adv. Stud. Pure Math.* **39**, 283-306 (2004). MR2073337
[KO01] W. König and N. O’Connell, Eigenvalues of the Laguerre process as non-colliding squared Bessel processes, *Elec. Comm. Probab.* **6**, Paper no. 11, 107-114 (2001). MR1871699
[KOR02] W. König, N. O’Connell and S. Roch, Non-colliding random walks, tandem queues, and discrete orthogonal polynomial ensembles, *Elec. Jour. Probab.* **7**, Paper no. 5, 1-24 (2002) MR1887625
[K05] W. König, Orthogonal polynomial ensembles in probability theory, *Prob. Surv.* **2**, 385-447 (2005). MR2203677
[OC03] N. O’Connell, Random matrices, non-colliding processes and queues, *Séminaire de Probabilités XXXVI*, 165–182, Lecture Notes in Math. **1801**, Springer, Berlin (2003). MR1971584
[Pe75] V.V. Petrov, *Sums of Independent Random Variables*, Springer, Berlin (1975). MR0388499 | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
1550,
1
],
[
1550,
5054,
2
],
[
5054,
9398,
3
],
[
9398,
12956,
4
],
[
12956,
16170,
5
],
[
16170,
20150,
6
],
[
20150,
23752,
7
],
[
23752,
26655,
8
],
[
26655,
30145,
9
],
[
30145,
33340,
10
],
[
33340,
36661,
11
],
[
36661,
39625,
12
],
[
39625,
43217,
13
],
[
43217,
46540,
14
],
[
46540,
49396,
15
],
[
49396,
53255,
16
],
[
53255,
56181,
17
],
[
56181,
59322,
18
],
[
59322,
62763,
19
],
[
62763,
65577,
20
],
[
65577,
68430,
21
],
[
68430,
71896,
22
],
[
71896,
76841,
23
],
[
76841,
80583,
24
],
[
80583,
83448,
25
],
[
83448,
86812,
26
],
[
86812,
89732,
27
],
[
89732,
92788,
28
],
[
92788,
95209,
29
],
[
95209,
97305,
30
]
]
} |
43ee06837933e22e8b234bfe5d4d85cf9eab4012 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 21,
"total-fallback-pages": 0,
"total-input-tokens": 59140,
"total-output-tokens": 19263,
"fieldofstudy": [
"Medicine",
"Political Science"
]
} | Concepts of health in different contexts: a scoping review
V. P. van Druten1,2*, E. A. Bartels2,3, D. van de Mheen2, E. de Vries1,2, A. P. M. Kerckhoffs4,5 and L. M. W. Nahar-van Venrooij1
Abstract
The rationale of our study was that the World Health Organization's (WHO) definition of health from 1947 which includes “… complete physical, mental and social wellbeing…” does not fit the current societal viewpoints anymore. The WHO’s definition of health implies that many people with chronic illnesses or disabilities would be considered unhealthy and complete wellbeing would be utopian and unfeasible for them. This is no longer uniformly accepted. Many alternative concepts of health have been discussed in the last decades such as ‘positive health’, which focusses on someone’s capability rather than incapability. However, the question remains whether a general health concept can guide all healthcare practices. More likely, health concepts need to be specified for professions or settings. The objective of our study was to create a structured overview of published concepts of health from different perspectives by conducting a scoping review using the PRISMA-ScR guideline. A literature search was conducted in Pubmed and Cinahl. Articles eligible for inclusion focussed on the discussion or the conceptualisation of health or health-related concepts in different contexts (such as the perspective of care workers’ or patients’) published since 2009 (the Dutch Health Council raised the discussion about moving towards a more dynamic perspective on health in that year). Seventy-five articles could be included for thematic analyses. The results showed that most articles described a concept of health consisting of multiple subthemes; no consensus was found on one overall concept of health. This implies that healthcare consumers act based on different health concepts when seeking care than care workers when providing care. Having different understandings of the concepts of health can lead to misunderstandings in practice. In conclusion, from every perspective, and even for every individual, health may mean something different. This finding stresses the importance that care workers’ and healthcare consumers’ meaning of ‘health’ has to be clear to all actors involved. Our review supports a more uniform tuning of healthcare between healthcare providers (the organisations), care workers (the professionals) and healthcare consumers (the patients), by creating more awareness of the differences among these actors, which can be a guide in their communication.
Keywords: Health, Health concept, Health definition, Positive health, Health-related concepts, Health perception, Perceived health, Scoping review
Introduction
The World Health Organisation’s (WHO) definition of health does not fit the current societal viewpoints anymore [1]. The WHO definition of health is formulated as “Health is a state of complete physical, mental and social wellbeing and not merely the absence of disease or infirmity” [2]. Due to the word ‘complete’ in this definition, many people would not be considered healthy, because...
of their chronic illnesses or disabilities [1, 3]. For them, complete wellbeing would be utopian and unfeasible [4]. This is no longer uniformly accepted. Perspectives on people with physical disabilities are changing; they are no longer seen as ‘unhealthy’. On the other hand, the focus has shifted to the fact that people, when they get a chronic illness or disability, do need to adapt to their new situation; being able to do this is part of the recently developed paradigm of ‘positive health’ [5].
Many alternative concepts of health have been discussed in the last decades in philosophical and policy-oriented health and medicine debates, changing from health as being free from disease to health as someone’s capabilities. Prominent concepts of health which have been widely discussed and criticized by philosophers were developed by Boorse, Nordenfelt, and Nussbaum, respectively. Boorse’s biostatistical theory of health is a purely descriptive quality of an organism [6], which focusses on the functioning of body parts and on physiological systems being free from disease [7]. Nordenfelt discharged Boorse’s biostatistical theory and focussed on the ‘second-order ability to achieve vital goals’ in which actions are oriented to achieve minimal happiness, being a condition that the person prefers [8]. Like Nordenfelt, also Nussbaum’s capability approach is about achieving a set of capabilities in things that are important in a person’s life [9]. However, Nordenfelt focusses on a person’s health relating to human flourishing and achieving vital goals, while Nussbaum focusses on defining components of a person’s life that equally reflect human dignity as well as being able to be and to do certain things [10]. More recently, the International Classification of Functioning, Disability and Health (ICF) focussed on performance as well as capacities taking a broader set of aspects into account: body functions, activity and participation, environmental and personal factors, and body structures [11, 12].
These broader views on health were further extended since the positive health concept was postulated by Huber et al. in 2011 [5, 12]. Positive health focusses on someone’s capability rather than incapability, which means that people with chronic diseases or disabilities are no longer automatically seen as ‘not healthy’. Besides, there is a clear focus on resilience and self-management in social, physical and emotional challenges [5, 12]. To further operationalise the concept of positive health, Huber et al. conducted survey research among several stakeholders, asking what they considered important aspects of health. This resulted in the identification of 32 aspects categorized into six dimensions: 1) bodily functions, 2) mental functions and perception, 3) spiritual/existential dimension, 4) quality of life, 5) social and societal participation, and 6) daily functioning [12]. This concept has had a strong influence on healthcare policy in the Netherlands. Furthermore, since 2020 the Eastern Institute of Health (HSA) in Iceland has also started the implementation of positive health [13].
Reactions to the concept of positive health in the literature are mixed. The dimensions are seen as meaningful, however, the terms ‘adapt’ and ‘self-manage’ are being questioned. Jambroes et al. [14] discussed that several groups of people like frail elderly or people with mental disorders may not have the capacity to adapt or to manage their own health. Furthermore, giving people the responsibility for their own health management can cause people to feel guilty when health problems occur [14]. Prinsen and Terwee [15] tried to develop an instrument for measuring positive health. The results showed that the aspects of the ‘positive health’ concept had not yet been worked out clearly. The experts involved questioned whether the operationalisation of the conceptual model is a reflection of health or a reflection of aspects of life that influence health (i.e., are determinants of health) [15]. Also, Hafen [16] sees the ‘ability to adapt and self-manage’ as a determinant instead of part of the concept of ‘health’ itself. Motives for including aspects in the six dimensions were unclear, nor was it always clear to which dimension certain aspects belonged. Overlap was seen across aspects within dimensions [16].
It can be concluded that a clear alternative concept of health to replace the WHO definition has not yet been found. To our knowledge, no reviews have been conducted on this topic yet. However, it is important to have a clear and understandable general health concept for management, designing and redesigning policy, research and healthcare practices [5, 17]. It may help policymakers to establish and implement effective health policies to improve health status, quality of life, morbidity and mortality [18]. Clear understanding of the meaning of health by healthcare professionals and patients will foster active participation and will increase patient empowerment [18]. However, it is questionable whether a general health concept can guide all practices. More likely, health concepts need to be specified for specific professions or settings [1]. To answer this question, we conducted a scoping review, to create a structured overview of published concepts of health from different perspectives that can support a more uniform tuning of healthcare between healthcare providers and healthcare consumers. The research question was: How is the concept of health defined in different contexts and from different perspectives? (For example, from the perspective of healthcare providers and healthcare consumers).
Method
Design
This scoping review was conducted using the PRISMA-ScR guideline, which follows a systematic approach to map evidence and identify main concepts and theories on a topic [19]. This design was used because our research question was broad. In line with the design of a scoping review, our review did not have the intention to perform a structured evaluation of the research quality, but focussed on all publications available about our topic.
Eligibility criteria
Articles eligible for inclusion focussed on the discussion or conceptualisation of health or health-related concepts. We included original research articles (interview or focus group discussions in qualitative design studies, surveys and concept mappings, quantitative or mixed methods studies exploring the concept), but also literature reviews, books, and letters to the editor. We excluded intervention studies using health or wellbeing related terms as one of their outcome measures. These studies do not focus primarily on discussing the concept of health. Validation studies of questionnaires or instruments evaluating health or wellbeing related terms not primarily focussing on the concept or definition of health were also excluded. Articles needed to be published in English between 2009 (the Dutch Health Council raised the discussion about moving towards a more dynamic perspective on health [5, 12] in that year) and May 2020.
Information sources
The search was conducted in two databases: Pubmed and Cinahl, on May 25, 2020. The search was conducted by the first author (VvD) and was peer reviewed within the research team. These databases were chosen because of their focus on social behaviour and medical sciences. A snowball method was conducted on the references of the collected articles. Finally, four experts in the field were asked for additional papers that might have been missed.
Search
The exact search string for PubMed is shown in Table 1 and for Cinahl in Table 2.
Selection of sources of evidence
Results of the search were uploaded in Rayyan, a free web application for independent selection of articles by multiple researchers. Two researchers (VvD and EB)
Table 1 The search string as conducted in PubMed
| Search term | Variations of the search terms entered in pubmed | Field |
|-----------------------------------|-----------------------------------------------------------------------------------------------------------------|------------------|
| OR | Health-related wellbeing OR health-related wellbeing OR health-related well-being | [Title/abstract] |
| Health perception | OR health perception OR health perceptions | [Title/abstract] |
| Attitude to health | OR attitude to health OR attitude health | [Title/abstract] |
| Health concepts | OR health concepts OR health concept | [Title/abstract] |
| Conceptualisation of health | OR conceptualisation of health OR conceptualisation health OR conceptualisation of health OR conceptualisations | [Title/abstract] |
| Positive health | OR positive health | [Title/abstract] |
| Dimensions of wellbeing | OR dimensions of well-being OR dimensions of wellbeing OR dimensions well-being OR dimension of wellbeing OR | [Title/abstract] |
| Perceived health | OR perceived health | [Title/abstract] |
| Concept | concept* | [Title/abstract] |
| Definition | OR defin* | [Title/abstract] |
| NOT | Child | [Title/abstract] |
| Kid | OR kid* | [Title/abstract] |
| Adolescent | OR adolescent* | [Title/abstract] |
| Newborn | OR newborn* | [Title/abstract] |
| Infant | OR infant* | [Title/abstract] |
| Baby | OR baby OR babies | [Title/abstract] |
| Animals | OR animals | [Title/abstract] |
| Filter | English | [Title/abstract] |
| | 11 years | [Title/abstract] |
independently screened all titles, abstracts and full-text articles for in- or exclusion. In addition, they discussed the articles on which there was disagreement. If no agreement was reached after discussion, a third researcher (LN-vV) was asked. Simultaneously, three senior researchers (LN-vV, EdV, DvdM) independently screened 10% of the articles for in- or exclusion in the first two phases, the title and abstract selection, in order to validate the process.
**Data items**
Preceding the coding process, a list of themes of interest was developed in consensus by the research team based on the aim of the scoping review and research question consisting of: 1) concept of health (a description of a health (—related) concept or definition, or what a health (—related) concept or definition should contain); 2) dimensions of health (category of health indicators for operationalisation in healthcare); 3) perspective (the perspective from which the concept of health was explored or the article written).
**Data charting process**
For data extraction and synthesis, a thematic analysis was conducted to identify patterns within the data. First, a form including characteristics of the article and the list of themes was developed. The characteristics consisted of: country, article type/study design and perspective population/theoretical approach. The list of themes of interest was pilot tested on three articles by the first (VvD) and the last author (LN-vV). Second, the first author (VvD) started data extraction. Third, within the themes of interest, an open coding process was started using a bottom-up approach by the first author (VvD). The program ATLAS.ti (version 8) was used when coding the data. Codes were extracted from the data using the exact words from the original article. After coding all articles, the codes were categorised into potential subthemes, which fit into the overarching themes (i.e. concept of health, dimensions of health, perspective). We introduced a minimum level of appearance for subthemes in at least three articles as threshold for relevance. In case a subtheme was represented in at least 3 articles a description in detail of the subtheme was given. This threshold was based on consensus within the research team with the aim to keep our focus on the most relevant results. During the entire process, four researchers (EB, LN-vV, EdV, DvdM) were repeatedly consulted to discuss the analytic process and the development of the results.
**Synthesis of results**
The articles were first divided into the retrieved subthemes for theme 3 (perspective), resulting in an overview of the results of theme 1 (concept of health) and theme 2 (dimensions of health) per subtheme of perspective (theme 3). In Fig. 1, the process for synthesis of results is shown.
**Results**
**Selection of sources of evidence**
In Fig. 2, the flowchart with the number of retrieved articles in Pubmed and Cinahl and in-/exclusion per
### Table 2 The search string as conducted in Cinahl
| Search term | Variations of the search terms entered in pubmed | Field |
|----------------------|---------------------------------------------------------------------------------------|------------------------------|
| OR | health-related wellbeing OR-related well-being | [Title/abstract] |
| Health perception | OR health perception OR health perceptions | [Title/abstract] |
| Attitude to health | OR attitude to health OR attitude health | [Title/abstract] |
| Health concepts | OR health concepts OR health concept | [Title/abstract] |
| Conceptualisation of health | OR conceptualisation of health OR conceptualisation health OR conceptualisations of health OR conceptualisations health | [Title/abstract] |
| Positive health | OR positive health | [Title/abstract] |
| Dimensions of wellbeing | OR dimensions of well-being OR dimensions wellbeing OR dimension of wellbeing OR dimension wellbeing | [Title/abstract] |
| Perceived health | OR perceived health | [Title/abstract] |
| AND | concept* | [Title/abstract] |
| Definition | OR defn* | [Title/abstract] |
Filter
English
11 years
selection step is shown. Articles that did not fulfil the inclusion criteria after screening title, abstract or full text, respectively were not included for the next step. In the first step (title screening), there was an initial agreement of 94% between the authors VvD and EB. Simultaneously, the initial agreement with the senior researchers (LN-vV, EdV, DvdM) was 94%. In the second step (abstract screening), the initial agreement was 77% between the authors VvD and EB. In addition, the initial agreement with the senior researchers (LN-vV, EdV, DvdM) was 82%. In the third step (full-text screening), the initial agreement was 87% between the authors VvD and EB. In total, 75 articles were included for thematic analysis. Fifty-six articles were excluded in full-text screening, because they did not meet the inclusion criteria: 29 articles were not focusing on the concept or definition of
health, 12 articles were intervention studies using health or wellbeing related terms as one of their outcome measures, 4 articles focussed on validation studies of questionnaires or instruments evaluating health or wellbeing related terms, for 8 articles no full texts were available, 2 articles were excluded because they were duplicates and 1 article was in Spanish.
Characteristics of sources of evidence
For theme 1 (concept of health) 159 codes (210 quotes) were created during the analysis process. For theme 2 (dimensions of health) 72 codes (148 quotes) were created. For theme 3 (perspective) 68 codes (92 quotes) were created. Table 3 shows the coding scheme with the identified subthemes and codes of theme 1 concept of health. Table 4 shows the coding scheme with the identified subthemes and codes of theme 2 dimensions of health. To see details of Table 3 the supplementary Table 1 shows the same coding scheme, but includes also all related quotations from the 75 articles.
Themes 1 and 2: concepts of health and dimensions of health
From the data for theme 1 (concepts of health) 159 codes were extracted and categorised. Nine subthemes arose by categorising the codes: multi-sided, adapting to change, complete wellbeing or functioning, participation, daily functioning, wellbeing, satisfying life, self-management, and subjective (see Table 3). Most articles (58/75) described a concept of health consisting of multiple subthemes. From the data for theme 2 (dimensions of health) 72 codes were extracted and categorised. Eight subthemes arose by categorising the codes for this theme: physical, mental, social, spiritual, individual, environmental, functional, and other dimensions (see Table 4). Almost half of the articles (36/75) described multiple dimensions of health. Similarities and differences in subthemes between theme 1 (concepts of health) and theme 2 (dimensions of health) were seen, represented by the related subthemes (see Tables 5, 6, 7, 8, 9, 10 and 11). An overview of the presented concepts and dimensions of health in more detail can be found in Supplementary Tables 2A to 2G (S2A-S2G). An overview table of the numbers of articles representing subthemes identified in the articles for theme 1 and theme 2, respectively, grouped per subtheme of perspective (theme 3), can be found in Supplementary Tables S3A and S3B.
Theme 3: concept of health from different perspectives
From the data for theme 3 (perspective) 68 codes were extracted and categorised. Seven subthemes arose by categorising the codes: general population (articles which do not specify a specific perspective in their study), care workers, patients, older people, philosophical, theological, and context specific (articles which define a specific context or viewpoint such as ‘Māori spiritual healers’). In the next paragraphs the similarities and differences between theme 1 (concepts of health) and theme 2 (dimensions of health) are outlined per perspective, in line with Tables 5, 6, 7, 8, 9, 10 and 11. We reviewed every subtheme mentioned in the included articles. We did not take into account the importance or weighting of a certain subtheme in our analyses although it was considered of higher importance in that specific article.
Health from a general population perspective
Thirteen articles were written from a general population perspective [20–32]. These articles were mostly literature studies, discussion articles or commentaries in which health concepts were discussed. Detailed characteristics of the included articles are shown in Table 5.
In the next paragraph, illustrative quotes are given for the subthemes of theme 1 (concept of health) which were identified in at least three different articles. Examples of quotes are also given of associations seen between the results of theme 2 (dimensions of health) and theme 1 (concept of health). For more detailed information and all quotes see supplementary Table S2A.
Content belonging to four subthemes were identified in at least three articles written from the general population perspective: multi-sided, self-management, participation, and subjective. The subtheme multi-sided view on health, i.e., health not only related to the physical dimension, was identified in five articles (5/13) written from a general population perspective. For example, Amzat and Razum [21] wrote: “the concept of health presents a form of ambiguity because it is multidimensional, complex, and sometimes elusive”. The multi-sided view on health from this perspective was also identified by the multiple dimensions of health (theme 2) being reported in six articles (6/13). For example, Lipworth et al. [27] wrote: “… balance among the physical, spiritual, cognitive, emotional, and/or social domains of life”. The subtheme self-management as part of a health concept was identified in three articles (3/13) written from a general population perspective. For example, Makoul et al. [28] wrote about the concept of health: “Health is the result of an individual’s behaviors, and is embodied in the self-control it takes to enact the behaviors”. The subtheme participation, i.e., being active and participating in life, as part of a health concept was identified in three articles (3/13) written from a general population perspective. For example, Makoul et al. [28] wrote: “Health is the means to living an active life”. Participation as part of a health concept was also identified in the dimension social (theme 2). For example, Makoul et al. [28] wrote: “... the biopsychosocial
Table 3 The coding scheme; identified subthemes and codes for theme 1, the concept of health
| Subtheme (explanation) | Codes |
|------------------------|-------|
| Complete wellbeing or functioning (Functioning without any disturbance of diseases or infirmities) | Absence of disease and functioning | Absence of disease or illness | Absence of health problems | Adopting the biomedical view |
| Biomedical interpretation of health | Complete physical | Getting off or maintaining desistance from harmful substance | Health as a condition to be fixed |
| Health merely as absence of disease or infirmity | No tension | Normal functional ability | Normal physiological functional ability |
| Not getting sick | Theoretical health is value free | | |
| Liberating and expansive way of being | Overall wellbeing | Physical-psychological wellbeing | Positive concept of wellbeing |
| Sense of wellbeing | Spiritual and emotional wellbeing | State of wellbeing | Subjective wellbeing |
| Wellbeing | | | |
| Liberating and expansive way of being | Overall wellbeing | Physical-psychological wellbeing | Positive concept of wellbeing |
| Sense of wellbeing | Spiritual and emotional wellbeing | State of wellbeing | Subjective wellbeing |
| Wellbeing | | | |
| Adapting to change (Being able to adapt to personal or environmental health-related changes and circumstances) | Ability to adapt | Acceptance and adjustment with optimism | Adapt and accept limitations as part of ageing | Adaptation to worsening life conditions |
| Adaptive system | Balance among dimensions | Dynamic nonlinear interaction | Dynamic over time |
| Emotional balance | Flow of energy, listening to and respecting its rhythms | Functional adaptation | Health and peace are dynamic |
| Health as a process | Health as a state of balance | Health can be fleeting both lost and regained | Health is a dynamic state |
| Interactions | Maximal functional adaptation to illness or disability | Never-ending system of events | Overcoming health problems |
| Process individuals go through during illness and health | Rhythmic pattern of living | | Subject to change |
| Multi-sided (Health is not related only to the physical dimension, but involves several dimensions) | Extends beyond the physical | Health as complex system | Health as holistic | More than physical |
| Health is not merely the absence of disease or infirmity | Health is not only normal physical function | Mind, body, soul or spirit concept | |
| More than the absence of disease or illness | Multi-facetted concept | Multidimensional | Multidimensional, complex, elusive |
| Not just focus on illness/disease elimination | Not merely the absence of problems | Person is more than his illness | Salutogenic health concept |
| Tried to quality of life concept | Ability to do something independently | Ability to handle daily life activities | Ability to make health-related decisions | Ability to self-manage |
| Self-management (Having self-control in life and in the health process) | Ability to handle daily life activities | | | |
| Absence or management of symptoms | Action and repetition of action in the health process | Autonomy | Autonomy and independency |
| Being able to trust one's ability | Capability to cope and manage malaise and wellbeing conditions | Control their lives | Experiencing enough energy in their own world |
| Focus on a person's strength | Independence | Manage daily activities | Manage one's daily tasks |
| Positive thinking and resourcefulness | Responsibility for yourself and others | Self-acceptance | Self-control |
| Self-esteem | Self-esteem, self-concept | To be aware of one's worth | To feel secure in oneself |
Table 3 (continued)
| Subtheme (explanation) | Codes |
|------------------------|-------|
| Participation (Being active and participating in life) | Ability to be active and participating Ability to live an active life Being able to work Being able to perform activities of daily living |
| Capacity to perform tasks and full societal roles | Participation | Ability to live a life that makes sense Capacity to fulfill societal roles |
| Dynamic participation in the world | Ability to participate in daily life Ability to take care of children Caring for others |
| Ability to satisfy by themselves the needs of daily life | Dynamic participation in the world Health as basic necessity or requirements to engage in activities |
| Capacity to realize creatively flourishing | Ability to take care of children Caring for others |
| Adjusting the world | Health as a commodity Experience meaningfulness in life Experience worth of equal human dignity Purpose in life To live the good life |
| Partaking in daily life | Health as a commodity Experience meaningfulness in life Experience worth of equal human dignity Purpose in life To live the good life |
| Satisfying life (Values that contribute satisfaction in life) | Satisfying life (Values that contribute satisfaction in life) |
| Ability to flourish | Satisfying life (Values that contribute satisfaction in life) |
| Feelings for the future | Satisfying life (Values that contribute satisfaction in life) |
| Health as a value | Satisfying life (Values that contribute satisfaction in life) |
| Health is about the whole life | Satisfying life (Values that contribute satisfaction in life) |
| Life satisfaction | Satisfying life (Values that contribute satisfaction in life) |
| Life worth of equal human dignity | Satisfying life (Values that contribute satisfaction in life) |
| Purpose in life | Satisfying life (Values that contribute satisfaction in life) |
| To live the good life | Satisfying life (Values that contribute satisfaction in life) |
| Connectedness with others | Connectedness with others Contextual features of human society Experience harmony in life |
| Relationships with family | Connectedness with others Contextual features of human society Experience harmony in life |
| Experience of the being | Connectedness with others Contextual features of human society Experience harmony in life |
| Health is subjective | Connectedness with others Contextual features of human society Experience harmony in life |
| Health beliefs | Connectedness with others Contextual features of human society Experience harmony in life |
| Personal and social resources | Connectedness with others Contextual features of human society Experience harmony in life |
| Health as a commodity Experience meaningfulness in life Experience worth of equal human dignity Purpose in life To live the good life |
| Health as a commodity Experience meaningfulness in life Experience worth of equal human dignity Purpose in life To live the good life |
| Subjective (Personal perceptions and experiences about health) | Subjective (Personal perceptions and experiences about health) |
| Bodily phenomena | Subjective (Personal perceptions and experiences about health) |
| Experience of the being | Subjective (Personal perceptions and experiences about health) |
| Health is subjective | Subjective (Personal perceptions and experiences about health) |
| Health beliefs | Subjective (Personal perceptions and experiences about health) |
| Personal and social resources | Subjective (Personal perceptions and experiences about health) |
| Subjective wellbeing | Subjective (Personal perceptions and experiences about health) |
| Personal experience | Subjective (Personal perceptions and experiences about health) |
| Subjective experience | Subjective (Personal perceptions and experiences about health) |
| Subjective wellbeing | Subjective (Personal perceptions and experiences about health) |
| Subjective experience | Subjective (Personal perceptions and experiences about health) |
| Subjective wellbeing | Subjective (Personal perceptions and experiences about health) |
| Personal evaluation of wellbeing | Personal evaluation of wellbeing |
| Personal and social resources | Personal evaluation of wellbeing |
| Objective features of human biology | Objective features of human biology |
model encompasses mental, emotional, social, and spiritual elements as well". The subtheme subjective view on health as part of a health concept was identified in three articles (3/13) written from a general population perspective. For example, Kaldjian [25] wrote: “... we can endorse a concept of health that incorporates ... subjective features of human valuing”. The other subthemes for the concepts of health were not identified in three articles or more and thus not further described here (see S2A).
**Health from a care worker’s perspective**
Ten articles were written from a care workers perspective [12, 33–41]. The care workers in these articles were for example general practitioners, social workers, and staff in mental health. Characteristics of the included articles are shown in Table 6.
Content belonging to six subthemes were identified in at least three articles written from a care worker’s perspective: multi-sided, subjective, adapting to change, satisfying life, wellbeing and complete wellbeing and functioning. The subtheme multi-sided view on health was identified in six articles (6/10) written from a care worker’s perspective. For example, Hunter et al. [36] wrote; “health is more multidimensional” and Merry [40] wrote; “health is viewed from a holistic perspective”. The multi-sided view on health from this perspective was also identified by multiple dimensions of health (theme 2) being reported in six articles (6/10). For example, Ashcroft and Van Katwijk [34] wrote; “… health is physical, mental and emotional well-being—as determined by relationships with others and with the constructed and natural environments ...”. The second subtheme, health is subjective, i.e., the concept of health depends on personal perceptions and experiences, was identified in four articles (4/10) written from a care worker’s perspective. For example, Merry [40] wrote; “… each person is unique and that how health is defined by a person, group, or community is subjective”. The subtheme adapting to change, i.e., being able to adapt to personal or environmental health-related changes and circumstances, as part of a health concept was identified in three articles (3/10) written from a care worker’s perspective. For example, Huber et al. [5] wrote; “… health as ‘the ability to adapt and to self-manage ...’”. The subtheme satisfying life, i.e., values that contribute satisfaction in life, as part of a health concept was both identified in three articles (3/10) written from the perspective of care workers. For example, Hunter et al. [36] wrote; “… the most advanced conception of ‘health that is more than the absence of disease’ was a liberating and
expansive way of being...". However, they also referred to health as "... health being understood only as the absence of disease", which relates to complete wellbeing. Notably, the subtheme complete wellbeing or functioning was never used as a concept of health on its own by care workers but always in combination with other subthemes for the concept of health. The other subthemes for the concepts of health were not identified in at least three articles and are not further described here (see S2B).
### Health from a patient's perspective
Eleven articles were written from a patient's perspective [12, 36, 38, 42–49]. The patients in these articles were for example patients with chronic illnesses, patients in mental health services, patients with psychosis, and patients with pressure ulcers. Characteristics of the included articles are shown in Table 7.
Content belonging to six subthemes were identified in three articles or more from a patient's perspective: subjective, daily functioning, self-management, satisfying life, adapting to change, and multi-sided. The first subtheme health as subjective as part of the health concept was identified in five articles (5/11) written from a patient's perspective. For example, Post [45] wrote: "... conceptualization of health encompassed ... personal evaluations of well-being" and Ebrahimi et al. [43] wrote: "... health is a subjective and dynamic phenomenon". The subjective view on health from this perspective was also seen by the dimension individual (theme 2). For example, Schrank et al. [46] wrote: "... the domain of individual well-being represents the subjective part of the concept". The second subtheme daily functioning, i.e., daily functioning in life, as part of the health concept was identified in four articles (4/11) written from a patient's perspective. For example, Warsop [48] wrote: "Health is always in the background, letting us do what we always do" and
### Table 5 Included articles discussing health from a general population perspective
| Authors, year | Country | Article type/ study design | Perspective (population) | Subthemes of Concept of health | Subthemes of Dimensions of health |
|---------------------|---------|----------------------------|--------------------------|-------------------------------------------------------|-----------------------------------|
| Abuelaish et al., 2020 [20] | Canada | Literature debate | NA | Multi-sided, adapting to change | Social, environmental |
| Amzat & Razum, 2014 [21] | Nigeria | Book chapter | NA | Multi-sided | |
| Conner et al., 2019 [22] | USA | Survey research | African American, Asian American, European American, and Latin American men and women of lower and higher socioeconomic status (SES) | Complete wellbeing or functioning | Functional, physical, mental, social, spiritual, others |
| Downey & Chang 2013 [23] | USA | Empirical mixed-method study | American adults | Multi-sided | |
| Frenk & Gómez-Dantés, 2014 [24] | USA, Mexico | Commentary | NA | Multi-sided | |
| Kaldjian, 2017 [25] | USA | Forum discussion | NA | Daily functioning, subjective, satisfying life | |
| Karimi & Brazier, 2016 [26] | Switzerland | Current opinion | NA | Daily functioning, wellbeing | |
| Lipworth et al., 2011 [27] | Australia | Qualitative literature review | NA | Adapting to change | Physical, spiritual, mental, social |
| Makoul et al., 2009 [28] | USA | Survey research | American adults | Participation, self-management, complete wellbeing or functioning | Physical, mental, social, spiritual, functional, others |
| Pietersma et al., 2014 [29] | The Netherlands | Three-stage Delphi-procedure | Patients, family members of patients, clinicians, scientific experts, and general population | Self-management, satisfying life, participation | Mental, social, physical |
| Shilton et al., 2011 [30] | Australia, France | Letter to the editor | NA | Self-management | Physical, mental, social, spiritual, environmental |
| Thumboo et al., 2018 [31] | Singapore, Finland | Qualitative research design | General public in Singapore | Subjective, participation, multi-sided | |
| Williamson et al., 2009 [32] | Canada | Literature study | NA | Subjective | |
Post [45] wrote: “... health encompassed how well people function in everyday life ...”. Daily functioning as part of a health concept was also identified in the dimension functional (theme 2) by Post [45]: “Functional health, including both physical functioning in terms of self-care, mobility, and physical activity level and social role functioning in relation to family and work”. The subtheme self-management as part of a health concept was identified in four articles (4/11) written from a patient’s perspective. For example, Jormfeldt [38] wrote: “… to be able to manage ones daily tasks”. The subtheme satisfying life as part of a health concept was identified in three articles (3/11) written from a patient’s perspective. For example, Jormfeldt [38] wrote about the attitudes towards health: “... to experience meaningfulness in life...” and “… to have a peaceful and positive feeling inside...”. The subtheme adapting to change as part of a health concept was identified in three articles (3/11) written from a patient’s perspective. For example, Shearer et al. [47] wrote: “Health was characterized by a rhythmic pattern of living with the paradox of chronic illness; that is, constructing meanings about one’s health that enhance personal strengths while acknowledging the losses and changes brought on by their illness”. The subtheme multi-sided view on health was identified in three articles (3/11) written from a patient’s perspective. For example, Hunter et al. [36] wrote: “... health that is more than the absence of disease ...”. The multi-sided view on health from this perspective was also identified by multiple dimensions of health (theme 2) being reported in four articles (4/11). For example, Gorecki et al. [44] wrote: “We developed a conceptual framework of HRQL [Health-Related Quality of Life] in PUs that includes four domains: PU-specific symptoms, physical functioning, psychological well-being and social functioning”. The other subthemes for the concepts of health were not identified in at least three articles and are not further described here (see S2C).
**Health from the perspective of elderly people**
Nine articles were written from the perspective of elderly people [18, 43, 47, 49–54]. The elderly people in these articles were for example elderly people with chronic illnesses. Characteristics of the included articles are shown in Table 8.
Content belonging to five subthemes were identified in at least three articles written from the perspective of elderly people: adapting to change, self-management, subjective, satisfying life, and participation. The subtheme adapting to change as part of a health concept was identified in six articles (6/9) written from...
| Authors, year | Country | Article type/ study design | Perspective (population) | Subthemes of Concept of health | Subthemes of Dimensions of health |
|------------------------|------------------------------------------|------------------------------------------------|------------------------------------------------------------------------------------------|--------------------------------------------------|--------------------------------------------------|
| Bickenbach, 2013 [42] | Switzerland | Literature study | Persons with disabilities | Subjective, daily functioning | |
| Ebrahimi et al., 2012 [43] | Sweden, USA | Phenomenological approach | Elders in emergency treatment, 80 years and older, or 65 years and older with chronic diseases | Subjective, adapting to change | Individual, environmental |
| Gorecki et al., 2010 [44] | United Kingdom | Review of the literature and qualitative approaches | Patients with pressure ulcers | Adapting to change, self-management, multi-sided | Physical, mental, functional, social, others |
| Huber et al., 2016 [12] | The Netherlands | Mixed method study, qualitative approach | Physicians, physiotherapists, policymakers, insurers, public health professionals, researchers, nurses, patients | Functional, physical, mental, social, spiritual, others | |
| Hunter et al., 2013 [36] | Australia | Phenomenography method | Patients and practitioners in integrative medicine clinic | Complete wellbeing or functioning, wellbeing, multi-sided | |
| Jormfeldt, 2009 [38] | Sweden | Cross-sectional study | Patients and staff in mental health services | Satisfying life, self-management | |
| Post, 2014 [45] | The Netherlands | Narrative review | NA | Functioning, subjective | Physical, mental, social, functional |
| Schrank et al., 2013 [46] | United Kingdom, Austria, Canada | Systematic review and narrative synthesis | People with psychosis | Daily functioning, participation, self-management, subjective | Individual |
| Shearer et al., 2009 [47] | USA | Qualitative descriptive design | Older women with chronic illness | Participation, satisfying life, adapting to change, self-management, subjective | |
| Warsop, 2009 [48] | United Kingdom | Phenomenological approach | NA | Satisfying life, daily functioning | Multi-sided, self-management |
| Zhang et al., 2014 [49] | China | Qualitative descriptive design | Chinese elderly with chronic illness, aged over 60 | | |
| Authors, year | Country | Article type/ study design | Perspective (population) | Subthemes of Concept of health | Subthemes of Dimensions of health |
|--------------|---------|-----------------------------|--------------------------|-------------------------------|----------------------------------|
| Boggatz, 2016 [50] | Austria | Concept analysis | Older adults | Subjective, adapting to change, satisfying life | |
| Cresswell-Smith et al., 2018 [51] | Finland/Italy/Norway/ Spain | Rapid review | Older adults, 80 years and older | Adapting to change, self-management, daily functioning | |
| Ebrahimi et al., 2012 [43] | Sweden, USA | Phenomenological approach | Elders in emergency treatment, 80 years and older, or 65 years and older with chronic diseases | Subjective, adapting to change | Functional, social, individual, environmental |
| Fange & Ivanoff, 2009 [52] | Sweden | Grounded theory method | Old age, between 80 and 89 years old | Participation, self-management | |
| Goins et al., 2011 [53] | USA | Qualitative approach | Community dwelling persons aged 60 years or older in west Virginia | Participation, subjective, adapting to change, satisfying life, multi-sided | Physical, functional, mental, spiritual |
| Noghabi et al., 2013 [54] | Iran | Theoretical analysis of literature and empirical observation. Hybrid concept analysis. | Old people, 65 years and older | Self-management | Physical, mental, social, spiritual, environmental |
| Shearer et al., 2009 [47] | USA | Qualitative descriptive design | Older women with chronic illness | Participation, satisfying life, adapting to change, self-management, subjective | |
| Song & Kong, 2015 [18] | Republic of Korea | Systematic review | Older adults | Self-management, adapting to change, satisfying life | Physical, mental, social, spiritual |
| Zhang et al., 2014 [49] | China | Qualitative descriptive design | Chinese elderly with chronic illness | Multi-sided, self-management | |
Table 9 Included articles discussing health from a philosophical perspective
| Authors, year | Country | Article type/ study design | Perspective (theoretical approach) | Subthemes of Concept of health | Subthemes of Dimensions of health |
|---------------|---------|----------------------------|------------------------------------|--------------------------------|----------------------------------|
| Bauer et al., 2020 [55] | Switzerland, Canada, Kenya, Italy, United Kingdom, Sweden, Norway, Denmark, Spain, Israel, Austria, Singapore, Netherlands, | Literature study | Salutogenic | Wellbeing, adapting to change, multi-sided | Environmental, individual, social |
| Bircher & Kuruvilla, 2014 [3] | Switzerland | Multi-grounded theory method | Multi-grounded theory | Wellbeing, adapting to change, multi-sided | Environmental, individual, social |
| Cloninger et al., 2012 [56] | USA | Literature study | Holistic | Multi-sided, adapting to change | Physical, mental |
| de Araújo et al. 2012 [57] | Brazil | Theoretical study | Hermeneutics | Subjective, adapting to change | Physical, mental |
| Elliot, 2016 [58] | United Kingdom | Literature study | Eudaimonistic | Multi-sided | Physical, mental, social |
| Ereshefsky, 2009 [59] | Canada | Paper | Naturalist/ normativist | Physical, mental, social, others | |
| Haverkamp et al., 2018 [7] | The Netherlands | Practice-oriented review | Philosophical | Adapting to change, self-management | Physical, mental, social |
| Huber et al. 2011 [5] | The Netherlands | Analysis | Positive health | Satisfying life, adapting to change | Physical, mental, social, spiritual, others |
| Leonardi, 2018 [1] | Italy | Literature study | Epistemological | Self-management, adapting to change, daily functioning | Physical, mental, social, functional |
| Misselbrook, 2014 [60] | Bahrain | Note | Human flourishing | Satisfying life, adapting to change | Physical, mental, social, spiritual, others |
| Misselbrook, 2016 [61] | Bahrain | Literature study | Human flourishing | Satisfying life, multi-sided, adapting to change | Physical, mental, social, spiritual, others |
| Prinsen & Terwee, 2019 [15] | The Netherlands | Mixed-method study including a literature search, a qualitative and quantitative ranking study, followed by a content validity study | Positive health | Satisfying life, adapting to change | Physical, social |
| Reed, 2019 [62] | USA | Review | Philosophical | Subjective, satisfying life | Physical, social |
| Van Spijk, 2015 [63] | Switzerland | Scientific contribution | Philosophical anthropology | Satisfying life | Physical, mental, social, functional |
| Sturmberg et al., 2010 [17] | Australia/USA | Literature study | Philosophical | Adapting to change, multi-sided | Environmental |
| Sturmberg, 2014 [64] | Australia | Commentary | Philosophical | Subjective, wellbeing, multi-sided | |
| Tengland, 2016 [65] | Sweden | Critical discussion | Holistic/ capability approach | Multi-sided, subjective, adapting to change, participation | |
| Tyerman, 2011 [66] | United Kingdom | Literature study | Phenomenological/ hermeneutics | Multi-sided, subjective, adapting to change, participation | |
| Venkatapuram, 2013 [4] | United Kingdom | Debate | Capability approach | Daily functioning, subjective, satisfying life | |
### Table 9 (continued)
| Authors, year | Country | Article type/study design | Perspective (theoretical approach) | Subthemes of Concept of health | Subthemes of Dimensions of health |
|---------------|------------|---------------------------|-----------------------------------|-------------------------------|-----------------------------------|
| Included articles discussing health from a biomedical science perspective |
| Boorse, 2011 [67] | USA | Conceptual analysis | Naturalist | Complete wellbeing or functioning |
| Boorse, 2014 [68] | USA | Reactions to critics | Naturalist | Complete wellbeing or functioning |
| Hafen, 2016 [16] | Switzerland | Sociological systems theory | Health/health impairment-continuum | Complete wellbeing or functioning |
| Schroede, 2013 [89] | United Kingdom | Literature study | Comparative | Daily functioning |
the perspective of elderly people. For example, Goins et al. [53] wrote: “... defining health as a value indicates it can be fleeting, both lost and regained” and Cresswell-Smith et al. [51] wrote about the concept of health: “... older adults have been seen to adapt and accept limitations as part of the ageing process”. The second sub-theme self-management as part of a health concept was identified in six articles (6/9) written from the perspective of elderly people. For example, Ebrahimi et al. [43] wrote: “... older adults experience health when they have the ability to do something independently...”. That health is subjective was identified in four articles (4/9) written from the perspective of elderly people. For example, Goins et al. [53] wrote: “... defining health as a value indicates it can be fleeting, both lost and regained” and Cresswell-Smith et al. [51] wrote about the concept of health: “... older adults have been seen to adapt and accept limitations as part of the ageing process”. The second sub-theme self-management as part of a health concept was identified in six articles (6/9) written from the perspective of elderly people. For example, Ebrahimi et al. [43] wrote: “... older adults experience health when they have the ability to do something independently...”. That health is subjective was identified in four articles (4/9) written from the perspective of elderly people. For example, Goins et al. [53] wrote: “... defining health as a value indicates it can be fleeting, both lost and regained” and Cresswell-Smith et al. [51] wrote about the concept of health: “... older adults have been seen to adapt and accept limitations as part of the ageing process”. The second sub-theme self-management as part of a health concept was identified in six articles (6/9) written from the perspective of elderly people. For example, Ebrahimi et al. [43] wrote: “... older adults experience health when they have the ability to do something independently...”. That health is subjective was identified in four articles (4/9) written from the perspective of elderly people. For example, Goins et al. [53] wrote: “... defining health as a value indicates it can be fleeting, both lost and regained” and Cresswell-Smith et al. [51] wrote about the concept of health: “... older adults have been seen to adapt and accept limitations as part of the ageing process”. The second sub-theme self-management as part of a health concept was identified in six articles (6/9) written from the perspective of elderly people. For example, Ebrahimi et al. [43] wrote: “... older adults experience health when they have the ability to do something independently...”. That health is subjective was identified in four articles (4/9) written from the perspective of elderly people. For example, Goins et al. [53] wrote: “... defining health as a value indicates it can be fleeting, both lost and regained” and Cresswell-Smith et al. [51] wrote about the concept of health: “... older adults have been seen to adapt and accept limitations as part of the ageing process”. The second sub-theme self-management as part of a health concept was identified in six articles (6/9) written from the perspective of elderly people. For example, Ebrahimi et al. [43] wrote: “... older adults experience health when they have the ability to do something independently...”. That health is subjective was identified in four articles (4/9) written from the perspective of elderly people. For example, Goins et al. [53] wrote: “... defining health as a value indicates it can be fleeting, both lost and regained” and Cresswell-Smith et al. [51] wrote about the concept of health: “... older adults have been seen to adapt and accept limitations as part of the ageing process”. The second sub-theme self-management as part of a health concept was identified in six articles (6/9) written from the perspective of elderly people. For example, Ebrahimi et al. [43] wrote: “... older adults experience health when they have the ability to do something independently...”. That health is subjective was identified in four articles (4/9) written from the perspective of elderly people. For example, Goins et al. [53] wrote: “... defining health as a value indicates it can be fleeting, both lost and regained” and Cresswell-Smith et al. [51] wrote about the concept of health: “... older adults have been seen to adapt and accept limitations as part of the ageing process”.
| Authors, year | Country | Article type/ study design | Perspective (population) | Subthemes of Concept of health | Subthemes of Dimensions of health |
|--------------|---------|---------------------------|--------------------------|------------------------------|----------------------------------|
| **Included articles discussing health from a cultural specific perspective** | | | | | |
| Kendall et al., 2019 [75] | Australia | Community collaborative participatory action research | Aboriginal mothers in metropolitan regional, and remote prisons | Complete wellbeing or functioning, adapting to change, self-management, multi-sided | |
| Mark & Lyons, 2010 [76] | New Zealand | Phenomenological approach | Māori spiritual healers | Multi-sided, satisfying life | Spiritual, environmental, others |
| Seyyedfatemi et al., 2014 [77] | Iran | Systematic review | Iranian women’s health concepts | Multi-sided, adapting to change | Environmental, social, individual, physical, spiritual |
| Yang et al., 2016 [78] | Republic of Korea/USA | Qualitative method | Nepalese women, had lived in the Dadeldhura district for more than 5 years | Complete wellbeing or functioning, satisfying life, participation | |
| **Included articles discussing health from an immigrant’s perspective** | | | | | |
| Cha, 2013 [79] | South-Korea | Grounded theory method | Korean migrant women who migrated to North-America or Canada for their children’s education while their husbands remained in Korea | Satisfying life, daily functioning, complete wellbeing or functioning | |
| Martin, 2009 [80] | USA | Phenomenology | Older Iranian immigrants | Adapting to change, multi-sided | Mental, physical, spiritual, social, others |
| Tirodkar et al., 2011 [73] | USA | Qualitative research design | South Asian immigrants in Chicago / religion | Multi-sided | Functional, social, physical, spiritual |
| **Included articles discussing health from an educational perspective** | | | | | |
| Jensen, 2013 [81] | Denmark | Qualitative approach | Women with low levels of education | Wellbeing, complete wellbeing or functioning, multi-sided, satisfying life | |
| Stronks et al., 2018 [82] | The Netherlands | Concept mapping | Lay persons with a lower educational level | Complete wellbeing or functioning, daily functioning, multi-sided, satisfying life | |
| | | | Lay persons with an intermediate educational level | Complete wellbeing or functioning, daily functioning, multi-sided, satisfying life, self-management, | |
| | | | Lay persons with a higher educational level | Complete wellbeing or functioning, daily functioning, multi-sided, satisfying life, subjective, self-management | |
| **Included articles discussing health from other context specific perspectives** | | | | | |
| Mayer & Bones, 2011 [83] | Germany, South-Africa | Multi-method research | South-African managers and expatriates | Wellbeing, multi-sided, subjective | Mental, physical, spiritual |
| Rawolle et al., 2016 [84] | Australia | Descriptive qualitative study | South-Australian farmers | Daily functioning, participation, complete wellbeing or functioning | Individual, social, environmental |
identified by multiple dimensions of health (theme 2) being reported in six articles (6/19) with a social science perspective. For example, Misselbrook [61] wrote: “But if we truly believe in a multi-sided model of health, which includes the biomedical, social, psychological, anthropological and spiritual dimensions, then we are swimming against the stream”. That health is subjective was identified in five articles (5/19) written from a social science perspective. For example, Sturmberg et al. [17] wrote: “The perception of being healthy is an emergent phenomenon based on individual and collective understandings of everyday realities”. The subtheme satisfying life as part of a health concept was identified in five articles (5/19) with a social science perspective. For example, Misselbrook [60, 61] wrote: “… health can be seen as the ability to flourish …”. In the articles from a biomedical science perspective content belonging to only one subtheme was identified in at least three articles: complete wellbeing or functioning. For example, Boorse [67] wrote about the concept of health as: “… each internal part to perform all its normal functions …”. The other subthemes for the concepts of health were not identified at least three times in the articles with a biomedical science perspective and are not further described here (see S2E).
Health from a theological perspective
Five articles were written with a theological perspective [70–74]. The perspectives in these articles were for example United Methodist church clergy and Islamic philosophy. Characteristics of the included articles are shown in Table 10.
Content belonging to onesubtheme was identified in at least three articles: multi-sided. The subtheme multi-sided view on health was identified in four articles (4/5) written from a theological perspective. For example, Proeschold-Bell et al. [71] wrote: “... we define our final health outcome holistically to indicate that health is not merely the absence of problems but is, rather, the presence of multiple life satisfactions”. The multi-sided view on health from this perspective was also identified by multiple dimensions of health (theme 2) being reported in four articles (4/5). For example, Proeschold-Bell et al. [71] wrote: “... spiritual, emotional, physical, mental well-being”. The spiritual dimension was identified in a theological perspective in four articles (4/5). For example, Proeschold-Bell et al. [71] wrote: “Although spiritual well-being may not have the rigorous definition and tradition of physical and mental health, participants considered it essential ...”. The other subthemes for the concepts of health were not identified at least three times and are not further described here (see S2F).
Health from a context specific perspective
Eleven articles were written from a context specific perspective. We divided these articles with a context specific perspective in four groups: cultural perspectives (4 articles) [75–78], immigrant perspectives (3 articles) [73, 79, 80], educational level perspectives (2 articles) [81, 82], and other perspectives (2 articles) [83, 84] (see Table 11). These contexts are diverse and cannot be seen as one similar group. Because of heterogeneity, this subtheme was not included in supplementary Tables 3A and 3B. For characteristics of the included articles and more detailed information about these concepts of health related to their specific contexts see supplementary Table 2G.
Discussion
We posited the research question whether a general health concept can guide all healthcare practices. It seems more likely that specific health concepts are needed for different professions or settings instead. In this scoping review, we provide an overview of articles discussing various concepts and dimensions of health, which were either general or specified to a particular context. We observed relevant differences but also similarities in the concepts and dimensions of health per context.
The variety of concepts of health already suggests that no consensus can be made on one overall concept to replace the WHO definition of health. First of all, our analysis shows that the best fitting health concept depends on the context. Besides, healthcare consumers act based on different health concepts when seeking care than care workers when providing it. This could mean that there is a misfit in the aims of healthcare consumers, compared to care workers. It is remarkable that complete wellbeing or functioning is mentioned by care workers, while healthcare consumers barely mentioned this biomedical viewpoint. Healthcare consumers value self-management, while care workers do not focus on self-management in their health concepts. Furthermore, individual health experiences can change over the course of life, due to diverse life circumstances and events [55]. It was seen that patients in general tend to focus on daily functioning while elderly people specifically focus on participation. This shows that one health concept does not automatically fit all age groups. On the other hand, there were interesting similarities regarding the concepts of health. In the majority of the articles, health was conceptualised as multi-sided and subjective, and not merely as complete wellbeing or functioning as suggested in the biomedical model. Furthermore, in the majority of the contexts other prerequisites for health were adapting to change and satisfying life. Indeed, no consensus can be...
made on one general health concept; all health concepts capture aspects that seem relevant [7].
Nevertheless, it is important to be clear about which health concept is used as a basis for development and implementations in health management, for (re)designing health policy and for research. Health concepts developed in one context do not hold automatically in other contexts. As a result, the expectations of healthcare consumers and care workers might not align in care provision. Having different understandings of the concepts of health can lead to misunderstandings in practice. Our overview of health concepts gives insight in the variety of experiences with health concepts of people with diverse health, life, community and other environmental circumstances. Policy officers or healthcare providers can check the similarities and differences of their health concept with health concepts in other contexts included in this overview. Even better, the overview we provide can be used by care workers preparing their conversation about what health means for the healthcare consumer. However, it should be emphasized that health could mean something different for each individual; no concepts are intrinsically incorrect. As Haverkamp et al. [7] described, health concepts share different features or assumptions and should be understood as a member of a family of concepts. By exploring the health concept in dialogue, important purposes of health provision can be defined by the care worker and the healthcare consumer together. Through such conversation between actors, health provision can be customised for each individual. Tools such as the positive health dialogue tool [12] might be of use in these conversations. This dialogue tool consists of six dimensions of health which correspond to the dimensions found in our study. However, the environmental dimension was not included in the positive health dialogue tool and might be of additional value to the conversation about what health means to an individual.
Many perspectives shared a similar multi-sided approach as Huber’s positive health [12]. Taking a closer look, we noticed that ‘the ability to adapt and to self-manage,’ the main issues of the concept of positive health, were also recognised in other health concepts, independently of perspective. The concepts of health described the ‘ability to adapt’ for example as adapting to changing physical conditions, such as ageing, illness or disability, and also as emotional balance and as health being a dynamic state in which adaptation to circumstances is necessary. ‘The ability to self-manage’ was described for example as autonomy or independence. However, care workers had barely focussed on this. This indicates that for care workers, patient self-management has less priority. Furthermore, we noticed that subjectivity was not explicitly mentioned in Huber’s concept, while this was frequently mentioned in the articles included in our review. However, Huber et al. did explain that positive health focuses on people’s strengths rather than weaknesses. As Huber argues, people’s strengths are based on their perception of and experiences with health [12], which is subjective. Notably, as mentioned by Prinsen and Terwee [15], it is not entirely clear whether the positive health concept refers to patients’ experiences or to their satisfaction with their health, and overlap between dimensions and aspects of Positive Health exist; this was also seen in our results.
Methodological considerations
A few methodological considerations are worth mentioning. A limitation of the search strategy was that the keyword ‘health’ by itself led to too many results. To solve this, we used the keyword ‘health’ in combination with ‘concept’ and ‘definition’ and used more specific keywords such as ‘health perception’ and ‘perceived health’ to broaden the search strategy and capture all relevant articles for our research. Most research we found was conducted in Europe and North America. Fewer research articles from Central/South America, Australia, Africa and Asia were found. Their views on health may be underrepresented. To decrease the chance that articles were missed in the search, a snowball method was conducted on the results of the primary search. Four experts from the field were asked to check whether they missed any articles in the selection. Moreover, we did not include the weighting (importance) of a specific subtheme as was described in some articles. To compensate, we only incorporated a subtheme in our analyses by introducing a minimum level of appearance in multiple articles (> 3) as threshold. Strengths of the research were the thoroughly structured process of article selection, the inductive method of analysis, and the repeated consultation of four researchers (EB, LN-vV, EdV, DvdM) to discuss the process and the results by the first author (VvD).
Conclusion
We performed a scoping review to explore if one general health concept can guide all different care practice situations. Based on the variety of health concepts from different perspectives, we conclude that for every perspective, and even for every individual, health can mean something different. Thus, it seems impossible to choose or define one health concept appropriate for all contexts. However, in the interaction between care workers and healthcare consumers (and also in health policy) it is important that the meaning of ‘health’ is clear to all actors involved to avoid misunderstandings.
Our overview supports a more uniform tuning of healthcare between healthcare providers (the organisations), care workers (the professionals) and healthcare consumers (the patients), by creating more awareness of the differences among these actors, which can be a guide in their communication.
Supplementary Information
The online version contains supplementary material available at https://doi.org/10.1186/s12913-022-07702-2.
Additional file 1: Supplementary Table 1. The coding scheme; identified subthemes and codes for theme 1, the concept of health.
Additional file 2: Supplementary Table 2A. Included articles discussing health from a general population perspective.
Additional file 3: Supplementary Table 3A. Overview of number of articles per subtheme for theme 1 (concept of health) for different perspectives.
Acknowledgements
Not applicable.
Authors’ contributions
VvD conducted the research and wrote the main manuscript. EB assisted with the screening of all titles, abstracts and full-text articles for inclusion. DJ, EdV, DvdM and LN-vV were repeatedly consulted to discuss the analytic process and the development of the results. EF, EdV, DvdM, AK and LN-vV reviewed the manuscript. All authors read and approved the final manuscript.
Funding
No funding was received for conducting this research.
Availability of data and materials
The dataset (list of included articles) supporting the conclusions of this article is included within the tables in this article and in the supplementary files.
Declarations
Ethics approval and consent to participate
Since no humans participated nor any human data has been used in this research, ethics approval and consent to participate are not applicable.
Consent for publication
The manuscript does not include details of individual persons, thus written informed consent for the publication of these details is not applicable.
Competing interests
The authors declare that they have no competing interests.
Author details
1 Jeroen Bosch Academy Research, Jeroen Bosch Hospital, Jeroen Bosch Ziekenhuis, PO Box 90153, Henri Dunantstraat 1, 5331 DB, ‘s Hertogenbosch, the Netherlands. 2 Tranzo Scientific Center for Care and Wellbeing, Tilburg University, PO Box 90153, Professor Cobbenhagenlaan 125, Tilburg 5000 LE, the Netherlands. 3 TISEM Department of Management, Tilburg University, Tilburg, the Netherlands. 4 Department of Nephrology, Jeroen Bosch Hospital, ‘s Hertogenbosch, the Netherlands. 5 Department of Geriatric Medicine, Jeroen Bosch Hospital, ‘s Hertogenbosch, the Netherlands.
References
1. Leonardi F. The definition of health: towards new perspectives. Int J Health Serv. 2018;48(4):735–48.
2. Kelley L. The World Health Organization (WHO). World Heal Organ. 2008(April 1948):1–157.
3. Bircher J, Kuruvilla S. Defining health by addressing individual, social, and environmental determinants: new opportunities for health care and public health. J Public Health Policy. 2014;35(3):363–86.
4. Venkatapuram S. Health, vital goals, and central human capabilities. Bioethics. 2013;27(5):271–9.
5. Huber M, Knottnersus JA, Green L, Van Der Horst H, Jadad AR, Komhout D, et al. How should we define health? BMJ. 2011;343:j262:2:j2613.
6. Boorse C. Health as a theoretical concept. Philos Sci. 1977;44(4):542–73.
7. Haverkamp B, Bovenkerk B, Verweij MF. A practice-oriented review of health concepts. J Med Philos A Forum Bioeth Philos Med. 2018;43(4):381–401.
8. Nordenfelt L. Quality of life, health and happiness. Aldershot: Avebury Ashgate Publishing Limited; 1993.
9. Nussbaum MC. Woman and human development. The capabilities approach. Cambridge: Cambridge University Press; 2000.
10. Bickenbach J. Reconciling the capability approach. Eur J Disabil Res. 2014;8:10–23.
11. WHO. International Classification of Functioning, Disability, and Health (ICF). 2017. Available at: https://www.who.int/classifications/icf/en/.
12. Huber M, van Vliet M, Geigergen M, Winkens B, Heenkens Y, Dagolle PC, et al. Towards a patient-centred operationalisation of the new dynamic concept of health. Br Med J Open. 2016;6(1):1–12.
13. East Iceland Health Institute (HSA). JÁRKÝD HEILSA & HEILSUHÓLÚ. 2020.
14. Jambroes M, Nederland T, Kalljou M, Van Vliet K, Essink-Bot ML, Ruwaard D. Implications of health as “the ability to adapt and self-manage” for public health policy: a qualitative study. Eur J Pub Heal. 2016;26(3):412–6.
15. Prinsen CAC, Terwee CB. Measuring positive health for now, a bridge too far. Public Health. 2019;170:70–7.
16. Hafén M. Of what use (or harm) is a positive health definition? J Public Health (Bangkok). 2016;24(5):437–41.
17. Sturberg JP, Martin CM, Moses WM. Health at the center of health systems reform: how philosophy can inform policy. Perspect Biol Med. 2010;53(3):341–56.
18. Song M, Kong E-H. Older adults’ definitions of health: a meta-synthesis. Int J Nurs Stud. 2015;52(6):1097–106.
19. Tricco AC, Lillie E, Zarin W, O’Brien KK, Colquhoun H, Levac D, et al. PRISMA extension for scoping reviews (PRISMA-ScR): checklist and explanation. Ann Intern Med. 2018;169(7):467.
20. Aburukash J, Goodstadt MS, Mouhaffel R. Interdependence between health and peace: a call for a new paradigm. Health Promot Int. 2020;35(6):1590–600.
21. Amzat J, Razum O. Health, disease, and illness as conceptual tools: Medical sociology in Africa; 2014. p. 21–37.
22. Conner AL, Boles DZ, Markus HR, Eberhardt JL, Crum AJ. Americans’ health mindsets: content, cultural patterning, and associations with physical and mental health. Ann Behav Med. 2019;53(4):321–32.
23. Downey CA, Chang EC. Assessment of everyday beliefs about health: the lay concepts of health inventory, college student version. Psychol Health. 2013;28(7):818–32.
24. Frenk J, Gómez-Dantés O. Designing a framework for the concept of health. J Public Health Policy. 2014;35(3):401–6.
25. Kaldjian LC. Concepts of health, ethics, and communication in shared decision making. Commun Med. 2017;1(1):83–95.
26. Karimi M, Brazier J. Health, health-related quality of life, and quality of life: what is the difference? Pharmacoconomics. 2016;34(7):645–9.
27. Lipworth WL, Hooker C, Carter SM. Balance, balancing, and health. Qual Health Res. 2011;21(15):714–25.
28. Makoul G, Clayton ML, Lynch EB, Thompson JA. Four concepts of health in America: results of national surveys. J Health Commun. 2000;14(1):3–14.
29. Pietersma S, de Vries M, van den Akker-marle ME. Domains of quality of life: results of a three-stage Delphi consensus procedure among...
patients, family of patients, clinicians and scientists and the general public. Qual Life Res. 2014;23(5):1543–56.
30. Shilton T, Sparks M, McQueen D, Lamare MC, Jackson S. Proposal for new definition of health. BMJ. 2011;343:3aqua23 4d3559.
31. Thumboo J, Ow MYL, Lily EiB, Xin X, Chan ZVC, Sung SC, et al. Developing a comprehensive, culturally sensitive conceptual framework of health domains in Singapore. PLoS One. 2013;13(6):e0199881.
32. Williamson DL, Carr J. Health as a resource for everyday life: advancing the conceptualization. Crit Public Health. 2009;19(1):107–22.
33. Alslman ET, Ahmad MM, Bani Hani MA, Atiyeh HM. Health: a developing concept in nursing. Int J Nurs Knowl. 2017;2(2):64–9.
34. Ashcroft R, Van Katwyk T. Joining the global conversation: social workers define health using a participatory action research approach. Br J Soc Work. 2016;bcw005.
35. Bąk-Sosnowska M, Skrzypulec-Plinta V. Health behaviors, health definitions, sense of coherence, and general practitioners’ attitudes towards obesity and diagnosing obesity in patients. Arch Med Sci. 2017;2:433–40.
36. Hunter J, Marshall J, Corcoran K, Leider S, Phelps K. A positive concept of health – interviews with patients and practitioners in an integrative medicine clinic. Complement Ther Clin Pract. 2013;19(4):197–203.
37. Johansson H, Weinenthal H, Emmelin M. ‘It depends on what you mean’: a qualitative study of Swedish health professionals’ views on health and health promotion. BMC Health Serv Res. 2009;9(1):191.
38. Jormfeldt H. Attitudes towards health among patients and staff in mental health services: a comparison of ratings of importance of different items of health. Soc Psychiatry Psychiatr Epidemiol. 2009;45(2):225–31.
39. Lyon BL. Stress, coping, and health, a conceptual overview. In: Handbook of health psychology. 1st ed. Thousand Oaks: Sage Publications, Inc; 2012. p. 2–20.
40. Merry L. Global health for nursing...and nursing for global health. Can J Nurs Res. 2012;44(4):20–35.
41. Pace CS, Velotti P, Zavattini GC. Representations of health and illness by Eastern European, South American and Italian care workers: a qualitative study. J Health Psychol. 2011;17(4):490–9.
42. Bickenbach J. Being unhealthy, and rights to health. J Law Med Ethics. 2004;13(6):e0199881.
43. Birkendall DM. The home is the hub of health in very old age: findings from the ENABLE-AGE project. Arch Gerontol Geriatr. 2020;83:104–10.
44. Goins RT, Spencer SM, Williams K. Lay meanings of health among rural people. Qual Health Res. 2012;22(11):1513–23.
45. Spielberger CD, Carp J, Carolus J, Green S. Stress, coping, and health: implications for nursing research, theory, and practice. Thousand Oaks: Sage Publications; Inc; 2012. p. 2–20.
46. Huisman D, van Druten K, Janssen H. Determinants of multidimensional mental wellbeing in older adults in Appalachia. J Rural Health. 2011;27(1):13–20.
47. Schrank B, Bird V, Tylee A, Coggins T, Rashid T, Slade M. Conceptualising health – interviews with patients and practitioners in an integrative medicine clinic. Complement Ther Clin Pract. 2013;19(4):197–203.
48. Schroeder SA. Rethinking health: healthier or healthier than? Br J Philos Sci. 2013;64(1):131–59.
49. Shearer NBC, Fleury JD, Reed PG. The rhythm of health in older women with chronic illness. Res Theory Nurs Pract. 2009;23(2):148–60.
50. Shearer NBC, Fleury JD, Reed PG. We hide under the scriptures”: conceptualization of health among united methodist church clergy in Kenya. J Relig Health. 2015;54(6):2345–8.
51. Shearer NBC, Fleury JD, Reed PG. “We hide under the scriptures”: conceptualization of health among united methodist church clergy in Kenya. J Relig Health. 2015;54(6):2345–8.
52. Shearer NBC, Fleury JD, Reed PG. “We hide under the scriptures”: conceptualization of health among united methodist church clergy in Kenya. J Relig Health. 2015;54(6):2345–8.
53. Snell LM. Conceptualizations of health by incarcerated aboriginal women in New South Wales, Australia. Qual Health Res. 2019;29(11):1549–65.
54. Sturmberg JP. The happy genius of my household: phenomenological and poetic journeys into health and illness. Med Health Care Philos. 2009;50(3):700–30.
55. Szapocznik J, Scarr S. Customary versus modern parental role beliefs and childrearing practices in an urban developing nation: the case of Cuba. J Cross Cult Fam Stud. 2012;51(1):1–23.
56. Tyreman S. The happy genius of my household: phenomenological and poetic journeys into health and illness. Med Health Care Philos. 2009;50(3):700–30.
57. van Druten K, Janssen H, van den Boorn J. Determinants of multidimensional mental wellbeing in older adults in Appalachia. J Rural Health. 2011;27(1):13–20.
58. van Druten K, Janssen H, van den Boorn J. Determinants of multidimensional mental wellbeing in older adults in Appalachia. J Rural Health. 2011;27(1):13–20.
59. van Druten K, Janssen H, van den Boorn J. Determinants of multidimensional mental wellbeing in older adults in Appalachia. J Rural Health. 2011;27(1):13–20.
60. van Druten K, Janssen H, van den Boorn J. Determinants of multidimensional mental wellbeing in older adults in Appalachia. J Rural Health. 2011;27(1):13–20. | 2025-03-04T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
3135,
1
],
[
3135,
8803,
2
],
[
8803,
14619,
3
],
[
14619,
19429,
4
],
[
19429,
20328,
5
],
[
20328,
25877,
6
],
[
25877,
29575,
7
],
[
29575,
33924,
8
],
[
33924,
36605,
9
],
[
36605,
41707,
10
],
[
41707,
44422,
11
],
[
44422,
48600,
12
],
[
48600,
50570,
13
],
[
50570,
53874,
14
],
[
53874,
54852,
15
],
[
54852,
59309,
16
],
[
59309,
62471,
17
],
[
62471,
67965,
18
],
[
67965,
73483,
19
],
[
73483,
79982,
20
],
[
79982,
85144,
21
]
]
} |
12475b5446b2c5bfbcc30bf48403320052309733 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 11,
"total-fallback-pages": 0,
"total-input-tokens": 36191,
"total-output-tokens": 12901,
"fieldofstudy": [
"Geology"
]
} | DEEP WATER CYCLING AND DELAYED ONSET COOLING OF THE EARTH
JOHNNY SEALES\textsuperscript{1} AND ADRIAN LENARDIC\textsuperscript{1}
Department of Earth, Environment and Planetary Sciences, Rice University, Houston, TX 77005
Draft Version 11/13/2017
ABSTRACT
Changes that occur on our planet can be tracked back to one of two energy sources: the sun and the Earth’s internal energy. The motion of tectonic plates, volcanism, mountain building and the reshaping of our planet’s surface over geologic time depend on the Earth’s internal energy. Tectonic activity is driven by internal energy and affects the rate at which energy is tapped, i.e., the cooling rate of our planet. Petrologic data indicate that cooling did not occur at a constant rate over geologic history. Interior cooling was mild until 2.5 billion years ago and then increased (Figure 1). As the Earth cools, it cycles water between its rocky interior (crust and mantle) and its surface. Water affects the viscosity of mantle rock, which affects the pace of tectonics and, by association, Earth cooling. We present suites of thermal-tectonic history models, coupled to deep water cycling, to show that the petrologically constrained change in the Earth’s cooling rate can be accounted for by variations in deep water cycling over geologic time. The change in cooling rate does not require a change in the global tectonic mode of the Earth. It can be accounted for by a change in the balance of water cycling between the Earth’s interior and its surface envelopes. The nature and timing of that water cycling change can be correlated to a change in the nature of continental crust and an associated rise of atmospheric oxygen. The prediction that the rise of oxygen should then be correlated, in time, to the change in the Earth’s cooling rate is consistent with data constraints.
Keywords: thermal history; deep water cycle
Solid planet cooling, and how it connects to volcanic-tectonic evolution, defines the Earth’s thermal history. At present, the cooling of our planet’s interior is associated with plate tectonics. At mid-ocean ridges, plates are created by decompression melting of mantle rock. As plates spread, they cool and transfer heat. Oceanic plates eventually subduct back into the mantle, and cold rock is mixed into the progressively cooling interior of our planet. Heat transfer associated with macroscopic motion is, by definition, thermal convection. Plate tectonics is thus a component of mantle convection and the Earth’s convective cooling. Given this, a change in cooling rate (Figure 1) could reasonably be taken to indicate a change in the tectonic mode of our planet [Condie et al., 2016]. There is an alternative that does not require a change in the global tectonic mode of the Earth. The alternative hypothesis is connected to the cycling of water between Earth’s interior and surface.
Figure 2 shows petrological constraints [Condie et al., 2016; Herzberg et al., 2010] along with a thermal history model that couples thermal convection in a planet’s interior to deep water cycling [Sandu et. al., 2011]. This is one model case from thousands we have run (Figures 3 and 4). Our modeling suites account for temperature and hydration effects on mantle viscosity [Kohlstedt, 2006; Li et al., 2008], melting and volcanism that can dehydrate the mantle [Hirschmann, 2000; Katz et. al., 2003], and processes that recycle surface water to the mantle [Ulmer and Trommsdorff, 1995; Rupke et al., 2004]. Mantle de-watering occurs at mid ocean ridges and re-watering at subduction zones. The amount of water initially in the mantle is an initial condition. The fraction of water in melt that makes it to the surface, $\chi_d$, and the fraction of water carried into the deep mantle with subducting slabs, $\chi_r$, represent de- and re-watering efficiencies. Surface heat flow follows the scaling form of $Nu \sim Ra^\beta$, where $Nu$ is the nondimensional heat flux, $Ra$ quantifies the vigor of mantle convection, and $\beta$ is a scaling parameter that accounts for variations in plate strength affecting the motion of tectonic plates and associated mantle cooling [Conrad and Hager, 1999; Korenaga, 2003; Hoinik et al., 2013]. In all cases, plate velocity parameterizations are such that model plate velocities, after 4.6 Gy of evolution, match present day values. Further model description can be found in the supplemental material.
The coupling between deep water cycling and thermal convection in the Earth’s mantle leads to feedbacks that affect planetary evolution [Crowley et. al., 2011]. Internal temperature changes alter the nature of deep water cycling, which feeds back and alters mantle thermal evolution. If, for example, mantle temperature is relatively high, melt production can increase. Accompanying higher melt production are greater rates of mantle de-watering, leading to a stiffer mantle [Kohlstedt, 2006; Li et al., 2008] and a less efficient heat transfer. This, in turn, can act to increase mantle temperatures. Heating proceeds until temperature effects on mantle viscosity can outpace those of mantle dehydration, thereby reducing viscosity and allowing for faster convection, which acts to offset the heating effect associated with dehydration. Recycling water into the Earth’s interior is also associated with potential feedbacks. For cooler conditions, hydrated mineral phases are stable to greater
\texttt{[email protected]}
\texttt{[email protected]}
depth, [Ulmer and Trommsdorff, 1995; Rupke et al., 2004] and as a result, the ability to cycle water into the interior can increase with mantle cooling. Water cycled into the mantle lowers mantle viscosity, which decreases the resistance to plate overturn and, by association, increases mantle cooling. The strength of these coupled feedbacks evolve through time, and this opens the potential of a wider diversity of thermal histories as compared to a situation without deep water cycling.
The model of Figure 2 started warm, contained 1.5 present day ocean mass equivalents (OM) of water in the mantle and evolved as water cycled between the surface and interior. The evolution consisted of three phases: rapid initial cooling, near constant temperature, and a steady decrease to present day. The first phase was facilitated by a hot and hydrated mantle. These factors decrease mantle viscosity which increased convective vigor and mantle cooling. The second phase is highlighted by a flattening of the cooling curve consistent with the data of Condie et al. [2016]. The data of Herzberg et al. [2010] is associated with warmer temperatures but overall trends are similar. Mantle degassing continued beyond the initial rapid phase of mantle cooling. Continued mantle dehydration drove an increase in viscosity which damped the efficiency of heat transport. Decreased heat transport drove an increase in mantle temperature which offset the tendency for the mantle temperature to drop as internal heat sources decayed. This occurred to the point where there was a near balance between the two effects which lead to a flat line cooling phase. The flat line behavior correlated with a model water evolution phase during which surface water mass increased due to the dominance of outgassing from the interior (Figure 2b). Over time, the rate of mantle dehydration waned and could not maintain a flat line trend. As the mantle cooled, lithospheric plates thickened and the stability field for hydrated minerals deepened allowing a larger capacity of water rich rock to be transported back into the deep mantle (subduction zones transitioned from being dry to wet). At ~2.0 Gyr of model time, mantle de- and re-hydrated became comparable which terminated the flat line cooling phase. The final phase was characterized by internal temperature tracking the decay of radiogenic heat sources in the mantle. For a number of cases explored, rehydration exceeded mantle dehydration which lead to a steeper final cooling phase.
Figure 2 plots an illustrative case from a large number of models that were run over varied model assumptions, parameter values, and initial conditions. In Figure 3, each open circle represents the result of one model for a distinct combination of initial conditions and parameter values. The four plots represent the final mantle temperature, the age at which the most recent cooling phase initiated, the mantle temperature after 1.5 Gyr of model evolution, and the present day ratio of mantle heat sources to mantle heat loss (referred to as the mantle Urey ratio). The Urey ratio values account for the effects of present day continental area [Grigné et al., 2001; Lenardic et al., 2011]. There are six column sets of model cases for each value of $\beta$. Decreasing $\beta$, from left to right, parameterizes the effects of plate strength progressively offering enhanced resistance to plate motion [Conrad and Hager, 1999]. The three red column sets, for each fixed $\beta$ suite, represent an initial mantle heat source density that is chondritic [e.g., Schubert et al., 1980] while the blue sets represent reduced mantle heat source density [Jackson and Jellinek, 2013]. The three different columns, for each fixed $\beta$ and heat source density sub-suite, represent increasing initial thermal conditions (from right to left columns, the starting temperature is 900 K, 1600 K, and 2300 degrees). Each individual model set column uses the results of 128 cases that varied initial water volume along with de- and re-gassing parameters. Initial water volumes ranged from 0.1 to 6 ocean mass equivalents. Re- and de-gassing efficiency parameters spanned the high to low parameter ranges from Sandu et al. [2011].
Figure 3 demonstrates the diversity of model behavior associated with feedbacks between deep water cycling and thermo-tectonic evolution. Differing combinations of de- and re-watering efficiencies, together with variable thermal parameters and initial conditions, can produce a range of thermal histories. The green transparent rectangles in Figure 3 delineate the range of model cases that are consistent with data constraints. Petro-
**Figure 1.** Petrological data from Condie et al. [2016] along with their conceptual interpretation of the data.
**Figure 2.** Representative thermal evolution with deep water cycling effects compared to petrologic data (a). The blue curve is the thermal evolution model. The red and black dots are data from Condie et al. [2016] and Herzberg et al. [2010]. (b) Model surface water evolution.
logical data provide a constraint for onset time of the Earth’s most recent cooling phase and mantle potential temperatures in the flat line cooling phase. Although the absolutes for different petrologic data sets are not in exact agreement, the trends match reasonably well (figure 2a). In particular, both data sets indicate that from the onset of the most recent cooling phase to the present day, the mantle has cooled by 100-200 °C.
Another constraint on thermal evolution is the present day Urey ratio (Ur) which, within data uncertainty, is between 0.2 and 0.5 [Jaupart et al., 2007].
Grouping model results into variable β sets reflects the fact that different values of β are associated with different hypothesis regarding solid planet dynamics. A model with β = 0.33 is based on the hypothesis that the dominant resistance to the motion of tectonic plates comes from interior mantle viscosity [Davies 1980; Schubert et al., 1980]. A model that with β = 0 is based on the hypothesis that the dominant resistance to the motion of tectonic plates comes from the strength of plates themselves with any changes in internal mantle viscosity having no effect on plate velocity [Christensen, 1984; 1985]. Intermediate values reflect variable hypotheses regarding the balance between internal mantle and plate sourced resistance to plate motion [Conrad and Hager, 1999]. Our modeling strategy follows that of McNamara and VanKeken [2000]: running a large number of models, under varied assumptions, allows different hypotheses to be assessed against each other in a statistical manner. It is no surprise, given parameter and initial condition uncertainties, that cases can be found that match data constraints from models that are based on fundamentally different physical assumptions. Given this, a probabilistic approach becomes necessary to: 1) determine if the ability of any hypothesis to match data is statistically meaningful (that is, to determine if model results, that match data, may be outliers in parameter space), and 2) to discriminate between competing hypothesis.
The Urey ratio has come to be seen as a key value that can be used to discriminate between competing thermal evolution hypotheses [Conrad and Hager, 1999; Korenaga, 2003; Jaupart et al., 2007]. Model Urey ratio values (Figure 3d) can be viewed probabilistically as in Figure 4. Model output distribution, when all β cases are plotted together, is not uni-modal. The model Ur peak at ∼0.6 is close to that obtained by first generation thermal history models that did not account for deep water cycling and/or the effects of strong plates resisting motion [Davies 1980; Schubert et al., 1980]. The peak at ∼0.35 is more in line with data constraints [Jaupart et al., 2007].
Including deep water cycling into classic thermal history models that do not include the effects of strong plates can lower Urey ratio values to a point such that the data constraints can be matched. This was already noted by Sandu et al. [2011]. A probabilistic approach, which covers larger parameter space allowing distribution functions to be constructed, shows that although this conclusion is valid, the model distribution peak is located outside the data window (Figure 4, top...
Figure 4: Distribution of present day Urey ratios. The top set of panels is for cases with chordritic heat sources [e.g., Schubert et al., 1980]. The bottom set is for cases with reduced mantle heat source density [Jackson and Jellinek, 2013]. The large plot at the left, for the upper and lower sets, shows results for all $\beta$ values. The smaller plots to the right of each large plot show the individual $\beta$ value distributions.
Non-classical assumptions regarding initial heat source density can bring the distribution peak within the data window (Figure 4, bottom panel). None the less, models that allow plate strength to provide a component of resistance to plate motion are statistically preferred as they bring the distribution peak deeper into the data window (Figure 4, smaller panels). As $\beta$ decreases, the model Ur distribution peak shifts towards lower values. When $\beta$ is equal to 0.20, the model distribution becomes uni-modal with a peak Urey ratio of $\sim$0.35 (Figure 4). However, there is a limit to this behavior. As $\beta$ is lowered towards zero, model output loses a uni-modal character and spans a wider Urey ratio range.
Shifting $\beta$ towards zero means that plate velocities progressively do not scale with convective vigor and as such, become constant over the full evolution time. Any enhanced cooling potential, due to enhanced subduction under hotter mantle conditions, is thus damped. This weakens a negative, i.e., buffering, feedback within the system. Weakening this negative feedback means that final model results become more sensitive to initial conditions [Korenaga, 2016]. If the negative feedback is removed altogether, $\beta \leq 0$, then the model system has no stable attracting state and results become highly sensitive to assumed initial conditions and the effects of parameter uncertainties become large [Moore and Lenardic, 2015]. This is reflected in Figure 4 for the lowest $\beta$ suites which are characterized by model outputs with a multi-modal distribution. Removing a thermal feedback also alters water cycling. Cooler conditions allow for enhanced water cycling into the mantle (water cycling into the mantle is also a cooling feedback as it lowers viscosity which allows for enhanced convective overturn and heat loss). The lack of a subduction cooling feedback can move the system towards one that
is dominated by mantle de-watering over larger portions of model evolution. Thus, de-watering can outweigh re-watering over a larger portion of potential parameter space. This tends to shift cooling times closer toward present day and can also lead to model distributions that allow for higher Urey ratio values [Crowley et al., 2011].
Many of the model cases explored do not match observational constraints for the Earth. However, the range of potential solutions that can match data constraints, given uncertainties in the data, initial conditions, model parameter values, and variable hypotheses regarding the role of plate strength, is significant (the percentage breakdown of models that can match data constraints is provided in the supplemental material). A very low $\beta$ hypothesis is associated with an extreme sensitivity to parameter uncertainty. In addition, the lowest $\beta$ cases all run too hot relative to data constraints (Figure 3). Collectively, this makes a low $\beta$ hypothesis statistically weak and cases with a $\beta$ range between 0.33-0.20 are favored. Within that model range, an initial heat source distribution lower than chondritic is also favored, whereas very cool starting conditions are not. Of the models subject to those statistical preferences, 13.3 percent match data constraints (the total number of models in that subset still exceeds 1000 cases). That is to say, solutions of the type shown in Figure 2 are not outliers. From this statistical perspective, petrologic data trends can be accounted for if deep water cycling and strong subduction zones are considered in tandem. Subduction zones that are so strong that they provide the dominant resistance to plate motion are not statistically preferred (that is, mantle viscosity remains an important variable for determining plate velocities). A change in tectonic regime is not required to account for the petrologic data trends.
There are added model implications that can provide enhanced layers of hypothesis testing. The cases from our modeling suite, that can match thermal constraints, suggest a change in the balance of mantle de- and re-watering at 2.0-2.5 Gya as subduction zones became cool enough to recycle a level of water that could keep pace with or outweigh mantle de-watering. This implies a switch from relatively dry to wet subduction, here caused by a thickening of the hydrated layer in subducting plates as the Earth cooled. An increase in water volume entering into the mantle at subduction zones can result in the production of felsic rather than mafic crust. As the amount of Earth’s surface area covered by felsic crust increases, its oxidative efficiency decreases, leading to a rise in atmospheric $O_2$ [Lee et al., 2016]. A rise in atmospheric $O_2$ should then be coincident with the onset of the Earth’s most recent cooling phase as constrained by petrological data [Condie et al., 2016; Herzberg et al., 2010]. Available data constraints [Lee et al., 2016] are consistent with this model implication.
In order for our models to match present day Urey ratio values, mantle re-watering needs to be in balance with or exceed de-watering from the termination of a flat line cooling phase to the present day (i.e., from 2.0 Gya to the present). Models in which re-watering is exceeding mantle de-watering over this time scale lead to lower Urey ratio values [Crowley, 2011] putting them deeper into the allowable data constraint range from Jaupart et al. [2007]. The balance of mantle de-watering and re-watering over geologic time is difficult to constrain. Efforts to do so do, however, suggest that mantle re-watering has exceeded de-watering over the last 500-600 Million years [Rupke et al., 2004; Parai and Mukhopadhyay, 2012]. This is consistent with the water balance implications from our model cases that can match thermal history constraints.
As a final word, we offer a caution on extrapolating our results to other terrestrial planets. Although observations can constrain the range of viable model solutions for the Earth’s thermal evolution, this does not mean that the same range needs to hold for terrestrial planets in general - be they planets in this solar system or in others. Theoretical models applied over geologic time frames need to effectively tune a range of parameter uncertainties by using Earth constraints. Model cases that fall out of the Earth viable range are not considered physically implausible. They are, instead, potential model paths for a terrestrial planet’s evolution that are not in line with constraints on the evolution of a particular terrestrial planet (Earth). Thermo-tectonic history models have been and continue to be extrapolated to terrestrial planets orbiting stars other that our own. Often this is done by adjusting only a few variables, e.g., planetary size, while leaving others constant. The diversity of solutions for models that couple water cycling to planetary thermal evolution (Figures 3 and 4) highlight a deficiency in this approach and argue for a shift toward a fully statistical/probabalistic approach that does not hinge on Earth tuned results.
REFERENCES
Christensen, U.R., 1984. Heat transport by variable viscosity convection and implications for the Earth’s thermal evolution. Phys. Earth Planet. Int. 35, 264282.
Christensen, U.R., 1985. Thermal evolution models for the earth. J. Geophys. Res. 90 (29953007), B4.
Condie, K., Aster, R.C., and van Hunen, J., 2016, A great thermal divergence in the mantle beginning 2.5 Ga: Geochemical constraints from greenstone basalts and komatiites, Geoscience Frontiers, 7, 543-553.
Conrad, C. and Hager, B., 1999. The thermal evolution of an earth with strong subduction zones, Geophysical Research Letters, 26, 3041-3044.
Crowley, J.W., Gerault, M., and O’Connell, R.J., 2011, On the relative influence of heat and water transport on planetary dynamics, Earth Planet. Sci. Lett., 292, 79-88.
Davies, G., 1980, Thermal histories of convective earth models and constraints on radiogenic heat production of earth, J. Geophys. Res. 85, 2517-2530.
Grigne, C., Labrosse, S., 2001. Effects of continents on Earth cooling: thermal blanketing and depletion in
radioactive elements. Geophys. Res. Lett. 28, 2707-2710.
Herzberg, C., Condie, K., and Korenaga, J., 2010, Thermal history of the Earth and its petrological expression, Earth Planet. Sci. Lett., 310, 380-388.
Hirschmann, M. M., 2000, Mantle solidus: Experimental constraints and the effects of peridotite composition, Geochim. Geophys. Geosyst., 1(10), 1042, doi:10.1029/2000GC000070.
Hoink, T., Lenardic, A. and Jellinek A. M., 2013, Earth’s thermal evolution with multiple convection modes: A Monte-Carlo approach, Phys. Earth Planet. Int., 221, 22-26.
Jaupart, C., Labrosse, S., Mareschal, J., 2007. Temperatures, heat and energy in the mantle of the earth, treatise on geophysics. Mantle Dynam. 7, 253303.
Lenardic, A., Cooper, C., Moresi, L., 2011. A note on continents and the Earths Urey ratio. Phys. Earth Planet. Int. 188, 127130.
Katz, R.F., Spiegelman, M. and Langmuir, C.H., 2003, A new parameterization of hydrous mantle melting, Geophys. Geosyst., 4(9), 1073.
Kohlstedt, D. L. 2006, The role of water in high-temperature rock deformation, Rev. Mineral. Geochem., 62, 377396, doi:10.2138/rmg.2006.62.16.
Korenaga, J., 2003, Energetics of mantle convection and the fate of fossil heat, Geophysical Research Letters, 30, 1437-1440.
Korenaga, J., 2016, Can mantle convection be self-regulated?, Sci. Adv., 2016, 2:e1601168.
Lee, C. A., Yeung, L. A., McKenzie, N. R., Yokoyama, Y., Ozaki, K. and Lenardic, A., 2016, Two-step rise of atmospheric oxygen linked to the growth of continents, Nat. Geosci., 9, 417-424.
Li, Z.-X. A., Lee, C.-T. A., Peslier, A.H., Lenardic, A. and Mackwell, S.J., 2008, Water contents in mantle xenoliths from the Colorado Plateau and vicinity: Implications for the mantle rheology and hydration-induced thinning of continental lithosphere, J. Geophys. Res., 113, B09210.
McNamara, A. K., and P. E. van Keken (2000), Cooling of the Earth: A parameterized convection study of whole versuslayered models, Geochem. Geophys. Geosyst., 1, 1027, doi:10.1029/2000GC000045.
Moore, W.B., and A. Lenardic, 2015, The efficiency of plate tectonics and non-equilibrium dynamic evolution of planetary mantles, Geophys. Res. Lett., 42, doi:10.1002/2015GL065621, 2015.
Parai, R., and Mukhopadhyay, S., 2012, Water in the oceanic upper mantle: Implications for rheology, melt extraction and the evolution of the lithosphere, Earth Planet. Sci. Lett., 317-318, 396406.
Rupke, L. H., J. P. Morgan, M. Hort, and J. A. D. Connolly, 2004, Serpentine and the subduction zone water cycle, Earth Planet. Sci. Lett., 223, 1734, doi:10.1016/j.epsl.2004.04.018.
Sandu, C., Lenardic, A. and McGovern, P.J., 2011, The effects of deep water cycling on planetary thermal evolution, Journal of Geophysical Research, 116, B12404.
Schubert, G., Stevenson, D., Cassen, P., 1980. Whole planet cooling and the radiogenic heat source contents of the earth and moon. J. Geophys. Res. 85, 25312538.
Ulmer, P., and V. Trommsdorff, 1995, Serpentine stability to mantle depths and subduction-related magmatism, Science, 268(5212), 858861, doi:10.1126/science.268.5212.858.
1. APPENDIX: METHODS
1.1. Convection
Here we use the one-dimensional energy equation [Schubert et al., 1979; Schubert et al., 1980] to obtain the time rate of change of the Earth’s average mantle temperature ($T$)
$$\rho CV \dot{T} = -3Aq_m + VQ(t)$$ \hspace{1cm} (1)
where $\rho$ is mantle density, $C$ is mantle heat capacity, and $q_m$ is the mantle surface heat flux. Mantle volume, $V$ and surface area $A$ are calculated as $R_m^3 - R_c^3$ and $R_m^2 - R_c^2$, respectively, where $R_m$ is the radius of the mantle and $R_c$ is the radius of the core. In this equation $T$ is the spherically averaged mantle temperature sense. In [1] it is assumed that the system is internally heated with an insulating bottom boundary. Heat is produced by radiogenic decay according to
$$Q(t) = Q_0 e^{-\lambda t}$$ \hspace{1cm} (2)
where $Q_0$ and $\lambda$ are constants and $t$ is the current time.
The Urey ratio ($U_r$), which defines the ratio of heat produced within to heat transferred through the mantle surface, is defined as
$$U_r = \frac{VQ}{Aq_m}.$$ \hspace{1cm} (3)
When $U_r > 1$, the planetary mantle is heating up. Alternatively, a value of $U_r < 1$ means heat flow out of the mantle exceeds heat generated within the mantle and thus the mantle cools.
The Rayleigh number ($Ra$), a ratio of forces driving convection to those resisting it, is defined as
$$Ra = \frac{g \alpha \Delta T Z^3}{\eta \kappa}$$ \hspace{1cm} (4)
where $g$, $\alpha$, $Z$, $\eta$ and $\kappa$ are gravity, thermal expansivity, depth of the convecting layer, kinematic viscosity and thermal diffusivity, respectively. The value $\Delta T$ is the temperature difference driving convection defined as $T - T_s$, the difference between the mantle and surface temperatures. The relationship between a nondimensional heat flux ($Nu$) and $Ra$, which takes the form
$$Nu = \frac{q_m Z}{k \Delta T} = \left( \frac{Ra}{Ra_{cr}} \right)^{\beta}$$ \hspace{1cm} (5)
is used to solve for $q_m$, where $k$ is thermal diffusivity, $Ra_{cr}$ is the critical Rayleigh number which determines the onset of convection and $\beta$ is a scaling exponent. The value of $\beta$ for classic thermal history models is assumed to be $1/3$ [Turcotte et al., 1967; Solomatov 1995]. This assumes a plate tectonics mode of behavior in which the dominant resistance to plate motion comes from mantle viscosity. Lower values are also considered to mimic the effects of enhanced resistance coming from the strength of plates and/or plate margins [Christensen, 1985; Conrad and Hager, 1999; Korenaga, 2008].
A velocity scale ($u_s$) is needed to compute degassing and regassing of the mantle. Fourier’s law is rearranged to determine the lithospheric thickness according to the equation
$$D_b = k \frac{(T_b - T_s)}{q_m}$$ \hspace{1cm} (6)
where $k$ is thermal conductivity. The temperature $T_b$ represents the temperature at the base of the lithosphere and is equivalent to $T_m$. We use boundary layer theory [Schubert et al., 2001] to derive a boundary layer breakthrough time associated with subduction of the lithosphere according to
$$t_s = \frac{1}{5.38 \kappa_m D_b^2}$$ \hspace{1cm} (7)
From here, an equation for convective velocity is expressed as
$$u_c = \frac{(R_m - R_c)}{t_s}.$$ \hspace{1cm} (8)
The convective velocity scaling is of the form of $u_c \sim Ra^{2\beta}$, or more fully
$$u_c = \frac{a_1 \kappa}{2 (R_m - R_c)} \left( \frac{Ra}{Ra_{cr}} \right)^{2\beta}$$ \hspace{1cm} (9)
where $a_1$ is a scaling parameter. It has a value of 5.38 for the classic case of $\beta = 1/3$ [Schubert et al., 1979; Schubert et al., 1980]. As can be seen in [9], velocity has a power dependence on $\beta$. In the endmember case that $\beta = 0$, a constant velocity would be maintained. That is to say that for any value of $Ra$, the velocity will not change. To account for variable $\beta$, in a manner that allows all model to match present day plate velocities, a velocity scale must be set. To set this scale, we use the present day values of convective vigor and velocity, $Ra_{now}$ and $u_{now}$, respectively, with the $\beta = 1/3$ scaling used as a reference. This leads to
$$u_{now} = a_1 \frac{\kappa}{2 (R_m - R_c)} \left( \frac{Ra_{now}}{Ra_{cr}} \right)^{1/3}$$ \hspace{1cm} (10)
$$u_{now} = a_2 \frac{\kappa}{2 (R_m - R_c)} \left( \frac{Ra_{now}}{Ra_{cr}} \right)^{2\beta}$$ \hspace{1cm} (11)
$$a_2 = a_1 Ra_{cr}^{2\beta - 2} \left( Ra_{now}^{\beta - 2} \right)$$ \hspace{1cm} (12)
This value of $a_2$ can be computed for each $\beta$ and provide calibrated velocity scalings that will result in comparable present day velocity for model suites with variable $\beta$ values.
1.2. Volatile Cycling
Volatile cycling between the interior and surface has a direct influence on thermal evolution. The calculation of volatile cycling follows Sandu et al. [2011]. Water leaves the mantle as an incompatible element participating in the batch melting process, which only occurs at mid-ocean ridges in our simplified model. Water is returned to the mantle via subduction processes.
To track mantle melting, the average mantle temperature calculated from [1] is converted to a temperature versus depth profile consisting of two parts: the conductive, lithospheric profile and the adiabat from the convecting mantle. The near surface temperature gradient is defined by the temperature at the surface and heat flux at the base of the lithosphere by
$$T(z)|_{z \leq D_b} = T_s + \frac{q_m}{k} z.$$ \hspace{1cm} (13)
The adiabat contribution to the thermal profile is calculated by converting the average mantle temperature to a potential temperature and projecting to depth according to
\[ T(z)|_{z>D_h} = T_p + \frac{\gamma T_m}{C_p} z. \] (14)
Although a depth dependent temperature profile is being calculated, it does not influence the convective dynamics.
The thermal profile is compared to a solidus to compute the amount of melt generated by upwelling mantle. Two second-order polynomial functions are used to track melt fraction [Hirschman, 2000]. The solidus defines the temperature depth profile below which all mantle material will remain in its solid phase. As temperature warms beyond the solidus, a greater fraction of the mantle will melt until the liquidus, the temperature at which the entire mantle parcel becomes melted, is reached. In the case of hydrous melting, these functions take the form
\[ T_{\text{sol-hyd}} = T_{\text{sol-dry}} - \Delta T_{H_2O} \] (15)
\[ T_{\text{liq-hyd}} = T_{\text{liq-dry}} - \Delta T_{H_2O} \] (16)
where \( T_{\text{sol-dry}}, T_{\text{liq-dry}}, T_{\text{sol-hyd}} \) and \( T_{\text{liq-hyd}} \) are the dry solidus and liquidus and hydrated solidus and liquidus, respectively. The last term of both equations is the temperature shift of each curve brought on by consideration of hydrous melting. This adjustment temperature scales with water concentration in the melt according to
\[ \Delta T_{H_2O} = K X_{\text{melt}}^\gamma \] (17)
where \( K \) and \( \gamma \) are constants which were calibrated by Katz et al. [2003]. The parameter \( X_{\text{melt}} \) is the ratio of water in the melt fraction expressed in kg of water per kg of melt and is calculated as
\[ X_{\text{melt}} = \frac{C_{mv}}{D_{H_2O} + F_{\text{melt}} (1 - D_{H_2O})} \] (18)
where \( C_{mv}, D_{H_2O} \) and \( F_{\text{melt}} \) are the bulk water composition in the solid mantle expressed as a weight fraction, the bulk distribution coefficient which takes the value of 0.01 — highlighting it behaves as an incompatible trace element — and the degree of melting expressed as melt fraction, respectively. The melt fraction is parameterized in power-law form as
\[ F_{\text{melt}} = \frac{T - (T_{\text{sol-dry}} - \Delta T_{H_2O} (X_{\text{melt}}))^\beta}{T_{\text{liq-dry}} - T_{\text{sol-dry}}}. \] (19)
This definition of \( F_{\text{melt}} \) is valid from the surface to a depth of 300 km as constrained by observation and melting experiments. The values of melt fraction and water concentration were integrated over the melt zone thickness to provide an average to be used in the water budget calculation.
The melt zone thickness is dependent upon the relative positioning of the thermal profile and the solidus. The lower boundary of the melt zone is defined where a parcel of upwelling mantle reaches a temperature hot enough to begin producing partial melt. This depth will be identified by the intersection between the mantle thermal profile and solidus. The upper bound of the melt zone is defined by the near surface intersection of the solidus and thermal profile. At this depth, the upwelling mantle has cooled enough such that no more melt is being produced. The depth difference between these two cross over points defines the thickness of the mantle undergoing partial melting and contributes to the mantle degassing calculation.
Water is degassed at mid-ocean ridges (MOR). The rate at which water is degassed depends on the volume of mantle transiting the melt zone below the ridge, the amount of melt produces, what fraction of that melt is water and how much of that water makes it to the surface. In equation form, the degassing rate \( r_{\text{MOR}} \) is
\[ r_{\text{MOR}} = \rho_m F_{\text{melt}} X_{\text{melt}} D_{\text{melt}} S \chi_d \] (20)
where \( F_{\text{melt}} \) is the integrated melt fraction in the melt zone and \( \chi_d \) is the degassing efficiency factor. Both \( D_{\text{melt}} \) and \( X_{\text{melt}} \) are calculated according to the parameterization of Katz et al. [2003]. The areal spreading rate, \( S \), is derived from a boundary layer model [Schubert et al., 2001] and is represented as
\[ S = 2L_{\text{ridge}} u_c \] (21)
which assumes symmetrical spreading along a constant length of ridge. \( L_{\text{ridge}} \). Velocity, \( u_c \), is solved within the model according to equation \( [8] \).
Water is assumed to be returned to the mantle at subduction zones. This water is bound in the serpentinized and thin sedimentary layers of the slab [Rupke et al., 2004]. Since most water held in the sedimentary layer is lost back to the surface, the serpentinized layer is the more important factor in our calculation. The rate at which water is subducted back into the mantle \( r_{\text{SUB}} \) is
\[ r_{\text{SUB}} = f_h \rho_{\text{hydr}} S \chi_r \] (22)
where \( f_h, D_{\text{hydr}}, \) and \( \chi_r \) are the mass fraction of volatiles in the serpentinized layer, thickness of the serpentinized layer and regassing efficiency factor, respectively. In this case, \( D_{\text{hydr}} \) is defined as the depth of the 700°C isotherm as the hydrous phase of serpentinite decomposes around this temperature [Ulmer and Trommsdorff, 1995].
Individually, equations (20) and (22) tell what is occurring independently. The overall flow rate of mantle water \( r_{\text{MmVw}} \) is
\[ r_{\text{MmVw}} = r_{\text{SUB}} - r_{\text{MOR}}. \] (23)
This tracks the balance of water between the interior and surface reservoirs. When \( r_{\text{MmVw}} \) is positive, the mantle is being replenished with water. When it is negative, the mantle is losing water. If \( r_{\text{MmVw}} \) is zero, there is a balance between the two and the mass of water in each reservoir remains constant.
### 1.3. Viscosity
The temperature dependence of mantle viscosity takes the Arrhenius form
\[ \eta = \eta_0 \exp \left( \frac{A}{RT_m} \right) \] (24)
where \( \eta_0 \), \( A \), \( R \) are a reference viscosity, activation energy for creep (Weertman and Weertman, 1975) and the
Table 1
Model Parameters
| Parameter Name | Symbol | Value | Units |
|--------------------------------------|--------|----------------|--------|
| Initial mantle temperature | $T_{mi}$ | 1300, 2300, 3300 | K |
| Initial surface temperature | $T_{sa}$ | 300 | K |
| Initial radioactive heat | $Q_{mi}$ | 4.51, 3.157 | J/(m³·yr) |
| Radioactive decay constant | $\lambda$ | $3.4*10^{-10}$ | yr⁻¹ |
| Lower mantle boundary (Earth) | $R_c$ | 3471 | km |
| Upper mantle boundary (Earth) | $R_m$ | 6271 | km |
| Initial lithospheric thickness | $Z_{lith}$ | 0 | km |
| Mantle density | $\rho$ | 3000 | kg/m³ |
| Thermal conductivity | $k$ | 4.2 | W/(m*K) |
| Specific heat | $C_p$ | 1400 | J/(kg*K) |
| Coefficient of thermal expansion | $\alpha$ | $3*10^{-5}$ | K⁻¹ |
| Viscosity constant | $\eta_0$ | $1.7*10^{17}$ | Pa*s |
| Viscosity material constant | $Acre$ | 90 | MPa⁻¹/s |
| Viscosity exponent constant | $r$ | 1.2 | - |
| Activation energy for creep | $AE_c$ | 4.8*10⁵ | J/mol |
| Degassing efficiency factor | $\chi_d$ | 0.002, 0.02, 0.04, 0.4 | - |
| Regassing efficiency factor | $\chi_r$ | 0.001, 0.003, 0.01, 0.1 | - |
| Initial Mantle Ocean Masses | $OM_i$ | 0.1, 0.25, 0.5, 0.75, 1, 2, 4, 6 | - |
| Fraction of volatile in basalt | $f_{bas}$ | 0.03 | - |
| Density of basalt | $\rho_{basalt}$ | 2950 | kg/m³ |
| Average thickness of basalt | $Z_{basalt}$ | 5000 | m |
| Critical Rayleigh number | $Ra_{crit}$ | 1100 | - |
| Nusselt-Rayleigh scaling parameter | $\beta$ | 0.1, 0.15, 0.2, 0.25, 0.3, 0.33 | - |
universal gas constant.
Experiments have shown hydration effects have a power law effect on mantle viscosity [Carter et. al., 1970; Chopra and Paterson, 1984; Mackwell et. al., 1985; Karato and Wu, 1993] The power law was further refined to include dependence on water fugacity in olivine [Hirth and Kohlstedt, 1996; Mei and Kohlstedt, 2000]. Assuming Newtonian behavior and an empirical relation for water fugacity based on concentrations [Li et. al., 2008], the effective viscosity is given by
$$\eta_{eff} = \frac{\tau}{\dot{\varepsilon}} = \eta_0 A_{cre}^{-1} \left( \exp\left(c_0 + c_1 \ln C_{OH} + c_2 \ln^2 C_{OH} + c_3 \ln^3 C_{OH} \right) \right)^{-r} \exp\left(\frac{A}{RT}\right)^{-r}$$
(25)
where $\tau$, $\dot{\varepsilon}$ are stress and strain rate. Experimentally determined constants from Li et al. [2008] are $c_0$, $c_1$, $c_2$ and $c_3$ and $C_{OH}$ is the water concentration expressed as $H/10^6$ Si. Here $\eta_0$ and $A_{cre}$ are a calibration and material constant.
2. APPENDIX: MODEL OUTPUT STATISTICS
Table 1 shows the range of model parameters, and Table 2 shows the models that can match data constraints broken into model subsets by variable $\beta$, initial heat source density, and initial temperatures. Of all the model cases, 3.7 percent can match data constraints. None of the cases with a $\beta$ value below 0.2 can match all the constraints. Once those cases are removed, 5.6 percent of the remaining cases can match data constraints. Statistically, models with initial heat source densities lower than chondritic [Jackson and Jellinek, 2013] are preferred. Once the higher heat source density cases are removed.
8.9 percent of the remaining cases can match data constraints. Once the coolest initial condition cases, which are not statistically preferred, are removed, 13.3 percent of the remaining cases can match data constraints. The number of cases within that reduced set is 1024. Model cases with low initial mantle water have a statistically lower chance of allowing for a mantle dewatering effect that can drive a flat line cooling phase and associated delayed mantle cooling (Figure 2). If models are further limited to an initial mantle water content of at least one ocean mass equivalent, then 19.14 percent of the remaining models (512 total) can match data constraints.
Figure 5 shows final water distributions. The sensitivity of final surface water on assumed initial mantle water volume made this a weak discriminator between different model hypotheses. It should be further noted that the surface water in our models represents water that is degassed from the mantle. Late stage water delivery could alter the final surface volume of water without having a significant effect on our thermal evolution models provided the initial mantle water is not significantly lower than one ocean mass (it was only the lower initial mantle cases that allowed mantle re-watering to be limited due to the lack of surface water). This further weakens the use of the final surface water as a constraint that can discriminate between competing hypothesis regarding thermal evolution.
APPENDIX: REFERENCES
Carter, N.L., and Ave Lallemant, H.G., 1970, High temperature flow of dunite and peridotite, Geol. Soc. Am. Bull., 81, 2181-2202.
Chopra, P. N., and M. S. Paterson (1984), The role of water in the deformation of dunite, J. Geophys. Res., 90, 7861-7876.
Christensen, U., 1985, Thermal evolution models for the earth, Journal of Geophysical Research, 90, 2995-3007.
Conrad, C. and Hager, B., 1999, The thermal evolution of an earth with strong subduction zones, Geophysical Research Letters, 26, 3041-3044.
Hirschmann, M. M., 2006, Water, melting, and the deep Earth H2O cycle, Annu. Rev. Earth Planet. Sci., 34, 629-653.
Hirth, G., and Kohlstedt, D.L., 1996, Water in the oceanic upper mantle: Implications for rheology, melt extraction and the evolution of the lithosphere, Earth Planet. Sci. Lett., 144, 93108.
Karato, S., and Wu, P., 1993, Rheology of the upper mantle: A synthesis, Science, 260, 771-778.
Katz, R.F., Spiegelman, M. and Langmuir, C.H., 2003, A new parameter- ization of hydrous mantle melting, Geochem. Geophys. Geosyst., 4(9), 1073.
Korenaga, J., 2008, Urey ratio and the structure and evolution of earth’s mantle, Reviews of geophysics, 46.
Li, Z.-X., Lee, C.-T., A., Peslier, A.H., Lenardic, A. and Mackwell, S.J., 2008, Water contents in mantle xenoliths from the Colorado Plateau and vicinity: Implications for the mantle rheology and hydration-induced thinning of continental lithosphere, J. Geophys. Res., 113, B09210.
Mackwell, S.J., Kohlstedt, D.L., and Paterson, M.S., 1985, The role of water in the deformation of olivine single crystals, J. Geophys. Res., 90, 11319-11333.
Mei, S., and D. L. Kohlstedt, 2000, Influence of water on plastic deformation of olivine aggregates 2. Dislocation creep regime, J. Geophys. Res., 105, 21,471-21,481.
Rupke, L.H., Morgan, J.P., Hort, M. and Connolly, J.A.D., 2004, Serpentine and the subduction zone water cycle, Earth Planet. Sci. Lett., 223, 1734.
Sandu, C., Lenardic, A. and McGovern, P.J., 2011, The effects of deep water cycling on planetary thermal evolution, Journal of Geophysical Research, 116, B12404.
Schubert, G., P. Cassen, and R. E. Young, 1979, Sub-solidus convective cooling histories of terrestrial planets, Icarus, 38, 192211.
Schubert, G., D. Stevenson, and P. Cassen, 1980, Whole planet cooling and the radiogenic heat source contents of the Earth and Moon, J. Geophys. Res., 85, 2531-2538.
Schubert, G., D. L. Turcotte, and P. Olson, 2001, Boundary layer theory, in Mantle Convection in the Earth and Planets, pp. 350361, Cambridge Univ. Press, Cambridge, U. K.
Solomatov, V.S., 1995, Scaling of temperature- and stress-dependent viscosity convection, Phys. Fluids, 7, 266-274.
Turcotte, D.L. and Oxburgh, E.R. Finite amplitude convective cells and continental drift, J. Fluid Mech. 28 (1967) 2942.
Ulmer, P. and Trommsdorff, V., 1995, Serpentine stability to mantle depths and subduction-related magmatism, Science, 268(5212), 858-861.
Weertman, J. and Weertman, J.R., 1975, High temperature creep of rock and mantle viscosity. Annual Review of the Earth and Planetary Sciences 3: 293-315. | 2025-03-06T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
5471,
1
],
[
5471,
10587,
2
],
[
10587,
13831,
3
],
[
13831,
16212,
4
],
[
16212,
22420,
5
],
[
22420,
25503,
6
],
[
25503,
31026,
7
],
[
31026,
37094,
8
],
[
37094,
40764,
9
],
[
40764,
45067,
10
],
[
45067,
45359,
11
]
]
} |
83e94160a9ddf650e25c040a37f79858d3ea3467 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 35025,
"total-output-tokens": 11762,
"fieldofstudy": [
"Mathematics"
]
} | Abstract
We study the local Hopf bifurcations of codimension one and two, which occur in the Shimizu–Morioka system. This system is a simplified model proposed for studying the dynamics of the well-known Lorenz system for large Rayleigh numbers. We present an analytic study and their bifurcation diagrams of these kinds of Hopf bifurcation, showing the qualitative changes in the dynamics of its solutions for different values of the parameters.
Keywords
Hopf bifurcation · Limit cycles · Bifurcation diagram
Mathematics Subject Classification Primary 34C35 · 58F09 · Secondary 34D30
1 Introduction
In this paper, we study the local Hopf bifurcations of codimension one and two and the kind of stability of the Hopf periodic orbits in the dynamics of the Shimizu–Morioka system given by
\[
\dot{x} = y, \quad \dot{y} = x - \lambda y - xz, \quad \dot{z} = -\alpha z + x^2, \quad (1)
\]
where \((x, y, z) \in \mathbb{R}^3\) are the state variables, and \(\alpha\) and \(\lambda\) are real parameters. System (1) is a simplified model proposed in [18] for studying the dynamics of the well-known Lorenz system [9]. Later, the system gained self-interest, and several articles have appeared in the literature, dealing mainly with the chaotic behavior of the solutions and the emergence of strange attractor, see, for instance [6,17,18,20–22]. It was shown in [17] among other properties that system (1) presents Lorenz-like strange attractors, for example, taking \(\alpha = 0.45\) and \(\lambda = 0.75\) (see Figure 1 of [13]).
In this note, we perform an analytic bifurcation analysis of dynamical aspects of the solutions of system (1), when the parameters vary, aiming to give a contribution to the understanding of its complex behavior. Our approach permits a geometric synthesis of the bifurcation analysis, based on the algebraic expression and geometric location of the codimension 2 Hopf point leading to the bifurcation of periodic orbits.
The study presented here is close to those realized in some papers, which was performed in [12] (see also [3]). But our approach is different, mainly in the computations of the Lyapunov coefficients, which are necessary to study the Hopf bifurcations. In [12], the authors study the system.
\[ \dot{x} = y - x, \quad \dot{y} = \beta x - xz, \quad \dot{z} = -\chi z + \eta x^2. \]
This system and system (1) are equivalent if \( \beta = \lambda = 1 \) and \( \eta > 0 \), taking \( \alpha = \chi \) and doing the change of variables \((x, y, z) \mapsto (\sqrt{\eta} x, -\sqrt{\eta} x + \sqrt{\eta} y, z)\) in system (1), but when \( \beta \neq \lambda \) or \( \eta \leq 0 \), these systems are not equivalent.
Our main result is the following one.
**Theorem 1** Let denote \( h(\lambda) = 3 \lambda^4 - 5 \lambda^2 - 1 \). The following statements hold for system (1):
(a) For \( \alpha = \frac{2-\lambda^2}{\lambda} \) and \( \lambda \in (0, \sqrt{2}) \), system (1) has two non-hyperbolic singular points \( Q_- \) and \( Q_+ \), and if \( h(\lambda) \neq 0 \), a one codimension Hopf bifurcation takes place at these points, permitting the existence of limit cycles near them. These cycles on the central manifolds of \( Q_- \) and \( Q_+ \) are unstable if \( h(\lambda) < 0 \) and stable if \( h(\lambda) > 0 \).
(b) For \( \alpha = \frac{2-\lambda^2}{\lambda} \) with \( \lambda \in (0, \sqrt{2}) \) and \( h(\lambda) = 0 \), a two codimension Hopf bifurcation takes place at the points \( Q_- \) and \( Q_+ \), with the creation of two limit cycles, one unstable and the other stable on the central manifolds of \( Q_- \) and \( Q_+ \).
The paper is organized as follows. In Sect. 2, through a linear analysis of system (1), we present a study of the bifurcations, which occurs with its singular points. In Sect. 3, we describe a method to compute the focus quantities, related to the stability of the limit cycles, which appear in the Hopf bifurcations. In Sect. 4, we present a brief review of the theory used to study codimension one and two Hopf bifurcations. These methods are used in Sect. 5 to prove statements (a) and (b) of Theorem 1. For some extensions of the Hopf bifurcation, see [1].
**2 Analysis of the singular points**
The statement (a) and (b) of the next proposition are not new, in fact, they are well known in the literature see, for instance, [5, 13].
**Proposition 1** The following statements hold for system (1).
(a) For \( \alpha < 0 \), the origin of system (1) is the unique hyperbolic singular point. It is a saddle with a one-dimensional stable manifold and two-dimensional unstable manifold;
(b) For \( \alpha = 0 \), the \( z \)-axis of system (1) is filled of singular points. The origin becomes a non-hyperbolic singular point, and a degenerate pitchfork bifurcation occurs on it. More precisely, for \( \alpha > 0 \) sufficiently small, this line of singular points disappear, the origin becomes a hyperbolic saddle with a two-dimensional stable manifold and an one-dimensional unstable manifold, two new singular points \( Q_- \) and \( Q_+ \) are created, and they are symmetric with respect to the \( z \)-axis. These new equilibria are hyperbolic and asymptotically stable if \( \alpha > \frac{2-\lambda^2}{\lambda} \) and \( \lambda > 0 \). For either \( \alpha = \frac{2-\lambda^2}{\lambda} \) and \( \lambda \in (-\infty, -\sqrt{2}) \) or \( \alpha < \frac{2-\lambda^2}{\lambda} \) and \( \lambda \in (0, \sqrt{2}) \cup (0, \sqrt{2}) \), \( Q_- \) and \( Q_+ \) are unstable singular points.
**Proof** For \( \alpha < 0 \), the origin \((0, 0, 0)\) is the unique singular point of system (1) and the eigenvalues of its linear part are
\[ \sigma_0 = -\alpha, \quad \sigma_{\pm} = -\lambda \pm \frac{\sqrt{\lambda^2 + 4}}{2}, \]
with eigenvectors given by \( v_0 = (0, 0, 1) \), \( v_{\pm} = (1, \sigma_{\pm}, 0) \), respectively. As the eigenvalues are all reals and \( \alpha < 0 \), \( \sigma_+ \sigma_- < 0 \), by the Invariant Manifold Theorem and the Hartman Theorem (see for instance [7]), the origin is a hyperbolic saddle with an one-dimensional stable manifold tangent to the line generated by \( v_- \) and a two-dimensional unstable manifold tangent to the plane generated by \( v_0 \) and \( v_+ \) for all \( \lambda \). Note that for \( \alpha < 0 \) the solutions in the invariant \( z \)-axis go away from the origin.
If \( \alpha = 0 \), the invariant \( z \)-axis is filled by singular points of system (1). Then, the origin is a non-isolated degenerate singular point. Moreover, the eigenvalues of the linear part of system (1) at this point are 0 and \( \sigma_{\pm} \).
When the parameter \( \alpha \) crosses the zero value, the vector fields associated with system (1) cross this degenerate situation transversally. On the other words, for \( \alpha > 0 \), the \( z \)-axis filled of singular points that exist for \( \alpha = 0 \) disappears, and system (1) has only the singular points \( Q_0 = (0, 0, 0) \), \( Q_\pm = (\pm \sqrt{\alpha}, 0, 1) \).
The eigenvalues of the linear part of system (1) at \( Q_0 \) are given in (2), and we have \( \sigma_0 < 0 \) and \( \sigma_- < 0 \) and \( \sigma_+ > 0 \). Therefore, \( Q_0 \) is a hyperbolic saddle with a two-dimensional stable manifold and an one-dimensional unstable manifold for all \( \lambda \). Thus, under
the creation and subsequent elimination of the line of singular points when $\alpha$ crosses the zero value, the origin $Q_0$ of system (1) gains one dimension in the stable manifold and loses one dimension in the unstable one, as stated in statement (b) of the proposition.
Under the change of coordinates $(x, y, z) \mapsto (-x, -y, z)$, system (1) is invariant. Hence, the kind of stability of the singular point $Q_+$ follows from the kind of stability of $Q_-$. The characteristic polynomial of the linear part of system (1) at $Q_-$ is
$$p(\sigma) = -\sigma^3 - (\alpha + \lambda)\sigma^2 - \alpha\lambda\sigma - 2\alpha.$$
The rest of proof follows from the next proposition.
**Proposition 2** Consider $\alpha > 0$. The singular point $Q_-$ is asymptotically stable to system (1) if $\alpha > \frac{2-\lambda^2}{\lambda}$ and $\lambda > 0$, and unstable if either $\alpha = \frac{2-\lambda^2}{\lambda}$ and $\lambda \in (-\infty, -\sqrt{2})$ or $\alpha < \frac{2-\lambda^2}{\lambda}$ and $\lambda \in (-\infty, -\sqrt{2}) \cup (0, \sqrt{2})$.
**Proof** The proof follows easily from the Routh–Hurwitz stability criterion (see [14, p. 58]).
The next proposition is a straightforward consequence of the relations between roots and coefficients of a polynomial in one variable.
**Proposition 3** Consider $\alpha > 0$. If $\alpha = \frac{2-\lambda^2}{\lambda}$ and $\lambda \in (0, \sqrt{2})$, then the linear part of system (1) at the singular point $Q_-$ has one negative eigenvalue and two conjugated pure imaginary eigenvalues.
Following [12], the symmetric bifurcation that occurs when the parameter $\alpha$ crosses the zero value is called degenerate pitchfork bifurcation, due to the line of equilibria which exists for $\alpha = 0$, and it has already been observed in other systems, which also present chaotic behavior (see, for instance, [16, p. 4] and [12]).
### 3 Center Theorem and focus quantities
In this section, we summarize the method described in [4] (see also [10,11]) for studying the center problem on a center manifold for vector fields in $\mathbb{R}^3$. Let $X : U \rightarrow \mathbb{R}^3$ be a real analytic vector field, such that $DX(0)$ has two pure imaginary eigenvalues and one nonzero. By a linear change of variables and a possible rescaling of the time, the system of differential equations $\dot{u} = X(u)$ can be written as
$$\dot{u} = -v + P(u, v, w) = \bar{P}(u, v, w),$$
$$\dot{v} = u + Q(u, v, w) = \bar{Q}(u, v, w),$$
$$\dot{w} = \beta w + R(u, v, w) = \bar{R}(u, v, w),$$
where $\beta$ is a real nonzero number. We denote again by $X$ this new vector field.
A non-constant $C^1$ function $H$ from a neighborhood of the origin of $\mathbb{R}^3$ into $\mathbb{R}$ is a local first integral of system (3) if it is constant on the orbits of (3), i.e., $H$ satisfies
$$XH = \bar{P}\frac{\partial H}{\partial u} + \bar{Q}\frac{\partial H}{\partial v} + \bar{R}\frac{\partial H}{\partial w} = 0,$$
(4)
in a neighborhood of the origin. A non-constant formal power series $H$ in $u, v,$ and $w$ is a formal first integral for system (3) if when $\bar{P}, \bar{Q},$ and $\bar{R}$ are expanded in power series at the origin, every coefficient in the formal power series in (4) is zero. If $w$ and $\dot{w}$ do not appear in system (3) the system is in $\mathbb{R}^2$, the singular point at the origin is either a focus (every trajectory near the origin spirals toward the origin, or every trajectory does so in reverse time) or a center (a punctured neighborhood is composed entirely of periodic orbits). The problem of distinguishing between these two cases is the center problem. It was solved by Poincaré and Lyapunov in terms of the nonexistence or existence of a local first integral. A proof is given in [15].
From Theorem 5.1 page 152 of [7], we know that system (3) admits a local center manifold $W^{c\text{loc}}$ at the origin. The following theorem provides one the main tools for detecting a center on a center manifold. See [4] for a proof.
**Theorem 2** The following statements are equivalent.
(a) The origin is a center for $X |_{W^{c\text{loc}}}$.
(b) There is a local analytic first integral at the origin for system (3) of the form $H(u, v, w) = u^2 + v^2 + \cdots$ (here the dots mean higher-order terms).
(c) There is a formal first integral at the origin for system (3) of the form $H(u, v, w) = u^2 + v^2 + \cdots$.
The Lyapunov Center Theorem corresponds to the equivalence of statements (a) and (b); for a proof, see also [2]. From this theorem, we can restrict our attention to investigate the conditions for the existence or nonexistence of a first integral of the form $H(u, v, w) = u^2 + v^2 + \cdots$, which is equivalent to
determine necessary and sufficient conditions for the existence of a center or a focus on the local center manifold, respectively.
In what follows, we consider that \( P, Q, \) and \( R \) in (3) are polynomials. We start by introducing the complex variable \( x = u + iv \). Therefore, the first two equations in (3) are equivalent to the unique equation \( \dot{x} = ix + \cdots \). Adding to this equation its complex conjugate, changing \( \bar{x} \) (where as usual \( \bar{x} \) denote the conjugate of \( x \)) by \( y \), thinking in \( y \) as an independent complex variable, and substituting \( w \) by \( z \), we obtain the following complexification of system (3)
\[
\begin{align*}
\dot{x} &= ix + \sum_{p+q+r=2} a_{pqr} x^p y^q z^r, \\
\dot{y} &= -iy + \sum_{p+q+r=2} b_{pqr} x^p y^q z^r, \\
\dot{z} &= \beta z + \sum_{p+q+r=2} c_{pqr} x^p y^q z^r, \quad (5)
\end{align*}
\]
where \( b_{pqr} = \bar{a}_{pqr} \) and the \( c_{pqr} \) are such that \( \sum_{p+q+r=2} c_{pqr} x^p \bar{x}^q w^r \) is real for all \( x \in \mathbb{C} \) and \( w \in \mathbb{R} \). Again, we denote by \( X \) the new vector field associated with system (5) on \( \mathbb{C}^3 \). Now, the existence of a first integral \( H(u, v, w) = u^2 + v^2 + \cdots \) for a system (3) is equivalent to the existence of a first integral of the form
\[
H(x, y, z) = xy + \sum_{j+k+l=3} v_{jkl} x^j y^k z^l \quad (6)
\]
for system (5).
By computing the coefficients of \( XH \) and equating them to zero, we investigate the existence of a first integral \( H \) for a system (5). When \( H \) has the form (6), we can calculate explicitly the coefficient \( g_{k_1k_2k_3} \) of \( x^{k_1} y^{k_2} z^{k_3} \) in \( XH \) (see [4]). But when \( (k_1, k_2, k_3) \neq (k, k, 0) \) for a positive integer \( k \), we can solved in a unique way for \( v_{k_1k_2k_3} \) the equation \( g_{k_1k_2k_3} = 0 \) in terms of the known quantities \( v_{\alpha\beta\gamma} \) such that \( \alpha + \beta + \gamma < k_1 + k_2 + k_3 \). Hence, if \( g_{kk0} = 0 \) for all \( k \in \mathbb{N} \), a formal first integral \( H \) exists. When the coefficient \( g_{kk0} \) is nonzero, an obstruction to the existence of the formal series \( H \) occurs. Such a coefficient is called the \( k \)th focus quantity.
The focus quantities \( g_{110} = 0 \) and \( g_{220} \) are determined in a unique way, but the others depend on the choices made for \( v_{kk0} \), \( k \in \mathbb{N} \), \( k \geq 2 \). Once such computations are made, \( H \) is determined and satisfies \( XH(x, y, z) = g_{220}(xy)^2 + g_{330}(xy)^3 + \cdots \).
It follows that if for one choice of the \( v_{kk0} \) at least one focus quantity is nonzero, the same is true for every other choice of the \( v_{kk0} \). A sufficient and necessary condition for the existence of a center on the center manifold is to vanish all focus quantities; otherwise, we have a focus (see [4]).
In rest of this work, we denote the \( k \)th focus quantity \( g_{kk0} \) by \( v_k \).
## 4 Hopf bifurcation method
Let \( (\theta, \rho) \) be polar coordinates on the local center manifold \( W_{loc}^c \), such that \( \rho = 0 \) corresponds to the origin in Cartesian coordinates. Consider system (3) restricted to its local center manifold and let \( \Pi(\rho) \) the respective Poincaré first return map on a sufficiently short segment of the axis \( \theta = 0 \) starting at \( \rho = 0 \). By the \( k \)th Lyapunov coefficient, we mean the coefficient \( l_k \) in the expansion of displacement map \( \Pi(\rho) - \rho \), i.e.,
\[
\Pi(\rho) - \rho = l_1 \rho + l_2 \rho^2 + \cdots.
\]
It follows by the proof of Theorem 6.2.3 of the page 261 of [15] that
\[
l_1 = c_1 v_1 \quad \text{and} \quad l_k \big|_{l_1=\cdots=l_{k-1}=0} = c_k v_k \big|_{v_1=\cdots=v_{k-1}=0}, \quad (7)
\]
where \( c_1, \ldots, c_k \) are positive constants.
A method to compute the Lyapunov coefficients can be found in the pages 177–181 of [7] or in [8, 12].
A singular point \((x_0, \mu_0)\) of a \( \mu \)-parameter family of vector fields \( X(x, \mu) \) in \( \mathbb{R}^3 \) is called a Hopf point if the Jacobian matrix \( DX(x_0, \mu_0) \) has a real eigenvalue \( \lambda_1 \neq 0 \) and a pair of purely imaginary eigenvalues \( \lambda_{2,3} = \pm i \omega_0 \). There is a two-dimensional center manifold at a Hopf point, and it is invariant by the flow of the system \( \dot{x} = X(x, \mu) \), see [7, p. 152]. If varying the parameters, the complex eigenvalues cross the imaginary axis with nonzero derivative and the Hopf point is called transversal, i.e., if \( \mu \) is one-dimensional parameter, then \( \frac{d\xi}{d\mu}(\mu_0) \neq 0 \) (where \( \xi(\mu) = i \omega(\mu) \) are the conjugated complex eigenvalues of the linear part of \( X(x, \mu) \) at singular point \( x_\mu \) when \( |\mu - \mu_0| \) is enough small). At a neighborhood of transversal Hopf point with \( l_1(\mu_0) \neq 0 \) the system \( \dot{x} = X(x, \mu) \), restricted to a center manifold, is orbitally topologically equivalent to the following complex normal form
\[
\dot{w} = (\xi + i \omega) w + \sigma w |w|^2,
\]
where $w \in \mathbb{C}$, $\sigma = \text{sign } l_1(\mu_0) = \pm 1$, $l_1(\mu_0)$ the first Lyapunov coefficient at the Hopf point, and $\xi$, $\omega$ are real functions having derivatives of arbitrary higher order, which are continuations of 0 and $\omega_0$, see [7, p. 98]. There is one family of stable (unstable) periodic orbits if $l_1 < 0$ ($l_1 > 0$) on the space of phases variables and parameters shrinking to a singular Hopf point.
A Hopf point of codimension 2 is a Hopf point where $l_1(\mu_0) = 0$ and $l_2(\mu_0) \neq 0$. It is called transversal if the manifolds $\xi(\mu) = 0$ ($\xi(\mu)$ is the real part of the conjugated complex eigenvalues) and $l_1(\mu)$ have transversal intersections, i.e., the map $\mu \mapsto (\xi(\mu), l_1(\mu))$ is regular at $\mu_0$. The codimension two Hopf bifurcation is also called of Bautin bifurcation or degenerated Hopf bifurcation. The system $\dot{x} = X(x, \mu)$ restricted to a center manifold at a neighborhood of a transversal Hopf point of codimension 2 is orbitally topologically equivalent to
$$\dot{w} = (\xi + i\omega_0)w + \tau w|w|^2 + \sigma w|w|^4,$$
where $\xi$ and $\tau$ are the unfolding parameters and $\sigma = \text{sign } l_2(\mu_0) = \pm 1$, see [7, p. 311]. The bifurcation diagram of system (8) on the space of parameters $(\xi, \tau)$ for $\sigma = 1$ is shown in Fig. 1, where the lines $H_1^\pm = \{ \pm \tau > 0 \}$ correspond to the Hopf bifurcation of codimension one with negative and with positive Lyapunov coefficient, respectively. Along these lines, the singular point has eigenvalues $\lambda_{1,2} = \pm \omega_0 i$. Moreover, the singular point is stable for $\xi < 0$ and unstable for $\xi > 0$. The first Lyapunov coefficient is $l_1(\xi, \tau) = \tau$. Therefore, the point of the Hopf bifurcation of codimension two $H_2$ occurs when $\xi = \tau = 0$ and separates the two branches, $H_1^-$ and $H_1^+$ of $\tau$-axis. An unstable limit cycle bifurcates from the singular point if we cross $H_1^+$ from right to left, while a stable limit cycle appears if we cross $H_1^-$ in the opposite direction. These limit cycles collide and disappear on the curve
$$T = \left\{ (\xi, \tau) : 4\xi - \tau^2 = 0 \right\},$$
corresponding to a non-degenerate fold bifurcation of the cycles. Along this curve, the system has a semistable limit cycle of multiplicity one, see [7, p. 311].
The bifurcation diagrams for $\sigma = -1$ can be found in [7], page 313, and in [19].
From (7), the Hopf method described above can be applied changing the Lyapunov coefficients by the focus quantities. Thus, in rest of this paper, we shall use the focus quantities in place of the Lyapunov coefficients to study Hopf bifurcations of codimension one and two.
5 Hopf bifurcation in the Shimizu–Morioka system
In this section, we study the stability of the singular point $Q_-$ of system (1) under the conditions $\alpha = \frac{2-\lambda^2}{\lambda}$ and $\lambda \in (0, \sqrt{2})$ given in Proposition 3, i.e., on the Hopf axis correspondent to the $\tau$-axis of Fig. 1. We prove the following theorem.
**Theorem 3** Consider the two-parameter family of differential equations (1). The first focus quantity at the point $Q_-$ for parameter values satisfying $\alpha = \frac{2-\lambda^2}{\lambda}$ and $\lambda \in (0, \sqrt{2})$ is given by
$$v_1(\lambda) = \frac{\lambda^2 - \lambda^2 (3\lambda^4 - 5\lambda^2 - 1)}{4 (\lambda^4 - 2\lambda^2 - 4) (\lambda^4 - 4\lambda^2 - 1)}.$$
For $\lambda \in (0, \sqrt{2})$ such that $h(\lambda) = 3\lambda^4 - 5\lambda^2 - 1$ is different from zero, system (1) has a transversal Hopf point at $Q_-$ for $\alpha = \frac{2-\lambda^2}{\lambda}$.
Now for the parameter values $\lambda_c = \sqrt{\frac{5 + \sqrt{37}}{6}}$ and $\alpha = \frac{7 - \sqrt{37}}{\sqrt{6(5 + 37)}}$, system (1) has a transversal Hopf point of codimension 2 at $Q_-$, which is unstable because $v_2 > 0$.
**Proof** For simplify the computations, we introduce the new parameters $(\beta, \varepsilon)$ by
$$\lambda = \frac{-\varepsilon (\beta^2 + \varepsilon^2 + 2) + \sqrt{(-\beta^2 - \varepsilon^2 + 2)(\beta^4 + (\beta^2 + 2) \varepsilon^2)}}{\beta^2 + \varepsilon^2},$$
$$\alpha = \frac{-\varepsilon - \sqrt{(-\beta^2 - \varepsilon^2 + 2)(\beta^4 + (\beta^2 + 2) \varepsilon^2)}}{\beta^2 + \varepsilon^2 - 2}.$$
The Jacobian determinant of this change of parameters in the point $(0, \beta)$ is
$$\frac{2\beta^5 (\beta^4 - 2\beta^2 - 4)}{(-\beta^4 (\beta^2 - 2))^{3/2}}.$$
Thus, the change of parameters is well defined for $(\varepsilon, \beta) \in (-\delta, \delta) \times (0, \sqrt{2})$, with $\delta$ enough small. In this new parameters, the linear part of system (1) at the singular point $Q_-$ has a real eigenvalue and two conjugated complex given by $\pm i\beta$. Furthermore, the conditions $\alpha = \frac{2-\lambda^2}{\lambda}$ and $\lambda \in (0, \sqrt{2})$ correspond to $\varepsilon = 0$ and $\beta \in (0, \sqrt{2})$. Hence, in this case, we have
$$\alpha = \frac{\beta^2}{\sqrt{2} - \beta^2} \quad \text{and} \quad \lambda = \sqrt{2 - \beta^2} \quad (9)$$
in system (1). Now, doing the change of coordinates $(x, y, z) \mapsto (\tilde{x} - \sqrt{\alpha}, \tilde{y}, \tilde{z} + 1)$, the singular point $Q_-$ is translated to the origin $(0, 0, 0)$. Now, we shall write the linear part of system in the coordinates $(\tilde{x}, \tilde{y}, \tilde{z})$ at the origin in its real Jordan normal form. For this, we introduce the variables $(u, v, w)$ by
$$\begin{pmatrix} \tilde{x} \\ \tilde{y} \\ \tilde{z} \end{pmatrix} = \begin{pmatrix} 1 \\ \frac{1}{2} \sqrt{2 - \beta^2} \\ \frac{1}{2} \sqrt{2 - \beta^2} \end{pmatrix} \begin{pmatrix} \beta \\ -2 \beta \sqrt{2 - \beta^2} \\ 2 (\beta^2 - 1) \end{pmatrix} \begin{pmatrix} u \\ v \\ w \end{pmatrix},$$
and so system (1) becomes
$$\begin{align*}
\dot{u} &= -v - \beta \sqrt{2 - \beta^2} (6 + \beta^2) u^2 \\
\phantom{\dot{u}} &= -16 - 8 \beta^2 + 4 \beta^4 \\
\dot{v} &= 2 (\beta^2 - 1) (\beta^2 - 2) (\beta^4 + (\beta^2 + 2) \beta^2) \beta^2 (\beta^4 - 1) v w \\
\phantom{\dot{v}} &= 16 (\beta^4 - 4 \beta^2 + 2 \beta^4) \\
\dot{w} &= 16 (\beta^4 - 4 \beta^2 + 2 \beta^4) w^2 \\
\phantom{\dot{w}} &= 64 - 32 \beta^4 + 8 \beta^6 \\
\end{align*}$$
\[ \varepsilon \text{ Springer} \]
Note that the above system is in the form (3). Now, we apply the method described in Sect. 3.
Firstly, we introduce the change of variables \((u, v, w) \mapsto (x, y, z) = (u + iv, u - iv, w)\) with inverse given by \((x, y, z) \mapsto (u, v, w) = \left(\frac{1}{2}(x + y), -\frac{i}{2}(x - y), z\right)\). Hence, we obtain system (1) in the complex form (5). Again let denote by \(X\) the vector field associated with this last system in complex form and let \(H\) be given by (6). We have that
\[
XH(x, y, z) = \sum_{m \geq 2} H_m(x, y, z),
\]
where \(H_m\) are homogeneous polynomials of degree \(m\) in the variables \((x, y, z)\). It is easy to see that \(H_2 \equiv 0\).
Denoting the coefficients of \(H_m\) by \(g_{jkl}\) with \(j + k + l = m\), we can solve easily the equations \(g_{jkl} = 0\) with \(j + k + l = 3\) in terms of the coefficients \(v_{\alpha \beta \gamma}\) of \(H\) such that \(\alpha + \beta + \gamma \leq 3\). For instance, the equation \(g_{000} = 0\) is given by
\[
-\frac{6v_{000}}{\beta\sqrt{2} - \beta^2} = 0,
\]
which solution in terms of the coefficients of \(H\) is \(v_{000} = 0\). Analogously, we can solve the equations \(g_{jkl} = 0\) with \(j + k + l = 4\) in terms of the coefficients \(v_{\alpha \beta \gamma}\) of \(H\) with \(\alpha + \beta + \gamma \leq 4\), except the equation \(g_{220} = 0\), because this equation does not depend on the coefficients of \(H\), only on the coefficients of \(X\). Hence, we have that the first focus quantity is \(g_{220} = v_1\) given by
\[
v_1 = \frac{\sqrt{2 - \beta^2} \left(3\beta^4 - 7\beta^2 + 1\right) \beta}{4 \left(\beta^4 - 2\beta^2 - 4\right) \left(\beta^4 - 2\beta^2 - 1\right)}.
\]
Following the above ideas, we obtain the second focus quantity \(g_{330} = v_2\), i.e.,
\[
v_2 = \left(\sqrt{2 - \beta^2} \left(-162\beta^{22} + 2268\beta^{20} - 14289\beta^{18}
+ 47071\beta^{16} - 80155\beta^{14}
+ 63495\beta^{12} - 20967\beta^{10} + 16999\beta^{8} - 23136\beta^{6}
+ 9300\beta^4 + 9760\beta^2\right) - 80\right)(96\beta^3 - 2\beta^2 - 4)^3\left(\beta^4 - 2\beta^2 - 1\right)^2
\times \left(9\beta^2 \left(\beta^2 - 2\right) - 4\right)\).
\]
Note that the polynomial \(\beta^4 - 2\beta^2 - 4\) has only two real roots, \(\pm \sqrt{1 + \sqrt{5}}\), and so it has negative sign in \((-\sqrt{1 + \sqrt{5}}, \sqrt{1 + \sqrt{5}})\). Now, the polynomial \(\beta^4 - 2\beta^2 - 1\) also has only two real roots, \(\pm 1 + \sqrt{2}\), and so it has negative sign in \((-\sqrt{1 + \sqrt{2}}, \sqrt{1 + \sqrt{2}})\).
Therefore, the sign of the first focus quantity is determined by the sign of \(h(\beta) = 3\beta^4 - 7\beta^2 + 1\), since we are considering \(\beta \in (0, 1)\) and so the denominator of (10) is positive. Observe that, for \(\beta \in (0, 1)\), the first focus quantity vanishes on \(\beta_c = \sqrt{\frac{1}{6} \left(7 - \sqrt{37}\right)}\), and the second is different from zero, i.e., \(v_1(\beta_c) = 0\) and \(v_2(\beta_c) = \frac{\sqrt{274249\sqrt{37} - 591726}}{15568}\). Moreover, \(v_1 > 0\) for \(\beta \in (0, \beta_c)\) and \(v_1 < 0\) for \(\beta \in (\beta_c, \sqrt{2})\).
Clearly, in the plane of parameters \((\varepsilon, \beta)\), we have a transversal Hopf point in \(Q_-\) for \(\varepsilon = 0\) and \(\beta \in (0, \sqrt{2}) \setminus \{\beta_c\}\). Now, as the map \((\varepsilon, \beta) \mapsto (v_1(\beta))\) is regular in \((0, \beta_c)\), since
\[
\frac{dv_1}{d\beta}(\beta_c) = -\frac{\sqrt{37} \left(14066\sqrt{37} - 84205\right)}{1946},
\]
it follows that we have a transversal Hopf point of codimension two in \(Q_-\) for \(\varepsilon = 0\) and \(\beta = \beta_c\).
In the parameter \(\lambda\), by (9), the function \(h\) becomes
\[
h(\lambda) = 3\lambda^4 - 5\lambda^2 - 1 \neq 0,
\]
\[
v_1(\lambda) = \frac{\lambda \sqrt{2 - \lambda^2} (3\lambda^4 - 5\lambda^2 - 1)}{4 \left(\lambda^4 - 2\lambda^2 - 4\right) \left(\lambda^4 - 2\lambda^2 - 1\right)}
\]
and \(v_1(\lambda)\) is zero in the \((0, \sqrt{2})\) only for the value \(\lambda_c = \sqrt{\frac{5 + \sqrt{37}}{6}}\). Moreover, in this point, by (9), \(\alpha = \frac{7 - \sqrt{37}}{\sqrt{6(5 + 37)}}\).
The same results stated in Theorem 1 are valid also for the point \(Q_+\), due to the symmetry of the system under the change \((x, y, z) \mapsto (-x, -y, z)\). The statements (a) and (b) of Theorem 1 follow from the above results.
The bifurcation diagram on the space of parameters \((\lambda, \alpha)\) of system (1) on the neighborhood of the
two codimension Hopf point $H_2 = \left( \frac{\sqrt{5 + \sqrt{37}}}{6}, \frac{7 - \sqrt{37}}{\sqrt{6(5 + 37)}} \right)$ is described in Fig. 2, where by Sect. 4 the curves $H_1^\pm$ and $T$ correspond, respectively, with the curves of Fig. 1. Note that
$$H_1^- \cup H_2 \cup H_1^+ = \left\{ (\lambda, \alpha) \mid \alpha = \frac{2 - \lambda^2}{\lambda}, \lambda \in (0, \sqrt{2}) \right\}.$$
Acknowledgments The first author was partially supported by the Grants MINECO/FEDER MTM 2008-03437, AGAUR 2014SGR 568, ICREA Academia and FP7 PEOPLE-2012-IRSES-316338 and 318999. The second author was partially supported by Program CAPES/DGU Process 8333/13-0 and by FAPESP Project 2011/13152-8.
References
1. Aguirre, L., Arredondo, J.H., Lópe, R., Siebert, P.: On certain generalizations of the Hopf bifurcation. Ann. Mat. Pura Appl. 186, 509–524 (2007)
2. Bibikov, Y.: Local Theory of Nonlinear Analytic Ordinary Differential Equations. Lecture Notes in Mathematics, vol. 702. Springer, New York (1979)
3. Dias, F.S., Mello, L.F., Zhang, J.-G.: Nonlinear analysis in a Lorenz-like system. Nonlinear Anal. Real World Appl. 11(5), 3491–3500 (2010)
4. Edneral, V., Mahdi, A., Romanovski, V.G., Shafer, D.S.: The center problem on a center manifold. Nonlinear Anal. Theory Methods Appl. 75, 2614–2622 (2012)
5. Islam, N., Mazumdar, H.P., Das, A.: On the stability and control of the Schimizu– Morioka system of dynamical equations. Differ. Geom. Dyn. Syst. 11, 135–143 (2009)
6. Kokubu, H., Roussarie, R.: Existence of a singularly degenerate heteroclinic cycle in the Lorenz system and its dynamical consequences: part I. J. Dyn. Differ. Equ. 16(2), 513–557 (2004)
7. Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory. Springer, New York (2004)
8. Kuznetsov, Y.A.: Numerical normalization techniques for all codim 2 bifurcations of equilibria in ODE’s. SIAM J. Numer. Anal. 36, 1104–1124 (1999)
9. Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963)
10. Mahdi, A.: Center problem for third-order ODEs. Int. J. Bifurc. Chaos Appl. Sci. Eng. 23(5), 11 (2013)
11. Mahdi, A., Romanovski, V.G., Shafer, D.S.: Stability and periodic oscillations in the Moon–Rand systems. Nonlinear Anal. Real World Appl. 14(1), 294–313 (2013)
12. Mello, L.F., Messias, M., Braga, D.C.: Bifurcation analysis of a new Lorenz-like chaotic system. Chaos Solitons Fractals 37, 1244–1255 (2008)
13. Messias, M., Gouveia, M.R.A., Pessoa, C.: Dynamics at infinity and other global dynamical aspects of Shimizu-Morioka equations. Nonlinear Dyn. 69, 577–587 (2012)
14. Pontryagin, L.S.: Ordinary Differential Equations. Addison-Wesley, Reading (1962)
15. Romanovski, V.G., Shafer, D.S.: The Center and Cyclicity Problems: A Computational Algebra Approach. Birkhäuser, Boston (2009)
16. Rubinger, R.M., Nascimento, A.W.M., Mello, L.F., Rubinger, C.P.L., Manzanares Filho N., Albuquerque, H.A.: Inductorless Chua’s circuit: experimental time series analysis. Math. Probl. Eng. 2007 (2007). doi: 10.1155/2007/83893
17. Shilnikov, A.L.: On bifurcations of the Lorenz attractor in the Shimizu–Morioka model. Phys. D Nonlinear Phenom. 62, 338–346 (1993)
18. Shimizu, T., Morioka, N.: On the bifurcation of a symmetric limit cycle to an asymmetric one in a simple model. Phys. Lett. A 76(3,4), 201–204 (1980)
19. Takens, F.: Unfoldings of certain singularities of vector-fields: Generalized Hopf bifurcations. J. Differ. Equ. 14, 476–493 (1973)
20. Tigan, G., Turaev, D.: Analytical search for homoclinic bifurcations in the Shimizu-Morioka model. Phys. D Nonlinear Phenom. 240(12), 985–989 (2011)
21. Vladimirov, A.G., Volkov, D.Y.: Low-intensity chaotic operations of a laser with a saturable absorber. Opt. Commun. 100, 351–360 (1993)
22. Yu, S., Tang, W.K.S., Lü, J., Chen, G.: Generation of $n \times m$-wing Lorenz-like attractors from a modified Shimizu–Morioka model. IEEE Trans. Circuit Syst. 55(11), 1168–1172 (2008) | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2243,
1
],
[
2243,
7310,
2
],
[
7310,
12026,
3
],
[
12026,
17166,
4
],
[
17166,
19908,
5
],
[
19908,
23438,
6
],
[
23438,
27903,
7
],
[
27903,
30303,
8
],
[
30303,
31823,
9
]
]
} |
2c28d4bb40145dc5329a3613185e49abb0d5f62e | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 9,
"total-fallback-pages": 0,
"total-input-tokens": 41476,
"total-output-tokens": 10200,
"fieldofstudy": [
"Physics"
]
} | Density of condensates of two-component Bose-Einstein condensates restricted between two planar walls
Nguyen Van Thu¹, Pham The Song², Nguyen Thi Le³
¹Department of Physics, Hanoi Pedagogical University 2, Hanoi, Vietnam
²Tay Bac University, Son La, Vietnam
³Medical Physics, Hanoi Medical University, Hanoi, Vietnam
E-mail: [email protected]
Abstract. The density of condensates of a binary mixture of Bose gases restricted by two parallel planar walls is investigated within the framework of Cornwal-Jackiw-Tomboulis effective action approach in improved Hartree-Fock approximation. It results that the density of condensates strongly depend not only on the distance between two walls but also on the interspecies interaction strength and they are equal their expectation values of the field operators after adding a term associated with the quantum fluctuations.
1. Introduction
One of the most important quantities in studies on Bose-Einstein condensate (BEC) in both theory and experiment is the density of condensate. Based on it, all of static and dynamic properties of the BEC can be easily investigated.
The well-known theory of the BEC proposed by Gorss and Pitaevskii (GP) [1, 2], where the temperature is assumed to be zero so that all of atoms are condensed. The ground state is described by the wave function, which is the solution of a nonlinear differential equation called the GP equation. The density of condensate is defined as square of the wave function and called the profile [2, 4]. However, it is reported that we have never achieve the absolute zero temperature and even so, a number of particles will be in the excited state instead of the ground state [5]. Based on the GP theory, the density of condensate in the BEC have been investigated by many authors, for example, see Refs. [6, 7, 8] and so on. In a simple approximation called double-parabola approximation [9] and triple-parabola approximation [10], this aspect was also studied.
Taking into account the quantum fluctuations, quantum field theory is proposed in several levels of the accuracy. In the one-loop approximation, the density of condensate in the ideal and weakly interacting Bose gas was investigated [11]. The Cornwal-Jackiw-Tomboulis (CJT) effective action approach [12] can be applied to consider the contribution of two-loop diagrams. The authors of Ref. [13] employed this method to consider the scenarios of phase transition in a binary mixture of Bose gases (BECs).
The finite-size effect in the BEC(s) produces many amazing changes in properties of the BEC(s). Within the framework of the GP theory, the density of condensate of the BEC has
been researched [14, 15] and [16, 17] for BECs. One of the most interesting consequence of the finite-size effect is the Casimir effect, which has been studied widely in many scopes of physics. In the BEC field, this effect was investigated in the one-loop approximation [14, 15, 18], in which the expectation value of the field operator is assumed independence of the coordinate. The results showed that the expectation value of the field operator is not only independent of the coordinate but also of the size of system, which is usually the distance between two planar walls filled by the Bose gas. By the same way, this effect was also studied in BECs [19]. In higher approximation, called improved Hartree-Fock (IHF) approximation, the expectation value of the field operator was considered in BECs with lower-order terms in the momentum integrals [20]. The contribution of the higher-order terms is taken into account to investigated the density of condensate of the BEC [21]. The resulting the expectation value of the field operator depends on both the coordinate and the distance between two planar walls. In this paper, the density of condensate of the dilute Bose gas confined between two parallel plates is considered in the IHF approximation with the present of the high-order terms in the momentum integrals, which is named the higher-order improved Hartree-Fock (HIHF) approximation.
This paper is organized as follows. In Section 2, the density of condensate is derived in improved Hartree-Fock approximation. Section 3 devote the density of condensate of a weakly interacting Bose gas in the HIHF approximation. Conclusions are given in Section 4.
2. Density of condensate in the improved Hartree-Fock approximation
We start by considering a two-component Bose-Einstein condensates, which is described by the Lagrangian [2, 4],
\[ \mathcal{L} = \sum_{j=1,2} \psi_j^* \left( -i\hbar \frac{\partial}{\partial t} - \frac{\hbar^2}{2m_j} \nabla^2 \right) \psi_j - V, \]
with GP potential
\[ V = \sum_{j=1,2} \left( -\mu_j |\psi_j|^2 + \frac{g_{jj}}{2} |\psi_j|^4 \right) + g_{12} |\psi_1|^2 |\psi_2|^2, \]
in which the field operator \( \psi_j(\vec{r}, t) \) has the expectation value \( \psi_{j0} \) plays the role of the order parameter; \( \hbar \) is the reduced Plack’s constant; the chemical potential and atomic mass of \( j \)-component are denoted by \( \mu_j \) and \( m_j \), respectively. The particles of species \( j \) and \( j' \) interact weakly via s-wave scattering, quantified by a positive scattering length \( a_{jj'} \) and a coupling constant
\[ g_{jj'} = 2\pi \hbar^2 a_{jj'} \left( \frac{1}{m_j} + \frac{1}{m_{j'}} \right) > 0, \]
and the interspecies interaction are determined by
\[ g_{jj} = \frac{4\pi \hbar^2 a_{jj}}{m_j} > 0. \]
Let \( \psi_{j0} \) be the expectation value of the field operator, in tree-approximation, minimizing the potential (2) with respect to the order parameter, in broken phase one has
\[ \psi_{10}^2 = \frac{g_{12}^2 \mu_1 - g_{12} \mu_2}{g_{11} g_{22} - g_{12}^2}, \quad \psi_{20}^2 = \frac{g_{11} \mu_2 - g_{12} \mu_1}{g_{11} g_{22} - g_{12}^2}. \]
In order to consider in the Hartree-Fock (HF) approximation, the field operator is decomposed in terms of the order parameter and two real fields $\psi_1, \psi_2$ associated with the quantum fluctuation of the field \cite{11},
$$\psi_j \rightarrow \psi_{j0} + \frac{1}{\sqrt{2}}(\psi_{j1} + i\psi_{j2}).$$
(6)
Inserting (6) into Lagrangian (1) yields the free Lagrangian
$$\mathcal{L}_0 = \sum_{j=1,2} \left( -\mu_j \psi_{j0} + \frac{g_{jj}}{2} \psi_{j0}^4 \right) + \frac{g_{12}}{2} \psi_{10}^2 \psi_{20}^2,$$
(7)
which gives us the inversion propagator in tree-approximation in momentum space
$$D^{-1}_{j0}(k) = \begin{pmatrix} \frac{\hbar^2 k^2}{2m_j} + 2g_{jj} \psi_{j0}^2 - \omega_n & -\omega_n \\ -\omega_n & \frac{\hbar^2 k^2}{2m_j} \end{pmatrix},$$
(8)
in combining with (5). Here we denote $\vec{k}$ the wave vector, $\omega_n = 2\pi n/\beta$, $n = 0, \pm 1, \pm 2, \ldots$ stands for the Matsubara frequency for boson. At temperature $T$ one has $\beta = 1/k_B T$ with $k_B$ being the Boltzmann constant. Let the determinants of the inversion propagator be zero \cite{22}
$$\det D_{j0}^{-1}(k) = 0,$$
one gets the dispersion relation
$$E_j(k) = \sqrt{\frac{\hbar^2 k^2}{2m_j} \left( \frac{\hbar^2 k^2}{2m_j} + 2g_{jj} \psi_{j0}^2 \right)}.$$
(9)
It is obvious that there are Goldstone bosons associated with $U(1) \times U(1)$ breaking.
We now look for the CJT effective potential in double-bubble approximation. To do this, substituting the decomposition (6) into Lagrangian (1) one arrives at the interaction Lagrangian \cite{20},
$$\mathcal{L}_{\text{int}} = \frac{1}{\sqrt{2}} \sum_{j=1,2} \left[ g_{jj} \psi_{j0} \psi_{j1} + g_{12} \psi_{j0} \psi_{j2} \right] (\psi_{j1}^2 + \psi_{j2}^2) + \frac{1}{8} \sum_{j=1,2} g_{jj} (\psi_{j1}^2 + \psi_{j2}^2)^2$$
$$+ \frac{g_{12}}{4} (\psi_{11}^2 + \psi_{12}^2)(\psi_{21}^2 + \psi_{22}^2).$$
(10)
and the CJT effective potential can be easily read off from (10)
$$V_{CJT}^\beta = \sum_{j=1,2} \left( -\mu_j |\psi_{j0}|^2 + \frac{g_{jj}}{2} |\psi_{j0}|^4 \right) + g_{12} |\psi_{10}|^2 |\psi_{20}|^2$$
$$+ \frac{1}{2} \int_\beta \text{tr} \left\{ \sum_{j=1,2} \left[ \ln D_j^{-1}(k) + D_{j0}^{-1}(k)D(k) \right] - 2 \mathbb{I} \right\} + \frac{3g_{11}}{8} (P_{11}^2 + P_{22}^2) + \frac{g_{11}}{4} P_{11} P_{22}$$
$$+ \frac{3g_{22}}{8} (Q_{11}^2 + Q_{22}^2) + \frac{g_{22}}{4} Q_{11} Q_{22} + \frac{g_{12}}{4} (P_{11} Q_{11} + P_{12} Q_{22} + P_{22} Q_{22} + P_{22} Q_{22}),$$
(11)
where $D(k)$ is the propagator in the double-bubble approximation and notations
$$\int f(k) = \frac{1}{\beta} \sum_{n=-\infty}^{+\infty} \int \frac{d^3 \vec{k}}{(2\pi)^3} f(\omega_n, \vec{k}),$$
$$P_{aa} = \int_\beta D_{1aa}(k), \quad Q_{bb} = \int_\beta D_{2bb}(k),$$
$$P_{ab} = \int_\beta D_{1ab}(k), \quad Q_{ab} = \int_\beta D_{2ab}(k),$$
$$\int D(k) = \int_\beta D_{11}(k), \quad \int_\beta D_{22}(k).$$
are employed. It is confirmed in our previous papers [20] that the CJT effective potential (11) breaks the Goldstone theorem. In order to restore it, the method proposed by Ivanov et. al. [23] is invoked therefore the CJT effective potential (11) is replaced by a new one [21],
\[ \tilde{\mathcal{V}}_{\beta}^{\text{CJT}} = \sum_{j=1,2} \left( -\mu_j |\psi_{j0}|^2 + \frac{g_{jj}}{2} |\psi_{j0}|^4 \right) + g_{12} |\psi_{10}|^2 |\psi_{20}|^2 \\
+ \frac{1}{2} \int \text{tr} \left\{ \sum_{j=1,2} \left[ \ln D_j^{-1}(k) + D_j^{-1}(k)D(k) \right] - 2 \right\} \int \frac{d^3 k}{(2\pi)^3} \left[ \ln D_0^{-1}(k) + D_0^{-1}(k)D(k) \right] - 2 \right\} + \frac{g_{11}}{8} (P_{11}^2 + P_{22}^2) + \frac{3g_{11}}{4} P_{11}P_{22} \\
+ \frac{g_{22}}{8} (Q_{11}^2 + Q_{22}^2) + \frac{3g_{22}}{4} Q_{11}Q_{22} + \frac{g_{12}}{4} (P_{11}Q_{11} + P_{12}Q_{22} + P_{22}Q_{11} + P_{22}Q_{22}). \] (12)
As it was pointed out in Ref. [20], this CJT effective potential (12) ensures that the Goldstone theorem is valid and the Goldstone bosons have the new dispersion relation [21],
\[ E_j(k) = \sqrt{\frac{h^2 k^2}{2 m_j} \left( \frac{h^2 k^2}{2 m_j} + M_j^2 \right)}, \] (13)
with \( M_j \) being the effective mass and the approximation associated with the effective potential (12) is called the IHF approximation. The inversion propagator is now
\[ D_j^{-1}(k) = \left( \frac{h^2 k^2}{2 m_j} + M_j^2 - \omega_n \frac{h^2 k^2}{2 m_j} \right). \] (14)
Eqs. (12) and (14) give us the momentum integrals
\[ P_{11} = \frac{1}{2} \int \frac{d^3 k}{(2\pi)^3} \sqrt{\frac{h^2 k^2/2m_1 + M_1^2}{h^2 k^2/2m_1 + M_1^2}}, \]
\[ P_{22} = \frac{1}{2} \int \frac{d^3 k}{(2\pi)^3} \sqrt{\frac{h^2 k^2/2m_1 + M_1^2}{h^2 k^2/2m_1 + M_1^2}}, \]
\[ Q_{11} = \frac{1}{2} \int \frac{d^3 k}{(2\pi)^3} \sqrt{\frac{h^2 k^2/2m_2 + M_2^2}{h^2 k^2/2m_2 + M_2^2}}, \]
\[ Q_{22} = \frac{1}{2} \int \frac{d^3 k}{(2\pi)^3} \sqrt{\frac{h^2 k^2/2m_2 + M_2^2}{h^2 k^2/2m_2 + M_2^2}}. \] (15)
From (12) it is easy to derive the gap equations
\[ -\mu_1 + g_{11} \psi_{10}^2 + g_{12} \psi_{20}^2 + \Sigma_2^{(1)} = 0, \]
\[ -\mu_2 + g_{22} \psi_{20}^2 + g_{12} \psi_{10}^2 + \Sigma_2^{(2)} = 0. \] (16)
The effective masses are solution of the and Schwinger-Dyson (SD) equations
\[ M_1^2 = -\mu_1 + 3g_{11} \psi_{10}^2 + g_{12} \psi_{20}^2 + \Sigma_1^{(1)}, \]
\[ M_2^2 = -\mu_2 + 3g_{22} \psi_{20}^2 + g_{12} \psi_{10}^2 + \Sigma_1^{(2)}, \] (17)
in which
\[ \Sigma_1^{(1)} = \frac{1}{2} (g_{11} P_{11} + 3g_{11} P_{22} + g_{12} Q_{11} + g_{12} Q_{22}), \]
\[ \Sigma_1^{(2)} = \frac{1}{2} (g_{22} Q_{11} + 3g_{22} Q_{22} + g_{12} P_{11} + g_{12} P_{22}), \]
\[ \Sigma_2^{(1)} = \frac{1}{2} (3g_{11} P_{11} + g_{11} P_{22} + g_{12} Q_{11} + g_{12} Q_{22}), \]
\[ \Sigma_2^{(2)} = \frac{1}{2} (3g_{22} Q_{11} + g_{22} Q_{22} + g_{12} P_{11} + g_{12} P_{22}). \] (18)
The pressure is defined as
$$P = -\hat{V}_{\beta}^{CJT} \bigg|_{\text{at minimum}}.$$ \hfill (19)
Using Eqs. (16)-(18), the pressure (19) can be easily obtained
$$P = -\sum_{j=1,2} \left( -\mu_j |\psi_{j0}|^2 + \frac{g_{jj}}{2} |\psi_{j0}|^4 \right) - g_{12}|\psi_{10}|^2|\psi_{20}|^2 - \frac{1}{2} \int_{\beta} \text{tr} \left[ \ln D_1^{-1}(k) + \ln D_2^{-1}(k) \right]$$
$$- \frac{1}{2} \left( -M_1^2 - \mu_1 + 3g_{11}\psi_{10}^2 + g_{12}\psi_{20}^2 \right) P_{11} - \frac{1}{2} \left( -\mu_1 + g_{11}\psi_{10}^2 + g_{12}\psi_{20}^2 \right) P_{22}$$
$$- \frac{1}{2} \left( -M_2^2 - \mu_2 + 3g_{22}\psi_{20}^2 + g_{12}\psi_{10}^2 \right) Q_{11} - \frac{1}{2} \left( -\mu_2 + g_{22}\psi_{20}^2 + g_{12}\psi_{10}^2 \right) Q_{22}$$
$$- \frac{g_{11}}{8} (P_{11}^2 + P_{22}^2) - \frac{3g_{11}}{4} P_{11} P_{22} - \frac{g_{22}}{8} (Q_{11}^2 + Q_{22}^2) - \frac{3g_{22}}{4} Q_{11} Q_{22}$$
$$- \frac{g_{12}}{4} (P_{11}Q_{11} + P_{11}Q_{22} + P_{22}Q_{11} + P_{22}Q_{22}).$$ \hfill (20)
The density of condensates in the IHF approximation is determined by
$$\rho_j = \frac{\partial P}{\partial \mu_j}.$$ \hfill (21)
Plugging Eq. (20) into (21) one obtains the density of condensates in the IHF approximation
$$\rho_1 = \psi_{10}^2 + \frac{1}{2} (P_{11} + P_{22}),$$
$$\rho_2 = \psi_{20}^2 + \frac{1}{2} (Q_{11} + Q_{22}).$$ \hfill (22)
3. Influence of the compactification on the density of condensates
We now consider the two-component Bose-Einstein condensates filling space between two larger parallel planar walls. These planar walls are perpendicular to 0z-axis at a distance $\ell$ and this distance is very small than the size of each wall. The compactification in $z$-direction leads to the quantization of the wave vector
$$k^2 \rightarrow k_{\perp}^2 + k_n^2,$$ \hfill (23)
in which the wave vector component $k_{\perp}$ is perpendicular to 0z-axis and $k_n$ is parallel with 0z-axis. Along 0z direction, the periodic boundary condition is applied [21], the $k_n$ component of the wave vector has the form
$$k_n = \frac{2\pi n}{\ell}, \quad n \in \mathbb{Z}.$$ \hfill (24)
In this paper, we adopt the dimensionless quantities for the purpose of seeking for simplicity: the distance between two plates is scaled by the healing length $\xi_j = \hbar / \sqrt{2mg_{jj}n_{j0}}$ with $n_{j0}$ being the bulk density of $j$-component thus the dimensionless distance is $L_j = \ell / \xi_j$. The dimensionless wave vector is $\kappa_j = k \xi_j$ and Eq. (23) becomes
$$\kappa_j^2 \rightarrow \kappa_{j\perp}^2 + \kappa_{jn}^2,$$ \hfill (25)
with the dimensionless form of (24) being \( \kappa_j = n/L_j \), \( L_j = L_j/(2\pi) \). In terms of these dimensionless quantities, the momentum integrals (15) are rewritten in form
\[
P_{11} = \frac{1}{2\xi_1^2} \int \frac{d^3\kappa_1}{(2\pi)^3} \frac{\kappa_1}{\sqrt{\kappa_1^2 + M_1^2}}, \quad P_{22} = \frac{1}{2\xi_1^2} \int \frac{d^3\kappa_1}{(2\pi)^3} \frac{\sqrt{\kappa_1^2 + M_1^2}}{\kappa_1},
\]
\[
Q_{11} = \frac{1}{2\xi_2^2} \int \frac{d^3\kappa_2}{(2\pi)^3} \frac{\kappa_2}{\sqrt{\kappa_2^2 + M_2^2}}, \quad Q_{22} = \frac{1}{2\xi_2^2} \int \frac{d^3\kappa_2}{(2\pi)^3} \frac{\sqrt{\kappa_2^2 + M_2^2}}{\kappa_2}.
\]
(26)
Because of the quantization of the wave vector (25), the momentum integration perpendicular to the plates is replaced by a discrete sum
\[
\int \frac{d^3\kappa_j}{(2\pi)^3} f(\kappa_j) \rightarrow \sum_{n=-\infty}^{+\infty} \int \frac{d^2\kappa_{j\perp}}{(2\pi)^2} f(\kappa_{j\perp}, \kappa_{jn}),
\]
therefore Eqs. (26) become
\[
P_{11} = \frac{1}{2\xi_1^2} \sum_n \int_0^L \frac{d^2\kappa_{1\perp}}{(2\pi)^2} \sqrt{\frac{\kappa_{1\perp}^2 + (2\pi n/L_1)^2}{\kappa_{1\perp}^2 + (2\pi n/L_1)^2 + M_1^2}},
\]
\[
P_{22} = \frac{1}{2\xi_1^2} \sum_n \int_0^L \frac{d^2\kappa_{1\perp}}{(2\pi)^2} \sqrt{\frac{\kappa_{1\perp}^2 + (2\pi n/L_1)^2}{\kappa_{1\perp}^2 + (2\pi n/L_1)^2 + M_1^2}},
\]
\[
Q_{11} = \frac{1}{2\xi_2^2} \sum_n \int_0^L \frac{d^2\kappa_{2\perp}}{(2\pi)^2} \sqrt{\frac{\kappa_{2\perp}^2 + (2\pi n/L_2)^2}{\kappa_{2\perp}^2 + (2\pi n/L_2)^2 + M_2^2}},
\]
\[
Q_{22} = \frac{1}{2\xi_2^2} \sum_n \int_0^L \frac{d^2\kappa_{2\perp}}{(2\pi)^2} \sqrt{\frac{\kappa_{2\perp}^2 + (2\pi n/L_2)^2}{\kappa_{2\perp}^2 + (2\pi n/L_2)^2 + M_2^2}}.
\]
(27)
Note that in the above equations, the dimensionless effective mass is defined as \( M_j = M_j/\sqrt{g_{jj}^2} \). In addition, the integrations over the perpendicular components of the wave vectors are ultraviolet divergent so that a momentum cut-off \( \Lambda \) is introduced. The sum over the parallel component \( \kappa_j \) of the wave vector can be dealt by using the Euler-Maclaurin formula [24],
\[
\sum_{n=0}^{\infty} \theta_n F(n) - \int_0^{\infty} F(n) \, dn = -\frac{1}{12} F'(0) + \frac{1}{720} F''(0) - \frac{1}{30240} F^{(5)}(0) + \cdots,
\]
(28)
with
\[
\theta_n = \begin{cases}
1/2, & \text{if } n = 0; \\
1, & \text{if } n > 0.
\end{cases}
\]
After performing the integration and then taking the sum, let the cut-off \( \Lambda \) tends to infinity one has [20],
\[
P_{11} = Q_{11} = 0, \quad P_{22} = \frac{g_{11} m_1^2 M_1}{12\hbar^2 \ell}, \quad Q_{22} = \frac{g_{22} m_2^2 M_2}{12\hbar^2 \ell}.
\]
(29)
According to Eq. (22), in order to calculate the density of condensates one needs to know the order parameters. To do that, the momentum integrals (29) are plugged into (16) and (17). The gap and SD equations in dimensionless form are
\[
\begin{align*}
-1 + \phi_1^2 + K \phi_2^2 + \frac{m_1 g_{11} M_1}{24 h^2 \ell} + K \frac{m_2 g_{22} M_2}{24 h^2 \ell} &= 0, \\
-1 + \phi_2^2 + K \phi_1^2 + \frac{m_2 g_{22} M_2}{24 h^2 \ell} + K \frac{m_1 g_{11} M_1}{24 h^2 \ell} &= 0, \\
-1 + 3\phi_1^2 + K \phi_2^2 + \frac{3m_1 g_{11} M_1}{24 h^2 \ell} + K \frac{m_2 g_{22} M_2}{24 h^2 \ell} &= \mathcal{M}_1^2, \\
-1 + 3\phi_2^2 + K \phi_1^2 + \frac{3m_2 g_{22} M_2}{24 h^2 \ell} + K \frac{m_1 g_{11} M_1}{24 h^2 \ell} &= \mathcal{M}_2^2,
\end{align*}
\]
(30)
where the reduced order parameter \( \phi_j = \frac{\psi_j}{\sqrt{n_j}} \) is introduced and the dimensionless gas parameter \( K = \frac{g_{12}}{\sqrt{g_{11} g_{22}}} \) is defined. Solving Eqs. (30) one easily finds the solution in dimensionless form
\[
\begin{align*}
\phi_1 &= \frac{1}{K + 1} + \frac{m_1 g_{11}}{12 \sqrt{2(K + 1) h^2 \ell}}, \\
\phi_2 &= \frac{1}{K + 1} + \frac{m_2 g_{22}}{12 \sqrt{2(K + 1) h^2 \ell}}, \\
\mathcal{M}_1^2 &= \mathcal{M}_2^2 = \frac{2}{K + 1}.
\end{align*}
\]
(31)
Defining the reduced density of condensate
\[
\vartheta_j = \frac{\rho_j}{n_j} \quad (32)
\]
then combining Eqs. (31) and (22) yields the reduced density of condensates
\[
\begin{align*}
\vartheta_1 &= \frac{1}{K + 1} + \frac{m_1 g_{11}}{6 \sqrt{2} \sqrt{K + 1} h^2 \ell}, \\
\vartheta_2 &= \frac{1}{K + 1} + \frac{m_2 g_{22}}{6 \sqrt{2} \sqrt{K + 1} h^2 \ell}.
\end{align*}
\]
(33)
It is not difficult to see that both the density of condensates and square of the order parameters are equal their values in the one-loop approximation after adding a corrected term associated with the contribution of the two-loop diagrams.
\textbf{Figure 1.} The dimensionless distance dependence of the order parameters at \( K = 3 \). The red and blue lines correspond to first component \( (\phi_1) \) and second one \( (\phi_2) \).
Let us illustrate for above calculations by numerical computations for a mixture of Bose gasses, which consists of the first component (rubidium Rb 87) and second one (cesium Cs 133) [25] with parameters $m_1 = 86.909 \text{ u}$, $a_{11} = 100.4a_0$, $m_2 = 132.905 \text{ u}$, $a_{22} = 280a_0$, $a_0 = 0.529 \text{ nm}$, with $u$ and $a_0$ being atomic mass unit and Bohr radius, respectively. Fig. 1 shows the order parameters as a function of the dimensionless distance $L = \ell/\xi_1$ between two plates at $K = 3$. The first thing one easily sees is the fast decay of the order parameters as the distance increases and which approach their values associated with those of the infinite system $\phi_1 = \phi_2 = 1/\sqrt{K+1}$ (black line).
The evolution of density of condensates as a function of the dimensionless distance are sketched in Fig. 2 for the first component (rubidium Rb 87) and Fig. 3 for the second component (cesium Cs 133). In these figures, the solid and dashed lines correspond to the density of condensate and square of the order parameter, black lines associate with those in the one-loop approximation. Similar to the order parameters, the density of condensates decay fast as the distance increases and approach to their values for the infinite system. Both the density of condensates are divergent when the distance tends to zero. There is no doubt that the contribution of the quantum fluctuations into the density of condensates is not small, especially in region of the small distance. Amount of difference between the solid and dashed lines correspond to contribution of the term $(P_{11}+P_{22})^2$ for the first component and $(Q_{11}+Q_{22})^2$ for the second one and which is $\frac{m_jg_{jj}}{12\sqrt{2(K+1)}}\ell$.
4. Conclusions
In the foregoing Section, the density of condensates of two-component Bose-Einstein condensates restricted between two planar walls is investigated in the improved Hartree-Fock approximation. The ultraviolet divergence in integrating over the perpendicular component of the wave vector is eliminated by introducing the momentum cut-off whereas the sum over all value of quantized component of the wave vector is dealt by using Euler-Maclaurin formula.
Our main results are in order:
- The compactification of space strongly affects on the density of condensate of the BECs, especially in region of the small distance. The density of condensates diverge as the distance between two planar walls approaches zero.
Figure 2. (Color online) The evolution of the reduced density of condensate (solid line) and square of the order parameter (dashed line) of the first component (rubidium Rb 87) versus the dimensionless distance at $K = 3$.
Figure 3. (Color online) The evolution of the reduced density of condensate (solid line) and square of the order parameter (dashed line) of the second component (cesium Cs 133) versus the dimensionless distance at $K = 3$.
- The contribution of the quantum fluctuations into the density of condensates are remarkable. This contribution is not negligible when the distance is sufficiently small.
Acknowledgments
This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 103.01-2018.02.
References
[1] Gross E P 1961 Structure of a Quantized Vortex in Boron Systems *Nuovo Cimento* 20 454.
[2] Pitaevskii L P 1961 Vortex lines in an imperfect Bose gas *Sov. Phys. JETP* 13 451.
[3] Pitaevskii L, Stringari S 2003 *Bose-Einstein Condensation* Oxford University Press, Oxford.
[4] Pethick C J, Smith H 2008 *Bose-Einstein Condensation in Dilute Gases* Cambridge University Press, Cambridge.
[5] Annett J F 2004 *Superconductivity, superfluids, and condensates* Oxford University Press, Oxford.
[6] Ao P and Chui S T 1998 *Phys. Rev. A* 58 4836.
[7] Brankov R A 2002 *Phys. Rev. A* 66 013612.
[8] Mazets I E 2002 *Phys. Rev. A* 65 033618.
[9] Indekeu J O, Lin C -Y, Thu N V, Schaeybroeck B V, Phat T H 2015 *Phys. Rev. A* 91 033615.
[10] Deng Z, Schaeybroeck B V, Lin C -Y, Thu N V, Indekeu J O 2016 Interfacial tension and wall energy of a Bose-Einstein condensate binary mixture: Triple-parabola approximation *Physica A* 444 1027.
[11] Andersen J O 2004 Theory of the weakly interacting Bose gas *Rev. Mod. Phys.* 76 599.
[12] Cornwall J M, Jackiw R, Tomboulis E 1974 Effective action composite operators *Phys. Rev. D* 10 2428.
[13] Phat T H, Hoa L V, Anh N T, and Long N V 2009 Bose-Einstein condensation in binary mixture of Bose gases *Ann. Phys.* 324 2074.
[14] Thu Nguyen Van 2018 The forces on a single interacting Bose-Einstein condensate *Phys. Lett. A* 382 1078.
[15] Biswas S, Bhattacharjee J K, Majumder D, Saha K, Chakravarty N. 2010 Casimir force on an interacting Bose-Einstein condensate *J. Phys. B* 43 085305.
[16] Thu N V, Phat T H and Song P T 2017 *J. Low Temp. Phys.* 186 127.
[17] Takahashi D A, Kobayashi M, Nitta M 2015 Nambu-Goldstone modes propagating along topological defects: Kelvin and ripple modes from small to large systems *Phys. Rev. B* 91 184501.
[18] Schiefle J. and Henkel C. 2009 Casimir energy of a BEC: from moderate interactions to the ideal gas *J. Phys. A* 42 045401.
[19] Thu Nguyen Van and Theu Luong Thi 2017 *J. Stat. Phys.* 168 1.
[20] Thu Nguyen Van and Theu Luong Thi 2019 Finite-size effect on Bose-Einstein condensate mixtures in improved Hartree Fock approximation *Int. J. Mod. Phys. B* 33 1950114.
[21] Thu Nguyen Van and Song Pham 2020 Casimir effect in a weakly interacting Bose gas confined by a parallel plate geometry in improved Hartree-Fock approximation *Physica A* 540 123018.
[22] Floerchinger S and Wetterich C 2009 Superfluid Bose gas in two dimensions *Phys. Rev. A* 79 013601.
[23] Ivanov Yu B, Rick F, Knoll J 2005 Gapless Hartree-Fock resummation scheme for the O(N) model *Phys. Rev. D* 71 105016.
[24] Arfken G B and Weber H J 2005 *Mathematical Methods for Physicists* 6th edn San Diego: Academic.
[25] McCarron D J, Cho H W, Jenkin D L, Koppinger M P, and Cornish S L 2011 *Phys. Rev. A* 84 011603.
[26] Biswas S 2007 Bose-Einstein condensation and the Casimir effect for an ideal Bose gas confined between two slabs *J. Phys. A* 40 9969. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
2653,
1
],
[
2653,
5784,
2
],
[
5784,
8657,
3
],
[
8657,
11477,
4
],
[
11477,
14040,
5
],
[
14040,
16677,
6
],
[
16677,
18770,
7
],
[
18770,
21703,
8
],
[
21703,
24961,
9
]
]
} |
fbb30092508f2fbf4624c8798ad2a0874970e9b8 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 11,
"total-fallback-pages": 0,
"total-input-tokens": 50251,
"total-output-tokens": 17639,
"fieldofstudy": [
"Physics",
"Engineering"
]
} | Unidirectional propulsion of planar magnetic nanomachines
Kevin-Joshua Cohen1, Boris Y. Rubinstein2, Oded Kenneth3, and Alexander M. Leshansky4*
1Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
2Stowers Institute for Medical Research, Kansas City, MO 64110, USA
3Department of Physics, Technion – Israel Institute of Technology, Haifa, 32000, Israel
4Department of Chemical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Steering of magnetic nano-/microhelices by a rotating magnetic field is considered as a promising technique for controlled navigation of tiny objects through viscous fluidic environments. It has been recently demonstrated that simple geometrically achiral planar structures can also be steered efficiently. Such planar propellers are interesting for practical reasons, as they can be mass-fabricated using standard micro/nanolithography techniques. While planar magnetic structures are prone to in-plane magnetization, under the effect of an in-plane rotating magnetic field, they exhibit, at most, propulsion due to spontaneous symmetry breaking, i.e., they can propel either parallel or antiparallel to the rotation axis of the field depending on their initial orientation. Here we demonstrate that actuation by a conically rotating magnetic field (i.e., superposition of in-plane rotating field and constant field orthogonal to it) can yield efficient unidirectional propulsion of planar and magnetized in-plane structures. In particular, we found that a highly symmetrical V-shape magnetized along its symmetry axis which exhibits no net propulsion in in-plane rotating field, exhibits unidirectional in-sync propulsion with a constant (frequency-independent) velocity when actuated by the conically rotating field.
I. INTRODUCTION
Controlled propulsion of artificial micro- and nano-structures that can be actuated and precisely navigated through a fluidic environment has recently attracted considerable attention. While many different approaches ranging from catalytic nanowires to thermally, light- and acoustically-driven nanomachines are being explored, driven propulsion powered by an external rotating magnetic field offering remote, engine-less and fuel-free steering of micro-/nanostructures, is particularly appealing for prospective biomedical applications (see [1, 2] for review).
Originally bio-inspired helical micro/nanopropellers were demonstrated [3, 4] and extensively studied, e.g., [5–8]. Such helical ‘swimmers’ are actuated by the weak (few milli Tesla) uniform in-plane rotating magnetic field and propel unidirectionally along the field rotation axis similar to a twirling bacterial flagella. However, fabrication of three-dimensional (3D) helical micro- and nanoscale structures typically requires complicated fabrication techniques, e.g., “top-down” approach [4], glancing angle deposition [3, 8], direct laser writing [9], biotemplated synthesis using biological spiral structures [10, 11], two-photon polymerization of a curable superparamagnetic polymer composite [12, 13], spiraling microfluidic flow lithography [14], etc. One interesting proposal to circumvent complicated microfabrication is to use one-dimensional soft magnetic nanowires [15, 16] that supposedly acquire helicity when actuated by rotating field due to an interplay of viscous and elastic forces. An alternative method that does not require sophisticated microfabrication involves spontaneous aggregation of magnetic nanoparticles into random-shaped 3D clusters [17, 18]. However, on average such random-shaped clusters appear to be significantly less efficient propellers in comparison to the structures with preprogrammed geometry and magnetization [19].
Another interesting option relies on the fact that geometric chirality is not required for driven propulsion based on rotation-translation coupling. It was recently demonstrated that geometrically achiral planar objects made of three interconnected magnetized microbeads can be steered quite efficiently by an in-plane rotating magnetic field [20, 21]. Such two-dimensional (2D) ferromagnetic propellers are of practical interest, as they can be mass-fabricated via standard photolithography methods [22]. Recently developed microfluidic stop-flow lithography can also be used for high-throughput fabrication of superparamagnetic 2D microstructures with high saturation magnetization [23].
The theory of magnetically driven propulsion of an arbitrary shaped object was developed in [24], suggesting that the notion of chirality should account not just for the object’s geometry, but also for orientation of the magnetic dipolar moment affixed to it. In particular it was predicted that specific magnetization of the geometrically achiral planar object can actually render it chiral resulting in unidirectional propulsion similar to helices. A combined theoretical and experimental study of planar V-shaped structures actuated by an in-plane rotating magnetic (or electric) field was recently conducted in Ref. [25]. The correspondence (depending on orientation of the dipolar moment) between different propulsive solutions was established based on symmetry arguments involving parity, $\hat{P}$, and charge conjugation, $\hat{C}$, as the in-plane rotating magnetic field is invariant under $\hat{P}$.
and $\hat{C}\hat{R}_z$. Here $\hat{R}_2$ stands for rotation by $\pi$ around the field rotation $z$-axis. In general, there could be two stable rotational solutions resulting in different propulsion velocities. In particular, it was found that highly symmetrical achiral ($\hat{P}$-even) V-shaped objects (e.g., with magnetization along $\hat{e}_3$ or $\hat{e}_2$, see Fig. 1a) exhibit no net propulsion at all. Furthermore, it was demonstrated that a V-shaped object, magnetized along any principal axis of rotation will exhibit no net in-sync propulsion regardless of its symmetry [25]. Individual magnetized in-plane (as in Fig. 1a) $\hat{C}\hat{P}$-even objects can efficiently propel due to spontaneous symmetry breaking. However, since $\hat{C}\hat{P}$-symmetry inverts linear velocities, the dual rotational solutions yield propulsion with equal, but opposite velocities (see illustration in Fig. 1b). It was also confirmed experimentally that in agreement with the prediction in [24] the off-plane magnetized V-shaped object with intrinsically broken ($\hat{C}\hat{P}$-and $\hat{P}$-) symmetry, i.e., chiral as well as $\hat{C}\hat{P}$-chiral, can propel unidirectionally.
Since planar micro/nano-structures are prone to in-plane magnetization while uniform off-plane magnetization of multiple samples is not an easy task, the interesting question is whether planar nanopropellers can be steered in a controllable fashion? As it will be shown below, controlled propulsion can be achieved using a conically rotating field, i.e., by adding an extra constant magnetic field along the field rotation $z$-axis breaking the $\hat{C}\hat{R}_z$-symmetry. The role of the constant field is to orient the magnetic moment along the $z$-axis and this results in selection of one of the dual solutions in Fig. 1b (on the left) over the other. We also shall demonstrate that a highly symmetrical planar V-object magnetized along its symmetry axis ($\hat{e}_1$-axis in Fig. 1a) which shows no net propulsion in an in-plane rotating field (see [25]), can be steered unidirectionally by the conically rotating field similar to a magnetic helix.
**II. PROBLEM FORMULATION**
We assume conical rotating magnetic field $H$
$$H = H(\hat{x}\cos \omega t + \hat{y}\sin \omega t + \hat{z}\delta),$$
where $H$ and $\omega$ are, respectively, the amplitude and angular frequency of the rotating field and $H_z = \delta H$ is the value of the constant magnetic field along the field rotation $z$-axis, such that $\tan^{-1}(1/\delta)$ is the cone angle.
We further assume that the motion of the magnetized object is force-free and driven solely by the magnetic torque $L = m \times H$, where $m$ is the magnetic moment affixed to the object. In the zero-Reynolds-number (Stokes) approximation, the condition of the balance of forces and torques acting on the particle reads
$$U = \mathbf{G} \cdot L, \quad \Omega = \mathbf{F} \cdot L.$$ \hspace{1cm} (2)
Here $U$ and $\Omega$ are the translational and angular velocities of body, $\mathbf{G}$ and $\mathbf{F}$ are the coupling and rotation viscous mobility tensors, respectively. The triad of unit eigenvectors, $\{\hat{e}_1, \hat{e}_2, \hat{e}_3\}$ of $\mathbf{F}$ makes up the body-frame principal rotation axes. We fix their order such that the corresponding eigenvalues satisfy $F_1 \leq F_2 \leq F_3$. The lab-frame unit vectors $\{\hat{x}, \hat{y}, \hat{z}\}$ are related to the body-frame axes $\{\hat{e}_1, \hat{e}_2, \hat{e}_3\}$ by a rotation matrix $R$ parameterized by, e.g., the three Euler angles $\varphi$, $\theta$ and $\psi$ (standard “3-1-3” parametrization) describing the instantaneous orientation of the object in the lab frame,
$$R = \begin{pmatrix}
\begin{array}{ccc}
c_\varphi & s_\varphi & 0 \\ -s_\varphi & c_\varphi & 0 \\ 0 & 0 & 1
\end{array}
\end{pmatrix} \cdot \begin{pmatrix}
\begin{array}{ccc}
c_\psi & 0 & 0 \\ 0 & c_\psi & 0 \\ 0 & 0 & 1
\end{array}
\end{pmatrix} \cdot \begin{pmatrix}
\begin{array}{ccc}
c_\theta & s_\theta & 0 \\ -s_\theta & c_\theta & 0 \\ 0 & 0 & 1
\end{array}
\end{pmatrix} = \begin{pmatrix}
\begin{array}{ccc}
c_\varphi c_\psi - s_\varphi s_\psi c_\theta & s_\varphi c_\psi + c_\varphi s_\psi c_\theta & s_\varphi s_\psi s_\theta \\ -c_\varphi s_\psi - s_\varphi c_\psi c_\theta & c_\varphi c_\psi + c_\varphi s_\psi c_\theta & c_\varphi s_\psi s_\theta \\ s_\varphi c_\psi s_\theta & -c_\varphi c_\psi s_\theta & c_\varphi s_\theta
\end{array}
\end{pmatrix},$$
where we use the compact notation: $s_\theta \equiv \sin \theta$, $c_\theta \equiv \cos \theta$, etc. For an arbitrary vector $\mathbf{A}$ we have $A^b = R \cdot A^l$ (or $A^l = R^T \cdot A^b$), where superscripts “$b$” and “$l$” stand for the body- and lab-frame of reference respectively.
The permanent magnetic moment in the body-frame axes is given by
$$m = m \left(n_1 \hat{e}_1 + n_2 \hat{e}_2 + n_3 \hat{e}_3\right),$$
where $n_i$ are projections of the unit vector $\mathbf{n} = m/m = s_\theta c_\psi \hat{e}_1 + s_\theta s_\psi \hat{e}_2 + c_\theta \hat{e}_3$ expressed via the spherical polar, $\Phi$, and azimuthal, $\alpha$, angles, respectively.
**Angular velocity.** It is most convenient to express the problem of driven rotation (the second equation in (2)) in the body-frame where $\mathbf{F} = \text{diag}(F_1, F_2, F_3)$ is fixed and...
the components of the angular velocity $\Omega$ are expressed through the Euler angles via the relations [24]:
$$\Omega_1^b = \dot{\varphi}s_\theta s_\psi + \dot{\theta}c_\psi, \quad \Omega_2^b = \dot{\varphi}s_\theta c_\psi - \dot{\theta}s_\psi, \quad \Omega_3^b = \dot{\varphi}c_\theta + \dot{\psi}, \quad (5)$$
where the dot stands for the time derivative. Expressing the magnetic field (1) in the body-frame components, $H^b = \mathbf{R} \cdot H^l$, the equation $\Omega = \mathbf{F} \cdot \mathbf{m} \times H$ after some algebra reduces to
$$\frac{1}{\omega_0} (\dot{\varphi} s_\theta s_\psi + \dot{\theta} c_\psi) = n_2 \zeta + n_3 [c_\varphi s_\psi + \chi c_\psi], \quad (6)$$
$$\frac{1}{\omega_0} (\dot{\varphi} s_\theta c_\psi - \dot{\theta} s_\psi) = -n_1 \zeta + n_3 [c_\varphi c_\psi - \chi s_\psi], \quad (7)$$
$$\frac{1}{\omega_0} (\dot{\varphi} c_\theta + \dot{\psi}) = -n_1 [c_\varphi s_\psi + \alpha + c_\psi \alpha], \quad (8)$$
where we denote $\zeta = s_\theta s_\varphi + \delta c_\theta$ and $\chi = s_\varphi c_\psi - \delta s_\theta$.
Here $\tilde{\varphi} = \varphi - \omega t$, $n_\perp = \sin \Phi$, $\omega_0 = m H F_\perp$ the characteristic angular frequency with $F_\perp$ being the geometric minor mobilities, $F_\perp^{-1} = (F_1^{-1} + F_2^{-1})/2$ and $p = F_3/F_\perp \geq 1$ and $\varepsilon = (F_2 - F_1)/(F_2 + F_1) \geq 0$ are, respectively, the transverse and the longitudinal anisotropy parameters. For the in-plane rotating field ($\delta = 0$) the Eqs. (6-8) reduce to Eqs. (5-7) in [24].
We look for solutions which turn in-sync with the magnetic field, i.e., rotating about the $z$-axis with angular velocity
$$\Omega = \omega \hat{z} = \omega (s_\theta s_\varphi e_1 + s_\theta c_\psi e_2 + c_\theta e_3), \quad (9)$$
From the comparison of (9) and (5) it follows that the in-sync regime corresponds to constant values of the three Euler angles $\psi, \theta$ and $\tilde{\varphi} = \varphi - \omega t$, so that Eqs. 8 simplify to
$$1 + \varepsilon) \tilde{\omega} s_\theta s_\psi = n_2 \zeta + n_3 [c_\varphi s_\psi + \chi c_\psi], \quad (10)$$
$$(1 - \varepsilon) \tilde{\omega} s_\theta c_\psi = -n_1 \zeta + n_3 [c_\varphi c_\psi - \chi s_\psi] \quad (11)$$
$$p^{-1} \tilde{\omega} c_\theta = -n_1 [c_\varphi s_\psi + \alpha + c_\psi \alpha] \quad (12)$$
where $\tilde{\omega} = \omega/\omega_0$ is the dimensionless actuation frequency.
The Eqs. (10)–(12) shall be used to make analytical progress in some particular cases, e.g., magnetization along principal rotation axes, where one may expect net propulsion (in comparison with the case of $\delta = 0$ where net propulsion is not possible [25]). In general numerical solution of (10)–(12) or time integration of (6)–(8) for some initial values of the angles is required.
Linear velocity. The linear velocity, $U$, can be found in the same way as was done for in-plane rotating field [19, 24, 25], as the constant component of the field $\delta H \hat{z}$ affects propulsion only through dynamic orientation of the propeller. Expressing the magnetic torque, $L$, from the second equation in (2) and substituting it into the first equation in (2), the translational velocity can be readily found as $U = \mathbf{G} \cdot \mathbf{F}^{-1} \cdot \Omega$. By symmetry the time-averaged linear velocity for in-sync actuation is along the $z$-axis. Taking a scalar product on both sides of this equation with $\Omega = \omega \hat{z}$ we readily obtain it in a compact covariant form as
$$\frac{U_z}{\omega \ell} = \mathbf{G} \cdot \mathbf{Ch} \cdot \mathbf{G} = \mathbf{G} \cdot \mathbf{Ch} \cdot \mathbf{G}, \quad (13)$$
where $\mathbf{Ch}$ is a dimensionless chirality matrix given by the symmetric part of $\frac{1}{\ell} \mathbf{G} \cdot \mathbf{F}^{-1}$ with $\ell$ being the characteristic length and $\mathbf{G} = \mathbf{G}/\omega = \hat{z}$ the normalized (unit) angular velocity. It is most convenient to write the RHS of (13) in the body frame whereas $\mathbf{Ch}$ is fixed and $\mathbf{G}$ being expressed via the Euler angles as in (9). Note that $\mathbf{Ch}$ (in contrast to $\mathbf{G}$) is independent of the choice of coordinate origin. Under rotation of the coordinate frame it transforms as a (symmetric) pseudo-tensor.
Applying Eq. (13) to the symmetric V-shaped object (see Fig. 2) whereas $\mathbf{Ch}$ has a pair of identical nonzero off-diagonal entries is straightforward. For such structures the easy rotation axis $e_3$ (corresponding to the largest eigenvalue $F_3$) is always parallel to the line connecting the arms of the V-shape, one minor axes coincides with the symmetry axis and another is perpendicular to the plane of the V-shape. For definiteness we choose the in-plane minor axis (along the symmetry axis) along the line bisecting the acute/obtuse angle formed by the arms of V-shape and pointing away from the vertex, as shown in Fig. 2. It should be noticed however that our convention of fixing the body frame in a way that $F_1 \leq F_2 \leq F_3$ can result in the interchange of minor axes, $e_1 \leftrightarrow e_2$ (and $e_3 \leftrightarrow -e_3$ to keep the frame right-handed) upon varying the V-shape opening angle or the aspect ratio $h:w$ as shown in Fig. 2. Considering for definiteness the case of chubby V-shape shown in Fig. 2b where the only nonzero elements of $\mathbf{G}$ are $G_{13} = G_{31}$, then (13) reduces to
$$\frac{U_z}{\omega \ell} = \mathbf{Ch}_{s_\psi s_\theta}, \quad (14)$$
FIG. 2. Planar V-shaped structures with 120-degree central angle together with their principal rotation axes ($e_1, e_2, e_3$): a) slim structure with rectangular cross section (height-to-width aspect ratio $h:w=1:3$); b) chubby structure (square cross section). The structures are magnetized in-plane and the red arrow stands for the magnetic dipolar moment $\mathbf{m}$.
\[ \begin{align*}
\Omega_1^b &= \dot{\varphi}s_\theta s_\psi + \dot{\theta}c_\psi, \quad \Omega_2^b = \dot{\varphi}s_\theta c_\psi - \dot{\theta}s_\psi, \quad \Omega_3^b = \dot{\varphi}c_\theta + \dot{\psi}, \\
\frac{1}{\omega_0} (\dot{\varphi} s_\theta s_\psi + \dot{\theta} c_\psi) &= n_2 \zeta + n_3 [c_\varphi s_\psi + \chi c_\psi], \\
\frac{1}{\omega_0} (\dot{\varphi} s_\theta c_\psi - \dot{\theta} s_\psi) &= -n_1 \zeta + n_3 [c_\varphi c_\psi - \chi s_\psi], \\
\frac{1}{\omega_0} (\dot{\varphi} c_\theta + \dot{\psi}) &= -n_1 [c_\varphi s_\psi + \alpha + c_\psi \alpha], \\
\Omega = \omega \hat{z} &= \omega (s_\theta s_\varphi e_1 + s_\theta c_\psi e_2 + c_\theta e_3), \\
1 + \varepsilon) \tilde{\omega} s_\theta s_\psi &= n_2 \zeta + n_3 [c_\varphi s_\psi + \chi c_\psi], \\
(1 - \varepsilon) \tilde{\omega} s_\theta c_\psi &= -n_1 \zeta + n_3 [c_\varphi c_\psi - \chi s_\psi], \\
p^{-1} \tilde{\omega} c_\theta &= -n_1 [c_\varphi s_\psi + \alpha + c_\psi \alpha], \\
\frac{U_z}{\omega \ell} &= \mathbf{G} \cdot \mathbf{Ch} \cdot \mathbf{G} = \mathbf{G} \cdot \mathbf{Ch} \cdot \mathbf{G}.
\end{align*} \]
where \( \widetilde{C}h = Ch_{13} = Ch_{31} = G_{13}(F_{1}^{-1} + F_{3}^{-1})/2\ell \) is the pseudo-chiral coefficient [24, 25].
When the same V-shaped propeller is not turning in-sync with the field, the propulsion velocity is given by (see Appendix A):
\[
\frac{U_{c}}{\ell} = \text{Ch}\psi \sin \phi \dot{\psi} + G_{13} \left( \frac{1}{F_{3}} s_{\psi} \sin \psi \dot{\psi} + \frac{1}{F_{1}} c_{\psi} c_{\theta} \dot{\theta} \right). \tag{15}
\]
Clearly, for in-sync actuation \( \dot{\psi} = 0, \dot{\phi} = \omega \) and (15) reduces to (14). When the minor axes interchange (see Fig. 2a) the similar equations apply with \( \psi \rightarrow \pi/2 - \psi \), \( \theta \rightarrow \pi - \theta \) and \( G_{23} \) replacing \( G_{13} \) everywhere.
### III. HYDRODYNAMIC MOBILITIES OF PLANAR V-STRUCTURES
We apply particle-based method [26] for computing mobility tensors \( \mathbf{F}, \mathbf{G} \), the resulting anisotropy parameters \( \rho, \varepsilon \) and the chirality matrix \( \text{Ch} \) for planar V-shaped propellers. This technique is based on multipole expansion of the Lamb’s spherical harmonic solution of the Stokes equations. The object is approximated by (i) monolayer of touching rigid spheres of radius \( a \), as shown in Figs. 3a–c, e or (ii) a hollow structure with beads retracing the perimeter (see Figs. 3d,f). Thickness of the propeller is controlled by varying the number of beads approximating the object. This particle-based approach was previously applied for modeling self-motion of an undulating flexible filament [27], magnetically driven propulsion of rigid helical [6, 8] and arc-shaped [24, 25] structures and random fractal-like aggregates [19].
The results of the computation are collected in Table I for different values of the central angle \( \gamma \) of the V-shape.
For straight stripes \( (\gamma = \pi) \) rotation-translation coupling vanishes, \( \mathbf{G} = 0 \), as can be anticipated from symmetry. Under the convention for the body frame selection (see Sec. II), for generic value of \( \gamma \) the coupling matrix \( \mathbf{G} \) has exactly two nontrivial off-diagonal elements \( G_{i3} = \widetilde{G}_{i3} \) with either \( i = 1 \) or, respectively, \( i = 2 \), depending on geometry of the structure. We find \( G_{13} < 0 \) for V-shapes with the opening angle \( \gamma = \pi/2 \), while for V-shapes with the opening angle \( \gamma = 2\pi/3 \) upon increasing the slenderness the minor axes interchange, \( e_{2} \leftrightarrow e_{1} \) (as illustrated in Fig. 2) leading to a sudden change of sign of \( G_{i3} \) and \( \text{Ch} \) in Table I, such that \( G_{23} > 0 \) becomes the only nontrivial entry.
As one may expect for Stokes flows, the computed rotational and coupling mobilities of hollow 2D structures (in Fig. 3d,f) are quite close to these found for the respective densely packed structures (in Fig. 3c,e).
FIG. 3. Planar V-shapes with 90-degree central angle and varying thickness (width-to-height aspect ration, \( w:h \)). Bead-made structures approximate hydrodynamic mobilities of the planar V-shapes. a) \( h: w = 1:1 \); b) \( h: w = 1:2 \); c) \( h: w = 1:3 \); d) \( h: w = 1:3 \) (hollow structure); e) \( h: w = 1:4 \); f) \( h: w = 1:4 \) (hollow structure).
### IV. ACTUATION OF V-SHAPED PROPELLERS BY A CONICAL MAGNETIC FIELD
In this section we shall consider a number of analytically tractable cases and approximate solutions. In the analysis below we assume, for definiteness, the orientation of the principal axes as shown in Fig. 2b. Modification of the present analysis for the slim structures (as in Fig. 2a) is straightforward.
#### A. Magnetization along the symmetry \( e_{2} \)-axis
Assuming magnetization along the symmetry axis \( e_{2} \), i.e., \( n_{1} = n_{3} = 0 \) and \( n_{2} = n_{\perp} = 1 \), we have \( \Phi = \alpha = \pi/2 \). Then from (11) it follows that \( \psi = \pm \pi/2 \) (it can be readily seen that \( \sin \theta = 0 \) is not a solution). Substituting these values of the magnetization angles and \( \psi \) into Eqs. (10,12) we obtain
\[
s_{2\theta} = \pm \frac{2\delta}{\omega(1 + \varepsilon - p^{-1})}, \tag{16}
\]
which imposes restriction on the value of \( \delta \) (or \( \omega \)) for which in-sync solution materializes. The \( \pm \) signs correspond to two rotational solutions with acute and obtuse wobbling angle \( \theta \), respectively. Then, knowing \( \theta \) the Euler angle \( \phi \) can be found from (10) as
\[
s_{\phi} = \pm (1 + \varepsilon)\omega - \delta \cot \theta. \tag{17}
\]
The larger root gives the step-out frequency:
\[
\tilde{\omega}_{\sigma_0} = \frac{1 + \varepsilon_p + \sqrt{(1 + \varepsilon_p)^2 - 4(1 + \delta^2)\varepsilon_p}}{2(1 + \varepsilon)},
\]
(19)
where \(\varepsilon_p = p(1 + \varepsilon)\). With \(\tilde{\omega}_{\sigma_0}\) at hand, one can readily determine the precession angle at the step-out, \(\theta_{\sigma_0}\), from, e.g., Eq. 16. It can also be shown that at the step-out the angle \(\beta\) between magnetization \(m\) and the field \(H\) attains its maximal value of \(\pi/2\), maximizing the magnetic torque.
As an example, for the V-structure with a cross-section aspect ratio \(h:w=1:2\) and central angle \(\gamma = 120^\circ\) (see Table I), we have \(p = 2.74\) and \(\varepsilon = 0.004\). For this sample propeller, the wobbling angle at the step-out, \(\theta_{\sigma_0}\), increases with \(\delta\) up to a maximum value \(\approx 31.1^\circ\) at \(\delta = 0.53\) (see Fig. 4a); above this value of \(\delta\) no in-sync solution exist. The step-out frequency in Eq. (19) slightly diminishes with \(\delta\) (see Fig. 4b). For instance for \(\delta = 0.1\) and 0.4 we have \(\tilde{\omega}_{\sigma_0} = 2.72\) and 2.44, respectively. Notice that no stable in-sync solutions can be found at \(\delta \gtrsim 0.478\) (see Fig. 4b and the stability analysis below).
Substituting the steady-state solution for \(s_{2g}\) from (16) and \(\psi = \pm \pi/2\) into (14) we readily obtain the in-sync propulsion velocity of a magnetic V-shape:
\[
\frac{U_z}{\omega_0} = \frac{1}{\varepsilon_p} \frac{2\delta}{(1 + \varepsilon - p^{-1})},
\]
(20)
which surprisingly is independent of the actuation frequency.
In contrast to helical propellers which swim the best when precession is minimized (similar to a corkscrew twirling around its long axis), efficient propulsion of planar structures requires considerable precession [24]. Since the wobbling angle, \(\theta\), diminishes with the actuation frequency as \(s_{2g} \sim 1/\omega\), while the propulsion velocity \(U_z \sim \omega s_{2g}\), reduction of the precession angle is compensated exactly by the increasing rotation rate, rendering \(U_z\) constant in a limited range of in-sync actuation frequencies \(\omega_s < \omega < \omega_{\sigma_0}\). We consider Eq. (20) as a major result of the present paper. Animations of the in-sync driven rotation and propulsion of the sample propeller (with \(\gamma = 120^\circ\) and \(h:w=1:2\), see Table I) are provided in [28] for \(\delta = 0.3\) and several values of the actuation frequency \(\omega/\omega_0\). Notice that in the movies the magnetic moment \(m\) rotates in the \(xy\)-plane of the field. A simple way to show that, is to note that for in-sync solution we have \(\Omega \parallel \hat{z}\), while the magnetic torque \(L = \mathbf{F}^{-1} \cdot \Omega \times m\).
Thus it follows that \(m \cdot \mathbf{F}^{-1} \cdot \hat{z} = 0\) and since \(\mathbf{F}\) is symmetric it means that \(\mathbf{F}^{-1} \cdot m \parallel \hat{z}\). For an object magnetized along one of the principal axes (i.e., eigenvectors of \(\mathbf{F}\)) we have \(\mathbf{F}^{-1} \cdot m \parallel m\) so that \(m \perp \hat{z}\).
The frequency dependence of the dimensionless propulsion velocity, \(U_z/v_0\) [29], of the same sample V-shape, where \(v_0 = \omega_0/2\pi\) stands for the characteristic (cyclic) frequency, is depicted in Fig. 5 for several values of \(\delta\). The Euler angles were obtained by numerical integration of Eqs. (6)-(8) and the propulsion velocity computed using Eq. (15). In agreement with the theory, the numer-
### TABLE I. Comparison of hydrodynamic mobilities of planar V-shaped structures. \(\gamma\) is the opening angle; \(t\) and \(h\) stand for either filled or hollow cluster, respectively; \(h:w\) is the height-to-width aspect ratio; \(\mathcal{F}\) are the eigenvalues of the respective dimensionless rotational mobility tensor \(\eta^2\mathbf{F}\); \(\mathcal{G}_i\) (\(i = 1\) or \(2\)) are the unique nonzero off-diagonal elements of the symmetrized coupling matrix \(\eta^2\mathbf{G}\); \(\mathcal{C}_h = \mathcal{G}_i(\mathcal{F}_i^{-1} + \mathcal{F}_j^{-1})/2\ell\) is the pseudo-chirality coefficient; \(\varepsilon\) and \(p\) are the transversal and longitudinal rotational anisotropy parameters, respectively.
| \(\gamma\) | \(h:w\) | \(t\) | \(h\) | \(\mathcal{F}_1\) | \(\mathcal{F}_2\) | \(\mathcal{F}_3\) | \(\mathcal{G}_3\times(\times 10^2)\) | \(\mathcal{C}_h\times(\times 10^2)\) | \(\varepsilon\) | \(p\) |
|--------------|----------------|----------------|-------|-----------------|----------------|----------------|----------------|----------------|----------------|----------------|
| \(\pi/2\) | | | | | | | | | | |
| 1:1 | f \(0.650\) | 0.755 | 0.118 | \(-0.470\) | \(-0.554\) | 0.068 | 1.685 | | | |
| 1:2 | f \(0.913\) | 1.050 | 0.175 | \(-0.578\) | \(-0.482\) | 0.070 | 1.790 | | | |
| 1:3 | f \(1.046\) | 1.161 | 0.195 | \(-0.620\) | \(-0.455\) | 0.052 | 1.780 | | | |
| 1:4 | f \(1.131\) | 1.219 | 0.206 | \(-0.641\) | \(-0.439\) | 0.037 | 1.760 | | | |
| 1:1 | f \(0.820\) | 0.861 | 0.207 | \(-0.933\) | \(-0.799\) | 0.024 | 2.410 | | | |
| 1:2\(^\ast\) | f \(1.069\) | 1.078 | 0.245 | \(-1.058\) | \(-0.675\) | 0.004 | 2.740 | | | |
| 1:3 | f \(1.164\) | 1.206 | 0.326 | 1.097 | 0.620 | 0.017 | 2.810 | | | |
| 1:4 | f \(1.275\) | 1.376 | 0.994 | 1.438 | 0.702 | 0.038 | 3.020 | | | |
| 1:1 | f \(0.942\) | 0.942 | 3.137 | 0 | 0 | 0 | 3.520 | | | |
| 1:2 | f \(1.037\) | 1.088 | 4.553 | 0 | 0 | 0.024 | 4.290 | | | |
| 1:3 | f \(1.086\) | 1.195 | 5.048 | 0 | 0 | 0.048 | 4.430 | | | |
| 1:4 | f \(1.105\) | 1.195 | 5.057 | 0 | 0 | 0.045 | 4.420 | | | |
| 1:1 | f \(1.113\) | 1.268 | 5.298 | 0 | 0 | 0.065 | 4.470 | | | |
| 1:4 | f \(1.141\) | 1.275 | 5.795 | 0 | 0 | 0.056 | 4.430 | | | |
\(\ast\) this sample is used in calculations throughout the paper
\(\ast\) rectangular stripes
In the regime we found that the solution converges to a stable closed orbit solution (limit cycle) in \((\theta,\psi)\)-plane (with \(\varphi\) periodic modulo \(2\pi\)) with average propulsion velocity described by the dashed line [30]. It should be noted however that the velocity oscillates strongly over the period of this limit cycle. Moreover it turns out that the convergence to the limit cycle is quite slow so that the standard deviation from the mean velocity for \(\delta = 0.2\) at \(\omega/\omega_0 = 3\) is \(\sim 10\%\) when averaging over 100 field revolutions while it drops to \(\sim 1\%\) when averaging over 1000 periods.
Notice that reversing the magnetization, \(\mathbf{m} \rightarrow -\mathbf{m}\) yields a parity-transformed object having the reverse propulsion velocity, \(U_z \rightarrow -U_z\). It can also be shown explicitly from Eqs. (10)-(12) since taking \(\alpha = -\pi/2\) and \(n_2 = -1\) yields, as before, \(\psi = \pm \pi/2\), while the corresponding \(\pm\) signs in Eqs. (16) and in (17) change to \(\mp\). Thus, the propulsion velocity \(U_z \sim s_\theta s_\varphi\) in (14) changes sign.
It should also be stressed that net propulsion occurs for the less symmetric (\(\tilde{P}\))-chiral propeller [25], while (\(\tilde{P}\))-achiral propeller (i.e., \(\mathbf{m}\) oriented along \(e_3\) or \(e_1\)) yields no propulsion even when a constant \(H_z\) field is present, as we shall see below. Please recall that for \(\delta = 0\) magnetization along any principal rotation axis yielded no net propulsion [25], while here we have shown that adding a static field along the field-rotation axis results in unidirectional propulsion similar to magnetic helices.
**Stability of the in-sync solutions.** To study stability of the above in-sync solution we substitute \(n_1 = n_3 = 0\), \(n_2 = n_\perp = 1\) and \(\Phi = \alpha = \pi/2\) into the Eqs. (6)-(8) governing the rotational dynamics and obtain:
\[
\frac{1}{\omega_0} (\dot{\varphi} s_\theta s_\varphi + \dot{\theta} c_\varphi) = s_\theta s_\varphi + \delta c_\theta, \quad (21)
\]
\[
\frac{1}{\omega_0} (\dot{\varphi} s_\theta c_\varphi - \dot{\theta} s_\varphi) = 0, \quad (22)
\]
\[
\frac{1}{\rho c_\theta} (\dot{\varphi} c_\theta + \dot{\psi}) = -c_\psi c_\varphi + s_\psi (s_\varphi c_\theta - \delta s_\theta). \quad (23)
\]
We further perturb the steady solution by adding small
disturbances to the steady-state values of the angles:
\[ \theta = \theta_0 + \theta_1 e^{\lambda t}, \varphi = \tilde{\varphi}_0 + \omega t + \varphi_1 e^{\lambda t}, \psi = \frac{\pi}{2} + \psi_1 e^{\lambda t}, \]
where \( \theta_0 < \pi/2 \) and \( \tilde{\varphi}_0 \) are the steady in-sync solutions of Eqs. (16) and (17), respectively, and \( \lambda \) is the perturbation growth rate. Substituting this ansatz into (21-23) and linearizing over the perturbation amplitudes, \( \mathbf{u} = (\theta_1, \psi_1, \varphi_1) \), we readily obtain the homogeneous system of equations, \( P \mathbf{u} = 0 \), where
\[
P = \begin{pmatrix}
\delta \csc \theta_0 & 0 & s_{\theta_0}(\tilde{\lambda} + \tilde{\lambda}c - c\tilde{\varphi}_0) \\
\lambda & \tilde{\omega} s_{\theta_0} & 0 \\
p \delta \sec \theta_0 & \tilde{\lambda} - pc\tilde{\varphi}_0 & c_{\theta_0}(\tilde{\lambda} - pc\tilde{\varphi}_0)
\end{pmatrix},
\]
where \( \tilde{\lambda} = \lambda/\omega_0 \). The solvability condition \( \det P = 0 \) yields the cubic equation \( \lambda^3 + q\lambda^2 + r\lambda + s = 0 \) where the coefficients after some algebra reduce to
\[
q = -\frac{(1 + p + \varepsilon p) \cos \tilde{\varphi}_0}{1 + \varepsilon},
\]
\[
r = \frac{p \cos^2 \tilde{\varphi}_0 + \delta \tilde{\omega}(\cot \theta_0 - p \tan \theta_0(1 + \varepsilon))}{1 + \varepsilon},
\]
\[
s = -\frac{2p \delta \tilde{\omega} \cot \theta_0 \cos \tilde{\varphi}_0}{1 + \varepsilon}.
\]
In general, the stability criterion, i.e., real part of all three roots \( \lambda \) should be negative, requires \( q, r, s > 0 \) together with the condition \( qr > s \) [31].
The condition \( q > 0 \) readily gives \( \cos \tilde{\varphi}_0 < 0 \). This condition is also evident from minimizing the magnetic energy, which in this case reduces to \( E = -\mathbf{m} \cdot \mathbf{H} = mH e\tilde{\varphi}_0 \). Notice that this condition ceases to hold exactly at the frequency \( \omega_{\lambda=0} \). The condition \( s > 0 \) then yields \( \cot 2\theta_0 > 0 \). Since we consider the solution with \( \sin 2\theta_0 > 0 \), it follows that \( \cos 2\theta_0 > 0 \) resulting in \( 0 < \theta_0 < \pi/4 \). Introducing \( x = \cot \theta_0 > 1 \) and using (16) we can write
\[
s_{2\theta_0} = \frac{2x}{1 + x^2} = \frac{2\delta p}{\tilde{\omega}(p + p\varepsilon - 1)} \equiv A^{-1}.
\]
Substituting \( x = A + \sqrt{A^2 - 1} > 1 \) into the expression for \( f(1 + \varepsilon) = c_{\tilde{\phi}_0}^2 + \tilde{\omega} \delta(x/p - (1 + \varepsilon)/x) \) and using \( s_{\theta_0} = (1 + \varepsilon)\omega - \delta x \) to eliminate \( \tilde{\varphi}_0 \), we obtain a condition on \( x \) from \( r/s > q > 0 \). The final stability criterion on \( \theta_0 \) reads
\[
\cot \theta_0 > \max \left[ 1, \frac{2p \delta \tilde{\omega}(1 + \epsilon_p + \epsilon_p^2)}{p^2(1 + \delta^2)(1 + \epsilon_p - 2\tilde{\omega}^2)} \right]. \tag{24}
\]
where \( \epsilon_p = p(1 + \varepsilon) \). The second condition in (24) imposes stricter restrictions on \( \theta_0 \) and \( \omega \) in comparison to those imposed by Eqs. (16), (17) at higher values of \( \delta \) and, in fact, no stable in-sync solutions can be found already for \( \delta \geq 0.478 \) (see Fig. 4).
The real part of the dimensionless growth rates \( \text{Re}(\lambda/\omega_0) \) corresponding to the in-sync solution with \( \theta_0 < \pi/4 \) for \( \delta = 0.1 \) (stable) and \( \delta = 0.48 \) (unstable) are depicted in Figs. 6a,b vs. scaled frequency \( \omega/\omega_0 \) for the V-shaped propeller shown in the inset in Fig. 5.
**FIG. 6.** Real part of the perturbation growth rate, \( \text{Re}(\lambda/\omega_0) \), vs. the actuation frequency \( \omega/\omega_0 \) for a V-structure in Fig. 5: a) \( \delta = 0.1 \) (stable); b) \( \delta = 0.48 \) (unstable).
B. Magnetization along the rotation easy-axis \( e_3 \)
When \( m \) is oriented along \( e_3 \), i.e., \( n_3 = 1 \) and \( n_1 = n_2 = n_\perp = 0 \), we have \( \Phi = 0 \). Then from Eq. (12) we immediately have \( \epsilon_0 = 0 \) and \( \theta = \pm \pi/2 \). Then from (14) it follows that \( U_z = 0 \). This regime corresponds to tumbling.
C. Off-plane magnetization along \( e_1 \)-axis
When \( m \) is parallel to \( e_1 \), i.e., \( n_1 = n_\perp = 1 \) and \( n_2 = n_3 = 0 \), we have \( \Phi = \pi/2 \) and \( \alpha = 0 \). Then from Eq. (10) we find that \( (1 + \varepsilon)\tilde{\omega} s_{\tilde{\phi}_0} s_{\psi_0} = 0.0 \), i.e., \( \psi = 0 \) or \( \pi \). For these values of \( \psi \) we have \( U_z = 0 \) in (14). Notice that the wobbling angle \( \theta \) found from (11) and (12) is nontrivial:
\[
s_{2\theta_0} = \mp \frac{2\delta}{\tilde{\omega}(1 - \varepsilon - p^2)}, \tag{25}
\]
where \( \mp \) holds for \( \psi = 0 \) and \( \pi \), respectively. This means that the object will undergo precession with a finite angle \( \theta \) which is not accompanied by net propulsion in contrast to magnetization along the symmetry axis [32].
D. Magnetization in $e_1 e_2$-plane, approximate solution
When $m$ is oriented perpendicular to the rotation easy-axis $e_3$ (i.e. $n_3 = 0, \Phi = \pi/2$), it is possible to find an approximate solution assuming $\varepsilon = 0$ (i.e. cylindrical approximation). In this case it readily follows from Eqs. (10)–(11) that $t_\psi = -t_\alpha$, meaning $\psi = -\alpha$ or $\psi = \pi - \alpha$. Then subtracting Eq. (12) multiplied by $s_\theta$ from (11) multiplied by $c_\theta/c_\psi$ we obtain
$$s_{2\theta} = \pm \frac{2\delta}{\omega (1 - p^{-1})},$$
(26)
where $\pm$ corresponds respectively to $\psi = \pi - \alpha$ (for $0 < \theta < \pi/2$) and $\psi = -\alpha$ (for $\pi/2 < \theta < \pi$). Thus using $s_\psi = \pm s_\alpha$ and (14) at the zeroth order approximation in $\varepsilon$ we arrive at
$$\frac{U_z}{\omega_0 \delta} \approx \bar{C}_n s_\alpha \frac{2\delta}{(1 - p^{-1})}.$$
(27)
The transverse (to $e_3$) magnetization also results in unidirectional propulsion with constant velocity as was found for the in-plane magnetization along $e_2$ in Sec. IV A. Notice that the propulsion velocity in (27) attains its maximum value at $\alpha = \pi/2$, corresponding to $m || e_2$, which agrees with the exact result (20) up to $O(\varepsilon)$.
The in-sync propulsion (27) persists in a limited range of actuation frequencies, $\bar{\omega}_s < \bar{\omega} < \bar{\omega}_w$, $\bar{\omega}$. Considering a solution corresponding to an acute precession angle $\theta$ and noting that the solution of the rotational problem assuming cylindrical anisotropy does not depend on $\alpha$, we find that $\bar{\omega}_s$ and $\bar{\omega}_w$ are given to the first approximation by the respective expressions (18) and (19) at $\varepsilon = 0$, such that
$$\frac{2\delta}{1 - p^{-1}} < \bar{\omega} < \frac{1}{2}(1 + p + \sqrt{(p - 1)^2 - 4p\delta^2}).$$
(28)
E. Arbitrary magnetization, $O(\delta)$ asymptotic theory
Although we could not find a closed form solution for an arbitrary magnetization for finite $\delta$, it is possible to to take advantage of the cylindrical approximation ($\varepsilon \approx 0$) for which an exact analytically solution is known for an in-plane rotating field for $\delta = 0$ (see [24]), and construct a small $O(\delta)$ expansion around it. This approximation provides closed-form solutions for the low-frequency “tumbling” ($\theta = \pi/2$) and high-frequency “wobbling” ($\theta < \pi/2$) regimes of in-sync actuation. The explicit form of the “tumbling” solution at low frequencies, $0 < \bar{\omega} < \bar{\omega}_w$, where $\bar{\omega}_w = c_d$, is given by
$$\theta = \pi/2, \quad \psi = -\alpha, \quad \bar{\phi} = -\Phi + \arccos \bar{\omega}.$$
(29)
At higher frequencies $\bar{\omega}_w < \bar{\omega} < \bar{\omega}_w$, where the step-out frequency is $\bar{\omega}_w = \sqrt{c_d s_d + s_d p^2}$, the two symmetric modes of the wobbling solution are given by
$$\theta_1 = \arcsin \left(\frac{\bar{\omega}}{c_d} \right), \quad \psi_1 = -\alpha - \arcsin \left(\frac{c_d \bar{\omega}}{ps_d} \right), \quad (30)$$
$$\theta_2 = \pi - \theta_1, \quad \psi_2 = -2\alpha - \psi_1.$$
(31)
where $\bar{\phi}_1 = \bar{\phi}_2 = 0$.
We therefore look for a solution to the rotational problem for finite $0 < \delta < \frac{1}{2}$ as regular perturbation in $\delta$ via $\theta = \theta^0 + \delta \theta^1 + \ldots, \psi = \psi^0 + \delta \psi^1 + \ldots, \bar{\phi} = \delta \phi^1 + \ldots$, where the superscript “$0$” stands for the zero-order “tumbling” solution (29). Substituting these expansions into Eqs. (10)–(12), collecting $O(\delta)$ terms and solving the resulting system of equations for the first-order corrections to the Euler angles in “tumbling” regime gives:
$$\{\theta^1, \psi^1\} = -\frac{\{ps_\phi, c_\psi\}}{(ps_\phi c_{\bar{\phi}_0} - c_\phi c_{\bar{\phi}_0} + \bar{\omega})}, \quad \varphi^1 = 0.$$
(32)
Analogous expansion around the zero-order “wobbling” solution in Eq. (30)-(31) yields the following $O(\delta)$-correction (identical for both solution branches):
$$\{\theta^1, \psi^1\} = \frac{\{\bar{\omega} \sqrt{p^2 s_{\bar{\phi}} + c_d^2 - \bar{\omega}^2}, \bar{\omega} \bar{\phi} \sec \Phi\}}{(p - 1)(c_d^2 - \bar{\omega}^2)}, \quad (33)$$
and
$$\varphi^1 = \frac{(\bar{\omega}^2 + (p - 1)c_d^2) \sqrt{\bar{\omega}^2 - c_d^2} \sec \Phi}{(p - 1)(c_d^2 - \bar{\omega}^2)}.$$
Although the regular asymptotic expansions in (32)-(33) break down in the vicinity of of the tumbling-to-wobbling transition, they are expected to closely approximate the solution elsewhere, i.e., except for the vicinity of $\bar{\omega}_w$.
To illustrate the applicability of this approximation we compute the propulsion velocity of V-shaped propeller magnetized in its plane by numerically integrating Eqs. (6)-(8) to find the solution of the rotational problem, and then compare these numerical result with $O(\delta)$ asymptotic prediction. When the V-shape is magnetized in its plane (but not along one of the principal rotation axes), it can efficiently propel even if actuated by an in-plane rotating magnetic field (i.e., for $\delta = 0$) above certain actuation frequency in a “wobbling” regime by a spontaneous symmetry breaking [25], whereas it can move in either ($\pm z$) direction depending on its initial orientation. The resultant symmetric velocity-frequency dependence is depicted in Fig. 7 (gray solid line). Turning on the constant $H_z$ field removes the degeneracy between two branches of the symmetric pitchfork “balloon” that bifurcates into a continuous (lower) branch and an isolated (upper) branch materializing over a limited range of actuation frequencies (red solid lines). In other words, symmetric pitchfork “balloon” is structurally unstable and it bifurcates similarly to the imperfection-sensitivity diagram of compressional buckling of an elastic rod [33].
The frequency range of the isolated solution branch shrinks as $\delta$ increases and disappears completely for
\[ \delta \approx 0.18 \] (see the blue curve in Fig. 7). The vanishing of the second branch of the solution can potentially be used for enhanced passive control of propulsion of planar magnetic micro/nanomotors. The effect of turning on the static \( H_z \) field is analogous to the effect of transverse rotational anisotropy of the magnetic propeller driven by an in-plane rotating field with \( \varepsilon \) (rather than \( \delta \)) playing a role of the “imperfection parameter” in bifurcation of the symmetric pitchfork “balloon” dependence (see Fig. 4 in [24]).
\[ \delta \approx 0.18 \] (see the blue curve in Fig. 7). The vanishing of the second branch of the solution can potentially be used for enhanced passive control of propulsion of planar magnetic micro/nanomotors. The effect of turning on the static \( H_z \) field is analogous to the effect of transverse rotational anisotropy of the magnetic propeller driven by an in-plane rotating field with \( \varepsilon \) (rather than \( \delta \)) playing a role of the “imperfection parameter” in bifurcation of the symmetric pitchfork “balloon” dependence (see Fig. 4 in [24]).
FIG. 7. The dimensionless propulsion velocity of the V-shape structure (the same as in Fig. 5) with in-plane magnetization for \( \Phi = \pi/4, \alpha = -\pi/2 \) (see the inset) as a function of the actuating frequency \( \omega/\omega_0 \) for different magnitudes of the constant magnetic field: \( \delta = 0 \) (gray), \( \delta = 0.1 \) (red) and \( \delta = 0.2 \) (blue). Solid lines stand for the stable in-sync numerical solution, long-dashed lines to asynchronous solutions and short-dashed lines to \( \mathcal{O}(\delta) \) asymptotic approximation.
The dashed color lines in Fig. 7 correspond to small-\( \delta \) approximation for the in-sync velocity (14) upon substituting the first-order expansions for the Euler angles, \( \theta = \theta^0 + \delta \theta^1, \psi = \psi^0 + \delta \psi^1 \) using Eqs. (29) and (32) at low frequencies or Eqs. (31) and (33) at high frequencies. It can be readily seen that the agreement between the numerical results and \( \mathcal{O}(\delta) \) asymptotic theory is quite accurate, except at the the vicinity of \( \tilde{\omega}_{1-w} \) where both expansions break down. The step-out frequency is only slightly altered by finite \( \delta \) and \( \varepsilon \) and can be predicted quite accurately by the expression \( \tilde{\omega}_{1-w} = \sqrt{c_{\theta}^2 + s_{\psi}^2 \delta^2} \).
V. CONCLUDING REMARKS
As a magnetized object is driven by an externally applied magnetic field, the equations governing its evolution are invariant only under symmetries which preserve this field. The in-plane rotating magnetic field \( H = H(x \cos \omega t + y \sin \omega t) \) is invariant under parity \( \hat{P} \) and \( \hat{C} \hat{R}_z \) that involves charge conjugation. It was demonstrated in [25] that highly symmetrical (achiral, i.e., \( \hat{P} \)-even) planar V-shaped objects exhibit no net propulsion while individual less symmetrical (\( \hat{C} \hat{P} \)-even) propellers can propel quite efficiently. In the latter case the propulsion direction, i.e., \( +z \) or \( -z \), is controlled by the object initial orientation which serves as to “spontaneously break the symmetry”, thus a large collection of such propellers having random initial orientations would at most exhibit symmetric spreading with zero ensemble average velocity. This finding is relevant to practical applications, as it indicates that a collection of 2D ferromagnetic micro/nanomotors that are prone to in-plane magnetization and can be fabricated using standard lithography methods, could not be steered in a controlled fashion. Particular orientation of the magnetic moment, \( \mathbf{m} \), rendering the V-shape \( \hat{C} \hat{P} \)-chiral does yield unidirectional propulsion typically associated with helical structures, however, it requires off-plane magnetization which is not easy to achieve.
It was pointed out in [25] that \( \hat{C} \hat{R}_z \)-symmetry is special to the case of plane rotating field and it would be interesting to explore modification of the actuating field that breaks this symmetry. In the present paper we examined how the results of [25] change upon adding a constant magnetic field along the field rotation \( z \)-axis that breaks the \( \hat{R}_z \)-\( \hat{C} \)-symmetry, but preserves \( \hat{P} \)-symmetry. Our analysis confirms that such modification of the actuating field removes the degeneracy of the plane rotating field and results in enantiomeric selection of the propulsion direction of magnetized in-plane symmetric V-shaped objects (see Fig. 7). Surprisingly, magnetization along the V-shape symmetry axis (rendering the 2D object \( \hat{P} \)-chiral) results in unidirectional in-sync propulsion with constant (frequency-independent) speed in a limited range of frequencies (see Fig. 5). Recall that for an in-plane rotating magnetic field, a magnetization along any principal axis yielded no propulsion. The \( \hat{P} \)-even object magnetized along a principal axis still exhibits no propulsion even when actuated by this less symmetrical conically rotating field.
Note that for highly symmetrical (\( \hat{C} \hat{P} \)-achiral) V-shaped propellers the orientation of the constant field controls the direction of propulsion, similar to what was observed for flexible magnetic nanowires in [16]. For instance, the direction of propulsion in Fig. 5 will not change upon reversal of the direction of the field rotation. The results shown in Fig. 7 demonstrate that the same holds more generally provided that \( \delta \) is not too small. For rigid magnetic helices, on the other hand, the propulsion direction is controlled by the rotation direction of the magnetic field and its intrinsic handedness, while reversal of propulsion is anticipated upon reversal of the field rotation. The flexible nanowires in [16] preserved the propulsion direction upon reversal of the field rotation because they had no intrinsic handedness and the acquired chirality was controlled by the direction of the field rotation.
The developed theory of magnetic actuation using a conically rotating field should be most relevant towards
enhanced control of propulsion of swarms of 2D micro/nanopropellers without the need of individual-level feedback control [20].
ACKNOWLEDGEMENT
This work was supported in part by the Israel Science Foundation (ISF) via the grant No. 1744/17 (A.M.L.). The authors wish to thank Johannes Sachs and Peer Fischer for fruitful discussions.
Appendix A PROPELLION OF A SYMMETRIC V-SHAPED PROPELLER
In the laboratory frame, the translational velocity of a propeller is $U^l = RF^T \cdot U^b$ where $R^T$ is the transposed rotation matrix. From Eqs. (2) we have $U^b = \mathbf{G} \cdot L^b = \mathbf{G} \cdot \mathbf{F}^{-1} \cdot \Omega^b$ where the components of the angular velocity $\Omega^b$ in the body-frame are determined by Eq. (5). For the chubby V-shape propeller (as in Fig. 2b), the only non-trivial entries of the coupling matrix $\mathbf{G}$ are $G_{13} = G_{31}$. Therefore the linear velocity in the body-frame reads
$$U^b = \frac{G_{13}}{F_3} \cdot c_0 e_1 + \frac{G_{31}}{F_1} \Omega_1^b e_3.$$ (A1)
Thus, the components of the translational velocity in the laboratory frame read:
$$U_x = \frac{G_{13}}{F_3} (c_0 c_\psi - s_\omega s_\psi c_\theta) \Omega_3^b + \frac{G_{13}}{F_3} s_\psi s_\theta \Omega_1^b,$$
$$U_y = \frac{G_{13}}{F_3} (s_\omega c_\psi + c_\omega s_\psi c_\theta) \Omega_3^b - \frac{G_{13}}{F_3} c_\psi s_\theta \Omega_1^b,$$
$$U_z = \frac{G_{31}}{F_1} s_\psi s_\theta \Omega_3^b + \frac{G_{31}}{F_1} c_\psi c_\theta \Omega_1^b.$$ (A2)
It is seen that in the in-sync regime where $\varphi = \omega t + \text{Const}$, $\psi = \text{Const}$, $\theta = \text{Const}$, the components $U_x$ and $U_y$ oscillate with the field frequency $\omega$ and have zero mean upon averaging over a period $T = 2\pi/\omega$. At the same time, the component $U_z$ does not depend on time.
Let us consider the propulsion velocity $U_z$ of the symmetric V-shape. Substituting the components of the angular velocity (5) into the third equation of Eqs. (A2) one readily finds
$$U_z = \frac{\text{Ch}s_\psi s_2 \varphi + \frac{G_{13}}{F_3} s_\psi s_\theta \psi + \frac{G_{31}}{F_1} c_\psi c_\theta \theta}{\ell},$$ (A3)
where $\text{Ch} = G_{13}(F_1^{-1} + F_3^{-1})/2\ell$.
[27] R. S. Berman, O. Kenneth, J. Sznitman and A. M. Leshansky, New J. Phys. 15, 075022 (2013).
[28] See Supplemental Material at http://link.aps.org/supplemental/... for animations.
[29] Nondimensionalization with $\nu_0$ complies with the definition of the propulsion efficiency $\delta^* = |U_z, \omega_0|/\nu_0 \ell$ introduced in Ref. [19] that ranks propellers according to their maximal speed (at the step-out) in body lengths per unit time.
[30] Sometimes a different limit cycle solution can be obtained, however its basin of attraction is rather narrow, so for most initial orientations the solution converges to the same limit cycle.
[31] The condition $qr > s$ follows from the fact that the roots of the cubic equation satisfy $(\lambda_1 + \lambda_2)(\lambda_1 + \lambda_3)(\lambda_2 + \lambda_3) = s - qr$.
[32] For a slim V-structure (as in Fig. 2a) magnetization along $e_1$ results in propulsion similar to that in Sec. IV A subject to some changes due to axes interchange, $e_2 \leftrightarrow e_1$. The in-sync propulsion velocity in this case is given by (14) with $\psi \rightarrow \pi/2 - \psi$, $\theta \rightarrow \pi - \theta$ and $Ch = Ch_{23}$, resulting in $U_z/\omega \ell = -Ch2\delta/(1 + \varepsilon - p^{-1})$. Since $Ch$ changes sign, the propulsion in the $+z$-direction will require magnetization along $-e_1$.
[33] J. E. Marsden and T. J. R. Hughes, Mathematical foundations of elasticity (Dover, 1983). | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
5363,
1
],
[
5363,
10683,
2
],
[
10683,
17647,
3
],
[
17647,
22228,
4
],
[
22228,
29766,
5
],
[
29766,
32157,
6
],
[
32157,
37189,
7
],
[
37189,
43197,
8
],
[
43197,
49474,
9
],
[
49474,
51668,
10
],
[
51668,
53115,
11
]
]
} |
cf751979b290b1e9ea86eabe468d3c9969f005d2 | {
"olmocr-version": "0.1.59",
"pdf-total-pages": 15,
"total-fallback-pages": 0,
"total-input-tokens": 37062,
"total-output-tokens": 10985,
"fieldofstudy": [
"Computer Science"
]
} | A dataset of mentorship in science with semantic and demographic estimations
Qing Ke\textsuperscript{1,\*}, Lizhen Liang\textsuperscript{1}, Ying Ding\textsuperscript{2}, Stephen V. David\textsuperscript{3}, and Daniel E. Acuna\textsuperscript{1,\*}
\textsuperscript{1}School of Information Studies, Syracuse University, Syracuse, New York 13244, US
\textsuperscript{2}School of Information, University of Texas, Austin
\textsuperscript{3}Oregon Hearing Research Center, Oregon Health and Science University, Portland, Oregon 97239, US
\textsuperscript{*}Corresponding authors: Qing Ke ([email protected]) and Daniel E. Acuna ([email protected])
ABSTRACT
Mentorship in science is crucial for topic choice, career decisions, and the success of mentees and mentors. Typically, researchers who study mentorship use article co-authorship and doctoral dissertation datasets. However, available datasets of this type focus on narrow selections of fields and miss out on early career and non-publication-related interactions. Here, we describe M\textsc{entorship}, a crowdsourced dataset of 743,176 mentorship relationships among 738,989 scientists across 112 fields that avoids these shortcomings. We enrich the scientists’ profiles with publication data from the Microsoft Academic Graph and “semantic” representations of research using deep learning content analysis. Because gender and race have become critical dimensions when analyzing mentorship and disparities in science, we also provide estimations of these factors. We perform extensive validations of the profile–publication matching, semantic content, and demographic inferences. We anticipate this dataset will spur the study of mentorship in science and deepen our understanding of its role in scientists’ career outcomes.
Background & Summary
Mentorship is a form of guidance provided by a more experienced person (mentor) to a less seasoned one (mentee). Likewise, mentors in science draw from their experiences to help mentees—who often are early-career researchers—navigate various issues inside and outside of academia. Mentorship is a crucial phase in a scientist’s development that has long-term effects throughout her career. Mentorship can occur formally through doctoral and postdoctoral advisor–advisee relationships or informally through collaborations. Mentees not only learn new knowledge and skills from mentors but also get involved in mentors’ social connections\textsuperscript{1}. Numerous studies have pointed out the association between mentor’s characteristics and mentee’s academic success, like productivity\textsuperscript{2–4}, career preference and placement\textsuperscript{2,5,6}, mentorship fecundity\textsuperscript{7,8}, and impact\textsuperscript{9}. Despite the large role of mentorship and interest in studying it, previous studies have relied on single-field datasets and indirect signals of mentorship (e.g., co-authorship) and therefore have limited generalizability. Large, curated, and open datasets on mentorship have the potential of bringing significant benefit to our understanding of the phenomenon, similar to how citation and publication datasets have accelerated the emerging field of science of science\textsuperscript{10,11}.
Studying mentorship requires access to a broad set of relationship types, including publication. There are a few data sources for mentorship in science (Table 1); here, we list a handful of them. The Mathematics Genealogy Project (MGP)\textsuperscript{12} is an online database for academic genealogy only in mathematics, though more broadly construed to include “mathematics education, statistics, computer science, or operations research”. MGP lacks publication records. The Astronomy Genealogy Project is a similar online database confined to astronomy that also does not have publication information\textsuperscript{13,14}. ProQuest is a database of theses and dissertations predominantly from the US\textsuperscript{15}. Although it is multi-disciplinary, it does not disambiguate researchers, making it hard to link advisor and advisee and construct lineages. Also, it does not provide publication information. More importantly, ProQuest is not publicly available, and its access is rate-limited. Apart from genealogy and thesis data, other researchers have proposed to use paper co-authorships as indirect signals of mentorship\textsuperscript{16}. However, mentorship can start much earlier than publishing works, and it does not necessarily lead to publications\textsuperscript{17}. To summarize, datasets about mentorship in science are in general fragmented.
Here, we start from the Academic Family Tree (AFT) website\textsuperscript{18} and extend it to create a large-scale dataset of mentorship relationships in science. The AFT is an online portal for mentorship in science. We match each AFT profile to the Microsoft Academic Graph (MAG), a leading bibliographic database\textsuperscript{19}. Moreover, we apply natural language processing techniques to extract semantic representations of researchers based on deep learning content analysis of their publications. Given the recent interest to understand the role of gender and race/ethnicity in science\textsuperscript{20}, we also provide estimations of researchers’ demographics. Compared to existing databases, our dataset, M\textsc{entorship} (M\textsc{entorship} with Semantic, Hierarchical, and...
demographic patterns), covers a wide range of disciplines with a richer set of features, making it ideal for studying generalizable mentorship patterns. We expect it to be the base of future studies covering various aspects of scientific mentorship, including semantic and demographic factors.
**Methods**
**Data sources**
The AFT website displays researchers’ profile information, like direct academic parents and children and a limited set of publication records in the PubMed. Originally focused on neuroscience\(^{21}\), AFT has been expanding to other areas such as chemistry, engineering, and education. As a crowd-sourcing website, contents on AFT are contributed by registered users. Contributions can be diverse, from adding a new researcher to adding mentors, trainees and collaborators of an existing researcher. Visitors can also indicate whether the website has correctly matched a profile with a publication. Due to the crowd-sourcing nature, researchers on AFT may not be a representative sample of the academic population.
In AFT, the user-contributed data are stored in a database consisting of several tables that are available online\(^{22}\). These tables are the starting point for the present work. In particular, we use four tables: (1) the *people* table storing researchers’ basic information, including person’s ID, name, degree, research area, etc.; (2) the *connect* table detailing mentorship relationships, including its ID, mentee and mentor person IDs, mentorship type (e.g., PhD, postdoctoral advising), and when and where the mentorship occurred; (3) the *authorPub* table enumerating researchers and their papers as well as meta data of papers; and (4) the *locations* table listing institutions and their geolocations.
We use the MAG dataset to find papers of AFT researchers. MAG contains information about papers, authors, journals, conferences, affiliations, and citations. One advantage of MAG is that all entities have been disambiguated and associated with identifiers. This dataset has been used in several recent works for author- and venue-level analyses\(^{20,23}\). Here we use four tables in MAG: (1) the *Affiliations* table that lists institution related information; (2) the *PaperAuthorAffiliations* table that records the name and the affiliation of each authorship; (3) the *Authors* table that contains author information including names; and (4) the *Papers* table that consists of paper-related metadata such as digital object identifier (DOI).
Fig. 1 provides an overview of how these data sources are used to assemble the dataset presented in our work.
**Normalizing researcher profiles**
The *people* table contains 778,367 researchers, uniquely identified by person IDs. We clean this table by ignoring (1) researchers without a first name or last name; (2) researchers who have the same name, institution, and major research area but different IDs as they are likely duplicates; and (3) researchers whose first, middle, or last name contain characters that are not likely to appear in a name, such as “&” and “;”. These steps leave us with 774,733 (99.5%) researchers.
Besides person IDs that are used internally in AFT, there are about 1,600 researchers whose Open Researcher and Contributor ID (ORCID), a persistent identifier to uniquely identify authors\(^{24}\), are available. Although this is a small fraction (0.2%), we use this information for later validation of our methods. This ORCID information needs cleaning before using it as it contains various “orcid.org” prefixes (“https://orcid.org/“, “http://orcid.org/“, and “orcid.org/”) and wrong format, which are manually corrected.
**Extracting mentor-mentee pairs**
From the *connect* table, we filter out mentorship pairs where mentee’s person ID or mentor’s person ID are not present in the curated list of researchers generated in the previous section. We then drop duplicate records and ignore records where the same relationship ID corresponds to a different mentee or mentor’s ID. We obtain 743,176 mentorship pairs among 738,989 researchers.
**Matching institutions between AFT and MAG**
To facilitate matching AFT researchers with MAG authors, we first match institutions. To do so, we generate a list of rules to normalize AFT institution names iteratively. More specifically, we perform a greedy matching where we sequentially select the unmatched AFT institution with the largest number of researchers associated with it. We then apply several rules to normalize the name so that we can find it in the MAG institution list (see Table 2 for the rules). For institutions that cannot be matched using these rules, we manually search them in the MAG if they have at least 200 researchers and discard the remaining institutions. These steps are iterated until no more matches are possible.
**Linking AFT researchers to MAG authors**
As described before, one unique feature of our dataset is that we provide lists of publications authored by AFT researchers. One motivation behind this is to access the entire co-authorship network of researchers and potentially understand the topics,
venues, and citation dynamics of this network. While AFT already has publication information, it is limited to PubMed only. By matching to MAG, we can access all research areas that are not limited to biomedicine.
There are two main strategies we follow to find matches. One approach is to find, for each mentor-mentee pair, the list of MAG papers where both of their names appear as co-authors. The other strategy is to match AFT researchers using their names and affiliation information. This second strategy is necessary because some mentees have not published a paper with a mentor yet.
We first elaborate on the first strategy: matching by co-authorship. This strategy involves the following three steps:
1. First, we prepare a list of mentor-mentee name pairs. To do so, for each AFT researcher, we consider her full name as presented in the AFT. If the first name has more than one character (i.e., not first initial), we also consider two possible variations: (1) first name, middle initial, last name; and (2) first name and last name. For a mentor-mentee pair, we then enumerate all possible name pairs.
2. Second, we scan the MAG to collect papers where the name pair of two co-authors appear in the list of name pairs prepared in the first step. Specifically, for a MAG paper, we collect its co-author names from the PaperAuthorAffiliations and Authors tables. Then, we use the nameparser Python library to parse a full name into first, middle, and last name. (Author names in the MAG are given as single text.) Next, we consider all possible name pairs of two co-authors and check if each pair is presented in the list of AFT name pairs prepared in the first step. Note that we only consider conference papers, journal articles, and unknown when performing the matching, ignoring the other five types of documents presented in MAG: book chapter, book, dataset, patent, and repository.
3. After scanning the MAG, we obtain a list of associated papers and the MAG author IDs for the mentor and the mentee for each mentor-mentee pair. In total, 359,238 AFT researchers have MAG papers associated with them and have at least one corresponding MAG author ID. Among these researchers, 295,630 (82.3%) have only one MAG author ID. For the rest, although multiple MAG ids are associated with them, only one of the ids accounts for more than half of the published works for the vast majority of those researchers. Therefore, we assign the most common MAG author ID to an AFT researcher if there is a single majority (98% of cases). We drop the remaining 2% and result in a total of 353,377 AFT researchers linked to MAG using co-authorship-based matching.
Next, we match the remaining 421,356 unmatched researchers with MAG using their name and institution information. The procedure is similar to co-authorship-based matching. First, we collect, for an AFT researcher, all possible name-institution pairs, by considering her name variations and institutions presented in the profile and mentorship tables (Fig. 1). We then aggregate those pairs across all researchers. Note that for only 928 (0.2%) unmatched researchers, their name-institution pairs are not unique. Next, we scan the MAG to find papers where the co-authors’ name-institution pairs are in the prepared list of name-institution pairs. Through this way, we additionally match 141,078 researchers, with the total matched researchers reaching to 494,455 (63.8%).
**Estimating semantic representations**
Our efforts so far have yielded a list of papers for each AFT researcher who we can match in MAG. Next, we use the titles and abstracts of these papers to construct vector representations of the researcher. Such models can capture semantics, allowing us to apply them in a wide range of scenarios such as comparing the content between researchers, recommendation, and matchmaking of scientists. Here we provide two types of representations; one is based on standard term frequency-inverse document frequency (TF-IDF) vectors, and the other is based on modern deep learning embeddings.
**TF-IDF representation:** The subset of researchers who we can match in MAG published a total of 169,424,159 papers in MAG. We concatenate the titles and abstracts of these papers. Then using scikit-learn, we preprocess the concatenated text by removing English stop words as well as words appearing only once and apply the TF-IDF transformation. This preprocessing results in a dense 169,424,159 × 227,5293 sparse matrix, with each row corresponding to a paper and each column a term. The vector of a researcher is the centroid (average) of the TF-IDF vectors of her documents.
**Deep learning embedding:** We employ SPECTER, a representation learning algorithm for scientific documents, to obtain dense vector representations of papers. We concatenate titles and abstracts and use the implementation reported in. Each article is represented by a dense vector of 768 dimensions, resulting in a dense 169,424,159 × 768 matrix for all documents. The vector of a researcher, again, is the average of the vectors of her papers.
**Estimating gender and race/ethnicity**
Gender in science has become an important subject of study. Here we provide researchers’ gender information inferred from their first names. To do so, we encode the character sequence using both the full string and sub-word tokenization as created by a pre-trained BERT model. The output of the BERT model is passed through a pooling layer which creates a vector of...
768 elements. This vector is then passed through a dropout layer and softmax layer to produce the final gender predictions. We have three genders in our dataset, two legal labels (female and male) and one unknown label, which attempts to capture potentially non-binary genders. For the training data, we use a combination of datasets. One dataset provides predicted gender of author names in the Author-ity 2009 dataset using the Genni and SexMac tools. We only maintain data points where Genni and SexMac agree with each other. This filtering step left us with 2793982 labeled data points. Another dataset for training comes from the Social Security Administration (SSA) and is about popular newborn names and their gender. The SSA dataset contained 95 026 names labeled as “male” and “female”. To reduce the generalization error, we sample each class from the aggregated dataset and obtain a relatively balanced dataset with 1500000 data points (male: 600000, female: 600000, unknown: 300000). When training, we sample each of all three labels equally. We use 80% for training and 20% for validating. The classes in both splits are also balanced.
We also provide race/ethnicity information of researchers inferred from their full name using a similar architecture. The deep learning architecture is identical to the one used in the gender prediction above: BERT → Max Pooling → Dropout → Softmax. We combine two data sources as our training set. The first one contains the predicted ethnicity of authors in the Author-ity 2009 dataset using the Ethnea tool. We map the predicted categories into four groups: Asian, Hispanic, Black, and White using the mapping described in Table 3. The second dataset consists of name and ethnicity information extracted from personal profiles on Wikipedia. We map the Wikipedia labels into the same four categories of ethnicity listed before. Finally, we get a dataset with 720000 data points (black: 180000, Asian: 180000, Hispanic: 180000, white: 180000). The training and validation schedule is similar to the one followed for the gender prediction.
Both models are incorporated in our Python package demographicx.
Data Records
The resulting dataset has 9 main tables, shared as the files described below. Fig. 2 presents the entity-relationship diagram of these tables.
1. researcher.csv is a comma-separated values (CSV) file listing 774733 researchers and contains the following variables: person ID (PID), first name, middle name, last name, institution, institution MAG ID, research area, ORCID, and MAG author ID. We also provide an auxiliary file named first_name_gender.csv that maps first name to inferred gender and an auxiliary file called full_name_race.csv that maps full name to inferred race/ethnicity.
2. mentorship.csv contains mentorship relationships between researchers and has 8 variables: relationship ID (CID), mentee’s person ID, mentor’s person ID, mentorship type, the institution where the mentorship happened, institution MAG ID, and the start year and stop year of the interaction.
3. authorship.csv lists all the MAG paper IDs of each researcher and has two columns: person ID (PID) and MAG paper ID.
4. paper.csv lists 3 types of IDs of each paper: MAG ID, PubMed ID (PMID), and DOI.
5. paper_tfidf.npz stores the sparse matrix for paper TF-IDF vectors in Compressed Sparse Row format.
6. researcher_tfidf.npz stores the sparse matrix for researcher TF-IDF vectors in Compressed Sparse Row format.
7. paper_specter.pkl stores SPECTER vectors of papers in the Pickle format.
8. researcher_specter.pkl stores SPECTER vectors of researchers.
9. researcher_neighbor_specter.csv lists the 9 nearest researchers and the distances to them of each researcher based on SPECTER vectors. It has 3 columns: person ID (PID), the neighbor’s person ID (NeighborPID), and their distance (SpecterDistance).
Fig. 3 provides a researcher-centric view of the different types of data available in our dataset.
Technical Validation
Validation of gender and ethnicity estimation
We report in Table 4 the performances of our gender prediction algorithm on the validation set and the SSA set. To validate the “unknown” class, we used “unknown” labels from Author-ity for names in the SSA dataset labeled “unknown” in the Author-ity
We validate researchers’ vectors by comparing distances between researchers who belong to different groups. Specifically, without DOI but with PMID, we query PubMed to get their DOI which of the two models better serves their analysis. (validation data: Black F1: 0.53, Asian F1: 0.64, Hispanic F1: 0.692, White F1: 0.52). We leave it to the user to determine which of the two models better serves their analysis.
Validation of mentorship
Our dataset covers mentorship relationships in multiple disciplines. Table 8 presents the top 20 most represented areas. Neuroscience is the one with the largest number of researchers, given that AFT was originally aimed for academic genealogy in neuroscience. Social sciences fields, like education, literature, sociology, and economics, are also well represented. Table 9 gives the count of each type of mentorship.
Validation of linking AFT researchers with MAG authors
Table 8 indicates that we can match the majority of researchers in natural sciences, but for social sciences fields like education, literature, we have lower percentages of researchers matched.
To validate our linking of AFT researchers to MAG authors, we take advantage of the fact that their publications are known to be genuinely authored by them for some AFT researchers. With these publications, we examine if they also appear in the publication list of the corresponding matched MAG author. Here we focus on two subsets of AFT researchers: (1) those with papers verified by AFT website users; and (2) those with ORCID available.
Let us describe the first subset. In our previous works, we have automatically linked AFT researchers to publications indexed in PubMed. Those matched papers are then displayed on researchers’ profile pages. AFT website users who have signed into the website can label whether the authorship is correct. We consider these labeled papers as a validation set to test the performance of our AFT-to-MAG matching of authors. To match these papers to MAG, we rely on their DOIs. For papers without DOI but with PMID, we query PubMed to get their DOI.
We can now introduce the measure used to quantify the performance of our matching. Let \( a \) be an AFT researcher who has at least one verified and \( P_a \) the list of her verified papers. Let also \( a' \) be the corresponding matched MAG author and \( P_{a'} \) the list of papers found on MAG. We calculate the fraction of \( P_a \) that appear in \( P_{a'} \), formally:
\[
O_a = \frac{|P_a \cap P_{a'}|}{|P_a|}.
\]
Fig. 4A, which plots the histogram of \( O_a \) for the first subset of researchers, indicates the validity of our matching process; for the vast majority of researchers, we can find most of their verified papers in the publication lists of their matched MAG authors.
Let us describe the second subset: papers listed on the ORCID website (\( P_a \)). To get these papers, we download the 2019 ORCID Public Data File (the most recent one), extract documents authored by researchers, and match extracted papers to MAG using their DOI. Fig. 4B shows the histogram of \( O_a \) for the second subset of researchers, indicating most of their papers also appear in publication lists of corresponding matched MAG authors.
Validation of author vector
We validate researchers’ vectors by comparing distances between researchers who belong to different groups. Specifically, in Fig. 5A, we show that the cosine distance of the TF-IDF vectors of a particular Ph.D. mentee, \( a \), and her mentor, \( b \), is much smaller than the distances between \( a \) and randomly selected researchers. Generalizing this systematically, for each Ph.D. mentee, we obtain a triplet \((a, b, c)\) where \( c \) is a randomly chosen researcher. We then calculate the difference of the distance between \( a \) and \( c \), \( d(a, c) \), and the distance between \( a \) and \( b \), \( d(a, b) \). As we expect, the semantics of a mentee is more similar to her Ph.D. mentor than to a random researcher, and the distance difference is expected to be larger than 0. This pattern is indeed
the case for the vast majority (97.4%) of Ph.D. mentees (Fig. 5B). We also replicate these analyses using SPECTER vectors, and the results remain similar (Figs. 5C–D): For 98.4% of Ph.D. mentees, they are semantically closer to their Ph.D. mentors than randomly selected researchers (Fig. 5D). The threshold 0 is located at 1.66 and 2.39 standard deviations away from the mean for the TF-IDF case and SPECTER case, respectively, suggesting that SPECTER is a better representation method.
To further show the structure of researchers’ SPECTER vectors, we run the UMAP dimension reduction technique to obtain 2-dimensional vectors and display them as a scatter plot for a 20% random sample of researchers in Fig. 6. As expected, researchers in the same research area are clustered, meaning that they are semantically closer to each other than researchers from other areas.
Usage Notes
Users can integrate our data set with MAG to study the role of mentor in mentee’s academic career. MAG provides detailed information about papers and citations, from which users can derive various indicators commonly used in the science of science. We can access MAG data by following the steps outlined on its website. In addition to MAG, other identifiers of publications we provide also facilitate integration with other scholarly databases. In particular, users can use CrossRef API to retrieve metadata of papers using DOI. Also, we can use the E-utilities API provided by the National Library of Medicine to obtain metadata of PubMed articles using PMID.
Users who want to use our released researcher vectors to perform semantic analysis can load the TF-IDF vector file using the SciPy library’s scipy.sparse.load_npz function.
Code availability
All the code for generating the dataset and figures is published as IPython notebooks on Github, https://github.com/sciosci/AFT-MAG. All the coding was completed using Python.
References
1. Austin, A. E. Preparing the next generation of faculty: Graduate school as socialization to the academic career. *The J. High. Educ.* 73, 94–122 (2002).
2. Long, J. S. & McGinnis, R. The effects of the mentor on the academic career. *Scientometrics* 7, 255–280 (1985).
3. Paglis, L. L., Green, S. G. & Bauer, T. N. Does adviser mentoring add value? a longitudinal study of mentoring and doctoral student outcomes. *Res. High. Educ.* 47, 451–476 (2006).
4. Baruffaldi, S., Visentin, F. & Conti, A. The productivity of science & engineering PhD students hired from supervisors’ networks. *Res. Policy* 45, 785–796 (2016).
5. Godechot, O. The chance of influence: A natural experiment on the role of social capital in faculty recruitment. *Soc. Networks* 46, 60–75 (2016).
6. Pinheiro, D. L., Melkers, J. & Newton, S. Take me where i want to go: Institutional prestige, advisor sponsorship, and academic career placement preferences. *PLOS ONE* 12, e0176977 (2017).
7. Malmgren, R. D., Ottino, J. M. & Amaral, L. A. N. The role of mentorship in protégé performance. *Nature* 465, 622–626 (2010).
8. Liénard, J. F., Achakulvisut, T., Acuna, D. E. & David, S. V. Intellectual synthesis in mentorship determines success in academic careers. *Nat. communications* 9, 1–13 (2018).
9. Ma, Y., Mukherjee, S. & Uzzi, B. Mentorship and protégé success in stem fields. *Proc. Natl. Acad. Sci.* 117, 14077–14083 (2020).
10. Fortunato, S. *et al.* Science of science. *Science* 359, eaao0185 (2018).
11. Zeng, A. *et al.* The science of science: From the perspective of complex systems. *Phys. Reports* 714-715, 1–73 (2017).
12. Mathematics Genealogy Project. https://www.mathgenealogy.org (2021).
13. Astronomy Genealogy Project. https://astrogen.aas.org (2021).
14. Tenn, J. S. Introducing astrogen: The astronomy genealogy project. *J. Astron. Hist. Herit.* 19, 298–304 (2016).
15. Proquest dissertations & theses global™. https://about.proquest.com/products-services/pqdtglobal.html (2021).
16. Wang, C. *et al.* Mining advisor-advisee relationships from research publication networks. In *Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining*, 203–212 (2010).
17. Acuna, D. E. Some considerations for studying gender, mentorship, and scientific impact: commentary on AlShebli, Makovi, and Rahwan (2020). OSF Preprints (2020).
18. Academic Family Tree. https://academictree.org (2021).
19. Wang, K. et al. A review of microsoft academic services for science of science studies. Front. Big Data 2, 45 (2019).
20. Huang, J., Gates, A. J., Sinatra, R. & Barabási, A.-L. Historical comparison of gender inequality in scientific careers across countries and disciplines. Proc. Natl. Acad. Sci. 117, 4609–4616 (2020).
21. David, S. V. & Hayden, B. Y. Neurotree: A collaborative, graphical database of the academic genealogy of neuroscience. PloS one 7, e46608 (2012).
22. David, S. V. Academic family tree data export (version 1.0) [data set]. zenodo. http://doi.org/10.5281/zenodo.4441298 (2021).
23. Peng, H., Ke, Q., Budak, C., Romero, D. M. & Ahn, Y.-Y. Neural embeddings of scholarly periodicals reveal complex disciplinary organizations. Sci. Adv. 7, eabb9004 (2021).
24. About ORCID. https://info.orcid.org/what-is-orcid (2021).
25. Name parser. https://github.com/derek73/python-nameparser (2021).
26. Achakulvisut, T., Acuna, D. E., Ruangrong, T. & Kording, K. Science concierge: A fast content-based recommendation system for scientific publications. PloS one 11, e0158423 (2016).
27. Achakulvisut, T. et al. neuromatch: Algorithms to match scientists. eLife (2020).
28. Pedregosa, F. et al. Scikit-learn: Machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011).
29. Cohan, A., Feldman, S., Beltagy, I., Downey, D. & Weld, D. S. Specter: Document-level representation learning using citation-informed transformers. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, 2270–2282 (2020).
30. https://github.com/allenai/specter (2021).
31. Devlin, J., Chang, M.-W., Lee, K. & Toutanova, K. BERT: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), 4171–4186 (2019).
32. Wolf, T. et al. Transformers: State-of-the-art natural language processing. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing: System Demonstrations, 38–45 (Association for Computational Linguistics, 2020).
33. Torvik, V. Genni + Ethnea for the Author-ity 2009 dataset. University of Illinois at Urbana-Champaign 10.13012/B2IDB-9087546_V1 (2018).
34. Social Security Administration. Beyond the top 1000 names. https://www.ssa.gov/oact/babynames/limits.html (2021).
35. Torvik, V. I. & Agarwal, S. Ethnea–an instance-based ethnicity classifier based on geo-coded author names in a large-scale bibliographic database (2016).
36. Ambekar, A., Ward, C., Mohammed, J., Male, S. & Skiena, S. Name-ethnicity classification from open sources. In Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 49–58 (2009).
37. Liang, L. & Acuna, D. E. demographicx: A Python package for estimating gender and ethnicity using deep learning transformers. Preprint https://doi.org/10.5281/zenodo.4898367 (2021).
38. Ke, Q., Liang, L., Ding, Y., David, S. V. & Acuna, D. E. A dataset of mentorship in science with semantic and demographic estimations. zenodo https://doi.org/10.5281/zenodo.4917086 (2021).
39. Black In Neuro. https://violin-porcupine-x6rg.squarespace.com/ (2021).
40. Bureau, U. C. Frequently occurring surnames from the census 2000. https://www.census.gov/topics/population/genealogy/data/2010_surnames.html (2014).
41. Get article metadata. https://www.ncbi.nlm.nih.gov/pmc/tools/get-metadat/ (2021).
42. ORCID public data file 2019. figshare https://orcid.figshare.com/articles/ORCID_Public_Data_File_2019/9988322/2 (2020).
43. McInnes, L., Healy, J. & Melville, J. UMAP: Uniform manifold approximation and projection for dimension reduction. arXiv preprint arXiv:1802.03426 (2018).
Acknowledgements
This work was partially supported by NSF grant #1933803. We thank Longfeng Wu for initial data explorations and Leah Schwartz for valuable discussions.
Author Contributions Statement
Q.K. and D.A. conceived the experiments, Q.K. conducted the experiments, L.L. performed gender and race/ethnicity estimations, Q.K. and D.A. analysed the results. All authors edited and reviewed the manuscript.
Competing Interests
The authors declare no competing interests.
Figures & Tables
Figure 1. Flowchart of the dataset generation process.
Figure 2. Entity-relationship diagram of our dataset.
Figure 3. Different types of data available for an exemplar researcher (Terrence J. Sejnowski).
Figure 4. Validation of matching AFT researchers with MAG authors. The measure $O$ considers, for an AFT researcher, $a$, the list of papers, $P_a$, genuinely authored by her, and measures the fraction of these papers that also appear in the list of papers of the corresponding matched MAG author. (A) Histogram of $O$ for 14,824 researchers with $|P_a| > 0$. Here $P_a$ refers to papers that registered AFT website users verify. (B) Histogram of $O$ for 1,262 researchers with ORCID identifiers. $P_a$ represents the list of papers extracted from the orcid.org website. In both cases, we observe that for the vast majority of researchers, most of their papers that they genuinely author can be found in the lists of publications of their matched MAG authors, indicating high accuracy of our matching procedure.
Figure 5. Validation of researcher vectors. (A) Histogram of cosine distances of TF-IDF vectors between one researcher $a$ and 10 thousand randomly selected researchers. The red vertical line marks the distance between $a$ and $a$’s Ph.D. mentor, $b$, indicating that $a$ is much closer to her mentor than expected. (B) For each PhD mentee, we calculate the difference of $d(a,c)$ and $d(a,b)$, where $d(a,c)$ is the cosine distance between $a$ and $c$, a randomly selected researcher. The figure shows the histogram of the differences for all Ph.D. mentees, indicating that they are semantically much closer to their mentors than to random researchers for the vast majority of Ph.D. mentees. (C–D) The same as A–B, except that researcher vectors are based on the SPECTER algorithm rather than TF-IDF.
Figure 6. The 2-dimensional projections of researchers’ SPECTER vectors, obtained using UMAP\textsuperscript{43}. The figure shows a 20% random sample of all researchers. An interactive version can be found at https://scienceofscience.org/mentorship.
| Database | Discipline | Country | Tree | Publication data | Open |
|------------------------------|------------|------------|------|------------------|------|
| MENTORSHIP | all | world-wide | ✓ | ✓ | ✓ |
| Mathematics Genealogy Project| Math | world-wide | ✓ | ✗ | ✓ |
| Astronomy Genealogy Project | Astronomy | world-wide | ✓ | ✗ | ✓ |
| ProQuest | all | US | ✗ | ✗ | ✗ |
**Table 1.** Comparison of existing datasets of mentorship in science with ours (MENTORSHIP).
| Race for prediction | Race in Ethnea |
|---------------------|-----------------------------------------------------------------------------|
| Asian | Arab, Chinese, Indian, Indonesian, Israeli, Japanese, Korean, Mongolian, Polynesian, Thai, Vietnamese |
| White | Baltic, Dutch, English, French, Greek, German, Hungarian, Italian, Nordic, Romanian, Slav, Turkish |
| Hispanic | Caribbean |
| Black | African |
**Table 2.** A list of rules to normalize AFT institution names used to match with MAG institutions.
| Validation set accuracy | AUROC | SSA names accuracy | AUROC |
|-------------------------|-------|--------------------|-------|
| Male | 0.961 | 0.972 | 0.993 |
| Female | 0.975 | 0.979 | 0.996 |
| Unknown | 0.889 | 0.862 | 0.966 |
**Table 3.** Mapping between race categories in the Ethnea and ours used for prediction.
**Table 4.** Performances of gender prediction.
| Gender | # researchers |
|--------|---------------|
| male | 374199 |
| female | 264263 |
| unk | 135732 |
Table 5. Number of researchers by gender. Here, the gender of the researcher is estimated by an algorithm using their first name. We acknowledge that there could be a great deal of noise and bias in this estimation. However, we believe it is better to open our algorithm to the community instead of analyzing proprietary software that does not publicize data used and performance metrics.
| | Validation set | | Wikipedia | |
|---------|----------------|----------|-----------|----------|
| | F-1 | ACC | AUROC | F-1 | ACC | AUROC |
| Black | 0.976 | 0.999 | 0.999 | 0.987 | 0.999 | 0.996 |
| Hispanic| 0.936 | 0.928 | 0.990 | 0.822 | 0.788 | 0.964 |
| White | 0.907 | 0.902 | 0.983 | 0.850 | 0.856 | 0.963 |
| Asian | 0.941 | 0.931 | 0.989 | 0.859 | 0.843 | 0.962 |
Table 6. Performances of race/ethnicity prediction.
| Race/ethnicity | # researchers |
|----------------|---------------|
| White | 508923 |
| Asian | 177649 |
| Hispanic | 68664 |
| Black | 18958 |
Table 7. Number of researchers by estimated race/ethnicity.
| area | researchers | % researchers | researchers matched | % matched |
|----------------|-------------|---------------|---------------------|-----------|
| neuroscience | 135756 | 16.7 | 93769 | 69.1 |
| chemistry | 104450 | 12.9 | 85585 | 81.9 |
| engineering | 56898 | 7.0 | 45004 | 79.1 |
| education | 56580 | 7.0 | 17978 | 31.8 |
| physics | 49582 | 6.1 | 37714 | 76.1 |
| math | 35651 | 4.4 | 22707 | 63.7 |
| literature | 28257 | 3.5 | 7449 | 26.4 |
| sociology | 25453 | 3.1 | 12618 | 49.6 |
| economics | 23497 | 2.9 | 12841 | 54.6 |
| computer science| 22399 | 2.8 | 18315 | 81.8 |
| cell biology | 20970 | 2.6 | 18087 | 86.3 |
| political science| 18914 | 2.3 | 8654 | 45.8 |
| theology | 17448 | 2.1 | 3726 | 21.4 |
| microbiology | 17230 | 2.1 | 14759 | 85.7 |
| phillosopy | 17035 | 2.1 | 6253 | 36.7 |
| linguistics | 13952 | 1.7 | 6685 | 47.9 |
| nursing | 13825 | 1.7 | 6207 | 44.9 |
| phtree | 13637 | 1.7 | 8986 | 65.9 |
| anthropology | 13471 | 1.7 | 6185 | 45.9 |
| evolution | 13417 | 1.7 | 10494 | 78.2 |
Table 8. The top 20 most represented major research areas.
| Mentorship type | Definition | Count |
|-----------------|-----------------|---------|
| 0 | Research assistant | 18850 |
| 1 | Graduate student | 630439 |
| 2 | Postdoctoral | 68652 |
| 3 | Research scientist| 7402 |
| 4 | Collaborator | 17833 |
**Table 9.** Mentorship type definition and statistics. | 2025-03-05T00:00:00 | olmocr | {
"pdf_page_numbers": [
[
0,
5408,
1
],
[
5408,
10539,
2
],
[
10539,
16043,
3
],
[
16043,
20334,
4
],
[
20334,
24424,
5
],
[
24424,
28553,
6
],
[
28553,
32589,
7
],
[
32589,
33140,
8
],
[
33140,
33291,
9
],
[
33291,
34103,
10
],
[
34103,
34905,
11
],
[
34905,
35156,
12
],
[
35156,
37033,
13
],
[
37033,
40325,
14
],
[
40325,
40727,
15
]
]
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.